Download A numerical study of recent tidal interactions between dwarf galaxies

Faculty of Sciences
Department of Physics and Astronomy
A numerical study of recent tidal
interactions between dwarf galaxies
Lars Bonne
Supervisor: Prof. Dr. S. De Rijcke
Dissertation advisor: R. Verbeke
Dissertation submitted to obtain the academic degree of
Master in Physics and Astronomy
Academic year 2015-2016
Contents
Acknowledgement
1 Introduction
1.1 The ΛCDM model . . . . . .
1.2 Dwarf Galaxies . . . . . . . .
1.2.1 Classification . . . . .
1.3 Tidal interactions . . . . . . .
1.4 Blue Compact Dwarfs . . . .
1.4.1 classification of BCDs
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2 Simulating and analysing dwarf galaxies
2.1 N -body/SPH simulations . . . . . . . .
2.2 Dwarf Galaxies and Initial Conditions . .
2.2.1 Included physics . . . . . . . . .
2.2.2 gogoIC, Kuzkut and Ganic . . . .
2.2.3 Initial conditions . . . . . . . . .
2.3 Interaction of dwarf galaxies . . . . . . .
2.3.1 Different interaction models . . .
2.3.2 The models . . . . . . . . . . . .
2.3.3 Initial velocity . . . . . . . . . . .
2.3.4 Amount of simulations . . . . . .
2.4 Hyplot . . . . . . . . . . . . . . . . . . .
2.4.1 Recognising the galaxy . . . . . .
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3 Results
3.1 Star formation history . . . . . . . . . . . . .
3.1.1 Burst factors in the interacting models
3.1.2 Prograde vs retrograde . . . . . . . . .
3.1.3 Duration of the bursts . . . . . . . . .
3.2 Velocity dispersion . . . . . . . . . . . . . . .
3.3 The gas mass . . . . . . . . . . . . . . . . . .
3.4 B-I . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Gas distribution and gas flow . . . . . . . . .
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3.6
3.7
Density profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B-band surface brightness profile . . . . . . . . . . . . . . . . . . . . . .
4 Discussion
4.1 Comparison with merger tree . . . .
4.2 Gas flow and burst duration . . . . .
4.3 Moment of the burst . . . . . . . . .
4.4 Classification of the bursting galaxies
4.5 Metallicity . . . . . . . . . . . . . . .
4.6 Effect of tidal stripping and bursts on
4.7 The amount of bursts . . . . . . . . .
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star formation
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5 Conclusion
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6 Nederlandstalige Samenvatting
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Appendices
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4
Acknowledgement
First of all I would like to thank prof. De Rijcke for several reasons. One of them is
providing this thesis subject and giving me the possibility to work on this topic. For me,
it has been an interesting year discovering the world of dwarf galaxies and their tidal
interactions. Further I would like to thank him for useful remarks during the year and
making it possible for me to attend the workshop on Computational Solar and Astrophysical Modeling in September. It provided me with an intensive training in astrophysical
simulations, which saved me a lot of time when fixing problems over the entire year such
that I had more time to focus on the results.
When talking about fixing problems, it is impossible for me not to thank Robbert.
Helping me out over and over again when I got stuck trying to fix a problem. Further
I also want to thank Robbert for answering all my questions, giving useful suggestions,
insights and providing me with several scripts making it a lot easier for me to perform
analysis of more complicated galaxy properties.
I would also like to thank my friends and girlfriend for reminding me that there is
more than finishing a dissertation.
Lastly I want to thank my family for making it possible for me to study here in Ghent
and showing interest in what I’m doing. In specific I want to mention my parents, giving
a teenager the freedom of choosing his study of interest starting from the age of 13 till
this moment. Even when he is ignoring the entire time advice from almost every high
school teacher he had.
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Chapter 1
Introduction
1.1
The ΛCDM model
Trying to understand the evolution of our universe has led to the so called ΛCDM model,
which is also known as the standard model of cosmology by now. The name refers to the
two main current constituents of the universe according to this model. The Λ refers to a
cosmological constant, associated with the unknown dark energy. And the CDM stands
for cold dark matter, where the preposition cold implies that the dark matter was not
relativistic at the moment it abandoned equilibrium.
The cosmoligical constant was first introduced by Einstein to be able to derive a static
universe from his equations. After his static universe lost all credibility when Edwin
Hubble observed the expansion of the universe (Hubble, 1929), the cosmological constant was eventually reestablished to explain the observed accelerating expansion of the
universe. This was discovered by looking at distant type Ia supernovae (Riess et al.,
1998; Perlmutter et al., 1999). These supernovae occur when a white dwarf in a binary
system superseeds the Chandrasekhar mass due to mass transfer in this binary system.
In the ΛCDM model, because of the fact that the dark matter is supposed to be cold,
the first dark matter halos that will be formed are the smallest ones. This implies that
dwarf galaxies will be the first structures formed in the early universe. Merging of these
smaller halos will lead to the formation of bigger structures.
1.2
Dwarf Galaxies
As the name already indicates, a dwarf galaxy is a galaxy which is considerably smaller
than some well known galaxies in our local group such as our own galaxy, M31 and M33.
A dwarf galaxy has a diameter of a few kiloparsec (kpc) while the larger galaxies have
diameters that can be expressed in units of 10 kpc.
The presence of a dark matter halo that embeds the system is a requirement proposed
for a while now (e.g. Mateo, 1998). This requirement would exclude globular clusters
since it is believed that these systems do not have a dark matter halo. Apart from the
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dark matter halo, efforts have been done to obtain a definition for dwarf galaxies. An
often used definition was proposed by Tammann (1994). This definition was based on
magnitudes in certain bands. Namely galaxies fainter than MV = -17 and MB = -16.
The fact that dwarf galaxies are small makes them very interesting study objects. The
first reason for this brings us back to the early stages of our universe when considering
the ΛCDM model since in this model dwarf galaxies are the first structures that were
formed. Because of their early formation and their small scale they are good study material for influences in the early universe, e.g. population III stars, the onset of the cosmic
ultraviolet background (UVB),...
Although dwarf galaxies should be the first systems that are formed, they produced
some conflicting results with the CDM model that was very successful at large scales.
Some of these successes were the large scale structure of galaxies (Davis et al., 1985)
and the anisotropy in the cosmic microwave background (Peebles, 1987). On the other
hand, one of the well known problems posed by dwarf galaxies is the ’missing satellites’
problem (Klypin et al., 1999; Moore et al., 1999). Since observationally there were less
satellite dwarf galaxies found around major galaxies than the amount of dark matter
substructures that were predicted by cosmological simulations. It was already proposed
then that the UVB and supernova feedback could suppress the formation of these dwarf
galaxies (e.g. Efstathiou, 1992; Haardt & Madau, 1996), such that this issue might be
resolved. This missing dwarf problem, together with some other problems, mostly seems
to be resolved now in simulations of Local Group environments due to ram pressure
stripping, UVB and supernova feedback (Sawala et al., 2016).
Another problem related to dwarf galaxies in this context is the existence of faint gasrich dwarf galaxies with rotational velocities of the order of 15 km/s, such as Leo P, Leo
T and Pisces A (e.g. Ryan-Weber et al., 2008; Giovanelli et al., 2013; Tollerud et al.,
2015), since more than 90 % of the dwarf galaxies with such rotational velocities are
predicted to be dark halos (Sawala et al., 2014). This can be expected since previously
mentioned effects remove gas from these low mass dwarf galaxies. However Tollerud et al.
(2015) found significantly more faint gas-rich dwarf galaxies compared to what would
be expected from cosmological simulations. This issue could be resolved by including
the effects of population III stars in merger tree simulations of dwarf galaxy formation
(Verbeke, Vandenbroucke & De Rijcke, 2015). The strong UV radiation coming from
these population III stars delays the star formation in low mass dwarf galaxies, such
that faint gas-rich dwarf galaxies can be found.
As should be explained by now, it is very difficult for dwarf galaxies to keep most of
their initial amount of baryons contained. This is in contrast with the more massive
galaxies for which this seems less difficult. Thus creating a qualitative distinction of
dwarf galaxies. An explanation for this is the fact that dwarf galaxies have a much more
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shallow gravitational potential than the more massive galaxies. Due to this shallow gravitational potential the UVB, supernovae,... eject large amounts of baryons out of the
dwarf galaxies (Tolstoy, Hill & Tosi, 2009).
Due to the fact that they do not succeed in containing most of their initial gas, dwarf
galaxies are heavily dark matter dominated. This attracted the attention from particle
physicists. They hope to detect the annihilation of dark matter in dwarf galaxies, more
specifically in dwarf spheroidal galaxies since they are even more dark matter dominated.
A thing one would almost forget when talking about dwarf galaxies due to their low
luminosity, is that they are more abundant in the universe than massive galaxies such
that they certainly deserve the necessary attention to be well understood.
Many observations of dwarf galaxies have led to their classification into different types
(Tolstoy, Hill & Tosi, 2009). This classification will be shortly discussed in the following
part.
1.2.1
Classification
- Dwarf ellipticals (dE): These dwarf galaxies don’t have a lot of gas left and barely
form any stars at the moment. They are mostly found in clusters of galaxies. Their
magnitudes in the blue band are in the interval: -18 < MB < -14. As can be seen,
this is not completely in agreement with the definition by Tammann (1994). However as
indicated as well before, there is no unique general definition for dwarf galaxies. Another
characteristic of dwarf elliptics are their smooth elliptical isophotes.
- Dwarf Spheroidals (dSph): There is basically not much difference with dwarf ellipticals. The main distinction is based on the magnitude, where dwarf spheroidals are
constrained by: -14 < MB < -8. Such that they are fainter than dwarf ellipticals. So
they are less massive and more dark matter dominated. Dwarf ellipticals and spheroidals
together are also classified as early type dwarf galaxies.
- Dwarf irregulars (dIrr): In contrast to the two previous types, dwarf irregulars are
still forming stars. They are also flattened by rotation (Côté, Carignan & Freeman,
2000) and are usually found in isolation in contrast to early type dwarf galaxies (e.g.
Côté et al., 2009). They are classified as irregulars due to their isophotes that are not as
smooth as the early type galaxies.
- Blue compact dwarfs (BCD): Just like dwarf irregulars, they have irregular isophotes.
However there is a difference with dwarf irregulars since they are generally bluer, more
compact and have a higher central surface brightness (Papaderos et al., 1996a; Salzer
& Norton, 1999). Together with the dwarf irregulars, they are referred to as late type
dwarf galaxies. These BCDs will be discussed in more detail later in the introduction,
since relations with tidal interactions are proposed.
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- Transition type dwarfs (TTD): They are still forming stars at a rather low rate and
possess properties of both early and late type dwarf galaxies. As their name suggests,
they are expected to connect the early and late type dwarf galaxies. It was shown by
Koleva et al. (2013) that with continued gas removal, these dwarf galaxies might evolve
to dwarf ellipticals.
- Ultra-faint dwarfs(uFd): Dwarf galaxies of this type have been observed rather recently. These dwarf galaxies have a very low metallicity (Kirby et al., 2008) and are
strongly dark matter dominated (Salvadori & Ferrara, 2009; Bromm & Yoshida, 2011).
It is assumed that they only had very few early star formation.
- Ultra compact dwarfs (UCD): These are dwarf galaxies with very small effective radii
and they are extremily faint (Penny et al., 2014). Compared to uFd, they are compacter
and less dark matter dominated. The formation of these galaxies is still poorly understood.
- Tidal dwarfs: Lastly one could mention this type of dwarf galaxy. These are formed in
the tidal tails of interacting galaxies, which leads to the fact that they don’t possess a lot
of dark matter. Because they are formed in tidal tails, they are formed out of enriched
gas. Therefore these dwarf galaxies generally have high metallicities (Duc et al., 2000;
Weilbacher, Duc & Fritze-v. Alvensleben, 2003; Sweet et al., 2014).
1.3
Tidal interactions
In this thesis, we will specifically look at tidal interactions of dwarf galaxies. The interest
in astronomy for tidal interactions between galaxies is certainly not new. This comes to
no surprise, since probably most galaxies are affected somewhere in their evolution by
interaction with other galaxies (e.g. Toomre, 1977). It was the Swiss astronomer Fritz
Zwicky, also known for e.g. the first proposal of unseen dark matter when observing
the Coma cluster, who first proposed that large extended stuctures seen in galaxies were
caused by tidal interactions (Zwicky, 1956). This was certainly not directly accepted as
an explanation, e.g. Gold & Hoyle (1959) suggested that electromagnetic interactions
would contribute as well.
That gravitational interaction could create these narrow extended structures was proved
afterwards by several investigations (e.g. Pfleiderer & Siedentopf, 1961; Toomre & Toomre,
1972). These calculations were performed using simplified assumptions, yet demonstrated that close passages of galaxies can create bridges and tails. These bridges and
tails are the most dominant features of tidally interacting galaxies.
Since many dwarf galaxies are found near massive galaxies, studying this tidal interaction could be interesting to see the effect on the evolution of the dwarf galaxies (e.g.
Mayer et al., 2001b, 2006; Klimentowski et al., 2009; Valcke, 2010).
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These simulations demonstrated that the presence of a Milky Way-like dark matter halo
has an influence on the evolution of the dwarf galaxies. In all studies tidal stripping
and tidal tails were observed. These interactions also led to star formation bursts in the
dwarf galaxies. And there was stated by Mayer et al. (2001a) that dwarf galaxies in the
Milky Way potential were transformed from low surface brightness dwarfs to dSphs and
from high surface brightness dwarfs to dEs.
In the context of dwarf galaxy interactions, mergers of dwarf galaxies have been studied (e.g. Bekki, 2008; Cloet-Osselaer et al., 2014; Starkenburg, Helmi & Sales, 2016).
However, the study of tidal interactions without eventual merger has never been done
in great detail. Only one numerical study was found mentioning non-merger tidal interactions of dwarf galaxies (Bekki, 2008). This study of tidal interactions was far from a
comprehensive study since there was mainly focussed on dwarf galaxy mergers triggering
a star burst. So only tidal interactions with a low eccentricity of e = 1.1 were discussed,
which is extremely close to a merging orbit. However, observational studies by Noeske
et al. (2001) indicate that a wide range of eccentricities are possible as could be expected.
This will be demonstrated in more detail in the next chapter.
The study of tidal interactions between dwarf galaxies reaches some interesting questions. Are tidal tails and bridges formed just like during the tidal interaction of massive
galaxies? Can these tidal interactions cause tidal stripping? Already for a long while
observational studies indicate that some BCDs are accompanied by other low mass halos (Brinks & Klein, 1988; Brinks, 1990; Campos-Aguilar & Moles, 1991; Noeske et al.,
2001). This was recently also confirmed with high resolution data from the Hubble Space
telescope (Lelli, Verheijen & Fraternali, 2014). So are these dwarf galaxy companions
possible triggers for the starburst occuring in these BCDs?,...
The lack of numerical study of these tidal interactions and the questions this poses was
the ground for the topic of this thesis.
1.4
Blue Compact Dwarfs
The definition for BCDs is not always the same, it mostly depends on the author. But
they generally include a few properties: it has a small optical size of maximally a few
kpc, it has a small magnitude compared to massive galaxies and a large fraction of the
light is emitted in the blue part of the spectrum caused by a starburst (e.g. Thuan &
Martin, 1981; van Zee, Skillman & Salzer, 1998).
Sevaral properties of these BCDs have been found by having a more detailed look at
these objects. First of all, these galaxies appeared to contain old stars as well (e.g. Loose
& Thuan, 1986; Kunth, Maurogordato & Vigroux, 1988; Papaderos et al., 1996a), implying it has a host galaxy. Surface brightness profiles of these BCDs have been created,
showing that these galaxies have a higher central surface brightness and a smaller scale
length (Papaderos et al., 1996b; Salzer & Norton, 1999).
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Many investigations found a large central concentration of gas (e.g. Taylor et al., 1994,
1995; van Zee, Skillman & Salzer, 1998). Another very interesting observation is that
BCDs can have very steep rotation curves, implying that there is a higher central density of dark matter (van Zee, Salzer & Skillman, 2001; Lelli et al., 2012a,b). It is also
generally found that BCDs have lower gas metallicities than dIrrs (e.g. Izotov, Thuan &
Lipovetsky, 1994; Izotov & Thuan, 1999; Hunter & Hoffman, 1999).
Tidal interactions are not the only triggering mechanism proposed for the creation of
BCDs. Mergers of dwarf galaxies in specific have been suggested as well to trigger a
starburst (Östlin et al., 2001). This mechanism was confirmed in numerical simulations
(Bekki, 2008; Cloet-Osselaer et al., 2014; Starkenburg, Helmi & Sales, 2016). Another
mechanism that was proposed is an inspiralling gas clump (Elmegreen, Zhang & Hunter,
2012; Sánchez Almeida et al., 2015). This inspiralling gas cloud could lead to a higher
central concentration of dark matter, stars and gas, which could cause a long-lived star
burst. This was further supported by Koleva et al. (2014). They noted very irregular
stellar kinematics in observed BCDs, which suggested that BCDs are experiencing a form
of interactions even when they are found in isolation. This mechanism was numerically
confirmed by Verbeke et al. (2014). So a couple of mechanisms have already been confirmed both observationally and numerically. For the tidal interactions between dwarf
galaxies not involved in a merger process, this still has to be confirmed. Even though
Bekki (2008) indicates that this mechanism should work as well, it was never studied in
full detail.
Based on the differences observed in BCDs, a classification scheme was proposed by
Loose & Thuan (1986). This classification scheme will be shortly discussed below.
1.4.1
classification of BCDs
- i0: This type of BCD seems to have no host galaxies. This would imply that they are
young objects experiencing a first star formation burst.
- nE: These BCDs are experiencing a nucleated burst in a host galaxy which has regular
elliptical outer isophotes.
- iE: Just like the previous type, this BCD has regular elliptical outer isophotes. But the
burst occuring in the host galaxy has an irregular shape.
- iI: This are BCDs that have an irregular burst in an irregular host galaxy. This class
contains two further subdivisions.
a) iI C: They have elongated hosts where the star formation is happening somewhere
near the side of the galaxy. The C refers to the cometary shape of the isophotes.
b) iI M: In this case the starbursting dwarf galaxy shows clear signs of a merger.
12
Chapter 2
Simulating and analysing dwarf
galaxies
Apart from observing dwarf galaxies, there are other ways to study these galaxies. A very
powerful tool to study dwarf galaxies is N -body/SPH simulations. One can implement
relevant physical processes in the code and study the effects of these processes on the
evolution of a dwarf galaxy and compare this with observations. The small scale of dwarf
galaxies is a particular advantage in the case of N -body simulations since this small scale
allows a very high resolution. A resolution that is by far not reachable for the larger and
more familiar galaxies with the same amount of resources. This again shows that dwarf
galaxies are very interesting objects to study since they allow that the physical processes
that govern galaxy evolution can be studied with a high resolution even when limited
resources are available.
In this chapter we will first discuss N -body simulations in general. A technique that is
used to study a wide variety of problems in astrophysics and many other applications not
directly related to astrophysics, such as ballistics and oceanography. In the second section
we will discuss its use in specific for simulating dwarf galaxies. The initial conditions
used for dwarf galaxies will be discussed in this section as well. The third section will
talk about how the interaction of the dwarf galaxies is initiated. The final section in
this chapter will shortly discuss the analysis tool HYPLOT that was used to analyse the
data obtained from simulations.
2.1
N -body/SPH simulations
In the simulations performed in this thesis, N -body systems were considered. To integrate these systems over time, an extended version of the freely available Gadget-2 code
(Springel, 2005) was used. The extra physics included in this code will be discussed
in the following part of this chapter. In this section the N -body techniques used and
smoothed particle hydrodynamics (SPH) will be discussed in some more detail.
The galaxies in our simulations consisted of dark matter, gas and stellar particles. All
13
the included particles interact gravitationally. For the gas particles, the pressure they
experience has to be included as well.
To calculate the gravitational force, the code is restricted to the non-relativistic case. In
this case, one could determine the gravitational force on a particle by summing all the
gravitational forces coming from the N-1 other particles.
N
X
Gmj (xi − xj )
ẍi = −
| xi − xj |3
j=1,j6=i
(2.1)
When a close encounter happens, this can lead to extreme accelerations of the particles
because the denominator in 2.1 becomes very small. To solve this problem, an extra
term was added to the denominator of the potential to avoid such problems, this is
called gravitational softening.
ẍi = −
N
X
j=1,j6=i
Gmj (xi − xj )
| xi − xj |2 )3/2
(2 +
(2.2)
This equation is then used to calculate the acceleration coming from gravitational interaction. The effect of gravitational softening on the acceleration of particles is plotted in
figure 2.1.
Gravitational softening brings some disadvantages since it can give rise to biases at small
scales. However it avoids the problem of extreme accelerations at close encounter requiring a very small time step. It also quickly gets very close to the standard gravitational
law at larger distances. In the case of our simulations, = 13 pc was used.
When simply applying equation 2.2 to all particles in the simulation, the simulation
time will scale with N2 . It is however possible to improve on this. This is done by using
a hierarchical multipole expansion e.g. in the form of a tree algorithm. This allows to
have a scaling like N log(N) instead of N2 .
The tree is constructed by dividing the first node which contains all particles into 8 cubes
with equal size and sides half the length of the original cube. This is division is done
untill the moment that the cube contains one particle. The cubes that don’t possess any
particles are left out. This is schematically shown for two dimensions in figure 2.2.
Forces are calculated by walking through the tree, starting at the root node. Then
it is checked if the the multipole expansion of the node provides an accurate enough
force. If the multipole expansion provides an accurate enough force, the walk through
that branch is stopped. If it is not accurate enough, the daughter nodes of this branch
are called and checked. This multipole expansion leads to an approximate force, but the
error on this force can be controlled by changing the criterion to call the daughter nodes.
The criterion is given by equation:
GM l 2
<α|α|
(2.3)
r2 r
14
Figure 2.1: The effect on the acceleration at close encouters when including gravitational
softening can be clearly seen in this plot. This plot was taken from the course on
Astrophysical Simulations of prof. Baes (Ghent University). On this plot the acceleration
is plotted as a function of the seperation between the two particles.
Where M is the mass in the node, l the size of the node and r the distance between
the particle and the center of mass of the node. | α | is the acceleration at the previous
timestep and α is the tolerance parameter. However it was shown that errors can become
large when standard opening criterions are used (Salmon & Warren, 1994). This happens
when the distance to the nearest particle in the node becomes very small. To protect
against these errors, a second opening criterion is added to the code.
| rk − ck |< 0.6l
(k ∈ {1, 2, 3})
(2.4)
Where r is the particle coordinate and c is the geometric centre of the node.
There are several possibilities to evolve the system in time such as the Runge-Kutta
integration, Gragg-Bulirsch-Stoer integration,... In the Gadget-2 code, a leapfrog integration was used. This integration scheme is a symplectic integration scheme, which
means that it preserves the Hamiltonian structure over the time integration. Integration schemes such as Runge-Kutta do not preserve the Hamiltonian structure. Using
a symplectic integration scheme leads to an extraordinary stabilitiy compared to e.g.
Runge-Kutta integration. This is shown by Springel (2005), where Runge-Kutta integration was compared with leapfrog integration for an elliptic orbit with high eccentricity, as can be seen in figure 2.3. The leapfrog integration shows a precession, while the
Runge-Kutta integration shows a drift in orbital energy. It has to be noted that the
fourth order Runge-Kutta integration requires several force computations for one time
step while leapfrog integration only requires one force computation per time step. This
15
Figure
2.2:
This
figure schematically shows the construction of
a particle tree in two dimensions.
This figure was taken from
http://http.cs.berkeley.edu/∼demmel/cs267/lecture26/lecture26.html
significantly reduces the computational cost while keeping a strong stability in the time
integration.
The timestep used in Gadget-2 depends on the gravitational softening , an accuracy
parameter η and the magnitude of the acceleration | α | of the particle. The timestep is
given by:
h
2η 1/2 i
(2.5)
∆t = min ∆tmax ,
|α|
Where ∆tmax ≈ 0.02 Gyr is the maximal timestep allowed in our simulations.
For simulating the behaviour of the gas, smoothed particle hydrodynamics (SPH) is
used. SPH is a Lagrangian approach for solving the hydrodynamics equations of a system. A Lagrangian method has the specific property that it uses co-moving spatial
coordinates of a fluid element. This is in contrast to the Eulerian method which follows
the state of a system at a fixed coordinate x.
In SPH, the fluid elements are represented by a limited amount of gas ’particles’. Then
the Lagrangian momentum equation has to be be solved for all these particles.
N
X
1
Gmj (xi − xj )
ẍi = − ∇pi −
ρi
| xi − xj |3
j=1,j6=i
(2.6)
Where pressure experienced by the hydrodynamical particles is the only difference in
this equation compared to the equation for the collisionless particles in the simulations.
This pressure is coming from the collisions on a microscopic level. The effect of this is
macroscopically represented by the pressure gradient.
16
Figure 2.3: The plot on the left shows the leapfrog evolution of the orbit, showing a
precession of the orbit. The plot on the right shows the Runge-Kutta evolution of the
orbit, showing a drift in the orbital energy. These plots were taken from Springel (2005)
Of great importance when working with SPH is the density estimate. In the Gadget-2
code this is done using
N
X
ρi =
mj W (r ij , hi )
(2.7)
j=1
Where r ij = r i - r j , hi is the smoothing length of the particle and W(r ij , hi ) is the SPH
smoothing kernel. In the case of the Gadget-2 code, the smoothing kernel is given by

2
3
r

1 − 6 h + 6 hr , 0 ≤ hr ≤ 12 ,


8
3
(2.8)
W (r, h) =
r
1
3
2 1− h ,
< hr ≤ 1,
πh 
2


r
0
>1
h
This smoothing kernel was proposed by Monaghan & Lattanzio (1985). The smoothing length hi of these particles is defined in Gadget-2 such that each kernel contains a
constant mass for the estimated density. This is constrained by
4π 3
h ρi = NSP H m
(2.9)
3 i
Where m is the average particle mass and NSP H the number of smoothing neighbours.
The first term in the Lagrange momentum equation used in the Gadget-2 code was
derived by Springel & Hernquist (2002):
"
#
N
X
1
Pi
Pj
∇pi =
mj fi 2 ∇i Wij (hi ) + fj 2 ∇i Wij (hj )
(2.10)
ρi
ρi
ρj
j=1
17
This equation conserves energy and entropy. Wij (h) stands for W(| r i − r j |, h) and
the particle pressure Pi = Ai ργi with Ai the entropy of the particle and γ the adiabatic
index. The coefficients fi are defined by
hi ∂ρi
fi = 1 +
(2.11)
3ρi ∂hi
To capture shocks that occur in the gas, an artificial friction term was added to the
Gadget-2 code.
N
X
(2.12)
ẍi,visc = −
mj Πij ∇i W ij
j=1
Where Πij ≤ 0 is non-zero when particles approach each other in space and W ij is
the average of the two kernels Wij (hi ) and Wij (hj ). This viscosity creates entropy,
transforming kinetic energy irreversibly into heat.
2.2
Dwarf Galaxies and Initial Conditions
As mentioned in the previous section, the N -body/SPH code that is used for the simulations is the freely available Gadget-2 code Springel (2005). This code was extended with
many relevant physical processes that govern (dwarf) galaxy evolution. These effects
include e.g. star formation, the heating and cooling of gas, chemical enrichment, feedback from stars and supernovae, the ionisation state of the gas, the cosmic ultra-violet
background (UVB) and the formation of population III stars in non enriched gas (Valcke,
de Rijcke & Dejonghe, 2008; Valcke et al., 2010; Schroyen et al., 2011; Cloet-Osselaer
et al., 2012; Schroyen et al., 2013; De Rijcke et al., 2013; Vandenbroucke et al., 2013;
Cloet-Osselaer et al., 2014; Verbeke, Vandenbroucke & De Rijcke, 2015; Verbeke et al.,
2014; Vandenbroucke, Verbeke & De Rijcke, 2016).
2.2.1
Included physics
Stellar particles
It is well known that collapsing gas clouds in a galaxy can lead to star formation under
certain conditions. To model this, star formation criteria have been included in the
simulation code (Valcke, de Rijcke & Dejonghe, 2008). These criteria are given by
∇·v<0
(2.13)
T < Tcrit = 15000K
(2.14)
ρg > ρcrit
(2.15)
18
These criteria are checked every time step for all gas particles. Equation 2.13 is
called the convergence criterion, which demands that the local gas flow is collapsing.
The second equation 2.14 is called the temperature criterion. This demands a minimum
temperature for the gas particle before it can be converted into a stellar particle. In
our simulations, Tcrit = 15 000 K is the critical temperature used for star formation
(Stinson et al., 2007). Apart from the gas being sufficiently cold, there is also need for
a high gas density to form stars. This is included using the last criterion, namely the
density criterion, with ρcrit the minimal density required. In our simulations, ρcrit = 100
amu cm−1 is used. This has been shown to be a good prescription for star formation
(Governato et al., 2010; Schroyen et al., 2013). Generally speaking, this is the most
stringent condition because it is rather unlikely that gas clouds reach such high densities
when they are not collapsing or if they have T > Tcrit .
If all these conditions are satisfied, the gas particle is allowed to transform into a stellar
particle. The star formation is implemented in the code using a Schmidt law (Schmidt,
1959).
dρg
ρg
dρ?
(2.16)
=−
= c?
dt
dt
tg
Where ρ? is the stellar density, ρg the gas density, c? the star formation efficiency and tg
is the dynamical time scale given by
tg = p
1
4πGρg
(2.17)
It was shown that c? only has a minor effect on the star formation history and that
models using a value around 0.2 for c? give dwarf galaxies that look most like observed
dwarf galaxies (Stinson et al., 2006; Revaz et al., 2009). In the case of our simulations,
c? = 0.25 is used (Cloet-Osselaer et al., 2014).
When a gas particle is converted into a stellar particle, this stellar particle needs to be
given certain properties. The stellar particle is assumed to represent a stellar population
of a certain mass. This stellar population then has the same metallicity and age. These
stars are modelled using an initial mass function, in the case of our simulations the one
of Chabrier (2003) is used. This function is compared with other initial mass functions
in figure 2.4.
These newly formed stellar particles have a strong impact on the interstellar medium
(ISM) of the dwarf galaxy. This happens through thermal feedback associated with type
II supernovae and stellar winds coming from young heavy stars. It is assumed that these
43
young stars inject 1050 ergs M−1
J M−1
(or 10
) into the interstellar medium via stellar
winds. The type II supernovae will inject 1051 ergs M−1
into the ISM. The effect of type
Ia supernovae on the galaxy is included as well. Since type Ia supernovae originate from
white dwarfs accumulating mass in a binary, a delay is included for this energy to be
injected in the ISM. To model this, a gaussian distribution is used with the mean at 4
Gyr and a standard deviation of 0.8 Gyr (Strolger et al., 2004). This distribution is cut
off at a standard deviation of 3σ.
19
Figure 2.4: A plot of the Chabrier initial mass function compared with other initial mass
functions that can be used (Mattsson, 2010). The green initial mass function is the initial
mass function used in Mattsson (2010).
The parameters given above only indicate the amount of energy released by these events.
However, this doesn’t say that much about its eventual effect on the interstellar medium.
To model this, one has to specify how easily this feedback can be absorbed by the ISM.
In the case of our simulations, an absorption efficiency of 0.7 is used (Cloet-Osselaer
et al., 2012). The feedback is distributed over the nearby gas particles using the SPH
smoothing kernel. In the simulations, the effect of feedback on a gas particle results in
the gas particle not being able to cool down radiatively during that time step.
Apart from feedback, the supernovae produced by these stellar particles also enrich
the dwarf galaxy with metals. In the case of these two types of supernovae included,
one only has to follow the abundances of Mg (magnesium) and Fe (iron). Following the
evolution of these two elements, one can deduce the entire chemical composition of the
galaxy (De Rijcke et al., 2013).
Population III stars
In 1944 Baade, who was working at the Mount Wilson Observatory at that time, devided
the observed stars in the universe in two types of stars (Baade, 1944). Namely population
I and population II stars. This division was based on the difference in metallicity of these
stars. Where population I stars have a higher metallicity than population II stars. It
was found that there was a correlation between the age of the stars and their metallicity.
The older stars seemed to have a lower metallicity. This led to the hypothesis of the so
20
called population III stars that were formed in the early universe. These stars that form
in the early universe have been a topic of research for a while. First investigations of
these stars include e.g. Ezer & Cameron (1971). They would have very low metallicity
since they were formed out of unenriched gas. Although theoretical research about these
objects has been done already, no stars with such a low metallicity have been observed
so far. This is not really surprising since it was shown in simulations that there is no
formation of population III stars at low redshift (Verbeke, Vandenbroucke & De Rijcke,
2015).
In figure 2.5 a plot is shown of the metallicity of the observed stars. This plot clearly
shows that one can expect that observations of nearby dwarf galaxies will not detect any
low metallicity stars.
Since no population III stars have been observed to date, the only possible input
for these stars is based on theoretical studies. This leads to some uncertainty whether
the effects of these stars in the simulations represent the reality. Yet it was shown by
Verbeke, Vandenbroucke & De Rijcke (2015) that the inclusion of these population III
stars can reproduce the most important observed quantities of gas rich dwarf galaxies.
There are some very important differences between the properties of the population III
stars and the stars forming out of enriched gas. First of all, they have a very different
initial mass function. The initial mass function used, can be found in figure 2.6. The initial stellar masses vary between 0.7 M and 300 M . The initial mass function is clearly
different from the Chabrier initial mass function, which contains a lot of low mass stars.
On the other hand the initial mass function used for population III stars contains much
more heavy stars (Susa, Hasegawa & Tominaga, 2014), this can be seen when comparing
figures 2.4 and 2.6 .
The assumption that population III stars form out of unenriched gas implies that
one has to put constraints on the metallicity of the gas that can form these population
III stars. When a stellar particle is formed in our simulations, it is assumed to be a
population III stellar particle if [Fe/H] < -5 for that particle. One can ask whether
this cut-off is at the ideal metallicity and probably the transition between population II
and population III stars will be smoother than the transition used in our simulations.
However not that much is known about population III stars for the moment. And it
is shown that simulations with this cut-off for population III stars are able to produce
dwarf galaxies that strongly resemble observed dwarf galaxies (Verbeke, Vandenbroucke
& De Rijcke, 2015).
Since these population III stars are clearly different from the population II stars, one
can expect that their effect on the environment will be different as well. For example,
the population III stars inject much more thermal energy into the galaxy. Their type II
supernovae would inject about 4 times as much energy in the ISM as type II supernovae
from the population II stars. The difference in energy injected by the young stars is even
21
Figure 2.5: This plot shows three different observations or theoretical observations of the
fraction of stars with a certain metallicity. The histogram is a real observation of LeoI, the
distribution that is rather nicely following this diagram is an observation of a simulation
that includes population III stars. It shows as well that no low metallicity stars will be
observed. The other graph is also an observation of a simulation, but this time without
population III stars included. This plot was taken from Verbeke, Vandenbroucke & De
Rijcke (2015)
larger. It is assumed that the energy injected by young population III stars is about 40
times higher than the energy coming from young population II stars (Heger & Woosley,
2010). The stellar winds and supernovae give lots of stellar mass back to the interstellar
medium. In the simulations a value of 45 % is used. The supernovae of population III
stars obviously give rise to enrichement of the interstellar medium. It is assumed that
the amount of Fe and Mg released is only 10 % of the chemical yield for these elements
coming from type II supernovae of population II stars (Heger & Woosley, 2010). This
yield has also been estimated based on observations of very low metallicity stars, since
these stars contain signatures from this yield (Nomoto, Kobayashi & Tominaga, 2013).
Cooling curves
For the cooling and heating curves of the gas, the calculations performed by De Rijcke
et al. (2013) were used. In this case the curves only depend on 5 parameters: temperature, density, redshift, [Fe/H] and [Mg/Fe]. Their calculations were done covering
a large interval of physical scales: densities up to 100 amu cm−3 , tempuratures ranging from 10 K to 109 K and including effects up to redshift z = 15. The ionisation of
14 elements is determined for this range of physics including radiative and collisional
ionization coming from the cosmic ultraviolet background and an interstellar radiation
field, and charge transfer reactions. These elements include e.g.: Fe, Mg, C, O, N, Ni,...
It concerns the elements that are mostly produced and/or released during type Ia and
type II supernovae, and by intermediate mass stars. A simplified model was used for the
22
Figure 2.6: The green function is a fit through the data points obtained by Susa,
Hasegawa & Tominaga (2014). This function is used as the initial mass function for
the population III stars. It can be seen that the initial masses vary between ± 1 M
and 300 M . This figure was taken from Verbeke, Vandenbroucke & De Rijcke (2015)
enrichment of the interstellar medium. In this model a distinction was made between
the fast contributions, coming from type II supernovae and young stars, and the slow
contributions, coming from type Ia supernovae and less massive stars.
A five dimensional interpolater was implemented by De Rijcke et al. (2013), allowing a
fast interpolation of the tabulated cooling and heating curves in the simulations. The
fact that only the Fe and Mg abundances need to be followed, reduces the memory requirements.
Another effect taken into account in the simulations is that part of the UVB and supernova energy injected in the gas leads to ionisation of this gas. Due to this ionisation,
the gas will be heated less since part of the energy is used to ionise this gas. This was
implemented by Vandenbroucke et al. (2013).
2.2.2
gogoIC, Kuzkut and Ganic
To set up the initial conditions, one uses gogoIC. This program calls two other programs,
namely Kuzkut and Ganic. Kuzkut sets up the initial conditions for the dark matter
23
halo of the galaxy using a Monte Carlo sampling method. The second program that is
called is Ganic. This programs adds gas particles to the previously created dark matter
halo, which is done as well using a Monte Carlo sampling method. Although a dark
matter halo is not required for Ganic to create a cloud of gas particles, but this feature
will not be necessary for this project. Many properties of the initial gas cloud can be
set, e.g. it is possible to give these gas particles an initial rotation. The initial rotation
can be generated based on different rotation profiles, e.g. a constant rotation profile,
a linearly increasing rotation velocity when moving away from the galaxy center or the
rotation velocity following an arctangential profile. This initial rotation can have a strong
influence on the galaxy observed in the current universe as will be explained later. This
influence will be discussed later when we go more into detail on the initial conditions.
Other properties of the gas cloud that can be set, are e.g. the initial temperature and
metallicity of the gas.
The gogoIC program can be used in two different ways. The first one is using a graphical
user interface. This graphical user interface is a very easy way to set up the initial
conditions, one simply has to select the desired dark matter halo, initial dark matter and
gas mass, feedback efficiency, critical density for star formation,... Using this graphical
user interface is however limited since it does not contain the latest updates. To really
make use of the full possibilities of gogoIC, one has to write an inputfile and then start
gogoIC using ’GOGOICmultiple.py’. An interesting possibility using the inputfile is that
one can generate several initial condition files at the same time. This is particulary useful
when working with a merger tree, since in this case lots of initial condition files have
to be generated. Using the graphical user interface the generation of initial conditions
has to be done one by one. Concerning our simulations, only the initial conditions of
one simulation was set up with the graphical user interface. This is mentioned here
because it will be shown later that there was something peculiar noticed about these
initial conditions. This peculiarity will be discussed later in this chapter.
2.2.3
Initial conditions
Cosmological parameters
When creating the initial conditions for the dwarf galaxies, there has to be decided at
which redshift one will set these initial conditions. This redshift will obviously be the
starting redshift for the simulation. A large initial redshift was chosen, namely z = 13.5.
From this redshift on, the created initial halo will evolve in a cosmological setting. The
cosmological setting is the ΛCDM model, the current standard model of cosmology. This
implies a flat universe currently dominated by the cosmological constant Λ. A flat universe implies that the current total critical density Ω0 is equal to 1. The critical density
of the so called dark energy ΩΛ is 0.7274. The universe being flat implies that ΩM =
0.2726, where matter consists of cold dark matter and baryonic matter. In the case of
our simulations ΩDM = 0.2250 and ΩBaryon = 0.0476. The Hubble constant is given
by H0 = 70.4 km s−1 Mpc−1 . These values are in agreement with the conclusions of
24
WMAP-9 (Hinshaw et al., 2013). The total evolution starting from z = 13.5 in this
cosmological setting takes 13.4 Gyr to arrive at z = 0. In the parameterfile of every
simulation, one can set after which time interval a new snapshot of the simulation has to
be saved. These snapshots contain all the information that can be used to analyse the
simulations. Making this time interval smaller, one can study the time evolution of the
galaxies with a higher resolution. Although using the birthtime parameter that is given
for every stellar particle, it is possible to achieve a higher time resolution in the star
formation rate without increasing the amount of snapshots per time interval. However
to study other parameters of the galaxy with higher time resolution such as the density
profile, the metallicity,... more snapshots are necessary.
The masses of the dark matter halos
It was found by many investigations both theoretical (Valcke, de Rijcke & Dejonghe,
2008; Revaz et al., 2009; Sawala et al., 2010) and observational (Tolstoy, Hill & Tosi,
2009; Mateo, 1998, and references therein) that the initial mass has a major influence
on the evolution of dwarf galaxies. Figure 2.7 shows the difference in star formation
depending on the initial mass of a dark matter halo. This figure was obtained from the
investigation by Valcke, de Rijcke & Dejonghe (2008). This implies that these simulations were by far not as accurate as current simulations. Yet the plot clearly shows an
effect of the initial mass on the star formation. This effect is obviously not limited to
star formation alone, it will also have its effect on luminosity, metallicity,... The effect of
the initial mass can be noted in our simulations as well. Figure 2.8 shows the difference
in star formation depending on the mass of the galaxies in our simulations. The two
star formation histories at the top of this figure are coming from two low mass dwarf
galaxies, which have a different initial rotation of the gas cloud.
By far the largest contribution to the mass of the galaxy is coming from the dark matter
halo. This comes to no surprise since it is generally accepted that there is way more dark
matter than baryonic matter in our universe. Since the initial gas mass of the galaxy is
based on the mass of the dark matter halo in our simulations, one can say that the choice
of the initial dark matter mass will have a major effect on the evolution of the galaxy.
Since the initial mass of the dark matter halo and the gas cloud are related and due to
the fact that the dark matter mass is much more dominant. When speaking about a
galaxy with a certain mass, we mean the initial dark matter mass, unless it is specified
differently.
For the eventual study of the tidal interactions, galaxies with 3 different masses were
used. Namely with masses: 1010 M , 2·1010 M and 4·1010 M . The magnitude in the
V-band of the most heavy model is close to MV = -17 and in the B-band close to MB
= -16. Which is an accepted rough working definition for dwarf galaxies proposed by
Tammann (1994). This can be seen in figure 2.9 where the evolution of the B-band
25
Figure 2.7: This plot shows the effect of the initial mass on the star formation history
of the galaxy. It contains 9 different mass models where C01 is the lightest model and
C09 the heaviest model. An important remark for noticing the effect of the initial mass
is the difference in scale on the y-axis. This plot was taken from Valcke, de Rijcke &
Dejonghe (2008)
and V-band magnitude are plotted for the 3 different masses used for the study of tidal
interactions. It should be noted that the gas cloud of the plotted low mass galaxy (1010
M ) has an initial rotation with vmax = 5 km/s. This note is important since two types
of low mass galaxies are used in the study of tidal interaction. One where the initial gas
cloud has no rotation and one where the maximal rotation velocity is 5 km/s. These two
galaxies have some different properties as will be discussed later.
However, models with these three masses are not the only models that were run in
isolation. Two models with an even lower mass of 2.5·109 M and 5·109 M were run
as well. These simulations proved useful, since they provided a lower limit for the mass
of the models that can be used for the main goals of this thesis. One of the main initial
goals of this thesis was to study if tidal interactions of dwarf galaxies could trigger starbursts in these dwarf galaxies. So it is necessary that the galaxies still contain enough
neutral hydrogen such that they can form a significant amount of stars. As can be seen
from figure 2.10, these galaxies barely (in case of 5·109 M ) or don’t (in case of 2.5·109
26
SFR [M /yr] SFR [M /yr] SFR [M /yr] SFR [M /yr]
0.010
0.008
0.006
0.004
0.002
0.000
0.008
0.006
0.004
0.002
0.000
0.040
0.035
0.030
0.025
0.020
0.015
0.010
0.005
0.000
0.25
0.20
0.15
0.10
0.05
0.00
sim5
sim6
sim30
sim59
2
4
6
8
10
12
t [Gyr]
Figure 2.8: This plot shows the star formation history of the galaxies used for the tidal
interactions. sim5 and sim6 are the low mass galaxies. Sim30 is the medium mass
galaxy and sim59 is the high mass galaxy. They show a clear difference in the rate of
star formation.
M ) form any stars after an initial burst. As can be noted from figure 2.10 as well, these
galaxies barely possess any neutral hydrogen near z = 0. Thus excluding a peak in the
star formation if no gas is captured e.g. by an inspiraling gas cloud. The capture of
gas from tidal interactions is rather unlikely for these galaxies since they don’t have a
lot of gas in their environment and neither possess enough mass to strip gas from other
galaxies and capture this gas. The fact that this is unlikely can be noted later, where it
can be seen that the low mass galaxies used in the interacting models don’t easily catch
a lot of gas from the other galaxy.
To be sure that this lack of remaining gas and star formation is no mass resolution
effect, a second simulation was done to check if this could be an issue. Certainly for
the galaxy with a halo mass of 5 · 109 M this could be interesting, since very rare star
formation is noted. However this led to the same results. After an initial star formation
peak both models almost completely stop forming stars. More information on the mass
resolution can be found later in this section about the initial conditions.
These low mass galaxies were run with the gas cloud having an initial rotation. This is
27
−18
−17
MB
−16
−15
−14
−13
−12
−11
−10
−18
−17
MV
−16
−15
−14
−13
−12
−11
low mass
medium mass
0
2
4
6
t [Gyr]
8
10
high mass
12
Figure 2.9: This figure shows the evolution of MV and MB for three models with different
masses as a function of time. The low mass model, is the galaxy with a high initial
rotation velocity of the gas cloud (see later).
done because simulations where the gas cloud has an initial rotation show a higher star
formation rate as was noted by Schroyen et al. (2013) and also seen in our simulations.
This implies that the low mass of the galaxies is probably the most important reason for
the lack of star formation. The observation of this lack of star formation is in accordance
with more realistic simulations involving a merger history by Verbeke, Vandenbroucke
& De Rijcke (2015). They noted a lack of star formation for dwarf galaxies with these
masses as well.
To make life easier, we will use short notations to describe the galaxies used in the
simulations of tidal interaction. There are four types of galaxies used in the simulations
of tidal interaction. Namely a low mass dwarf galaxy (1010 M ) where the gas cloud has
no initial rotation. To this dwarf galaxy will be referred with ”DG1”.
A second type of low mass galaxy (1010 M ) was used. But this time the gas cloud was
given an initial rotation with a maximal velocity of 5 km/s. To this dwarf galaxy will
be referred with ”DG2”.
The medium mass dwarf galaxy (2 · 1010 M ) used in the tidal interaction simulations,
has a gas cloud that was given an initial rotation with a maximal velocity of 2.5 km/s.
To this dwarf galaxy will be referred with ”DG3”.
The high mass dwarf galaxy (4 · 1010 M ) has a gas cloud that was given an initial
rotation with a maximal velocity of 2.5 km/s. To this dwarf galaxy will be referred with
”DG4”.
This is also summarised in table 2.1.
28
0.030
0.025
0.020
0.015
0.010
0.005
0.000
5
4
3
2
1
0
−1
−2
−3
−4
10
−53
0.030
0.025
0.020
0.015
0.010
0.005
0.000
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
−1
−2
−3
−4
10
−53
102
101
100
10−1
10−2
10−3
10−4
SFR [M /yr]
Mstar [106 M ]
[Fe/H]B
102
101
100
10−1
sim9 (high resolution)
MHI [106 M ]
MHI [106 M ]
[Fe/H]B
Mstar [106 M ]
SFR [M /yr]
sim21(high resolution)
0
2
4
6
t [Gyr]
8
10
12
0
2
4
6
t [Gyr]
8
10
12
Figure 2.10: The plot on the left shows a high mass resolution simulation of a galaxy
where the dark matter halo has a mass of 5·109 M . It can be clearly seen that the star
formation is almost completely shut down after 8 Gyr. On the right a galaxy is plotted
with a dark matter halo mass of 2.5·109 M . This is also coming from a simulation with
a higher mass resolution.
Density profile of the dark matter halo
The initial density profile used for all galaxies simulated in isolation is an NFW profile,
named after Navarro, Frenk and White, which is cusped (Navarro, Frenk & White, 1997).
This was proposed based on dark matter profiles obtained from large scale cosmological
simulations that only included dark matter. On the other hand, observations indicate
that dark matter profiles should have a core instead of a cusp (de Blok, 2010; Salucci
et al., 2012). The way to resolve this, is to include baryonic matter in the simulations.
It was found that through the gravitational interaction of the dark matter halo with the
baryonic matter that the halo transformed from being cusped to having a core (Read &
Gilmore, 2005; Governato et al., 2010; Cloet-Osselaer et al., 2012; Teyssier et al., 2013;
Brooks & Zolotov, 2014). We use the assumption that in the early stages of the universe
this baryonic effect did not really take place yet, such that the NFW profile is acceptable
to use for the initial conditions. The NFW-profile is given by
ρDM (r) =
ρs
(1 +
rDM,s
r
r
)2
rDM,s
(r < rDM,max )
(2.18)
This equation is used to generate the initial conditions for the dark matter halo. In this
equation rDM,s is the scale length and ρs is a characteristic density for the dark matter
halo. RDM,max is the radius where the profile is cut off.
By now, generalised NFW profiles have been proposed based on high resolution cosmological simulations. For low mass and high redshift halos such a generalised NFW profile
was proposed by Cen et al. (2004). For these halos, the density profile is dependent on
29
the halo mass and redshift. This generalised NFW profile is not necessary for the dwarf
galaxies used in the tidal interactions, since it only have to be used for a halo mass under
109 M .
The generalised NFW profile was used when constructing the merger tree simulations,
to compare with the galaxies obtained in isolation. This is necessary since in a merger
tree many low mass halos exist. And it was shown in the thesis by Cloet-Osselaer
(2015) that using a generalised NFW profile can have a significant effect on the early
evolution of these halos. In figure 2.11 the difference between a generalised NFW and an
Figure 2.11: The initial density profiles for the dark matter halo and the gas cloud in
Cloet-Osselaer (2015). These simulations where done with a halo mass of 0.9·109 M .
NFW profile can be seen, where the generalised NFW profile has a higher central density.
The creation of a generalised NFW profile is based on equation
ρDM =
( rrs )α (1
ρ0
+ rrs )4−2α
(r < rmax )
(2.19)
Where α and rs are dependent on the mass and redshift of the halo and rmax is the cutoff radius. Values for α and rs can be found in Cen et al. (2004). They obtained these
values by fitting a statistical distribution to many values obtained for these parameters
30
from different dark matter halos. To obtain the values needed for different masses in the
simulations the following function was used
f (M, z) = a(1 + z)b (
M
)(1+z)c
7
10 M
(2.20)
This function was fitted through their obtained data points for every parameter (CloetOsselaer, 2015).
The gas cloud
Not only a dark matter halo has to be created. As mentioned before a gas cloud has to
be added to the dark matter halo. The mass of this gas cloud is then fixed by the mass
of the dark matter halo. This is based on the ratio of baryonic and dark matter mass
in the universe. The initial density profile of the initial gas cloud is a pseudo-isothermal
profile (Revaz et al., 2009)
ρg (r) =
ρ0
2
1 + rr2
(r < rg,max )
(2.21)
g
In this equation ρ0 is the central gas density, rg is the scale length determined as in
Schroyen et al. (2013) and rg,max is the radius where the gas cloud is cut off. Since it is
determined as in Schroyen et al. (2013), the density of the gas cloud and the dark matter
halo are related as can be seen from figure 2.11. The density difference of the gas cloud
depending on the type of dark matter density profile will have its effect on the initial
star formation. This was shown by Cloet-Osselaer (2015), where it was found that the
higher central gas density for the generalised NFW profile led to a stronger initial star
formation peak.
It is possible to give the gas cloud an initial rotation. This initial rotation has a
crucial influence on the galaxy observed at z = 0 and its evolution (Schroyen et al.,
2011). It is also possible to have some different initial rotation profiles for the gas cloud.
Namely a uniform rotation profile, a linearly increasing rotation velocity or the velocity following an arctangential profile as mentioned already before. Building on previous
work done by Schroyen et al. (2013), the arctangential profile was chosen if an initial
rotation was given to the gas cloud.
vrot (r) =
r
2
vmax arctan(
)
π
rrot,s
(2.22)
Where rrot,s is the scale radius and vmax the maximal rotational velocity. This profile is
certainly favorable above the constant rotation profile, because this profile would give
the gas particles at the center of the initial galaxy an unnatural high rotation speed.
The influence of initial rotation can be seen in our simulations, namely in figures 2.12
and 2.13. First of all a more quiet start in the galaxy with an initial rotation is expected.
31
0.010
0.008
0.006
0.004
0.002
0.000
12
10
8
6
4
2
0
−1
−2
−3
−4
10
−53
0.010
0.008
0.006
0.004
0.002
0.000
25
20
15
10
5
0
−1
−2
−3
−4
10
−53
SFR [M /yr]
Mstar [106 M ]
[Fe/H]B
102
102
101
100
vinit,max = 5 km/s
MHI [106 M ]
MHI [106 M ]
[Fe/H]B
Mstar [106 M ]
SFR [M /yr]
vinit,max = 0 km/s
2
4
6
8
10
101
12
t [Gyr]
2
4
6
8
10
12
t [Gyr]
Figure 2.12: The evolution of the star formation rate, stellar mass, metallicity and neutral
hydrogen mass for the two low mass dwarf galaxies. On the left, the dwarf galaxy without
initial rotation is plotted and on the right the dwarf galaxy with initial rotation.
This can be explained by the fact that the initial rotation provides a barrier against immediate collapse of the gas. The initial rotation makes the gas spiral in, which makes
the star formation ignite more quietly (Schroyen et al., 2011). However this won’t be
compared here because of reasons explained later in this section. The first Gyr of the
galaxy evolution is also not plotted in figure 2.12 for aesthetic reasons due to the way
higher star formation in the first year of evolution. It can be seen that there is much less
neutral hydrogen expelled from the galaxy with initial rotation. Because there is lots of
neutral hydrogen continuously present in this galaxy, it is possible to have no significant
breaks in the star formation history. This is clearly not the case in the galaxy without
initial rotation.
The galaxies with a higher mass, namely with 2·1010 M and 4·1010 M , were given an
initial rotation as well, and don’t show any breaks in the star formation either. This
can be seen in figure 2.8. One could argue that this could be because of their deeper
gravitational potential such that not as much gas can escape. This might be part of the
story, yet the initial rotation helps as well igniting the star formation less burstlike such
that mass is not expelled in large amounts as would happen without initial rotation. The
maximal initial rotation that was given to these more massive dwarf galaxies is 2.5 km/s.
In Schroyen et al. (2011) it was shown that rotation has a strong effect on the star
formation history. It was noted that dwarf galaxies with higher rotation show a less
burstlike star formation history and have lower stellar mass. In our low mass galaxy
with initial rotation there is a slight burstlike behaviour on top of the continuous star
formation. This burstlike behaviour on top are statistical fluctuations in the star formation due to the formation of small clumps on top of the smeared out profile seen in
figure 2.14. This is not really the case in the galaxy without initial rotation, where only
32
MB
MV
MI
−16
−14
−12
−10
−8
−6
−4
−2
−160
−14
−12
−10
−8
−6
−4
−2
−16
−14
−12
−10
−8
−6
−4
−2
vrot = 0 km/s
0
2
4
6
t [Gyr]
8
10
vrot = 5 km/s
12
Figure 2.13: The evolution of the BVI magnitudes for the low mass dwarf galaxies with
initial and no initial rotation of the gas cloud. It can be seen that the galaxy with initial
rotation of the gas cloud is brighter in all bands.
the burstlike behaviour is observed. The continuous star formation in the galaxy with
initial rotation occurs because the gas is smeared out. This is not the case for the galaxy
without initial rotation where the gas is not smeared out as smoothly, but collapses into
clumps as seen in figure 2.14. Because of this, the star formation is more dependent on
the occasional collapse of the gas cloud in this galaxy.
The lower stellar mass with higher rotation is not observed in our simulations, as can be
seen in figure 2.12. Just like in Schroyen et al. (2013) a higher stellar mass is seen when
the gas cloud has an initial rotation. It has to be noted that in Schroyen et al. (2011) a
uniform gas profile was used instead of a pseudo-isothermal gas profile. An explanation
can be proposed then for this higher star formation. Since the pseudo-isothermal profile
is more compact in the center and the rotational velocity is lower at the center due to
the arctangential profile, it might be that the gas feels the centrifugal barrier less and
that this leads to higher star formation. Further this could lead to a more burstlike star
formation history of the galaxy, which can be observed in the star formation history
33
of our galaxy with initial rotation. This could be due to the fact that the initial star
formation is stronger. This higher initial star formation could lead to slight disturbances
on the smeared out galaxy. These clumps of higher density on top of the smeared out
gas can be seen in figure 2.14.
The higher star formation over the history of the galaxy with initial rotation obviously
leads to a higher stellar mass and slightly higher metallicity, as can be seen in figure 2.12.
In figure 2.13, a difference in the magnitudes between the two low mass galaxies is clearly
visible. The difference in magnitude is around 1 mag most of the time. Where the galaxy
with the higher brightness in all bands is as expected the galaxy with initial rotation,
since it has a higher star formation rate and a higher stellar mass. Other parameters of
the initial gas cloud are the same for all galaxies simulated. The gas cloud was given
an initial temperature of 104 K (Cloet-Osselaer et al., 2014) and zero initial metallicity
such that the gas was unenriched at the start of the simulations.
While checking the correctness of the simulations, an odd initial density profile of
the gas was found for the DG1 model as seen in figure 2.15. The initial conditions of
DG1 were created with the graphical user interface of gogoIC. When creating exactly
the same initial conditions with the inputfile, a completely different density profile for
the gas was obtained as can be seen as well in figure 2.15.
The initial dark matter density profiles are exactly the same up to some statistical
scatter. One could think that different initial gas profiles were used. But a thorough
search showed that they were both created using an pseudo-isothermal density profile
and that the other initial conditions were the same as well. A search through the code
that creates these initial conditions was done to find a reason for this strange behaviour.
A multiplicative difference of 0.01 was found for the central density when creating a
pseudo-isothermal profile. It is difficult to say that this is ’the’ reason for this odd behaviour. First of all because the central density of the gas should not be higher than
the central density of the dark matter, even with a multiplicative difference. Secondly,
the initial density profile of the gas created with the graphical user interface seems to
be divergent. This is not the case for a pseudo-isothermal density profile as can be seen
from equation 2.21. It also has to be noted that it is very weird that such a multiplicative
difference for the central density was found while no direct reason seemed to be available
for this. This doesn’t necessarily say that there is no reason for this difference, but this
reason was not found. So a completely satisfying answer for this problem was not found.
Since all tidal interactions with a DG1 galaxy are performed using the galaxy created
with the graphical user interface, one obviously has to wonder if this gives similar results
at the moment the tidal interactions will be studied. The tidal interactions were studied
starting after ± 10.5 Gyr of evolution. To do this, several properties are studied over
the evolution of the two galaxies. These properties are shown in figure 2.16. Looking at
these plots one can see that there is a difference in star formation rate up to ± 9 Gyr.
34
Figure 2.14: Plotted on the left plot is a snapshot of the gas density in the low mass
galaxy without initial rotation. The plot on the right shows the more smeared out low
mass galaxy with initial rotation. This galaxy also shows some higher gas densities, yet
it does not consist of two clear clumps like the plot on the left. The gas density in general
is more smeared out because of the rotation.
Afterwards the star formation rate gets very similar. This higher early star formation
obviously leads to more stars in the galaxy at z = 0. However this difference is ± 20
%, which is way less than when comparing the effect of initial rotation. It was found
that when the star formation becomes similar, the amount of neutral hydrogen is also
at the same level in both simulations. The galaxy created with the inputfile had more
neutral hydrogen up to ± 8 Gyr of evolution. But the higher star formation and thus
more feedback leads to a slow exhaustion of this extra neutral hydrogen. Also the magnitudes in the different bands are very close to each other, although generally the DG1
created with the inputfile is slightly brighter because there are more stars created in total.
The main difference can be seen when looking at the initial star formation shown in
figure 2.17. The gas density with the strong central peak has a very strong initial burst
compared to the pseudo-isothermal profile created with the inputfile. This comes to no
surprise seeing the high central density, since the star formation has a density criterion.
Mass resolution
The amount of particles used for the simulations in isolation of the galaxies depends
on the mass of the dwarf galaxy. This was done such that every galaxy was simulated
with the same mass resolution. For the low mass galaxies with a dark matter halo of
1010 M , 2·105 particles were used to model the dark matter halo. This implies that the
mass of every dark matter particle in the simulation is 5·104 M . For modelling the gas
cloud, 2·105 particles were used as well in the low mass galaxies. As mentioned before,
the amount of gas in the simulation is based on the ratio of the baryonic matter over the
35
104
DM (GUI)
gas (GUI)
DM (inputfile)
gas (inputfile)
ρDM [106 M /kpc3 ]
103
102
101
100
10−1
10−1
100
101
r [kpc]
Figure 2.15: The density profiles of the dark matter and the gas for DG1 when created
with the GUI or with the inputfile.
dark matter in the universe for which a value of 0.2115 is used. This implies a total gas
mass of 2.115·109 M in the initial galaxy. This leads to a mass resolution of 1.0575·104
M for the gas in the simulations.
To obtain the same mass resolution for the medium and high mass galaxies used in the
tidal interactions, they were simulated with respectively 4·105 and 8·105 dark matter and
gas particles.
The very low mass galaxies simulated, with masses of 2.5·109 M and 5·109 M , were
given the same resolution as well. This implies that 5·104 and 105 particles were used
to simulate the galaxies with respectively a dark matter halo of 2.5·109 M and 5·109
M . Although simulations with this mass resolution should be good enough for galaxies
in isolation (e.g. Schroyen et al., 2013; Verbeke et al., 2014; Vandenbroucke, Verbeke &
De Rijcke, 2016), a second simulation was run for the galaxies with a mass of 2.5·109
M and 5·109 M with respectively 105 and 2 · 105 particles. This was done since very
occasionally a gas particle was transformed into a stellar particle for the galaxy with a
halo of 5·109 M . So looking at this with a higher mass resolution was interesting since
simulations of this kind of galaxies do not require a lot of resources. The simulations
with higher resolution gave qualitatively and quantitatively the same results. Confirming
that the used resolution will be good.
2.3
Interaction of dwarf galaxies
To study the effects of tidal interactions of dwarf galaxies, two dwarf galaxies that were
simulated in isolation were put on a trajectory passing each other. The starting distance
36
0.010
0.008
0.006
0.004
0.002
0.000
12
10
8
6
4
2
0
−1
−2
−3
−4
10
−53
0.010
0.008
0.006
0.004
0.002
0.000
16
14
12
10
8
6
4
2
0
−1
−2
−3
−4
10
−53
SFR [M /yr]
Mstar [106 M ]
[Fe/H]B
102
102
101
100
inputfile
MHI [106 M ]
MHI [106 M ]
[Fe/H]B
Mstar [106 M ]
SFR [M /yr]
GUI
101
2
4
6
8
10
100
12
2
t [Gyr]
4
6
8
10
12
t [Gyr]
Figure 2.16: The evolution of DG1 constructed with the graphical user interface on the
left and the one constructed with the inputfile on the right. This plot starts after one
year of evolution, since the high initial star formation makes it difficult to create plots
that nicely show all properties.
between these galaxies was taken large enough such that tidal effects of both galaxies on
each other should be almost neglectable. So the initial conditions were constructed such
that the galaxies were initially seperated by at least 100 kpc. The specific models used
will be discussed later in this section.
Putting the galaxies together is a sort of balancing exercise. Since on one hand you
would like to have them starting as far as possible from each other, such that no tidal
effects are present at the moment these galaxies are put together. On the other hand if
you put these galaxies too far from each other. You spend a lot of computing time just
evolving galaxies that are in good approximation still evolving in isolation.
To obtain an idea if the initial seperation of more than 100 kpc is big enough, let’s
first have a look at the magnitude of tidal interaction. Where the tidal acceleration
experienced by a particle is given by
atidal =
2GMsource ∆r
R3
(2.23)
Msource is the mass of the source causing the tidal force, R is the distance between the
center of mass of the object experiencing tidal forces and the source, and ∆r is the
distance from the center of mass for the particle experiencing tidal accelaration.
It can be noted from this equation that tidal force is an R−3 law. Such that this force
drops extremely quick when increasing the distance of the source. 100 kpc is many times
the size of dwarf galaxies which have a radius of only few kpc. This implies that ∆r
R3
should make equation 2.23 relatively small for dwarf galaxies when R is higher than 100
kpc.
37
0.10
0.10
GUI
SFR (M /yr)
0.08
SFR (M /yr)
0.08
0.06
0.06
0.04
0.04
0.02
0.00
inputfile
0.02
0.2
0.4
0.6
time (Gyr)
0.8
0.00
1.0
0.2
0.4
0.6
time (Gyr)
0.8
1.0
Figure 2.17: The star formation in the first Gyr of evolution of the two DG1 dwarf
galaxies. On the left is the DG1 created with the graphical user interface. On the right
is the DG1 created with the inputfile.
2.3.1
Different interaction models
Trying to achieve a systematic study of tidal interactions of dwarf galaxies, one has to
cover a large parameter space. A first parameter one can vary is the mass of the interacting galaxies. As was shown in the section on the mass of the dark matter halo,
this can cover a large range of masses that lead to a different evolution of these galaxies.
However it was found that for initial halo masses lower than 5·109 M there is absolutely
no star formation and barely any gas present in the halo. It was also noted that 5·109
M was the absolute minimum for anything happening in the halo, but that even this
mass was too low for expecting effects in tidal interactions with other dwarf galaxies.
Halos with initial masses of 1010 M were the lowest mass halos that had a significant
star formation over their evolution and were able to keep a sufficient reservoir of gas that
could be affected by tidal interactions. The neutral hydrogen mass is of the order of 107
M . It thus seems fair to use this halo mass for the low mass halos in tidal interactions.
As was noted earlier, the halo with initial mass of 4·1010 M almost exactly satisfies
the limits of a dwarf galaxy that were proposed by Tammann (1994). So using the
galaxy obtained with this halo mass should be a good reference for a high mass dwarf
galaxy. The third halo mass used in the study of the tidal interactions has 2·1010 M as
initial mass. This is the dubbel of the low mass and half of the high mass galaxy, such
that it could be used as a medium mass dwarf galaxy.
Not 3 different galaxies in isolation are used for studying the effects of tidal interactions, but 4 as mentioned earlier. As demonstrated in Schroyen et al. (2011), the initial
rotation can have a big influence on the evolution and eventual galaxy observed. One
38
could expect that the effects of tidal interactions on these different galaxies would be
different as well. This is why tidal interactions on galaxies with the same initial halo
mass but with different initial rotation of the gas cloud are studied as well. The initial
mass and rotation are the two main parameters that influence the evolution of a galaxy.
So the division of the used galaxies is based on these two parameters. In table 2.1 the
main parameters of the galaxies run in isolation are given together with the name they
are referred to. One could wonder why only the effect of different initial rotation for
name initial mass of the dark matter halo initial rotation of the gas cloud
DG1
1010 M
vinit = 0 km/s
10
10 M
vinit = 5 km/s
DG2
2 · 1010 M
vinit = 2.5 km/s
DG3
DG4
4 · 1010 M
vinit = 2.5 km/s
Table 2.1: This table contains the initial mass of the dark matter halo and the initial
rotation of the gas cloud of the dwarf galaxies simulated in isolation that are used in the
tidal interaction simulations.
low mass galaxies is studied. This is purely based on the computational time needed for
the more massive galaxies. Simulating the evolution of these galaxies is very costly and
simulating the interactions with these heavier galaxies is even more costly. Such that it
would require more resources to do the same study for the more massive galaxies.
It could be questioned if this is sufficient to study the effect of rotation. But it was shown
in Schroyen et al. (2011) that initial rotation leads to quantitatively and qualitatively
different dwarf galaxies. Such that we should be able to study the general effects only
related to the initial rotation in the tidal interactions.
As one could expect, the main parameters of the galaxies are not the only parameters
that matter in tidal interactions. The effects could depend on the galaxy it is interacting
with. The effect of a more massive or a less massive galaxy could be completely different.
Furthermore one might expect that it could depend on the distance at the moment of
closest approach. The distance of closest approach already leads to a large parameter
space one could cover. But it might also depend on the eccentricity of the orbit.
One could try to reduce the size of this parameter space that has to be covered. For
example when looking at relatively close encounters one can avoid very high eccentricities since this would require extremely high relative velocities. Since we are looking at
tidal interactions, a lower limit can be put on the eccentricity. If the eccentricity is lower
than 1, the 2 galaxies form a bound gravitational system such that they should merge
after a while. Obviously the galaxies in this bound system will also experience tidal
forces. Yet it seems applicable to study these tidal forces in the context of the merging
process and not in the context of tidal interactions of two dwarf galaxies (Bekki, 2008;
Cloet-Osselaer et al., 2014; Starkenburg, Helmi & Sales, 2016). In practice this lower
39
limit can be pushed up even a little more. This is possible because of the interaction
of the gas clouds and the fact that we are considering N-body simulations, which could
lead to interactions with eccentricity just above 1 eventually leading to a merger. Such
that in our case a minimal eccentricity of 1.5 is used to study the tidal interactions. The
maximal eccentricity used is 3.5 such that a rather wide range of interaction paths are
covered. This can be seen in figure 2.18 where the paths for different eccentricities are
plotted. These plotted trajectories are idealisations of the true trajectories that would
be followed because of effects associated with the kinematics of the gas and the fact that
N-body systems are involved instead of point sources. Yet it gives a good visualisation
of the followed trajectories.
An earlier study of the effects of a gas cloud falling in by Verbeke et al. (2014) showed
great dependence on the way the gas cloud was falling in on the galaxy relative to its
rotation. It was shown that when the gas cloud fell in along a retrograde path a strong
burst in star formation was easily triggered. Yet a prograde path did not easily lead to
a strong burst in the star formation rate. This is a different study, but seeing this result
it is certainly worth to study this effect in tidal interactions.
Figure 2.19 shows the concept of a retrograde orbit. This is an orbit where the first
galaxy passes the other galaxy in the direction opposite to the rotation of that galaxy.
A prograde orbit is then a path where the relative motion is in the same direction as the
rotation of the object.
In comparison to the study by Verbeke et al. (2014) the definition of prograde and
retrograde is a bit more difficult since there are two galaxies involved and DG1 has no
initial rotation and no clearly defined rotation in the x-y plane. So it does not necessarily
mean that when a prograde interaction is chosen that this is prograde for both galaxies
when they have a rotation. So it has to be checked that all galaxies with a rotation have
the same rotation sense in the x-y plane. If they all have the same sense of rotation, this
would not pose a problem. Since in that case the interaction would be e.g. prograde for
both galaxies. If the two galaxies have opposite rotation sense, one galaxy will pass on
a prograde trajectory while the other galaxy will pass on a retrograde trajectory.
In case of our simulations this does not pose a problem since the rotation of all galaxies
with a rotation is in the same sense, such that prograde and retrograde are properly
defined. In the case DG1 is involved, it is put on a retrograde or prograde orbit of the
other galaxy. When two DG1 type dwarf galaxies are interacting, this is hard to define.
So when a prograde orbit is chosen, a track is used that would be prograde for one of
the galaxies with initial rotation. But for these galaxies no difference between prograde
and retrograde should be expected.
The paragraphs above give an overview of the different parameters considered for the
tidal interactions. To study the effects in a more systematic way, the simulations were
divided over 7 models. These 7 models were based on the characteristics of the galaxies
in isolation that were used in the interaction. In these seven models, simulations were
40
Figure 2.18: Plotted here are three orbits, with eccentricities ranging from 1.5 to 3.5,
showing the range of paths that are covered in our simulations.
run with a different orbit and different values for the pericenter distance and eccentricity.
These 7 models were used to have a clear view on the effect of interaction with different
galaxies. In the coming part, the specific properties of these 7 different models will be
discussed.
2.3.2
The models
In table 2.2, the specific properties of the interaction models are displayed. As was explained before, the galaxies used in our simulations depend on two parameters. Namely
mass of the dark matter halo and initial velocity of the gas cloud. It are these 2 parameters of the 2 galaxies that are listed in this table. The first three interaction models only
consider low mass galaxies. These are mainly used to study a possible effect of the initial
rotation of a galaxy in the interaction. So the effect on the galaxy with initial rotation
is studied when it is interacting with a galaxy without initial rotation but as well when
it is interacting with a galaxy with initial rotation of the same mass. The same is done
for the low mass galaxy without initial rotation.
The following three models , so I4, I5 and I6, introduce a galaxy with a higher mass,
referred to as medium mass galaxy or DG3. The gas cloud of this galaxy was given an
initial rotation of 2.5 km/s. These interactions make it possible to study the interaction
41
Figure 2.19: This plot shows a retrograde orbit of the red dot. Changing the direction
of rotation would lead to a prograde orbit of the red dot. This image was taken from
https://en.wikipedia.org/wiki/Retrograde and prograde motion
name
I1
I2
I3
I4
I5
I6
I7
Mgal1 (M )
1010
1010
1010
2 · 1010
2 · 1010
2 · 1010
4 · 1010
vinit,gal1 (km/s)
5.0
5.0
0
2.5
2.5
2.5
2.5
Mgal2 (M ) vinit,gal2 (km/s)
1010
0
1010
5.0
1010
0
10
10
5
1010
0
10
2 · 10
2.5
2 · 1010
2.5
Table 2.2: This table contains the mass of the dark matter halo and the initial rotation
of the gas cloud for both galaxies that are used in the interaction models.
of galaxies with a different mass. Studying the interaction of galaxies with different
masses is certainly important since one can expect that this could lead to different effects.
This expectation can be purely based on the higher mass leading to a higher gravitational
and tidal force exerted on the other galaxy. Again both low mass galaxies are put in
interaction with this medium mass galaxy to study the effect of their initial rotational
velocity. These two low mass galaxies will also be able to point to possible effects only
dependent on the mass of the halo. Not only is it possible to study the effects on a low
mass dwarf galaxy when it is interacting with a heavier galaxy. Looking at the more
massive galaxy can also tell us the effect of interacting with less massive galaxies. Model
I6 looks at the interaction of two medium mass dwarf galaxies, such that this can be
compared with the interactions with a low mass dwarf galaxy.
42
To make the study of the tidal interactions more complete, interactions with very heavy
dwarf galaxies would be interesting. This brings us to model I7. More than the models
before we are faced with computationally very demanding simulations, which strongly
limits the study of these interactions. This is why only one model of interactions with a
high mass dwarf galaxy is studied. Otherwise sufficient statistics on this model would be
impossible, and a lack of statistics would make the study of these models rather useless.
The question then is: which model to study? One could study the effect of the tidal
interaction of a high mass galaxy and a low mass galaxy. But to some extent this was
already achieved by models I4 and I5. It thus seemed more interesting to study the interaction of the medium mass dwarf galaxy with the high mass dwarf galaxy. This would
make the study of mass dependence of the tidal interactions more complete. Certainly
since the effect of rotation is already studied by the previous models.
It could be argued that taking the medium mass and high mass dwarf galaxies would be
far more computationally demanding than the interaction with low mass galaxies, since
this would include more particles in the simulation. However the most important reason
for the higher computational cost is dominantly that much more particles are in high
density areas of these galaxies. Since the time step is dependent on the density, this
leads to much more computations that have to be done. This was confirmed by noticing
that the simulation times of the galaxies in isolation with different masses and different
amount of particles clearly didn’t follow the N logN relation that only takes the amount
of particles (N) into account.
However some remarks should be made on this. First of all the difference in mass would
be bigger in case the low mass galaxies were used, such that the galaxies might need to
start with a larger distance between each other. Leading to the need for evolving this
simulation longer and thus increasing the amount of computations needed.
Secondly from the simulations of the galaxies in isolation it could be expected that the
dominant computational cost of these models would be the high mass dwarf galaxy. As
noted before, it not only has most particles but it also requires that more timesteps have
to be calculated. This increases the amount of computational time needed significantly
only because of the presence of the high mass galaxy. Taking into account that interactions with the low mass galaxy might need to evolve longer, these simulations might
grow as costly as interactions with the medium mass galaxy. It is thus fair to say that
computational costs should not be used as an argument not to study the interaction with
medium mass dwarf galaxies.
2.3.3
Initial velocity
When the two dwarf galaxies are put together such that they can interact, they are
also given an initial velocity towards each other. This initial velocity is based on the
trajectory of the galaxies and their masses. This mass was determined by looking at the
43
mass within a certain radius around the center of the galaxies. For DG1, DG2 and DG3
a radius of 20 kpc was used, for DG4 a radius of 30 kpc was used. These were rather
good radii, since even the dark matter denstiy at these radii was very low. Trajectories
with eccentricities between 1.5 and 3.5 were taken as mentioned before, since trajectories
with a higher eccentricity seem rather unplausible. The initial velocities generated vary
between minimally ± 60 km/s for the interactions of low mass dwarf galaxies and a
maximum of ± 145 km/s for the interaction of medium and heavy dwarf galaxies.
On itself these initial velocities don’t say that much since they are dependent on the
initial distance of the interacting system. But this can be used for a comparison with
observational data. For this we have a look at the observational data obtained by Noeske
et al. (2001). They determined the recession velocity difference relative to us for dwarf
galaxies within a projected distance of ± 100 kpc of one another. They found these
recession velocity differences could reach up to 250 km/s but with the larger amount of
velocity differences being way lower. The distribution can be seen in figure 2.20, which
was taken from their publication.
Looking at our initial velocities, they seem to be in the same interval as these observational measurements. The higher velocities in the observations could be explained
because the above mentioned speeds in our simulations are only the initial relative speeds,
thus the speeds at a distance of about 100 kpc and higher. But when the galaxies approach each other they will accelerate which will lead to higher relative velocities. To
have an estimate of the relative velocity at the moment of closest approach, conservation
of energy can be used. This is done using equation
=
v2 µ
−
2
r
(2.24)
Where is the specific orbital energy of the system. µ is given by G(M1 + M2 ) with G
the gravitational constant and M1 & M2 the two masses of the objects, in this case the
galaxies. The orbital velocity of the two objects is given by v and the r gives the radial
distance.
This formula is used to have an estimate of the maximal relative velocity that occured in
our simulations. To achieve this, formula 2.24 was applied to the system with the highest
initial velocity. The relative velocity of these galaxies was then determined when their
radial distance is 12 kpc. This is the radial distance of the two galaxies at the moment
of closest approach. The calculations gave a maximal relative velocity of 213 km/s. This
of the same order of magnitude of the maximal recession velocity differences proposed
by Noeske et al. (2001).
When having a detailed look at the velocity distribution in figure 2.20, one can see
that there is also a significant fraction of galaxies with recession velocity differences
smaller than 50 km/s. This is not really a huge problem. First of all, figure 2.20 only
shows the recession velocity difference which is not always a good representation of the
real relative velocity, such that the effective relative velocity might be higher. A second
44
Figure 2.20: Important is the continuous line in this plot which shows the observational
difference in recession velocity of the dwarf galaxies that are within a projected distance
of ± 100 kpc of each other.
remark is, that they were only looking at dwarf galaxies near each other. However it is
perfectly possible that some of these galaxies near each other will eventually merge, but
merging galaxies was not part of our study. So in conclusion, the fact that the relative
velocities in our simulations are roughly in the same interval as observational recession
velocity differences gives confidence that realistic tidal interactions of dwarf galaxies are
studied.
2.3.4
Amount of simulations
As stated before a huge parameter space has to be covered when studying these tidal
interactions. This leads to the requirement of a large amount of simulations for an indepth study. To achieve this, 140 different simulations of interactions were performed.
This in not including some simulations that were done a second time but with a higher
time resolution, which allows a deeper study of these simulations.
These 140 simulations were rather equally distributed over the 7 interaction models.
Only for model I7 less simulations were run due to the high computational cost. For
model I7 only 10 simulations were run, where for the other models ± 20 simulations were
done.
In these specific models about half of the simulations were done with prograde trajectories and the other half with retrograde trajectories. Thus allowing a study of these
45
effects. All the initial conditions of the performed tidal interactions are listed in appendix
6.
2.4
Hyplot
To analyse the data obtained from the simulations, scripts were written in python. These
scripts made use of the analysis tool called Hyplot. This tool is publically available 1 and
is designed for the analysis of N-body/SPH simulations. Very specifically for datafiles
coming from the Gadget-2 simulation code. It can directly give quantities of galaxies
evolved in isolation. This analysis tool is constructed using three programming languages. Namely C++, Fortran and Python. The C++ and Fortran code are used for
reading the data files and performing calculations. While Python is mainly used for
plotting and scripting (Valcke, 2010; Schroyen, 2013).
As noted already, it is rather easy using HYPLOT to plot any basic quantities of a
galaxy evolving in isolation. When working with two galaxies in the simulation, one has
to take care that you know on which galaxy you are centered and thus taking data from.
This extra care one has to take when more galaxies are involved will be discussed a little
deeper in the coming part.
2.4.1
Recognising the galaxy
HYPLOT has the built in function rcom(). Several arguments can be given to this
function depending on what you want, but we won’t go into detail about this. This
function doesn’t just calculate the center of mass in the data file but finds the center
of mass of a galaxy. It can then put this center of mass at the origin, thus shifting
the data. It can also give you the position of the center of mass with respect to the
origin. But this feature was not really used. It is also possible to choose on which type
of particle you want to center. You can look for the center of mass for the stars, gas or
dark matter. It is also possible to find the center of mass based on all three types of
particles. In most cases of the analysis, the centering is done based on the stellar particles. Since observationally, light coming from stars are a general way to identify a galaxy.
Since this function will center on a galaxy in the data file, two questions arise: On
which galaxy did it center? And secondly, how can you center on the other galaxy?
Let’s start with answering the second question.
After you centered on the first galaxy, you calculate the physical quantities of this galaxy.
This is done assuming the galaxy is contained within a certain radius. When you have
calculated the properties, you want to center on the second galaxy. This is done by
putting the calculation of this physical quantity in a loop over the amount of galaxies
1
https://sourceforge.net/projects/hyplot/
46
in the data, which is two in our case. Important to achieve recentering, is to use the
reset() function which resets certain flags. This makes sure that using rcom() again will
actually recenter the data. Otherwise the data will just stay at the same position since
rcom() function gets the signal that it has already centered and will not try to recenter.
You can expect that just using reset() and in the second part of the loop rcom() again,
will lead to centering on the galaxy it already centered on the first time. This can be
expected since this galaxy should still be the preferred center of mass. This can be
avoided by removing this galaxy from the data. This is done by applying limits on the
data based on the radius. When this galaxy is removed from the data, you can reuse
rcom() for centering on the second galaxy. This procedure can be extended for as many
galaxies as there are in the data. However one has to take care when two galaxies are
very close that you don’t remove both galaxies or part of the second galaxy based on the
radius.
The previous part answered the question on how to recenter on the second galaxy in
the data. But still you don’t know on which galaxy you centered during these processes.
In the case of galaxies with different masses it will generally center first on the most
massive galaxy and afterwards on the lower mass galaxy. However you want to be sure
about this and in the case of two galaxies with almost the same mass you can’t really
have an idea on which galaxy there was centered first.
To know on which galaxy you centered, you can use the identities of the particles.
The particles are namely identified by a number, so each particle in the simulations has
a number. And maybe most importantly, this number stays the same over the entire
lifetime of this particle.
To define what is the first and what is the second galaxy, we look at the first datafile
of this interaction. For which we perform the centering procedure explained above. But
instead of calculating physical properties for the galaxy centered on, the id numbers of
100 stellar particles in both of these galaxies are stored in two different lists.
Then when looking at the snapshots of interest, there is looped over the two galaxies to center on both of them. However except for calculating the physical properties
of this galaxy, a list of all the id numbers of the stellar particles in the galaxy is made
as well. It is checked for all these id numbers if they can be found in one of the two
arrays that contain the reference id numbers. After this is done for all stellar particles,
one could expect that this galaxy would contain 100 stars of a certain list and thus the
galaxy is identified. This could be end of story, but since galaxies are dynamic enviroments it is possible that one or a couple of these stellar particles get ejected out of the
galaxy. So a good criterion to identify this galaxy would be that the galaxy contains
at least 70 or 80 of these reference stars. Since normally not that many stars are lost
over the time we are looking at these galaxies, even when the galaxy is tidally interacting.
47
So to plot physical properties over the evolution of time for both galaxies, two arrays
were defined such that each array contained the physical property of the same galaxy
over its entire evolution. The allocation to these arrays was based on the identification
explained above.
48
Chapter 3
Results
In this chapter results obtained using the analysis tools will be presented and shortly
discussed. Since the first objective of this thesis was to study if tidal interactions could
trigger starbursts in dwarf galaxies, the first results to be discussed will be about the
star formation rate over the evolution of the interacting galaxies.
Afterwards other properties of these dwarf galaxies will be discussed as well. Such as the
density profiles at certain points in the evolution, the evolution of the velocity dispersion,
the gas mass available in the galaxy,...
It will be checked if certain events in the evolution of these galaxies can be related and
if certain events can be explained by other properties seen at the same time. This won’t
be always discussed in full detail since a more in depth study will be done in the next
chapter.
3.1
Star formation history
By several observational studies it was shown that there are dwarf galaxies that show
an extaordinary star formation who are accompanied by other dwarf galaxies (Brinks
& Klein, 1988; Brinks, 1990; Campos-Aguilar & Moles, 1991; Noeske et al., 2001). For
this reason it is of great interest to have a look at our simulations and see if these tidal
interactions are able to trigger remarkable bursts in these dwarf galaxies. It has to be
noted that it is not necessarily expected that both galaxies show star formation bursts
and certainly not at the same time. Since these studies note that in many cases it is
very hard to see the compagnon.
When speaking of starbursts it would be nice to have a definition to characterise this
burst. This is not that easy, since the star formation in the galaxies clearly varies over
the evolution of the galaxy as can be seen from figure 2.8. So a star formation rate that
would be characterised as a burst after 12 Gyr of evolution would not necessarily be
characterised as a burst after 3 or 4 Gyr. This is why we use the definition proposed
by Verbeke et al. (2014) to determine the burst factor of a certain star formation peak.
49
We can do this since both studies are about bursts at late stages of the dwarf galaxy
evolution.
Their definition only takes into account the star formation over the last 3 Gyr of the
host, so the galaxy in isolation. The star formation rate at the peak is then divided by
the average star formation rate of the host over the last 3 Gyr. This is expressed by
equation
(3.1)
b = SF Rpeak /SF Rhost
Where ’b’ is the burst factor. In their paper they also characterise these bursts based on
the burst factor. When the burst factor of the peak is higher than 5, they characterise
it as a burst. When the burst factor at the peak is larger than 10, they characterise it as
a strong burst. This definition was used for all galaxy models in their simulations. This
definition will not be used in this thesis. Why this definition is not used will be shortly
discussed in the coming part.
As already explained and you might have seen from figure 2.8, the star formation history
is highly dependent on the dwarf galaxy model that is used. Some models clearly have
a more burst like behaviour than other models, certainly after 10 Gyr of evolution. To
show this, we apply definition 3.1 to the galaxies in isolation. We only consider the star
formation history after 10 Gyr of evolution, since none of the tidal interactions in our
models take place before 10 Gyr of evolution. The results are shown in table 3.1.
name burst factor
DG1
4.19
DG2
2.84
DG3
1.61
DG4
2.24
SF R (M /yr)
4.2 · 10−4
1.3 · 10−3
1.2 · 10−2
4.3 · 10−2
Table 3.1: This table contains the burst factors of the galaxies in isolation.
Based on these numbers it could be claimed that there is not really a line in the
burst factors. But when looking in great detail to figure 2.8. It can be seen that there
is a small star formation peak in DG4 just after 10 Gyr of evolution. When looking at
the star formation history of DG3, it can be noted that there is a slightly higher star
formation rate just before 10 Gyr of evolution. Comparing this with the peak in DG4,
one could expect that peaks in DG3 just before 10 Gyr of evolution will have a similar
burst factor. This was checked by including 500 Myr extra in the analysis. In that case
a burst factor of 2.13 is found for the medium mass galaxy (DG3) in isolation. This
burst factor probably gives a more accurate representation for the medium mass galaxy.
In conclusion, it can seen that there is a difference in what can be classified as a burst
in each galaxy.
Another reason why not necessarily the same definitions have to be used is the fact that
new physical processes are included in the code used since the publication by Verbeke
50
et al. (2014). First of all an ultraviolet background is included and secondly, population III stars are included in the code used for this investigation. It is already shown
in publications that this has a significant influence on the galaxy evolution (Verbeke,
Vandenbroucke & De Rijcke, 2015; Vandenbroucke, Verbeke & De Rijcke, 2016).
As a last argument, in this thesis the star formation rate is determined by looking at time
intervals of 50 Myr. In each time interval the star formation rate is then determined. As
mentioned in the previous chapter, this star formation rate can also be determined with
other time resolutions. We will show later that this can lead to different burst factors.
This is another reason why the definition of a burst and a strong burst by Verbeke et al.
(2014) can not directly be applied to our simulations, since it is not immediatly clear if
the same time interval is used in this paper.
3.1.1
Burst factors in the interacting models
I1
All models had simulations where significantly higher burst factors were seen compared
to the same galaxy in isolation. This burst factor was dependent on the galaxy as stated
above.
Looking at model I1, some remarkable bursts were noted in DG1. In 4 of the 23 simulations of this model, a burst factor higher than 6 was obtained. With a maximal burst
factor of 6.99. As can be seen from figure 3.1, a burst factor bigger than 6 is certainly
noteworthy for this type of galaxy. Such that we will use this burst factor to define a
burst in DG1.
In the case of DG2, the burst factors are not that high in the I1 model. This can be
seen from figure 3.2, which shows the highest star formation peak in this model for DG2.
This star formation rate is not that much higher than the maximal star formation rate
in the model in isolation and neither remarkable enough to be classified as a burst.
In the two plots mentioned above, the peak in the star formation rate happens shortly
after the point of closest encounter. This closest approach occurs in all models after 11.4
or 11.5 Gyr of evolution. The bursts in the models with the low mass galaxies generally
occur around this time. But for the moment we won’t go into detail about this. The
moments that the bursts occur will be discussed in more detail in the following chapter.
I2
In this model, two low mass galaxies with initial rotation are interacting with each other.
Based on the maximal burst factor of the galaxy in isolation, it is not expected that these
galaxies will reach burst factors as high as DG1. However higher star formation peaks
are obtained in this model. The maximal burst factor obtained in these galaxies is 4.42,
51
Figure 3.1: This plot contains the comparison of the star formation rate of the galaxies
in isolation and the two galaxies in an I1 interacting model. On the left DG2 is plotted,
on the right DG1 is plotted. The burst factor at the peak of the galaxy on the right is
6.87, the maximal burst factor in the galaxy on the left is 3.09. The vertical line indicates
the moment of closest approach.
Figure 3.2: The plot on the left shows the highest star formation peak of the galaxy with
initial rotation in the I1 model. The burst factor of this peak is 3.86. The vertical line
indicates the moment of closest approach.
52
which is shown in figure 3.3. Over all the 22 simulations in total of this model, there are
3 simulations where a galaxy shows a peak with a burst factor higher than 4. The peak
with a burst factor of 4.42 is strong compared to the star formation in isolation and in
general any peak with a burst factor higher than 4 seems to be rather remarkable for
this type of galaxy. This is why peaks, in low mass galaxies with initial rotation, that
have a burst factor higher than 4 will be referred to as bursts in this thesis.
I3
In this model, two low mass dwarf galaxies without initial rotation are tidally interacting.
As mentioned before, a burst factor of 6 will be used to classify a peak as a burst. Of
the 21 simulations done, 4 contain a galaxy with a burst factor higher than 6. The
maximal burst factor that was obtained is 7.43. So it seems that it is possible to trigger
significant star bursts in DG1 with galaxies of similar mass irrespective of their initial
rotation. Based on model I1, this does not seem to be the case for DG2. This is not such
a big surprise since the initial rotation of DG2 provides a certain stability against collapse
of the gas (Schroyen et al., 2011). That in model I2 bursts occur might be attributed
to the fact that DG2 creates a higher tidal force than DG1 since more gas and stars are
contained within the galaxy. Although it could still be a statistical fluctuation due to
the small amount of bursts in this type of galaxy. But the large difference in maximal
burst factor for DG2 when comparing I1 and I2 doesn’t really support this last remark.
I4
This is the first model that also includes something else than only low mass galaxies,
namely DG3. In this specific model this medium mass dwarf galaxy is interacting with
the low mass dwarf galaxy with initial rotation. For the low mass galaxies in this model,
in 3 of the 23 simulations a peak with a burst factor higher than 4 is encountered which
is earlier defined as a burst in this type of galaxy. The maximal burst factor that was
obtained is 4.27. All these bursts occur when the distance at closest approach is larger
than 20 kpc, which is rather remarkable. It could be that DG2 gets disturbed too much
when it has a closer approach such that a burst can not occur. However no conclusive
proof was found for this when looking at other properties of the galaxy.
Also noteworthy peaks appear in the star formation history of the medium mass dwarf
galaxies during these interactions as shown in figure 3.4. The highest peak during the
interaction is remarkably higher than the star formation rate of the galaxy in isolation.
But also very noticable and rather surprising is the peak in this galaxy only 100 Myr
after the two galaxies were put together. To directly point at ’the’ explanation for this is
quite hard. Since the two galaxies are put together and this peak does not show up in the
galaxy in isolation it can be argued that this is caused by the second galaxy. However
the small galaxy being able to trigger a burstlike event in the medium mass galaxy
seems rather unlikely at that moment due to the small tidal forces then. Most likely
this peak should not be classified as a burst taking into account what was mentioned
53
Figure 3.3: The peak in the left plot has a burst factor of 4.42 and the peak in the
right plot has a burst factor of 3.76. The vertical line indicates the moment of closest
approach.
Figure 3.4: These star formation histories come from an I4 type interaction simulation.
Both galaxies are displaying strong star formation peaks, with a maximum of 2.57 for
DG3 and 4.12 for DG2. The vertical line indicates the moment of closest approach.
54
earlier. Namely that just before 10 Gyr this medium mass dwarf galaxy still has a slightly
higher star formation rate where the highest peaks would give burst factors up to ± 2.1,
although this is still lower than the burst factor of the early peak which is 2.31. It has
to be noted that this was the maximal burst factor seen that early in the evolution of
DG3 for all interaction simulations that were run.
A burst factor has to be defined to classify a specific peak as a burst in the medium
mass dwarf galaxies. We will use a burst factor of 2.5 to classify a peak as a burst in this
thesis. Using this definition only one of the 23 simulations has a medium mass dwarf
galaxy showing a burst. This burst has a burst factor of 2.57.
I5
In this interaction model, the medium mass dwarf galaxy is interacting again with a low
mass dwarf galaxy. But this time the low mass dwarf galaxy without initial rotation of
the gas cloud.
Based on the previously defined burst factors, there are bursts in both types of galaxies.
In 2 of the 20 simulations of this model a burst occurs in the low mass dwarf galaxies, with
the maximum burst factor being 6.36. Also in 2 of the 20 simulations, a burst occurs in
the medium mass dwarf galaxy. It has to be noted that these 2 simulations are different
simulations than the 2 with a burst in the low mass dwarf galaxy. The maximal burst
factor obtained in a medium mass dwarf galaxy is 2.72. The star formation history of
the simulation with the highest burst factor for the medium mass dwarf galaxy is plotted
in figure 3.5. As can be seen, this peak is way higher than all other star formation. The
peak occurs ± 150 Myr before the moment of closest approach. So in this case it seems
very plausible that the tidal interaction with the other dwarf galaxy triggers the star
formation burst.
I6
This model studies the interaction of two medium mass dwarf galaxies. In 5 of the
21 simulations, a burst in at least one of the two galaxies is detected. Where 3.15 is
the maximal burst factor that was obtained. It also has to be noted that in one of
the simulations both galaxies had a burst factor higher than 2.5. The star formation
histories for this simulation are plotted in figure 3.6. Also intersting to note is that this
simulation contains the two star formation peaks with the highest burst factor of this
model, namely 3.15 and 2.81. Remarkably these peaks occur at completely different
moments. One happens directly after closest approach and the one in the other galaxy
about 1 Gyr after closest approach.
I7
In this model only very few tidal interactions were studied. But still a star formation
peak was noticed in the medium mass dwarf galaxy. This peak had a burst factor of
55
Figure 3.5: This plot shows the strong star formation that is triggered in the medium
mass dwarf galaxy because of tidal interactions with a low mass dwarf galaxy. The
vertical line indicates the moment of closest approach.
Figure 3.6: Plot of the star formation rate where both medium mass dwarf galaxies have
a burst over their evolution. The vertical line indicates the moment of closest approach.
56
2.64, such that it is classified as a burst in our study. In the case of the high mass dwarf
galaxy, no really significant peaks were observed. The maximal star formation peak in
the interacting models still had a lower star formation rate than the small peak in the
galaxy in isolation just after 10 Gyr of evolution.
To classify a peak as a burst in DG4, a burst factor of 2.5 seems a fair requirement. Yet
this is by far not reached in the performed simulations, so one can not speak of a burst
in these galaxies. This doesn’t mean that no burst can occur since only 10 simulations
with a DG4 were run. But no peaks with a burstfactor higher than 2.2 were seen, which
indicates that it might be rather difficult to trigger a burst in DG4 with a less massive
dwarf galaxy.
3.1.2
Prograde vs retrograde
Looking at the orbit when a burst occurs, there is no unambiguous dependence on the
type of orbit found. For DG1, 6 burst were noted when it was on a prograde orbit and
4 were noted when it was on a retrograde orbit. Indicating that the type of orbit is of
no importance for this dwarf galaxy model, as was expected. For DG2, 4 galaxies had a
burst when they were in a prograde orbit and 2 galaxies with a burst were found with a
retrograde orbit. For DG3, 3 galaxies had a burst when they had a prograde orbit and
7 galaxies with a burst were found in a retrograde orbit.
Seeing these results it is not easy to point at a specific orbit that more easily causes a
burst in a dwarf galaxy. The small spread seen could be caused by rather poor statistics
in the amount that could be classified as a burst. When taking the statistics for DG2
and DG3 together, 7 galaxies were in a prograde orbit and 9 were in a retrograde orbit.
This doesn’t point to a dependence on the type of orbit for the dwarf galaxies to have a
burst. This is in contrast with the observations of a gas cloud falling in, where a strong
dependence on the type of orbit was found Verbeke et al. (2014). This doesn’t have to
be completely surprising, since in the case of our simulations the burst is triggered using
a different mechanism.
A dependence on the eccentricity wasn’t found either. The orbits that had a burst,
had eccentricities ranging between 1.8 and 3. That no bursts were found on an orbit
with an eccentricity higher than 3, doesn’t really say much since very few interactions
with an eccentricity higher than 3 were run.
3.1.3
Duration of the bursts
As already mentioned, it is possible to determine star formation rates in different time
intervals since the birthtime is stored. Looking at this might be interesting since it
could shed more light on e.g. the duration of bursts. Using the 50 Myr time interval to
determine the star formation rate didn’t really allow to determine the duration of the
bursts, since in almost every case the peak consisted of only one time interval. To study
the duration of these bursts, there was zoomed in on the bursts in time and using the
57
birthtime of the stars it was tried to determine the duration of the burst.
In case of DG1, these bursts are of very short duration in time with a maximal duration of the order of ± 10 Myr as can been seen in figure 3.7. When looking more into
detail to the gas flow at the moment of a burst in a DG1 dwarf galaxy we will try to
explain why this happens. The fact that this burst is of such a short duration leads to
a very strong sharp peak in the star formation history. When looking at the bursts of
DG2 with a higher time resolution, a very different behavious is observed. The bursts
occur during a longer time interval, going up to 50 Myr like in figure 3.8. Such that it
is not one sharp peak, but the burst consists of an increased star formation for a short
while. In the case of the burst in figure 3.8 the burst seems to be split into two by a very
short interval of 10 Myr where no star formation occurs.
In the case of DG3, two different types of burst were found when looking with a
higher time resolution. This is shown in figure 3.9. The first type of burst can take up
to 80 Myr, which has a strongly increased star formation over this time. This looks a
lot like the bursts seen in DG2 type galaxies. On the other hand, bursts with one sharp
peak have been found as well. These look more like the peaks observed in DG1 type
dwarf galaxies. A possible explanation for this behaviour could be the initial rotation of
the dwarf galaxy, since DG3 has a maximal initial rotation velocity of 2.5 km/s. This is
exactly between the initial rotation velocities of the two low mass dwarf galaxies.
3.2
Velocity dispersion
In the previous section it was shown that significant star formation peaks can occur while
two dwarf galaxies are tidally interacting. Due to the large feedback coming from the
young stars, one can expect that this will have a visible impact on the dwarf galaxies.
First we will look for its effect on the velocity dispersion in the galaxy. Where both
the velocity dispersion of the gas and the stars will be considered. When looking at the
effect of feedback, it can also be checked if the tidal interactions have any effect on the
velocity dispersion in the dwarf galaxies.
To determine the velocity dispersion, the following formula is used
r
σx2 + σy2 + σz2
(3.2)
σ=
3
P
2
Where σx2 = N1 N
i=1 (vx,i - vx,av ) . This is calculated, taking into account all stellar and
gas particles within a radius of 5 kpc. Such that N is the amount of gas or stellar particles within a 5 kpc radius from the galaxy center.
For DG1, there is a strong peak in the velocity dispersion of the gas after a burst.
This can be seen in figure 3.10. The effect on the stellar velocity dispersion is hardly
or not noticable. The velocity dispersion can show peaks up to about twice the average
58
Figure 3.7: A high time resolution of a burst in a DG1 dwarf galaxy. The time resolution
in this image is 5 Myr.
Figure 3.8: A higher time resolution of a burst in a DG2 dwarf galaxy. It is plotted with
a time resolution of 10 Myr.
59
Figure 3.9: The two types of bursts seen in the medium mass galaxy. These plots were
made with a time resolution of 10 Myr.
velocity dispersion of the galaxy. The time for the gas to recover to the normal velocity
dispersion for these galaxies is about 50 to 100 Myr. Also clearly noticable in these
dwarf galaxies, is the fact that the average velocity dispersion is significantly higher for
the stars than for the gas. It can also be seen that the velocity dispersion of the gas has
a peaked time evolution, where the peaks are related to small star formation seen in the
galaxy. This is caused by the lack of initial rotation of the gas cloud.
For DG2, also a peak in the velocity disperion of the gas is noted after a star formation burst. However a clear difference with the other low mass galaxy can be noted
in figure 3.11. The peak in the velocity dispersion of the gas is not much higher than
the average velocity dispersion of the gas. Certainly when comparing with the velocity
dispersion peaks obtained for DG1. As can be seen from the evolution of the velocity
dispersion in figure 3.11, it takes the gas about 50 to 100 Myr as well to come back to
the original velocity dispersion.
Noticable compared to the velocity dispersion of DG1 is the fact that the velocity dispersion of the gas and the stars are very similar, which happens because the average
velocity dispersion of the gas is higher. The average velocity dispersion of the stars in
the two low mass models is basically the same.
An example of the velocity disperion of DG3 while interacting is shown in figure 3.12.
As could be expected for a more massive dwarf galaxy, the average velocity dispersion is
higher compared to DG1 and DG2 (e.g. Valcke, de Rijcke & Dejonghe, 2008; Schroyen
et al., 2011). There is still a higher velocity dispersion of the gas when a starburst occurs, but it can not be characterised as a real strong peak. This is not really surprising
because there is more gas in this galaxy. Such that the feedback coming from the young
stars is more localised in the galaxy and doesn’t have a strong impact on all the gas in
the galaxy. The time needed to relax to the average velocity disperion takes ± 50 Myr
60
Figure 3.10: The velocity dispersion of the stars and the gas is plotted together with the
star formation rate (black line) for DG1, clearly showing a peak just after the burst.
Figure 3.11: The evolution of the velocity dispersion over time for the gas and stars in
DG2. This is plotted together with the star formation (black line.)
61
to 100 Myr, so rather similar to the low mass dwarf galaxies.
As stated at the start of this section about the velocity dispersion, it would be very
interesting to have a look at any effects on the velocity dispersion coming from the tidal
interaction. When having a quick look through the results, immediatly some very strong
and rather unnatural peaks in the stellar and gas velocity dispersion are observed at
the moment of closest approach such as in figure 3.13. These peaks can be noted when
galaxies are passing very close to each other. So close that the two galaxies are partly
passing through each other at moment of closest approach. In that case part of the second galaxy is taken into account for the determination of the velocity dispersion in the
first galaxy. This can lead to false peaks in the velocity dispersion. Normally this effect
can be noticed by looking at the second galaxy in the interaction, where a similar effect
is seen. Figure 3.14 shows the velocity dispersion of the galaxy which is interacting with
the galaxy for which the velocity dispersion is displayed in figure 3.13. It can be seen
that the velocity dispersion of the gas in this galaxy shows a strong sharp peak at the
moment of closest approach as well. This peak is not because part of the first galaxy is
included but because part of this second galaxy is cut out of the data when recentering
to the second galaxy. Finally it has to be noted that a clear signature of this false peak,
is the sharpness of it. It is only lasts for 50 Myr, afterwards the galaxies are seperated far
enough such that this effect does not occur anymore. So when trying to the determine
if there is an effect of tidal interaction on the velocity dispersion. There has to be taken
care that no part of the other galaxy is included in the data.
Some effects in the velocity dispersion were noted around closest approach for which
the above remark didn’t provide an explanation. An example is shown in figure 3.15, in
that case a strong increase in the velocity dispersion of the gas is noted for ± 400 Myr.
There is also an increase for the stellar velocity dispersion but less significant however.
A couple of times a similar behaviour was noted. Very remarkable is that all these events
occured in DG1 of the I5 interaction model. For DG2 and DG3 this increase is never
significantly seen. Why this happens, we hope to answer in the coming sections. Finally
it should be noted that for DG4 no significant increase in velocity dispersion was found
over their evolution. This is not really surprising since increase in velocity dispersion
was generally found when a burst occurred, which did not happen in DG4.
3.3
The gas mass
Apart from an effect on the velocity dispersion, one could also expect that the burst in
star formation will have an effect on the amount of gas in the galaxy. This would be
caused by the feedback ejecting gas out of the galaxy.
To have a look at this effect, plots were produced showing the evolution of the amount
of gas within a 5 kpc radius of the center of the galaxy. Again there has to be taken
care when analysing the results that part of the other galaxy is not included in the gas
62
Figure 3.12: The velocity dispersion for DG3 (including a star burst) in an interacting
model.
Figure 3.13: An enormous peak in the velocity dispersion at the moment of closest
approach in one of the galaxies at closest approach. The vertical line indicates the
moment of closest approach.
63
Figure 3.14: An enormous peak in the velocity dispersion of the second galaxy at the
moment of closest approach for a very close encounter. The vertical line indicates the
moment of closest approach.
Figure 3.15: Around the moment of closest approach, there is a strong increase for the
velocity dispersion of the gas for ± 400 Myr. The increase in velocity dispersion for
the stars is less strong but noticable as well. The vertical line indicates the moment of
closest approach.
64
mass of the galaxy when analysing these results. This will only happen at the moment
of closest encounter just like for the velocity dispersion, such that this effect was easily
noticed.
In this context, there was very regularly an increase in gas mass inside the galaxy when
the two galaxies were getting close to closest approach. This can be seen in e.g. figures
3.16 and 3.18. One could try to attribute this to gas originally belonging to or hanging
around the other galaxy that is now found in the galaxy we are looking at. However
there are some odd things about this when one has a more detailed look. First of all,
this effect is also seen when galaxies are passing by at more than 20 kpc. This is a very
large distance to note such an effect, since only extremely rare gas can be found at such
distances. Secondly looking at figures 3.16 and 3.18 it can be seen that this effect can be
rather big. A lot of gas seems to show up in the galaxies up to ± 107 M even for low
mass galaxies. This is a rather high gas mass. These amounts are even found for very
large distances of closest approach.
So based on the identity numbers of the gas particles, the amount of gas originally belonging to the other galaxy and now found in the galaxy near closest approach could be
determined. It turned out that this was by far not close to the increase seen in the gas
mass. The values for this comparison are given in appendix 6. This is only done for the
low mass galaxies that had a burst since this burst generally occurred near the moment
of highest mass accretion such that this might be related. The values for the low mass
galaxies that don’t experience a burst are not given there, but for these galaxies similar
gas accretion was found near closest approach as can be seen in figure 3.17. For the
medium mass galaxies this was not done since the gas mass behaviour is generally more
complex such that it is difficult to define this increase and the bursts in DG3 generally
don’t occur near closest approach. But this will be discussed in more detail in the next
chapter. So to compare this increase in gas mass with the accreted mass from the other
galaxy, the gas increase was determined by comparing the maximal gas mass near closest
approach with the moment the gas mass starts to increase monotonically towards this
maximum. Never more than 43 % of the mass increase is coming from the other galaxy.
And generally speaking about 80 - 90% of the gas increase is not coming from the other
galaxy in the interaction. It has to be noted that after closest approach all galaxies
seem to lose a lot of gas as well. One reason for this can be the starbursts that are
sometimes initiated by this gas capture of the galaxy. Another reason that seems rather
plausible is tidal stripping after closest approach which we hope to confirm by looking
at the gas flow later. Certainly in figure 3.17 this seems the most plausible explanation
for the gas lost.
What can be seen as well in figure 3.18 is the effect of feedback when a large amount of
stars are formed. This clearly leads to a sharp decrease in gas content of the galaxy. In
figure 3.16, this effect is less clear since one could expect that tidal stripping is starting
at that moment as well. The complete effect of feedback is however dependent on the
65
Figure 3.16: In black, the evolution of the gas mass in a DG1 and in red the evolution
of the star formation rate. The moment of closest approach is indicated by the vertical
line.
Figure 3.17: The evolution of the amount of gas (shown in black) in a DG1 that is not
experiencing a burst. This can be seen from the star formation history (shown in red).
The moment of closest approach is indicated by the vertical line.
Figure 3.18: In black, the evolution of the gas mass in a DG2 and in red the evolution
of the star formation rate. The moment of closest approach is indicated by the vertical
line.
66
mass of the galaxy. Where in the low mass galaxies the gas lost after a strong burst
or tidal stripping is generally never retrieved, the gas lost by the medium mass galaxy
can be partly retrieved after a while as in figure 3.19. For the high mass dwarf galaxies
nothing different should be expected since they have an even deeper gravitational potential. However for the bursts there is no direct confirmation since no burst was found in
the massive galaxy. The recapture of gas can be rather significant for DG3, such that a
sequence of burst like events can be triggered as can be seen in figure 3.19. Since the gas
is generally never retrieved for low mass dwarf galaxies, it is rather difficult for low mass
galaxies to achieve a sequence of burst like events. Although not necessarily impossible,
sometimes when the galaxy seems to stop losing gas after the burst a smaller burstlike
event can be triggered even though the amount of gas in the galaxy does not seem to
increase just before this. This could be because this gas never left the 5 kpc radius and
is at that moment collapsing somewhere in the galaxy.
3.4
B-I
At the moment of the burst, it can be expected that the galaxy will look bluer because
of the young stars that were created recently. In the I-band on the other hand one can
mostly see old stars. Such that a B-I map can show where the young stars will be found
in the galaxy. Making use of the B-band and I-band magnitude of the stellar particles,
maps of the galaxies are plotted at specific moments during the evolution.
To produce B-I maps that look more like what would be seen observationally, the luminosity in both bands of the stellar particles is smeared out using a gaussian since stellar
particles are unresolved during observations. In our case, the particles are smeared out
with a standard deviation of 80 pc. This value for smoothing is chosen since it delivers
a smooth B-I map, but also allows to identify the B-I substructure in the galaxy.
From these B-I maps, it is then possible to obtain a B-I colour profile. This B-I profile can be deduced from this map using a technique similar to isophotal integration
(Papaderos et al., 1996b; Micheva et al., 2013a,b; Verbeke et al., 2014). This isophotal
integration is done in steps of 0.01 for the B-I values to obtain a smooth profile. The
integration is done by looking for each B-I value to the cartesian grid cells of the B-I
map. For each of these B-I values, the number of grid cells are determined that are
bluer than this value. The area of these grid cells is then added together. Knowing the
total area which is bluer, this is converted to a radius of a circle with the same area. It
has to be noted that this radius is not the physical distance from the center of the galaxy.
In figure 3.20, a B-I map is plotted of a DG1 before, after and at the moment of the
burst. Before the burst, almost no blue spots are noticable in the galaxy since it barely
forms any stars. When the strong burst occurs, it seems to happen near the center close
to one dominant peak. Afterwards the peaks get less blue and are spread a bit more over
the galaxy. In DG1, the burst doesn’t necessarily happen at the center of the galaxy, but
67
Figure 3.19: In black, the evolution of the gas mass in a DG3 and in red the evolution
of the star formation rate. The moment of closest approach is indicated by the vertical
line.
Figure 3.20: The B-I map of a DG1 before (t = 11.76 Gyr), during (t = 11.82 Gyr) and
after (t = 11.85 Gyr, t = 11.97 Gyr) the burst.
68
it takes place very concentrated as shown in figure 3.21. This is probably a consequence
of a large amount of gas collapsing towards a small area in the galaxy. If starbursts occur
at two different points, these points are rather close to each other.
A difference between DG1 and DG2 can be seen in the B-I maps at the moment of
a star burst. Where DG1 has one or two spots of strong star formation in the galaxy, the
star formation in DG2 seems to be more distributed over the entire galaxy. An example
of this is shown in figure 3.22. Where at the moment of the burst the star forming
regions are distributed over the galaxy, indicating smaller clouds are collapsing to form
stars around the same time. This might be a good explanation why the bursts in DG2
seem to last longer in time than DG1, where the burst is one strong and short peak.
Due to the strong feedback on the large collapsing cloud in DG1, one can expect that
star formation is immediatly shut down after the first stars are formed. Where in DG2
feedback of young stars formed in one cloud will not stop the star formation in another
area of the galaxy.
The distribution of peaks in the B-I map of DG3 during a burst is rather similar to
the one of DG2. One can see several star forming areas distributed over the galaxy in
figure 3.23. This is not really surprising when looking at Schroyen et al. (2011), which
states that the star formation is more smeared out over the galaxy when the gas cloud
has an initial rotation.
As mentioned before, B-I profiles can be constructed from these maps. Figure 3.24
shows such a B-I profile before, during and after the burst of a DG1. It can be seen that
there is a strong blue peak during the burst. However, this peak is not more compact
than at other stages in the galaxy evolution. So during a burst in this type of galaxy
it seems like the star forming area is larger in comparison with no burst. Except for
the peak for R < 0.5 kpc, the profile is extremely flat. Indicating that star formation
in this type of galaxy occurs very concentrated. This is in agreement with the fact that
the star formation is dependent on the occasional collapse of the gas cloud in a certain
region. When looking at B-I profiles of DG2 in figure 3.25, it can be noted that these
profiles are slightly different from the B-I profiles of DG1. They are bluer up to a larger
radius, normally around 1 kpc. This is in agreement with the fact that the star formation
happens continuously and is smeared out over the galaxy. A strong blue peak is also
noticable during the burst just like in DG1.
During a burst in a DG3, the B-I profiles also show a blue peak as can be expected, this
is shown in figure 3.26. Compared to the low mass galaxies, the B-I profile has a smooth
evolution up to higher radii than 3 kpc. These higher radii are very dominant in the
infrared, implying that very old stars are found there.
In general it can be noted that the bursts in the galaxies show a blue peak on the
background of older stars. The B-I magnitudes obtained during bursts are of the order
of 0.6, with the strongest peaks going down to 0.5. Although these values are dependent
on the radius used for the smoothing.
69
Figure 3.21: The B-I map of a DG1 at the moment of the star burst. On the left the
galaxy is plotted edge one and on the right face on.
Figure 3.22: The B-I map before (t = 11.47 Gyr), during (t = 11.53 Gyr) and after (t
= 11.55 Gyr, t = 11.61 Gyr) the burst of a DG2.
70
Figure 3.23: The B-I map of a DG3 before (t = 11.47 Gyr), during (t = 11.59 Gyr) and
after (t = 11.61 Gyr, t = 11.7 Gyr) the burst.
71
Figure 3.24: The B-I profile of a DG1 before (red), during (blue) and after (green) a
burst.
Figure 3.25: The B-I profile of a DG2 before (red), during (blue) and after (green) a
burst.
72
Figure 3.26: The B-I profile of a DG3 before (red), during (blue) and after (green) a
burst
3.5
Gas distribution and gas flow
In the context of tidal interactions, the gas distribution in and around the dwarf galaxies
can be studied for many purposes. It was noted in the B-I maps that the starbursts in
different types of dwarf galaxies show different signatures. One could expect that this
will be reflected in the gas distrution of these galaxies.
Studying the tidal interaction of galaxies, many authors noted already long ago the existance of tidal tails around these galaxies (e.g. Pfleiderer & Siedentopf, 1961; Toomre &
Toomre, 1972). One might expect a similar behaviour for the interaction between dwarf
galaxies. While studying the velocity dispersion of the gas earlier in this thesis, it was
noted that in some galaxies the gas has a significant increase in velocity dispersion at
the moment of closest approach. One can hope that the distribution of the gas might
teach something about what happens at that moment. A last thing one can look for, is
the effect of feedback from a strong burst on the gas in the galaxy. Since the study of
the velocity dispersion clearly showed strong peaks immediatly after the burst.
First let’s have a look at the gas distribution in the galaxies when a burst occurs. In
figure 3.27 an example of a burst in a DG1 is shown. Just before the burst, the gas becomes extremely concentrated in a small area where the burst will occur. The feedback
from the recently formed stars has an immediate impact on the concentrated gas clump,
which get disrupted. Leading to a strong increase in spread of the gas for ± 100 Myr
and an irregular distribution of the gas inside the galaxy.
This is perfectly in agreement with the observations of the velocity dispersion. Where it
was noted that there is a strong increase in velocity dispersion of the gas up to 100 Myr
73
Figure 3.27: A plot of the gas column density in a DG1. It is shown before (t = 11.60),
during (t = 11.65) and after (t = 11.70) the burst. The yellow dots show the positions
of the stars formed in the previous 50 Myr.
after the burst. Afterwards, the gas will start to get more concentrated again and show
a distribution similar to the normal observed distribution in this type of galaxies.
In the galaxy with initial rotation, it appeared that the burst occurs more spread out
over the galaxy based on the B-I maps in figure 3.22. To confirm this, it is necessary
that the gas is more spread out over the galaxy at the moment of burst. However one
also expect strong clumps showing up in this galaxy where the new stars will be formed.
These strong clumps might be formed because of the generally higher gas mass in the
galaxy at the moment a burst occurs. This is also what is seen in these galaxies. Not
one highly concentrated clump, but several high density clumps at different places in the
galaxy are observed just before and during the star burst in figure 3.28. This could give
an explanation for the lower peak in the velocity dispersion. Since in DG1 the burst
has a huge impact coming from one star formation peak on almost all gas in the galaxy
that is collapsing towards a small area. On the other hand in DG2, the burst occurs
in smaller clumps where the star formation is a bit spread over time. This gives rise to
less strong feedback on the gas involved such that the peak in the velocity dispersion is
smaller. Even though not all the gas is collapsing to one clump, it can be noted from
figure 3.28 that just before and during the burst the gas gets very compact for this type
of dwarf galaxy while still having an irregular clumpy gas distribution. This was also
seen in observations (e.g. van Zee, Skillman & Salzer, 1998). It was also noted that the
bursts show wider peaks in DG2 when comparing with DG1, where the star formation
is completely shut down after a burst. This can also be seen in figure 3.28, where it is
shown that it is possible that directly after the first stars are formed that other clumps
can occur at different places in the galaxy. This can lead to extra stars formed and wider
star formation peaks.
After this star formation peak the gas gets strongly dispersed as well for ± 100 Myr,
although less strong than in DG1. This is again in accordance with the previously ob74
Figure 3.28: A plot of the gas column density in a DG2. It is shown before (t = 11.45),
during (t = 11.50) and after (t = 11.55) the burst. The yellow dots show the positions
of the stars formed in the previous 50 Myr.
tained behaviour of the velocity dispersion of the gas in this type of galaxy, which is
shown in figure 3.11. Where peaks in the velocity dispersion after a star burst are less
strong than in DG1 and also lasted up to ± 100 Myr.
A DG3 galaxy also shows compact gas clumps rather spread out over the galaxy as
was expected. And again the feedback from the young stars has a less significant impact
on the interstellar medium as shown in figure 3.29. In the case of these dwarf galaxies,
not all gas in the galaxy seems to be involved in the starburst. This will be a reason for
the less strong peak in the velocity dispersion.
One would also like to have an explanation for the increase in velocity dispersion in
the low mass dwarf galaxies in model I5 at the moment of closest encounter. When looking at figure 3.30, it gets clear quickly why there is such an increase in velocity dispersion
of the gas. The gas of the low mass dwarf galaxy forms a large tidal tail when passing by
the medium mass dwarf galaxy. Thus strongly increasing the velocity dispersion of the
gas within a radius of 5 kpc. Also something looking like a bridge is formed near closest
approach. The medium mass galaxy doesn’t really form a tidal tail, but something close
to a small tidal tail is formed as well in this system. This can be seen in figure 3.31.
However this happens at radii of 5 kpc and higher, such that this can’t be noted in the
velocity dispersion. Since the formation of this small structure behind the medium mass
dwarf galaxy was not seen in the velocity dispersion, it is certainly worth having a look
if the formation of a tidal tail is also possible for galaxies other than DG1.
First we will have a look if tidal tails can be formed during the tidal interaction of
DG3 and DG2. In this case a bridge is formed between the galaxies and tidal tails are
observed in both galaxies 3.32. This even occurs when both galaxies have rather large
75
Figure 3.29: A plot of the gas column density in a DG2. It is shown before (t = 11.30),
during (t = 11.35) and after (t = 11.40) the burst. The yellow dots show the positions
of the stars formed in the previous 50 Myr.
Figure 3.30: The construction of a tidal tail near closest approach of a DG1. The final
box zooms in on the small galaxy, showing the effect within 5 kpc.
76
Figure 3.31: In DG3, something close to a small tidal tail is formed after the passage of
the low mass galaxy.
Figure 3.32: The formation of a bridge and tidal tails in an I4 model.
77
distances at closest approach. Even in simulations where the closest encounter had a
seperation of 20 kpc a bridge and tidal tails were observed. Since bridges are seen, one
would expect that a significant amount of gas can be transferred. The effect of these
tidal tails is not significantly seen in the velocity disperion of the DG2 and DG3 dwarf
galaxies since the formation of these tails mainly starts at the outskirts of the galaxy.
So at radii generally higher than 5 kpc. There also seems to be no link between a burst
occuring and no tidal tails for DG2, since tidal tails were also observed in simulations
where a burst occurred.
When looking at the models with only low mass galaxies, generally no tidal tails or
bridges are seen. With the exception of encounters closer than 10 kpc in models where
a DG2 is included. Then small tidal tails or bridges can be observed. This seems to
indicate that for dwarf galaxies with a low mass it is hard to give rise to tidal tails in
the other galaxy.
This seems rather contradictory with the study of the I4 model where tidal tails were
observed after closest encounter in both dwarf galaxies. But it has to be noted since
the DG3 has an initial rotation, the gas is spread out. Such that tidal tails could be
formed from this gravitationally less bound gas. The tidal tail of the DG3 is not necessarily completely caused by the gravitational perturbation coming from DG2. But a
contribution could also come from gas originally belonging to DG2 that is now falling in
on DG3 and so enlarging the tail. This can be seen from figure 3.33, where it is shown
that a large part of the gas in the tail originally belonged to DG2. Looking at the gas
distribution when two DG3 galaxies are interacting in figure 3.34, it can be seen that
tidal tails and bridges are formed. Only when going to tidal interactions with a closest
approach at ± 25 kpc no tidal tails are visible anymore. Implying that these medium
mass dwarf galaxies seem much stronger in the creation of tidal tails than the low mass
dwarf galaxies. For the I7 interacting model this is rather similar, where tidal tails can
also be formed when the closest approach is larger than 20 kpc. Tidal tails can be noted
in the high mass dwarf galaxy as well.
Regarding the effect of rotation on the formation of tidal tails and bridges, it looks
like an initial rotation more easily gives rise to tidal tails and bridges. This is not completely surprising since this initial rotation gives rise to a more smeared out dwarf galaxy.
Because of this, more gas is available that is continuously not that tightly bound to the
galaxy. In that case, the tidal acceleration will have a bigger effect on this gas leading to
formation of bridges and tidal tails. An extra reason can be found when looking at the
equation of tidal acceleration 2.23. When gas is found at higher radii, there are more
particles with a higher ∆r such that the tidal acceleration is bigger for these particles.
Seeing the bridges formed between tidally interacting dwarf galaxies, it seems very plausible that the dwarf galaxies might capture gas originally belonging to the other galaxy.
That this is possible can be seen in figure 3.35, where two DG3 dwarf galaxies are shown
78
Figure 3.33: On the left, the gas particles of the interacting system are shown. The
particles belonging to different galaxies are in a different color. It shows a strong concentration of gas particles coming from the second galaxy in the tidal tail.
Figure 3.34: The tidal interaction between to DG3 galaxies, showing the formation of a
bridge and tidal tails.
79
± 1.5 Gyr after the closest approach. Both dwarf galaxies contain gas originally belonging to the other galaxy, although the amount of gas transferred is rather low. In the
case that low mass galaxies are involved in the interaction this effect is generally even
smaller as can be seen in figure 3.36, which shows this property for a DG2 interacting
with a DG1.
3.6
Density profiles
The plots of the gas distribution show a more compact and higher density of the gas just
before and during the burst. The feedback coming from the young stars then disperses
the interstellar medium. Quantifying this effect is done by looking at the density profiles. These density profiles are constucted by determining the density of the different
particles in spherically symmetric shells around the center of the galaxy. For the gas, it
is already pretty clear what will happen around the moment of the burst. But what can
we expect for the dark matter and stellar density, will they also become more compact?
The theoretical investigation by Verbeke et al. (2014) about starbursting dwarf galaxies found a slightly more compact and a higher central stellar and dark matter density
when a starburst occurred. This compactification was however way less than for the gas.
This phenomenon could be explained by the deeper gravitational potential created by
the compact gas cloud. Since in their investigation gas clouds of 107 M were captured
by the system, the gas could have a significant effect on the gravitational potential. In
the case of our simulations it does not necessarily have to be that big. Although gas
was tunneled into the galaxy, it was not necessarily 107 M . It is also not known if gas
hanging around the galaxy is tunneled into the galaxy when a gas cloud is captured. So
in our simulations one can not immediatly expect that this effect will be significant when
the gas becomes very compact.
At the moment of burst in a DG1, the gas density shows a compact strong peak. The
stellar and dark matter particles get a slight density peak as well at the center as can
be seen in figure 3.37. When the feedback coming from the newly formed stars had its
impact on the gas, this shows a way flatter and dispersed gas profile. This has its effect
as well on the dark matter and stars for which the density at the center of the galaxy
has a small drop. This is caused by the slightly shallower gravitational potential when
the gas is dispersed. In the case of DG2 and DG3 a central peak in the stellar and dark
matter density profile can be observed as well when a burst occurs. In contrast to DG1 a
compactification is noted sometimes as well, although this is not always very significant.
This can be seen in figure 3.38 where the stellar density is slightly more compact, but the
dark matter density profile does not appear more compact in this case. It can be seen
that the dark matter density profile still has a higher central density, which is oberved
for all simulatutions.
The density profiles of DG4 are not studied in this section since no starbursts were noted
in this galaxy. Such that there was not immediatly a reason why one would study the
80
Figure 3.35: The gas particles of two DG3 dwarf galaxies that interacted with each other
about 1.5 Gyr earlier. Showing that some gas from the other galaxy can be captured.
Figure 3.36: The gas particles of a DG2 (left) and a DG1 (right) that interacted with
each other about 1.5 Gyr earlier. Showing that generally very few gas is captured when
low mass dwarf galaxies are interacting.
81
ρstar [106 M /kpc3 ]
10−1
ρgas [106 M /kpc3 ]
101
10−32
10
101
100
10−1
10−2
10−32
10
t = 11.75Gyr
t = 11.8Gyr
t = 11.9Gyr
100
ρDM [106 M /kpc3 ]
10−2
101
100
0.0
0.5
1.0
1.5
2.0
2.5
3.0
R [kpc]
Figure 3.37: The stellar, gas and dark matter density profile of a DG1 before (t = 11.75
Gyr), during (t = 11.8 Gyr) and after (t = 11.9 Gyr) the burst.
82
density profiles of these galaxies in detail. This higher central density observed for all
particles, will give rise to steeper rotation curves which were found in BCDs by van Zee,
Salzer & Skillman (2001). The feedback coming from the formed stars disperses the gas.
This leads to a drop in stellar and dark matter density and flattening of the rotation
profiles (Verbeke et al., 2014). Such that this steep rotation profile is not a permanent
property of galaxies hosting a starburst.
3.7
B-band surface brightness profile
In the previous sections of this chapter, the galaxies having a burst show properties that
are also observationally seen in dwarf galaxies that are experiencing a starburst. Seeing these results it would be interesting to look at the surface brightness profiles in the
B-band. It is namely noted by observational studies that the surface brightness profiles
have a smaller scale length in dwarf galaxies experiencing a starburst (e.g. Papaderos
et al., 1996b; Salzer & Norton, 1999). To construct these profiles, again isophotal integration is used. And just like for the B-I maps produced earlier, the luminosity coming
from the stellar particles is smeared out using a gaussian with a standard deviation of
80 pc.
First of all, looking at the surface brightness of the DG1 type dwarf galaxies, a central peak is observed. But the profile doesn’t get significantly more compact when going
to higher radii like in figure 3.39. This could be expected from the stellar density profiles
discussed in the previous section. Just like in the B-I profiles at radii higher than 0.5 kpc,
the profile is independent on a burst happening or not. This implies that the I-band
magnitude won’t show a drop in surface brightness at higher radii as well. Since the
host galaxy does not seem to be more compact, these bursts do not completely satisfy
all the properties generally found for BCDs. The surface brightness profile in the case
of a DG2 type dwarf galaxy is somewhat different. It does show a peak within a small
radius similar to the DG1 type dwarf galaxies. But in contrast to the DG1 dwarf galaxies
showing a burst, the DG2 dwarf galaxies their surface brightness shows a drop at higher
radii like in figure 3.40 such that surface brightness profiles are more compact. This is in
agreement with the observations of the density profile. When looking at the B-I profiles
in figure 3.25, there is no difference at higher radii. This would imply that the surface
brightness profile in the I-band should be more compact as well. To test this, the surface
brightness profile was also plotted in the I-band. This is shown in figure 3.41 where the
I-band surface brightness profile is also more compact as could be expected from the B-I
profile. The peak is slightly less strong, but this comes to no surprise since the recently
formed stars barely contribute to the I-band luminosity, so this can only be caused by a
higher central stellar density.
During the bursts in the DG3 type dwarf galaxies, two types of surface brightness
profiles are observed. These two profiles are shown in figures 3.42 and 3.43. The first
type shows a strong central peak in the surface brightness profile, but it doesn’t get more
83
t = 12.05Gyr
t = 12.15Gyr
t = 12.3Gyr
101
100
10−12
10
101
100
10−1
10−2
10−32
10
ρDM [106 M /kpc3 ]
ρgas [106 M /kpc3 ]
ρstar [106 M /kpc3 ]
102
101
100
0.0
0.5
1.0
1.5
2.0
2.5
3.0
R [kpc]
Figure 3.38: The stellar, gas and dark matter density profile of a DG3 before (t = 12.05
Gyr), during (t = 12.15 Gyr) and after (t = 12.3 Gyr) the burst.
Figure 3.39: The surface brightness profile in the B-band of a DG1 before (t = 11.76
Gyr), during (t = 11.82 Gyr) and after (t = 11.91 Gyr) the burst.
84
Figure 3.40: The surface brightness profile in the B-band of a DG2 before (t = 11.5
Gyr), during (t = 11.61 Gyr) and after (t = 11.79 Gyr) the burst.
Figure 3.41: The surface brightness profile in the I-band of a DG2 before (t = 11.5 Gyr),
during (t = 11.61 Gyr) and after (t = 11.79 Gyr) the burst.
85
compact at higher radii like the DG1 dwarf galaxies. The second type shows a wider but
less strong peak and a lower surface brightness for higher radii, a bit like the DG2 dwarf
galaxies. Both profile types are seen a couple of times, implying that none of these two
profiles are one time events.
86
Figure 3.42: The surface brightness profile in the B-band of a DG3 before (t = 12.0
Gyr), during (t = 12.15 Gyr) and after (t = 12.3 Gyr) the burst.
Figure 3.43: The surface brightness profile in the B-band of a DG3 before (t = 11.2
Gyr), during (t = 11.35 Gyr) and after (t = 11.5 Gyr) the burst.
87
Chapter 4
Discussion
In this chapter, certain results will be discussed in more detail. For some of these more
in depth discussions, simulations of merger trees will be used as well. Because of this,
the simulations involving a merger tree will be discussed in the first section. There will
also be attempted to characterise the bursting galaxies using isophotal maps.
4.1
Comparison with merger tree
Although no merger tree was used when studying the tidal interaction of the dwarf galaxies, two simulations were run with a merger history. This was done to have a comparison
of our simulations that were run in isolation with these merger tree dwarf galaxies. These
two simulations were given the same initial mass, namely 2·1010 M , and were simulated
using 300 000 gas and dark matter particles. The mass was chosen such that at the end
of the galaxy evolution star formation would be still observed. It has to be noted that
a lower mass resolution is used than for the simulations in isolation and the study by
Verbeke, Vandenbroucke & De Rijcke (2015). This might pose some resolution effects for
the low mass halos in the merger tree, certainly the low resolution for the gas particles is
not ideal. But the final results show what could be expected. Namely gas-rich and low
metallicity dwarf galaxies were found. Also similar effects were seen as in Vandenbroucke,
Verbeke & De Rijcke (2016) where they used a higher resolution simulation performed for
Verbeke, Vandenbroucke & De Rijcke (2015) to do a comparison with their simulations
in isolation. This gives confidence that this resolution was not a major problem.
To construct the merger history, a modified version of the GALFORM algorithm was
used (Cole et al., 2000; Parkinson, Cole & Helly, 2008), which is based on the extended
Press-Schechter algorithm (Press & Schechter, 1974; Bond et al., 1991; Lacey & Cole,
1993). This constructs the density threshold for a halo to become virialised, based on a
Gaussian distribution of density fluctuations using a cosmological spherical collapse. For
a given halo mass and redshift it creates a conditional mass function of the progenitors
at a higher redshift. Then using a Monte-Carlo technique, the merger history is con89
structed based on the final mass of the galaxy. The modification by Parkinson, Cole &
Helly (2008) was done to fit the conditional mass function of the Millenium Simulation
(Springel et al., 2005).
These merger tree simulations were performed in the same cosmological setting as the
simulations in isolation, starting at a redshift of z = 13.5, and 20 redshift intervals were
used for the merger processes. A minimal halo mass of 0.5·108 M was taken for the
halos involved in the merger process. The two merger trees run for this thesis had a main
difference. The first merger tree (MT1) has a late merger involving two rather massive
halos and the other merger tree (MT2) that was run consists of many low mass halos
that are merged over time with a more massive halo. These two merger trees are shown
in figure 4.1.
First of all, the star formation in both merger trees is compared. In both cases only the
most massive halo can have star formation before the last merger in the tree, except for
the initial star formation although this is not shown in the plots. The magnitude of the
star formation in the two trees is however very different. MT2 shows on average a higher
star formation in the last 2 Gyr of evolution than MT1 as illustrated in figure 4.2. It also
has a slightly higher stellar mass and more neutral hydrogen at z = 0. The metallicity
is almost exactly the same. These results are compared with DG1, DG2 and DG3 in the
last 2 Gyr of their evolution, where DG1 and DG2 are shown in figure 2.12.
Some effects of a merger history are immediatly visible compared to simulations in isolation. First of all, there is a difference in the star formation. The star formation of MT1 is
around the same magnitude as the star formation in DG1 and slightly lower than the the
star formation in DG2. The star formation of MT2 is of similar magnitude as the star
formation in DG2. However since MT1 and MT2 have a double initial mass compared
to DG1 and DG2, this implies that a higher initial mass is necessary for the merger trees
to obtain a similar current magnitude of star formation as in isolation. When comparing
the star formation with DG3, which has the same initial mass as MT1 and MT2, it was
found that the star formation at z = 0 is way lower when the merger tree is involved.
This is not really surprising since the merger tree consists of smaller halos, where star
formation is immediatly shut down after the initial burst for most of these protogalaxies. Because of this, the star formation is mainly achieved by the protogalaxy with the
highest mass. These many low mass halos which don’t form any stars after the initial
burst also explain the lower stellar mass. Their stellar mass is even lower than in DG1.
This lower star formation and stellar mass obviously leads to a lower metallicity for the
merger trees.
The amount of neutral hydrogen in the galaxy when considering the merger tree shows
an interesting property. Although the merger trees retain less neutral hydrogen than
DG3, they retain more neutral hydrogen than the low mass galaxies. Since the star formation in these mergers is similar to the low mass galaxies, this could imply that higher
burst factors can occur when these galaxies are tidally interacting than in the case of
interaction between dwarf galaxies simulated in isolation.
90
Figure 4.1: The visualisation of the two merger trees that were run as a function of the
lookback time.
91
0.014
0.012
0.010
0.008
0.006
0.004
0.002
0.000
8.0
7.5
7.0
6.5
6.0
5.5
5.0
−1
−2
−3
−4
10
−52
0.014
0.012
0.010
0.008
0.006
0.004
0.002
0.000
11
10
9
8
7
6
5
−1
−2
−3
−4
10
−52
SFR [M /yr]
Mstar [106 M ]
101
100
11.5
MT1
[Fe/H]B
MHI [106 M ]
MHI [106 M ]
[Fe/H]B
Mstar [106 M ]
SFR [M /yr]
MT1
12.0
12.5
t [Gyr]
101
100
10−1
11.5
13.0
12.0
12.5
t [Gyr]
13.0
Figure 4.2: The comparison of the star formation, stellar mass, metallicity and neutral
hydrogen mass of the two merger trees in the last 2 Gyr of their evolution.
In work performed by Cloet-Osselaer et al. (2014) a comparison between isolated models
and merger trees was made as well. They also found a higher stellar mass for the isolated models at z = 0. However, they found a lower metallicity for most of the models
in isolation. This is not in agreement with what we find. This happens since in their
study, a lot of non-population III stars are formed in the initial burst leading to a high
stellar mass. This strong initial burst is followed by a low star formation rate at later
stages of the evolution, thus leading to a low metallicy. However recently, population
III stars have been included in the code (Verbeke, Vandenbroucke & De Rijcke, 2015).
In the case of a merger tree, it was shown that these population III stars delay the star
formation in the galaxy. The effects of population III stars might be less strong in an
isolated case, which leads to a stronger star formation history and thus a higher metallicity. This higher star formation rate in isolated models was very recently also found by
Vandenbroucke, Verbeke & De Rijcke (2016) when population III stars were included.
4.2
Gas flow and burst duration
In the previous chapter it was noted that depending on the type of galaxy, the bursts
that occured were different. In the case of DG1 a very sharp peak was observed for only
± 10 Myr. Since this star formation happened in maximally two rather close compact
clumps, it could be expected that feedback from the recently formed stars will shut this
star formation down in the collapsing cloud. The prescriptions for the feedback from
young stars can be found in Valcke, de Rijcke & Dejonghe (2008). The distribution of
feedback from stellar winds and type II supernovae over time was based on the main
92
sequence liftime of stars with a certain mass David, Forman & Jones (1990):
log τ (m) = 10 − 3.42log m + 0.88(log m)2
(4.1)
Where m is expressed in solar masses. When applying the appropriate boundary masses
for type II supernovae to this formula, which are 8 M and 70 M , one gets the following
time intervals:
- Stellar winds: 0 - 4.3 · 107 yr
- Type II supernovae: 4.8 · 106 - 4.3 · 107 yr
This provides a satisfying explanation for the short burst since stellar winds and supernovae from the most massive stars had their impact already. In the case two clumps
form stars, this implies that these clumps have to start forming stars within ± 5 Myr
time difference. Otherwise two distinct peaks would be observed. That this happens is
not that surprising since these compact clumps are rather close to each other and most
likely involved in the same collapse of the gas. This can be seen from the gas distribution
maps in figure 3.27.
In the case of DG2, this feedback from freshly formed stars can not directly explain
the duration of the bursts, which last up to 50 Myr. Since after ± 40 Myr all feedback
coming from massive stars has already been send into the ISM. Taking the gas flow into
account explains the duration nicely, since many compact clumps over the entire galaxy
can be seen in figure 3.28 just before the star formation is starting. Such that every
clump probably only experiences star formation for about 10 Myr just like in the DG1
type galaxies. But since many clumps are collapsing over the galaxy, these short bursts
together form one longer burst. This could also explain the short drop in star formation
for 10 Myr in the middle of the burst, where due to a statistical fluctuation no clumps
are collapsing.
In the case of one or two clumps collapsing this drop would be very difficult to explain.
If one clump was collapsing, the feedback shutting down the star formation would stop
the star formation for longer than 10 Myr because the feedback of the last formed stars
would still be too strong. In that case the gas can’t collapse in the same region. Two
clumps are unlikely as well since not that much more gas is contained, compared to a
DG1 dwarf galaxy. Such that two regions forming stars would have been shut down
after 10 Myr like in the DG1 type dwarf galaxies. This would at best lead to two shorter
peaks in the star formation.
In DG3, two types of bursts are seen similar to the two types just discussed. This
is not completely surprising since the initial rotation velocity was taken in the middle.
However in all the galaxies where a burst occurred several clumps appeared in the gas
maps. These gas maps are a bit misleading and it is important to look where te stars
actually form, this is illustrated in figure 4.3. This reveals that in case of a sharp peak,
most of the stars are formed in one small area, while for the wider star formation peak
the recently formed stars appear more distributed over the galaxy just like what is seen
93
Figure 4.3: The gas map on the left shows the recently formed stars in a long burst. The
gas map on the right shows the recently formed stars when a sharp burst occured.
in figure 3.28 for a burst in DG2. In the case of the sharp peak, there are some stars
formed elsewhere in the galaxy. This can be explained because the peak is not isolated
like for DG1, but there is continuous star formation for the dwarf galaxy of this mass. So
the other stars formed are a sort of continuous star formation background for the burst,
which is caused by the collapse of one massive cloud. A correlation with the observed
surface brightness profiles is found as well. The profile with the strong central peak
that is not getting more compact has one or two compact areas where a lot of stars are
formed. On the other hand, the more compact profile has a star formation spread over
the galaxy. This result is again completely in accordance with the observations in DG1
and DG2.
This short peak could also offer an explanation why no compact profile is observed
in that case. Since the peak is extremely short, the gas becomes compact only for a very
short time because it is immediatly dispersed again. This gives only a very short time
for the other matter in the galaxy to get more compact, such that the galaxy might not
have enough time to get significantly more compact.
Although this could provide an explanation, it could also just be the time resolution
used. If the compactification only happens for a short while, it might be that this is not
captured by the snapshots that were saved. Although the higher resolution simulations
using a time difference of ± 30 Myr per snapshot could not capture any compactification
either, giving small support to the suggestion that the galaxy doesn’t really have the
time to get significantly more compact.
Since this is rather noteworthy, we will try to obtain a rough estimate of the time scale
94
needed for the galaxy to become more compact in the hope to learn something from this.
For this, we will make use of the dynamical time scale given by equation 2.17. But ρg is
changed by the density of dark matter and stellar particles. To define ρ we will use the
simple assumption:
3M
ρ=
(4.2)
4πR3
Where M is the stellar and dark matter mass contained within radius R. This total
stellar and dark matter mass was determined within three different radii. Namely 1 kpc,
3 kpc and 5 kpc. This was done for several snapshots of the galaxy in isolation to have
a descent view on the usual mass within these radii. For DG1 and DG2 almost exactly
the same masses were found within these radii, respectively: 1.5 · 108 M , 109 M and
2 · 109 M . For DG3 these masses were higher: 1.7 · 108 M , 1.75 · 109 M and 3.5 ·
109 M . The values obtained for tdyn in DG1 and DG2 are respectively: ± 25 Myr, 40
Myr and 55 Myr. For DG3, this is respectively ± 20 Myr, 30 Myr and 40 Myr.
Since these values are determined on very simple grounds one should not pay too much
attention to these values. But they do provide an explanation why always a higher
central density is obtained but not always a more compact profile at higher radii. This
happens because the dynamical time scale is significantly smaller for the center of the
galaxy than at higher radii. Since the higher central density is always seen, this again
seems to support the explanation of the short burst.
To conclude this section it can be stated that two types of bursts appear to be possible
in tidal interactions. And the type of burst observed depends on the gas dynamics in
the dwarf galaxy.
4.3
Moment of the burst
In the introduction it was already stated that tidal interactions are considered as a possible trigger for starbursts because a companion dwarf galaxy is sometimes seen close to
a starbursting dwarf galaxy. So it is interesting to ask when the bursts in our galaxies
occur. Such that it can be checked if the galaxies are actually still close to each other
when the burst occurs.
A first remarkable feature when going through the moments of burst compared to the
moment of closest approach is that ± 80 % of the bursts occur after the moment of
closest approach. The results on the gas mass inside the galaxy point to an explanation
for this. As was shown there, a significant amount of gas hanging around the galaxy gets
tunneled into the dwarf galaxies when they are approaching each other due to the tidal
interaction. This generally reaches its maximum very close to closest approach. This
gas tunneling can then trigger a burst during this tunneling or afterwards. When the
galaxy has a burst before closest approach, the galaxy was already accreting a significant
amount of gas earlier, as is shown in figure 4.4. This accretion of the surrounding gas
before a burst obviously agrees with the observation that dwarf galaxies experiencing a
starburst are gas rich with a high central concentration (e.g. Taylor et al., 1994, 1995;
95
Figure 4.4: The gas mass evolution of a DG2 type dwarf galaxie having a burst before
closest approach. The moment of closest approach is indicated by the vertical line.
van Zee, Skillman & Salzer, 1998).
When the burst occurs is also dependent on the type of galaxy, this can be seen from the
data which is added in appendix 6. For the low mass galaxies, the burst almost always
occurs within ± 250 Myr around the closest encounter. While it appears rather rare that
a burst occurs within 250 Myr around the moment of closest approach in DG3. Bursts
in these dwarf galaxies can easily occur more than 1 Gyr after closest approach.
If a burst for the low mass galaxies occurs, the gas capture seems to initiate a burst
rather quickly if one occurs. Such that in observations a companion will be found close
to the starburst galaxy. For the more massive galaxies this immediate burst is not necessarily the case, such that the galaxies will easily have a separation of 100 kpc at the
moment of a burst. This is still in agreement with recent observations by Lelli, Verheijen
& Fraternali (2014) who found possible perturbers within a projected distance of 200
kpc. So not all perturbers are necessarily very close to the bursting galaxy. This delay
that can be found in DG3 can be related to the recapture of gas generally somewhere
after closest approach. So again these bursts can be related to the tunneling of gas into
the galaxy, but this time it can also be an indirect consequence of the gas accretion due
to tidal interactions.
4.4
Classification of the bursting galaxies
Trying to classify the burst galaxies, we will use isophotal maps in the B-band. These
isophotal maps are very useful since they give a great view on how the galaxy would be
observed and the substructure it has. To create these isophotal maps, smoothing of the
luminosity from the stellar particles is used with a standard deviation of 80 pc. This
is exactly the same as for the other luminosity maps and profiles created. Because this
resolution allows to see a lot of structure, also isophotal maps were produced with a
standard deviation of 160 pc. This makes it easier to see the coarser structure of the
96
bursting dwarf galaxy, without being distracted by all the substructure.
First the results for bursts in DG1 will be discussed. Both irregular and nucleated
bursts are seen in this dwarf galaxy type, which is shown in figure 4.5. In both cases
the outer regions are not that elliptical. When looking at the coarser map, they look
more elliptical but not completely. The high resolution isophotal map shows that for the
irregular burst two clumps are seen which are rather of center. In the coarser map, the
irregular burst stays of center and slightly irregular. When having a look at the classification scheme in the introduction, there is not really a place to put the nucleated bursts
with rather irregular outer isophotes. However it was already shown that the bursts in
this dwarf galaxy type do not show all properties seen in BCDs. This might be because
the gas cloud having absolutely no initial rotation could be a slightly extreme case to
study, such that obtained results might not be optimal.
For the DG2 dwarf galaxies, the burst is always irregular as could be expected from e.g.
the B-I and density maps. An example of this is shown in figure 4.6. When looking at
the coarser maps, the outer regions of DG2 galaxies appear rather elliptical. The inner
regions on the other hand still show an irregular shape. Even in the high resolution map
the outer region appears quite elliptical. Generally, the outer isophotes seem to be more
elliptical in DG2 than DG1 as can be seen for example in figures 4.5 and 4.6. But it is
hard to confirm this quantitatively. For the DG3 dwarf galaxies, rather irregular bursts
are expected as well due to the initial rotation. This is shown in the face on isophotal
map in figure 4.8. The outer regions in the coarse map are quite elliptical, but in the high
resolution maps there is still a lot of scatter on these elliptical shapes. When looking at
the edge on isophotal maps, iI C like burst galaxies can be seen like in figure 4.8. These
comet like edge on isophotal maps were not seen for DG2. This could be because not
that much bursts were seen and since not all DG3 burst galaxies show this comet like
profile. However there is also some difference between the two bursts. DG3 can have
a burst in one dominant area in contrast with DG2, such that a comet like profile can
be formed more easily in DG3. In DG2 the burst always happens spread out over the
galaxy, which is also reflected in a more spread burst in the edge on isophotal map in
figure 4.7.
4.5
Metallicity
The oxygen abundance of the ionised gas has been determined for the bursting dwarf
galaxies like it would be determined observationally. Such that it could be compared
with observational studies (e.g. Izotov, Thuan & Lipovetsky, 1994; Amorı́n et al., 2014).
They observed BCDs with respectively 7.37 < 12 + log(O/H) < 8.04 and 7.5 < 12 +
log(O/H) < 8.3.
When looking at the values obtained from our simulations, which are tabulated in appendix 6. One can see that that the oxygen abundances are on the high side for the low
mass dwarf galaxies, ± 8.1 for DG1 and ± 8.2 for DG2, and even too high for DG3, ± 8.5,
97
Figure 4.5: On top a nucleated burst is shown while below an irregular burst is shown
for DG1. The two different resolutions are plotted.
98
Figure 4.6: A typical burst for DG2 is plotted, which is always irregular. This is still
visible in the lower resolution isophotal map.
Figure 4.7: The edge on view of a DG2 burst galaxy. A rather irregular burst profile can
be seen, certainly in the high resolution map.
99
Figure 4.8: On top one can see the face on rather irregular burst. Below the rather
comet like behaviour of the edge on isophotal map.
100
compared with observations. However one does not immediatly expect that this would
be in the same region as the observations based on the section about the merger tree
simulations. It was shown there that merger galaxies with a certain star formation had a
significantly lower metallicity than the models in isolation with a similar star formation
rate. However, the determination of these metallicities was very basic and not how it
would be observed in reality. Because of this, the oxygen abundance of these two merger
trees was determined as well. This would give a better view on the actual magnitude of
the oxygen abundances observed. The oxygen abundances of the merger trees at z = 0,
are given in 6. These are around 7.6. Seeing this, one could expect that the metallicities
for the simulations in isolation are on the high side such that the medium mass dwarf
galaxies might fit in the observed range as well when using a merger tree.
Having a detailed look at the study by Verbeke, Vandenbroucke & De Rijcke (2015),
one of the only results that did not completely agree with observations was the oxygen
abundance. This abundance was somewhat on the high side as can be seen in figure
4.9 which was taken from their paper. This should also be the case in our merger tree
simulations, since the same code was used. So if this small issue would be resolved,
one could expect that simulations with merger trees would lead to even slightly lower
metallicities. The discussion so far only looked at the magnitude of the observed metallicities. However it was found that BCDs have a metallicity that is generally lower than
dIrrs (e.g. Izotov, Thuan & Lipovetsky, 1994; Izotov & Thuan, 1999; Hunter & Hoffman,
1999). This was not adressed so far in this discussion. When a low metallicity cloud is
falling in on the galaxy, obtaining a lower gas metallicity for the BCD is obviously no
problem. However in the case of tidal interactions it is not immediatly clear if a lower
metallicity will be obtained when a burst will occur.
We would like to check if this drop in metallicity is also possible with tidal interactions.
Since the burst is triggered by the capture from surrounding gas, one could explain this
by the gas falling in having a lower metallicity. When having a look at Schroyen et al.
(2013) a metallicity gradient was found for simulated dwarf galaxies. They found long
lived metallicity gradients in simulated dwarf galaxies even when they had an initial
rotation. This metallicity profile was however based on stars, and we are dominantly
interested in the gradient of the oxygen abundance in the gas. So a metallicity profile for
this was constructed. It has to be noted that the determination of the oxygen abundance
up to now was based on the oxygen abundance in ionised gas. However to construct the
profile it was not restricted to ionised gas, but all gas was used to have a better view
on the general oxygen abundance profile in the gas. The bins for plotting these profiles
were taken large (in steps of 5 kpc) to have no jumps in the profile due to a lack of gas
at a certain radius. Although this are very large bins, this is not really a big problem
since we are interested in the coarse oxygen abundance profile at higher radii. These
profiles were constructed for the host galaxies in isolation near times where generally
bursts occured in the interacting models.
101
Figure 4.9: The oxygen abundance obtianed by Verbeke, Vandenbroucke & De Rijcke
(2015) in their simulations compared with observations. Their oxygen abundance is
slightly on the high side.
When looking at these profiles in figures 4.10 and 4.11, it can be seen that the oxygen abundance profile is dropping at higher radii. Certainly at radii higher than 10 kpc.
The behaviour is rather smooth for DG2 and DG3, seen in figure 4.11. For DG1 there is
a bit more scatter on these results, which is shown in figure 4.10. Seeing these profiles,
it seems possible that when gas is falling in on the galaxy from radii higher than 5 kpc
that this could lead to lower oxygen abundances of the gas. However one can expect that
this effect will by far not be as strong as a low metallicity gas cloud falling in, since the
gas hanging around the galaxy is still enriched. To compare the gas oxygen abundance
of a burst with the oxygen abundance when no burst happens is very complicated to do
without biases. Since there is an evolution over time in the metallicity due to the star
formation. Such that it is very difficult to find a statistically significant and representative sample of snapshots from the performed simulations to compare with the galaxies
experiencing a burst. And since we can expect that the effect won’t be that big in our
simulations it might be difficult to get conclusive results.
It could be argued that one can try to study the evolution of the oxygen abundance in a
galaxy experiencing a burst. However since the gas falls in over a large time interval, it
should be difficult to see a significant drop in the evolution because the star formation
is continuously enriching the gas and the metallicity is not much lower at higher radii.
Although there is a drop at higher radii (r > 10 kpc) in the oxygen abundance, one
can ask if this gas will fall in on the galaxy. If this doesn’t happen there won’t be a drop
in the oxygen abundance. This would pose a problem for this model to create BCDs
since they generally have a lower oxygen abundance. However the results discussed so
far on the oxygen abundance gradient only considered the models in isolation. When
looking at our merger tree simulations, which should be more realistic, they seem to offer
102
Figure 4.10: The course oxygen abundance profile of the gas in DG1 in isolation at
different times during the evolution.
Figure 4.11: The course oxygen abundance profile of the gas in DG3 in isolation at
different times during the evolution.
103
a solution for this problem. As shown in figure 4.12 for MT2, the merger simulations
seem to show a strong drop in oxygen abundance towards higher radii. It has to be noted
that this is slightly less strong for MT1, but still way stronger than the simulations in
isolation.
4.6
Effect of tidal stripping and bursts on later star
formation
It was noted from the gas density maps and the evolution of the gas mass in the galaxy
that tidal tails can be formed and that there is some tidal stripping. Although significant
amounts of gas can be stripped from the galaxy, it is certainly not able to strip enough
gas from the galaxy to stop the star formation. This can be seen from the star formation
histories e.g. in figure 3.16. Even when bursts occur, triggered by tidal interactions,
the star formation maximally stops for 50-100 Myr in the DG1 model which is most
sensitive to the starbursts. For DG2 and DG3 a stop in star formation for 50 Myr is not
significantly seen in the star formation histories with a time interval of 50 Myr. In the
higher resolution star formation histories, sometimes intervals after the burst of up to
20 Myr without star formation can be seen for DG2 e.g. in figure 3.8. In DG3 a break
in the star formation is not really seen after a burst.
4.7
The amount of bursts
Over all simulations, 26 galaxies were having a burst based on the definitions from the
previous chapter. But it seems rather fair that one should not pay too much attention
to this number. These definitions were proposed by looking at the burst factor in many
simulations and comparing them with the star formation in these simulations and the
simulations in isolation of the host galaxy. However the burst factors might be defined
differently by another person so they are still slightly arbitrary, but this has been the
case for all studies so far both theoretical and observational, since there is no unique
definition for a starbursting dwarf galaxy. It was shown that galaxies with these burst
factors generally show properties that are also seen observationally in galaxies experiencing a burst, which gives confidence that the definitions used are quite good.
Although one should not pay too much attention to the number of bursts, one can
try to have an idea on how easy or difficult it is to trigger a starburst using tidal interactions. 140 simulations were considered, which implies that 280 galaxies experiencing
tidal interaction with another dwarf galaxy were studied. This implies that ± 10 % of
the galaxies experienced a burst. Again a lot of arguments can be proposed that this
number is not representative, it is also not claimed that this number is representative.
Some of these arguments might be:
- The definition of a burst is always slightly arbitrary.
104
Figure 4.12: The coarse oxygen abundance profile of the gas in MT2 at different times
during the evolution.
- It was attempted to study a representative range of orbits. But it is hard to put an
upper limit for the radius of closest approach on what can be considered as tidally interacting dwarf galaxies. So it was just attempted to make this range as large as possible.
- Other environmental influences were not included.
But seeing the amount of galaxies that did not experience a burst, it is fair to say
that tidal interaction is not a very efficient way to trigger a burst in a dwarf galaxy.
This is also not necessary since not that many starbursts are seen in dwarf galaxies. The
main reason why they are easily spotted is because of the higher luminosity caused by
the recently formed stars. That it is not so easy to initiate a starburst in a dwarf galaxy
was also noted by Verbeke et al. (2014), where only the most massive gas clouds could
trigger a star burst rather easily.
105
Chapter 5
Conclusion
In this thesis we numerically studied a wide range of recent tidal interactions between
dwarf galaxies, attempting to understand the impact of these interactions on the evolution of dwarf galaxies.
It was found that tidal tails and bridges can be formed if the galaxies passed each
other sufficiently close. But to create these structures easily, a high enough mass of the
galaxies is favorable. A dependence on the initial rotation of the gas cloud was found
for this creation as well.
Studying the amount of gas inside the galaxy, effects related to tidal interactions were
found. Before the moment of closest approach it turned out that the tidal interaction
generally led to the tunneling of surrounding gas into the galaxy. After closest approach
tidal stripping of significant amounts of gas was observed. It was found that the accumulation of gas before closest approach and the recapture of gas after tidal stripping could
initiate a starburst which again ejected a lot of gas out of the galaxy. The recapture of
this gas could initiate a sequence of burstlike events. Finally it should be noted that the
gas ejected out of the galaxy, both by tidal stripping and feedback, was never sufficient
to create a star formation break longer than 100 Myr.
Two types of bursts were found, depending on the dwarf galaxy dynamics. The first
type of burst involved the collapse of maximally two massive clumps very close to each
other, leading to a very short burst of maximally 10 Myr. The second type involved the
collapse of several clumps at different places in the galaxy spread over a time interval
of 40-80 Myr. Both bursts led to different features in e.g. the density profile and the
surface brightness profile.
It was found that the galaxies experiencing the second burst type show many properties that are observationally also seen in BCDs e.g. they are more compact, they are
gas rich,... The property that could pose a problem for this model seems to be the possible lack of a metallicity drop when the burst occurs. However it was shown that more
realistic simulations involving a merger tree could resolve this issue.
107
In the case of the first burst type, no compactification of the host galaxy was found.
This is not necessarily a huge problem since generally BCDs are more compact. And
it might be that a slight compactification is not noted in our simulations because of a
too big time gap between the snapshots. It could also be that this type of burst is over
abundant in our simulations due to the low mass dwarf galaxy without initial rotation,
which is possibly not an ideal way to get rather realistic dwarf galaxies.
108
Chapter 6
Nederlandstalige Samenvatting
Al geruime tijd zijn er observationele indicaties dat getijdenwerking tussen dwerggalaxieën
een mogelijke oorzaak kan zijn voor een verhoogde stervorming die soms wordt waargenomen
in dwerggalaxieën. Andere mogelijke oorzaken voor deze verhoogde stervorming, zoals
het invangen van een gaswolk en het mergen van dwerggalaxieën is reeds numeriek aangetoond door verschillende studies. Getijdenwerking tussen dwerggalaxieën en het mogelijk
effect hiervan op de stervorming is echter nog nooit diepgaand bestudeerd met computersimulaties.
Daarom werd in deze thesis een uitgebreide numerieke studie gedaan van deze getijdenwerking. Hiervoor werd de interactie tussen verschillende dwerggalaxieën op verschillende
relatieve trajecten bestudeert. Dit leverde enkele significante resultaten op.
Ten eerste werd soms de vorming van bruggen en langwerpige structuren waargenomen
rond de dichtste nadering van de twee galaxieën. Om deze structuren te vormen waren de
dwerggalaxieën bij voorkeur voldoende massief en was de onderlinge afstand bij dichtste
nadering van belang. Voor de vorming van deze structuren werd ook nog een andere
afhankelijkheid gevonden, gerelateerd aan de initiële rotatie van de gaswolk.
De getijdenwerking tussen de dwerggalaxieën had ook een effect op de hoeveelheid gas
in de galaxieën. Als de galaxieën elkaar naderden, werd een stijging van de hoeveelheid
gas in de galaxieën waargenomen. Dit was afkomstig van gas dat rond de galaxie hangt.
Na dichtste naderen werd er dan weer een significant verlies van gas waargenomen. Al
werd bij de meer massieve dwerggalaxieën een deel van het tijdelijk verloren gas na een
tijdje weer terug ingevangen.
Deze twee manieren van gas vangst konden tot een verhoogde stervorming leiden in
de dwerggalaxien. De verhoogde stervorming kon ook grote hoeveelheden gas uit de dwerggalaxieën verwijderen. Het verlies van gas kon nooit tot periodes langer dan 100 Myr
zonder stervorming leiden. Het deels terug invangen van het gas kon soms wel opnieuw
tot een verhoogde stervorming leiden.
Twee soorten verhoogde stervorming werden waargenomen, die bleken afhankelijk te zijn
109
van de interne dynamica van de dwerggalaxieën. Het eerste type burst, was een zeer korte
burst van maximaal 10 Myr. Het tweede type burst bestond over een tijdsinterval van
± 40-80 Myr. Er was een duidelijk verschil merkbaar in hoe deze bursts tot stand kwamen. Het eerste type burst bestond uit maximaal twee massieve gaswolken die heel dicht
bij elkaar sterren beginnen te vormen. Het tweede type burst bestond uit verschillende
gaswolken die gespreid over de galaxieën sterren beginnen te vormen. Deze stervorming
is iets meer gespreid in de tijd. Deze verschillende bursts leiden ook tot verschillende
observaties, bijvoorbeeld in het oppervlaktehelderheid profiel.
In het geval van het tweede type burst, hadden de dwerggalaxieën veel eigenschappen
die waargenomen zijn in BCDs: het compacter zijn van de galaxie, hogere gashoeveelheid,... Alleen de nodige lagere metalliciteit leek voor een mogelijk probleem te zorgen.
Meer realistische simulaties, gebruikmakende van een merger geschiedenis van de dwerggalaxieën, zouden dit probleem kunnen verhelpen.
Het eerste type burst was niet echt compacter, dit hoeft niet noodzakelijk een probleem
te zijn. Aangezien over het algemeen dwerggalaxieën met een verhoogde stervorming
compacter zijn. Het kan ook zijn dat in onze studie dit soort burst overbenadrukt wordt
door het bestuderen van het nogal extreme model zonder initiële rotatie van de gaswolk.
En het kan misschien zijn dat het compacter worden van de galaxie niet gemerkt wordt
door een gebrekkige tijdsresolutie in het wegschrijven van de snapshots.
110
Appendices
111
Appendix A
pro vs retro tinit (Gyr) tp (Gyr) rp (kpc)
prograde
9.95
1.0
15
9.95
1.0
15
retrograde
prograde
10.45
1.0
5
10.45
1.0
7
retrograde
retrograde
10.45
1.0
7
10.45
1.0
5
retrograde
prograde
10.45
1.0
6
10.45
0.8
8
prograde
prograde
10.45
0.9
7
10.45
1.0
7
prograde
retrograde
10.45
1.0
9
retrograde
10.45
1.0
17
10.45
0.9
16
prograde
10.45
0.9
11
prograde
prograde
10.45
0.9
12
retrograde
10.45
0.9
10
10.45
0.9
6
prograde
10.45
0.9
13
retrograde
10.45
0.9
17
prograde
retrograde
10.45
0.9
18
prograde
10.45
1.0
19
retrograde
10.45
0.9
19
e
2
2
2
1.6
3
2
1.9
2.6
3
2
2
2
3
2.2
3
2.5
3.4
3
2.5
2.8
2
3
Table 1: The initial conditions of the I1 model interactions. Where tinit is the starting
time of the interaction, tp the time after which the closest approach is achieved, rp the
distance at closest approach and e the eccentricity.
112
pro vs retro tinit (Gyr) tp (Gyr) rp (kpc)
prograde
10.45
1.0
7
prograde
10.45
0.8
5
10.45
0.9
6
retrograde
retrograde
10.45
0.9
5
10.45
0.9
11
retrograde
prograde
10.45
1.0
9
10.95
0.8
10
retrograde
retrograde
10.45
0.9
12
10.45
1.0
11
prograde
prograde
10.45
1.0
13
10.45
1.0
10
retrograde
prograde
10.45
1.0
12
10.45
1.0
15
prograde
retrograde
10.45
0.9
16
retrograde
10.45
1.0
18
retrograde
10.45
0.9
11
prograde
10.45
0.9
11
prograde
10.45
0.9
10
10.45
1.0
9
retrograde
prograde
10.45
0.9
17
10.45
0.9
15
retrograde
prograde
10.45
0.9
18
e
2.5
2.5
2
1.7
2
2
3
2.5
2
3
2
2
2
3
2
2.6
3.1
2.5
2
2.3
3
3
Table 2: The initial conditions of the I2 model interactions. Where tinit is the starting
time of the interaction, tp the time after which the closest approach is achieved, rp the
distance at closest approach and e the eccentricity.
113
pro vs retro tinit (Gyr) tp (Gyr) rp (kpc)
retrograde
10.45
0.9
6
retrograde
10.45
1.0
10
10.45
1.0
9
prograde
prograde
10.45
0.9
8
10.45
0.9
5
prograde
retrograde
10.45
0.9
5
10.45
1.0
7
retrograde
retrograde
10.45
1.0
4
10.45
1.0
8
prograde
prograde
10.45
0.9
6
10.45
1.0
7
prograde
retrograde
10.45
1.0
9
10.45
0.9
6
retrograde
prograde
10.45
0.9
6
prograde
10.45
0.9
13
retrograde
10.45
0.9
12
retrograde
10.45
0.9
5
retrograde
10.45
1.0
8
10.45
1.0
7
retrograde
prograde
10.45
1.0
7
10.45
1.0
12
prograde
e
1.9
2
2
2
2
1.7
3
3
3
3
2
2
3
2.4
2.8
2.1
3
2
2
1.5
2
Table 3: The initial conditions of the I3 model interactions. Where tinit is the starting
time of the interaction, tp the time after which the closest approach is achieved, rp the
distance at closest approach and e the eccentricity.
114
pro vs retro tinit (Gyr) tp (Gyr) rp (kpc)
retrograde
10.45
1.0
9
prograde
10.45
0.9
12
10.95
0.8
13
retrograde
prograde
10.45
1.0
20
10.45
1.0
16
retrograde
prograde
10.45
0.9
16
10.45
0.9
9
prograde
retrograde
10.45
1.0
8
10.45
0.9
11
retrograde
prograde
10.45
1.0
11
10.45
1.0
17
prograde
retrograde
10.45
0.9
18
10.45
1.0
19
retrograde
prograde
10.45
0.9
14
prograde
10.45
0.9
21
retrograde
10.45
0.9
22
prograde
10.45
1.0
10
prograde
10.45
1.0
22
10.45
0.9
23
retrograde
retrograde
10.45
0.9
24
10.45
0.9
23
prograde
retrograde
10.45
1.0
25
e
3
2.5
3
2
2.5
3
2.5
2
3
2
2
3
1.6
3
2.4
2.7
2
2.1
3
2.4
2.9
2
Table 4: The initial conditions of the I4 model interactions. Where tinit is the starting
time of the interaction, tp the time after which the closest approach is achieved, rp the
distance at closest approach and e the eccentricity.
115
pro vs retro tinit (Gyr) tp (Gyr) rp (kpc)
retrograde
10.45
0.8
8
retrograde
10.45
1.0
10
10.45
1.0
9
prograde
retrograde
10.45
0.9
16
10.45
0.9
18
prograde
retrograde
10.45
0.9
14
10.45
0.9
8
retrograde
prograde
10.45
0.9
12
10.45
1.0
11
retrograde
prograde
10.45
1.0
11
10.45
1.0
13
prograde
prograde
10.45
0.9
17
10.45
1.0
18
retrograde
prograde
10.45
0.9
14
retrograde
10.45
0.9
13
prograde
10.45
1.0
19
retrograde
10.45
1.0
18
retrograde
10.45
1.0
12
10.45
1.0
12
prograde
prograde
10.45
1.0
10
10.45
1.0
15
retrograde
retrograde
10.45
0.9
21
e
1.7
2
2.5
3.5
3
3
2.5
3
2
2
2
3
2
3
3
1.9
2.1
1.8
1.8
2.3
2.2
2.6
Table 5: The initial conditions of the I5 model interactions. Where tinit is the starting
time of the interaction, tp the time after which the closest approach is achieved, rp the
distance at closest approach and e the eccentricity.
116
pro vs retro tinit (Gyr) tp (Gyr) rp (kpc)
prograde
10.45
1.0
15
prograde
10.45
0.9
13
10.45
1.0
16
retrograde
retrograde
10.45
0.9
15
10.45
1.0
10
retrograde
prograde
10.45
1.0
11
10.45
0.9
12
retrograde
prograde
10.45
0.9
20
10.45
1.0
19
retrograde
prograde
10.45
1.0
17
10.45
1.0
20
retrograde
prograde
10.45
1.0
14
10.45
0.9
23
prograde
retrograde
10.45
0.9
13
retrograde
10.45
0.9
22
prograde
10.45
0.9
18
prograde
10.45
0.9
22
retrograde
10.45
0.9
14
10.45
0.9
24
retrograde
prograde
10.45
1.0
24
10.45
0.9
25
retrograde
e
2.5
3.5
2
3
2
2
3
3
2
2
2
2
2.1
2.6
2.8
3
2.6
2.2
2.5
2.1
2.3
Table 6: The initial conditions of the I6 model interactions. Where tinit is the starting
time of the interaction, tp the time after which the closest approach is achieved, rp the
distance at closest approach and e the eccentricity.
117
pro vs retro tinit (Gyr) tp (Gyr) rp (kpc)
prograde
10.45
1.0
15
retrograde
10.45
0.9
13
10.45
0.9
17
prograde
retrograde
10.45
1.0
18
10.45
0.9
20
retrograde
prograde
10.45
0.9
22
10.45
0.9
12
prograde
retrograde
10.45
1.0
24
10.45
1.0
20
prograde
retrograde
10.45
1.0
27
e
2
2.5
2.8
2
2.7
2.2
2.6
2.1
2.3
2.2
Table 7: The initial conditions of the I7 model interactions. Where tinit is the starting
time of the interaction, tp the time after which the closest approach is achieved, rp the
distance at closest approach and e the eccentricity.
Appendix B
200 Myr
DG1
-100 Myr
DG2
-250 Myr
DG1
0 Myr
DG3
300 Myr
DG2
200 Myr
DG2
1.1 Gyr
DG1
-150 Myr
DG1
150 Myr
DG3
400 Myr
DG2
Table 8: The times of the bursts in DG1, when the moment of closest approach is taken
as the zero point. Added directly below the time is the galaxy type it is interacting with.
150 Myr
DG2
150 Myr
DG2
1.5 Gyr
DG2
-150 Myr
DG3
50 Myr
DG3
250 Myr
DG3
Table 9: The times of the bursts in DG2, when the moment of closest approach is taken
as the zero point. Added directly below the time is the galaxy type it is interacting with.
118
1.1 Gyr
DG3
700 Myr
DG3
1.25 Gyr
DG3
150 Myr
DG3
750 Myr
DG2
1 Gyr
DG3
-200 Myr
DG5
1 Gyr
DG5
1.5 Gyr
DG30
0 Myr
DG4
Table 10: The times of the bursts in DG3, when the moment of closest approach is taken
as the zero point. Added directly below the time is the galaxy type it is interacting with.
Appendix C
12 + log(O/H)
[Fe/H]
12 + log(O/H)
[Fe/H]
8.12 8.07 8.16 8.03 8.09
-1.51 -1.58 -1.49 -1.56 -1.53
8.10 8.08 8.11 8.11 8.06
-1.54 -1.57 -1.57 -1.50 -1.52
Table 11: The 12 + log(O/H) and [Fe/H] values for DG1 experiencing a burst.
12 + log(O/H)
[Fe/H]
8.23 8.24 8.20 8.19 8.25 8.24
-1.45 -1.46 -1.47 -1.47 -1.46 -1.46
Table 12: The 12 + log(O/H) and [Fe/H] values for DG2 experiencing a burst.
12 + log(O/H)
[Fe/H]
12 + log(O/H)
[Fe/H]
8.58 8.55 8.56 8.52 8.59
-1.22 -1.24 -1.24 -1.30 -1.19
8.55 8.53 8.56 8.57 8.52
-1.24 -1.28 -1.22 -1.23 -1.30
Table 13: The 12 + log(O/H) and [Fe/H] values for DG3 experiencing a burst.
model
MT1
MT2
12 + log(O/H) [Fe/H]
7.51
-1.73
7.66
-1.66
Table 14: The 12 + log(O/H) and [Fe/H] values for the merger tree simulations.
119
appendix D
0.94 0.4 2.46 1.25 1.60 3.14 2.38 1.46 2.12
0.34 0.0 0.06 0.0 0.70 0.30 1.16 0.04 0.12
Table 15: On top the increase in gas mass in the galaxy around closest approach for the
DG1 dwarf galaxies having a burst. Immediatly below that, the gas mass coming from
the other galaxy at the moment of maximal gas mass in the galaxy. The values in the
table are in units of 106 M
5.82 6.31 7.91 8.79 4.40 8.53
0.40 0.59 0.11 1.25 1.05 0.0
Table 16: On top the increase in gas mass in the galaxy around closest approach for the
DG2 dwarf galaxies having a burst. Immediatly below that, the gas mass coming from
the other galaxy at the moment of maximal gas mass in the galaxy. The values in the
table are in units of 106 M
120
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