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Galaxies II – Dr Martin Hendry
10 lectures to A3/A4, beginning January 2008
3. Galaxy Formation and Evolution
How did galaxies form?…
o
A detailed explanation is one of the main unsolved
problems in astronomy.
o
We understand the general picture: gravity assembles
galaxies and clusters by causing growth of primordial
density perturbations
CMBR fluctuations are the
seeds of today’s galaxies
Galaxy formation is
sensitive to the pattern,
of CMBR temperature
fluctuations
3. Galaxy Formation and Evolution
How did galaxies form?…
o
A detailed explanation is one of the main unsolved
problems in astronomy.
o
We understand the general picture: gravity assembles
galaxies and clusters by causing growth of primordial
density perturbations
o
A recipe for galaxy formation has ingredients:
gravity
(dark matter)
gas physics
(stars)
background cosmological model
Studying the statistics of the present-day galaxy distribution
is a powerful tool for constraining cosmological parameters.
Can compare real observations with the results of computer
simulations – e.g. 2dF galaxy redshift survey
Studying the statistics of the present-day galaxy distribution
is a powerful tool for constraining cosmological parameters.
Can compare real observations with the results of computer
simulations – e.g. 2dF galaxy redshift survey.
Simulations follow the evolution of galaxies as structure grows
 Clear that mergers and interactions are
common.
Galaxy mergers and interactions
What happens when galaxies merge?
o Their stars don’t collide, but some of the galaxies’ K.E. is
transferred to the random motion of the stars.
o Galaxies experience a ‘drag’ force, known as
Dynamical Friction
Drag force on each galaxy depends
on:-
M,
mass of galaxy
v,
velocity of galaxy
,
mass density of neighbour
Mass of galaxy enters via Newton’s law of gravitation, so
the drag force will be a function of
GM
Can show via dimensional analysis that
GM 
2
Fdrag

v
2

(3.1)
Mass of galaxy enters via Newton’s law of gravitation, so
the drag force will be a function of
GM
Can show via dimensional analysis that
GM 
2
Fdrag

v
2

(3.1)
Mass of galaxy enters via Newton’s law of gravitation, so
the drag force will be a function of
GM
Can show via dimensional analysis that
GM 
2
Fdrag

v

(3.1)
2
(Can also use this formula to consider the lifetime of e.g.
globular clusters orbiting a parent galaxy – see example
sheets)
High speed ‘collision’ of 2 disk galaxies
 Galaxies are not slowed down enough to become a bound
pair.
 Galaxies separate, but their disks are ‘dishevelled’:
stars acquire random motions, causing disks to ‘puff up’.
 Can form spiral arms or bars
e.g. spiral arms of M81
e.g. bar of M95
High speed ‘collision’ or ‘fly-by’ of 2 disk galaxies
 Galaxies are not slowed down enough to become a bound
pair.
 Galaxies separate, but their disks are ‘dishevelled’:
stars acquire random motions, causing disks to ‘puff up’.
 Can form spiral arms or bars
 Multiple ‘close encounters’ may destroy disks all together;
explains lack of disk galaxies in the cores of rich clusters
Slower ‘collision’ or ‘fly-by’
 Much greater disturbance – particularly if co-planar and
direction of fly-by aligned with direction of motion
 Relative velocity of stars in galaxy A and
B is significantly smaller; stars spend a
long time in close proximity
 Interaction can draw out a long
tidal tail which may persist for
several Gyr
Slower ‘collision’ or ‘fly-through’
 Head-on collision can produce a polar ring galaxy
Slower ‘collision’ or ‘fly-through’
 Head-on collision can produce a polar ring galaxy
Computer model, by J. Toomre
Why should a polar ring form?
Suppose the galaxy is in virial equilibrium before the
interaction
2Kinit  U init
(3.2)
Why should a polar ring form?
Suppose the galaxy is in virial equilibrium before the
interaction
2Kinit  U init
(3.2)
If the interaction happens quickly (impulse approximation)
then the potential energy of the galaxy doesn’t have time to
change appreciably.
Stars in the galaxy gain K.E. from the disturber
K after  Kinit  K

Galaxy K.E. increases to

Galaxy thrown out of equilibrium
(3.3)
Why should a polar ring form?
After some time virial equilibrium will be restored.
When virialised, the galaxy’s total energy satisfies
E  K  U  K  2K  K
(3.4)
Why should a polar ring form?
After some time virial equilibrium will be restored.
When virialised, the galaxy’s total energy satisfies
E  K  U  K  2K  K
(3.4)
Just after the interaction,
Eafter  K after  U init  K init  K  U init
 Einit  K
(3.5)
Why should a polar ring form?
Once virial equilibrium has been restored
K final   Efinal  ( Einit  K )
 K init  K
Comparing with eq. (3.3) we see that, just after the
interaction, the galaxy has gained
K
the time it has virialised again it has lost
of K.E., but by
K
of K.E.
One way this can happen is to convert excess K.E. into
P.E. – e.g. a shell of galactic material expands outwards
(3.6)
Why should a polar ring form?
Once virial equilibrium has been restored
K final   Efinal  ( Einit  K )
 K init  K
Comparing with eq. (3.3) we see that, just after the
interaction, the galaxy has gained
K
the time it has virialised again it has lost
of K.E., but by
K
of K.E.
Tidal tails and streams can achieve a similar result.
(3.6)
Formation of dust lanes
 Sometimes, instead of the ‘disturber’ drawing out a tidal
tail from the first galaxy, the first galaxy can ‘tidally
strip’ gas and dust from the disturber
(the disturber becomes the disturbed)
 Can leave behind a dust lane – fresh supply of gas and
dust which can kick start new star formation (even in an
elliptical)
e.g. Centaurus A (also strong radio source)
Even slower ‘collision’, leading to a merger
 Interactions with lower approach velocities may lead to a
merger – possibly after an elaborate ‘courtship’
 Final appearance of galaxies depends on mass and speed
of the perturber, and orientation during interaction.
Even slower ‘collision’, leading to a merger
 Interactions with lower approach velocities may lead to a
merger – possibly after an elaborate ‘courtship’
 Final appearance of galaxies depends on mass and speed
of the perturber, and orientation during interaction.
 Close passage of two gas-rich spirals can produce a
Starburst galaxy:
* disk gas is pulled away from near circular orbits
* gas clouds collide at high speed, causing shocks
* compresses gas to very high density, triggering
large amounts of star formation
Star Formation Models
 Since galaxies contain stars, to understand galaxy
formation we need to understand star formation.
 This is a much more complicated problem than following the
evolution of the dark matter – which only needs gravity.
Star Formation Models
 Since galaxies contain stars, to understand galaxy
formation we need to understand star formation.
 This is a much more complicated problem than following the
evolution of the dark matter – which only needs gravity.
 We need to understand:
o
how and where do stars form in galaxies?
o
what determines stellar masses?
o
what determines stellar luminosities?
o
what determines stellar chemical compositions?
o
how do all of these depend on galaxy type, age, redshift ?
Star Formation Models
 A good way to compare star formation models with
observations is by spectral synthesis:
We can compute a synthetic spectrum for our model
galaxy, accounting for:





age of the galaxy
chemical composition (metallicity)
initial mass of stars and gas
rate at which new stars form
redshift of observation
We can then compare with observed spectrum to
‘best fit’ galaxy properties
Spectral energy distribution,
from the models of Bruzual &
Charlot (2003).
Assuming solar metallicity
(i.e. same chemical abundances
as the ISM in the vicinity of
the Solar System).
Single burst of star formation
at time t  0
Ages range from 1 million years
(0.001 Gyr) to 13 Gyr
Note that the spectrum shape
evolves very little between
about 4 Gyr and 13 Gyr
(See also examples sheet 5)
Although spectrum
shape varies little with
age, the strength of
spectral absorption lines
depends on metallicity:
Lines associated with
metals stronger in
metal-rich galaxies
(But some degeneracy
here, as older galaxies
are usually also more
metal-rich, as metals
build up after many
generations of star
formation)
Ca H, K
Fe, Mg
TiO O2
Note the sharp drop in flux
for   400 nm, known as the
Lyman Break
This occurs because:
a)
There aren’t many stars
hot enough to produce UV
photons in great numbers
b)
Any UV photons that are
produced can ionise HI
clouds, so a large fraction
of them are absorbed
before they reach us
We saw the Lyman break in
The spectra of S0 and Sb
Galaxies, in Section II
Ca H, K
Fe, Mg
TiO O2
Spectral fits to 2
galaxies from the
Sloan Digital Sky
Survey
(Note that the emission
lines in 385-118 are not
included in the fit; these
are the result of a
recent burst of star
formation in this galaxy)
Star Formation Models
We define the stellar birthrate function
B( M , t )dMdt
B( M , t ) :
number of stars per unit volume*
= with masses between M and M  dM ,
formed between t and t  dt .
* Equivalently, per unit surface
area for disk galaxies
Star Formation Models
We define the stellar birthrate function
B( M , t ) :
number of stars per unit volume*
= with masses between M and M  dM ,
formed between t and t  dt .
B( M , t )dMdt
* Equivalently, per unit surface
area for disk galaxies
Usually we assume
B( M , t )dMdt
  (t )  ( M ) dMdt
Star formation rate
Initial mass function
(3.7)
Various models can be adopted for
 (t )
:
a) Instantaneous burst (delta function)
b) Constant SFR
c) Steep rise + exponential decay
Or one can model a combination; e.g. (a) + (c) for
Feedback models
Various models can be adopted for
 (t )
:
a) Instantaneous burst (delta function)
b) Constant SFR
c) Steep rise + exponential decay
Or one can model a combination; e.g. (a) + (c) for
Feedback models
The IMF is generally modelled as a power law :
e.g. Salpeter (1955):
 ( M )  M  (1 x )
(3.8)
x  1.35
Miller-Scalo (1998):
Different values of x for
different mass ranges
M  0.1M
M  0.8M
 (M )  M 1.8
Miller-Scalo (1998):
Different values of x for
different mass ranges
 (M )  M 1.4
Chemical Evolution Models
As new stars form and old stars leave the main sequence, the
chemical composition of the ISM changes. This is most easily
modelled via a drastic over-simplification:
one zone, instantaneous recycling, closed box model
Galaxies II – Dr Martin Hendry
10 lectures to A3/A4, beginning January 2008
Chemical Evolution Models
As new stars form and old stars leave the main sequence, the
chemical composition of the ISM changes. This is most easily
modelled via a drastic over-simplification:
one zone, instantaneous recycling, closed box model
We assume:
o galaxy’s gas is well-mixed; same composition everywhere
o massive stars return their nuclear products to the ISM rapidly
o no gas escapes from the galaxy or is added to it
o all elements heavier than Helium maintain the same proportion
relative to each other
We define:
M g (t )
=
mass of gas in the galaxy at time
M s (t )
=
mass in lower mass stars +
remnants of high mass stars (WDs + NS + BHs)
M h (t )
=
mass of metals : elements heavier than Helium in the ISM
t
 metallicity, Z (t )  M h (t ) M (t )
g
We define:
M g (t )
=
mass of gas in the galaxy at time
M s (t )
=
mass in lower mass stars +
remnants of high mass stars (WDs + NS + BHs)
M h (t )
=
mass of metals : elements heavier than Helium in the ISM
t
 metallicity, Z (t )  M h (t ) M (t )
g
Suppose at time
t
a mass
M s
of stars is formed.
o The massive stars go through their lives rapidly, and leave behind
M s
o A mass
of low mass stars and remnants
p M s
of metals is returned (instantaneously) to the ISM
Hence
Also
M h  pM s  ZM s
(3.9)
M h  M g Z   ZM g  M g Z
(3.10)
So
Z

pM s  Z M s  M g 
(3.11)
Mg
If no gas enters or leaves the system, then
M s  M g  0
So we can rewrite eq. (3.11) as:
Z
M g
p
 
Mg
(3.13)
(3.12)
If
p
is independent of
Z
then we can solve eq. (3.13):
Z (t )   p ln M g (t )  const.
or
 M g (t  0) 
Z (t )  Z (t  0)  p ln 

 M g (t ) 
(3.14)
(3.15)
If
p
is independent of
Z
then we can solve eq. (3.13):
Z (t )   p ln M g (t )  const.
or
 M g (t  0) 
Z (t )  Z (t  0)  p ln 

 M g (t ) 
So the metallicity increases with time, as stars are formed
and the gas in the ISM is steadily used up.
(3.14)
(3.15)
If
p
is independent of
Z
then we can solve eq. (3.13):
Z (t )   p ln M g (t )  const.
or
(3.14)
 M g (t  0) 
Z (t )  Z (t  0)  p ln 

 M g (t ) 
(3.15)
So the metallicity increases with time, as stars are formed
and the gas in the ISM is steadily used up.
The mass of stars formed before time
is given by M (0)  M (t )
g
Re-arranging eq. (3.15)
t , and hence with Z  Z (t ) ,
g


M s ( Z )  M g (0)1  e

Z Z ( 0 )
p


(3.16)
Differentiating, the mass of stars with metallicity between
Z and Z  Z is
dM s
Z
dZ

M g (0)
p
 Z (t )  Z (0) 
exp 
Z

p


(3.17)
This model predicts that the distribution of metallicities should fall
off exponentially.
We can test the model using Galactic Bulge
observations (through Baade’s Window )
Reasonably good fit, with
Z  0 at t  0
p  0.7 Z
and
We can also apply the model to the solar neighbourhood.
Near to the Sun, the Milky Way disk contains about
-2
30  40 M pc-2 of stars, and about 13M pc of gas

 M g (t  0)  50M pc-2

(3.18)
We can also apply the model to the solar neighbourhood.
Near to the Sun, the Milky Way disk contains about
-2
30  40 M pc-2 of stars, and about 13M pc of gas


 M g (t  0)  50M pc-2
(3.18)
The Sun is more metal-rich than the solar neighbourhood gas:
Z  0.7Z
If we suppose that Z (0)  0 and no gas has entered or left
the solar neighbourhood, then from eqs. (3.15) and (3.18)
50
 
Z now  0.7Z  p ln 13
p  0.5Z
(3.19)
This is lower than for the Bulge.
Perhaps we need a ‘leaky box’ model: could some of the metal-enriched gas,
recycled by supernovae, have leaked away from the solar neighbourhood?
But there is another problem…
This is lower than for the Bulge.
Perhaps we need a ‘leaky box’ model: could some of the metal-enriched gas,
recycled by supernovae, have leaked away from the solar neighbourhood?
But there is another problem…
From eq. (3.16)
M s ( Z  0.25Z)
M s ( Z  0.7 Z )
1  exp  0.25Z

1  exp  0.7 Z




p
p
 0.52
if
p  0.5Z 
i.e. more than half of the stars in the solar neghbourhood should
have metallicities less than a quarter of the Sun’s.
This has not been observed in surveys
In a survey of 132 G-dwarfs:
only 33 had less than 25% of solar iron abundance
only 1 had less than 25% of solar oxygen abundance
This is known as the G-dwarf problem
The G-dwarf problem highlights the limitations of the one
zone, instantaneous recycling closed-box model.
o We can resolve the G-dwarf problem if we suppose that the
initial metallicity of the solar neighbourhood was not zero –
i.e. the gas was pre-enriched (by earlier star formation?)
when it arrived at the solar neighbourhood (see examples 6)
The G-dwarf problem highlights the limitations of the one
zone, instantaneous recycling closed-box model.
o We can resolve the G-dwarf problem if we suppose that the
initial metallicity of the solar neighbourhood was not zero –
i.e. the gas was pre-enriched (by earlier star formation?)
when it arrived at the solar neighbourhood (see examples 6)
o However, the abundances of different heavy elements vary
relative to each other. Also, abundances show a large scatter
even for stars of a given age.
This suggests that subsequent
inflow of fresh, metal-poor gas
may have diluted the ISM, but
may not have mixed evenly with
the gas already present
Increasingly, gas dynamics and sophisticated star formation
models are being incorporated into numerical galaxy simulations,
so we no longer need consider only simplified approximations
such as the closed-box models.
There is much yet to be done, however, and a lot of complicated
physics still remains to be treated properly.
Increasingly, gas dynamics and sophisticated star formation
models are being incorporated into numerical galaxy simulations,
so we no longer need consider only simplified approximations
such as the closed-box models.
There is much yet to be done, however, and a lot of complicated
physics still remains to be treated properly.
As we remarked previously, our recipe for galaxy formation also
depends on the background cosmology.
We develop this theme further in Section 4.