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Properties of Galaxies
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Many subjects here are covered superficially and I can give references
to review-type articles or even the original scientific papers if you
want. There is no single reference book that covers everything in
these lectures, mostly because research in this field is fairly rapidly
moving (for example about a quarter of what is covered was
discovered in the last few years).
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An outline is given below. This is not entirely a useful thing, because
everything is connected to everything else. The intention is to start
from the beginning and end up so that you can understand the
framework in which most current research into extragalactic
astronomy is placed.
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www.ast.cam.ac.uk/~trentham/course.ppt
1. Definition of a galaxy in terms of its components.
2. Fluxes, luminosities, magnitudes, wavebands
3. Types of Galaxies - ellipticals, spirals, and others - their gross properties.
4. Nomenclature
5. Components of Galaxies 1. Stars - formation, HR diagram, evolution,
remnants
6. Components of Galaxies 2. Active Galactic Nuclei - quasars, radio jets
7. Components of Galaxies 3. Gas - hot and cold
8. Components of Galaxies 4. Dark matter - properties, what it might be?
9. Local Galaxies
10. Distribution of galaxies in the Universe - environments, large-scale
structure
11. Emission mechanisms and spectral energy distributions – bolometric
luminosities
12. Luminosity functions
13. Light profiles and surface-brightnesses
14. Stellar and gas dynamics
15. Galaxy formation 1. Dark matter and cosmology
16. Galaxy formation 2. The high redshift Universe
17. Galaxy formation 3. The formation of stars in galaxies - the Madau Plot
1 Definition of a galaxy
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A galaxy is a self-gravitating collection of about 106 to 1011 stars, plus
an amount up to 1/2 of as much by mass of gas, and about 10 times
as much by mass of dark matter. The stars and gas are about 70%
hydrogen by mass and 25% helium, the rest being heavier elements
(called "metals").
Typical scales are: masses between 106 to 1012 solar masses (1 solar
mass is 2 x 1030 kg), and sizes 10 kpc (1 pc = 3.1 x 1016 m, 1 kpc =
1000 pc). Galaxies that rotate do so in about 10-100 Myr at about 100
km/s. The average separation of galaxies is about 1 Mpc.
Between galaxies there is very diffuse gas, called the intergalactic
medium. It was much denser in the past before galaxies formed and
took up all the gas and made it into stars.
The Milky Way is
known in a fair
amount of detail,
and both the gas
and stars split
cleanly into
different
populations or
phases.
Stars:
Disk: 5 1010 Msun
Bulge: 1
Halo:
1010
109
Msun
Msun
Globulars:
108
Msun
Gas:
Dark matter:
H2 clouds: 1 109 Msun
Halo: 2 1012 Msun
HI gas: 4 109 Msun
HII regions: 108 Msun
Cosmic Inventory (Fukugita & Peebles 2004, Read
& Trentham 2005)
73 % - dark energy or cosmological constant
23 % - dark matter, probably CDM
4 % - normal baryonic matter, about 10% of
which is in galaxies (mostly in the form of stars).
The rest is in the IGM.
2 Fluxes, luminosities, magnitudes,
wavebands
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The total light from a galaxy comes out at all wavelengths of the electromagnetic
spectrum. When we observe a galaxy, we usually consider the light from some waveband
(crudely thought of as all the light between two wavelengths lmin and lmax ; in fact a
more complex transmission function is usually required). For example the B band is a
narrow band between about 4200 and 4600 Angstroms, the K band is a band between
2.1 and 2.3 microns.
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mX = -2.5 log10 (FX / F0), where F0 is the flux measured in band X from the star Vega.
The magnitude we measure from a galaxy is called its apparent magnitude. A more
useful quantity for relating galaxies at different distances to each other is the absolute
magnitude MX = mX - 5 log10 (distance/10 pc). Absolute magnitudes for galaxies are
negative, the more negative the absolute magnitude, the brighter the galaxy. Typical
values range from - 7 (the faintest galaxies known) to -26 (the brightest galaxies known)
in the B band.
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As far as I can tell the way the magnitude scale is defined is purely historical. It is not
used at long (radio or far-infrared) wavelengths or at short (UV or X-ray or gamma ray)
wavelengths, where fluxes are usually quoted instead. One other system in use is the AB
magnitude system in which the zero-point is a flat spectrum (instead of the spectrum of
Vega).
Here as some of the quantities and
units that are currently in use. The
way in which people quote results is
often subjective.
Note in that in the penultimate
equation, the first transmission
coefficient is a function of the
physics of the Earth’s atmosphere,
the second transmission coefficient
is a function of the filter used, the
luminosity distance is a function of
the cosmology, and the attenuation
coefficient is a function of the line
of sight to the object in question.
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Apparent magnitudes
Values in the V-band (appropriate for the eye) are -27 for the Sun, -13 for the Moon,
-4 for Venus, -1 for Sirius, +6 for the faintest stars visible with the naked eye, +4
for Andromeda (this is difficult to see, because it is spread out over a large area of
the sky), +18 for the star-galaxy transition in the sky, and +30 for the faintest
galaxies observed in the Hubble Deep Field.
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Absolute magnitudes
Values in the V-band are -20 for the Milky Way, +5 for normal solar-type stars, -9
for globular clusters, -28 for bright quasars. The brightest object ever observed at
optical wavelengths, the prompt afterglow of GRB 990123, had an absolute
magnitude that reached -36.
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Colours
These can be computed from either apparent or absolute magnitudes. Typical B-V
values are 0.6 for the Sun, 0 for an A0 star, 1.0 for an elliptical galaxy and 0.5 for a
spiral galaxy.
Fukugita et al. (1995) PASP 107, 945
3 Types of galaxies
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In most galaxy samples there are roughly equal numbers of elliptical, spiral, and peculiar
(irregular) galaxies.
Elliptical galaxies come in two types - giant ellipticals, which have high brightnesses at their
centres and absolute B magnitudes between about -25 and -15, and dwarf ellipticals, which have
low brightnesses at their centres and absolute B magnitudes fainter than about -18. The faintest
galaxies known are dwarf ellipticals. Elliptical galaxies are featureless, with brightness profiles that
are high in the centre and lower far away from the centre.
Spiral galaxies like the Milky Way and Andromeda have absolute B magnitudes between about -24
and -18. They often look smooth near their centres (where the brightnesses are highest), and
have spiral arms at large radius from the centre. The spiral arms are often irregular in form and
one can see many condensations or knots, like HII regions which are making stars.
Irregular galaxies are irregular. They can be big systems of interacting galaxies, or (more
commonly) small blue galaxies with absolute blue magnitudes > -18 and no regular morphology,
usually just diffuse fuzz with a few condensations. The most famous examples are the Magellanic
clouds which can be seen from the Southern hemisphere.
If a galaxy has a bright quasar at the centre, the quasar is usually so bright that you can't see the
rest of the galaxy. Such objects therefore look pointlike (that is, like stars).
Finally, there do exist other, rarer, less classifiable galaxies, like giant low-surface-brightness
galaxies that can barely be seen above the sky brightness.
Spiral
Elliptical
Dwarf irregular
Dwarf elliptical
The Hubble sequence is normally used to classify giant galaxies and is illustrated in the tuning fork diagram.
For ellipticals, the classification seems to depend an orientation. Conventionally, many astronomers use the
classifications Sd and Sm to describe galaxies intermediate between Sc and irregular galaxies.
Many observational parameters correlate with Hubble type. For example:
•Bulge-to-disk ratio decreases towards later types
•Spiral arm pitch angle increases towards later types
•Star formation rate per unit mass increases towards later types
•HI mass fraction increases towards later types
•Colour gets bluer towards later types
•Total mass is approximately constant from S0 to Sc, then decreases towards later types
•Dark matter mass fraction increases towards later types
•Optical stellar mass-to-light ratio decreases towards later types
•Ratio of molecular to atomic gas mass decreases towards later types
X= Mrk 1460
4 Nomenclature
This is mostly historical, with apparently similar galaxies having very different-sounding
names. Names are usually taken from the following catalogs (if a galaxy appears in
more than one catalog, the name from the first-listed is usually adopted).
 Messier or M (bright local objects, many are star clusters)
 NGC (New Galaxy Catalog, about 8000 objects, many are star clusters)
 Zwicky catalogs (odd objects)
 Arp catalog (peculiar interacting systems)
 Markarian catalog (UV-bright systems)
 IC (Index catalog)
 UGC (Uppsala General Catalog)
 IRAS (infrared-loud, discovered by the IRAS satellite)
Most contemporary surveys like 2MASS and SDSS give names with the coordinates
implicit.
Failing all above, a galaxy can be named by its coordinates, which tell its position on the
sky. For example 01305+3305 would be an object at a right ascension of 01:30.5 and
a declination of +33:05.
5. Components of galaxies 1. Stars
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Stars like the Sun are massive spherical accumulations of gas that are
undergoing nuclear fusion and releasing energy in the form of (mostly visible)
electromagnetic waves. They have masses typically 0.1 to 100 times the mass
of the sun, and have a blackbody spectrum that peaks at longer wavelengths
for lower mass stars (it peaks at about 500 nm for the Sun).
The evolution of stars is depicted in the Hertzprung-Russell (HR) diagram
(alternatively called the color-magnitude diagram), which is historically one of
the most profound matches between theory and observation in astrophysics.
Different mass stars follow different tracks on the diagram.
Most gross photometric properties of galaxies can be understood in terms of
this diagram, remembering the fact that more massive stars evolve (that is,
move along their tracks in the diagram) much faster than less massive ones.
For example, a 10 solar mass star completes its track in about 0.01 billion
years, a 1 solar mass star in about 10 billion years.
BRIGHT
FAINT
BLUE
RED
Gas cloud – gravitational contraction - pre-main sequence – nuclear burning initiated - main sequence –
shell burning - subgiant – photon streaming limit - red giant branch ascent – core helium ignition – tip of
the red giant branch – vigorous helium core burning + weakened hydrogen shell burning – horizontal branch
– CO core and double shell burning – asymptotic giant branch – helium shell exhaustion – supergiant –
mass loss to become a planetary nebula and then CO white dwarf OR core collapse supernova to
become neutron star or black hole
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Young stars form in clouds of gas and tend to be enshrouded in these clouds
which contain lots of dust. Therefore we don't see these (very luminous) OB
stars directly, rather we infer their presence from the thermal (infrared or
submillimeter) radiation of dust which has absorbed the short-wavelength
radiation from the young stars and reradiates it as a cold blackbody.
The nuclear fusion in stars is responsible for making all the elements heavier
than helium that are seen in the Universe.
Remnants are white dwarfs, neutron stars, or black holes. These are
condensed matter, the last two are optically invisible and are remnants of the
most massive stars. Neutron stars are however visible as radio pulsars (and
maybe some gamma-ray bursts). The long-duration gamma ray bursts may be
linked to black holes in formation.
The color-magnitude for star cluster is that
for a single age population.
Here is the color-magnitude diagram of an
old globular cluster. Note:
1)
There are no blue stars on the main
sequence.
2)
The turn-off is well defined, and a
function of age (redder is older)
3)
White dwarfs will be below the
diagram to the left
4)
The two or three stars on the blue
side of the turn-off are blue
stragglers.
5)
That the morphology of the
horizontal branch. In general, older
and more metal-poor stars are bluer
here.
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Stellar population synthesis modeling of galaxies is used to predict
photometric properties of galaxies by combining the stellar evolution models
for different age populations with a stellar IMF.
Elliptical galaxies contain old populations of stars. All the massive stars in
these galaxies have completed their evolution and are remnants. The most
luminous stars in elliptical galaxies are red giants -- this is why elliptical
galaxies look red through a telescope. This is also true for the central parts of
spiral galaxies (the bulges).
Spiral galaxies (particularly the outer parts, also irregular galaxies) contain
young populations of stars. They have massive stars that haven't finished
their evolution. These are the most luminous stars in the galaxies. Recall
from the HR diagram that these are blue. This is why spiral galaxies look blue
through a telescope.
6 Components of galaxies 2. Active
galactic nuclei
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Nucleosynthesis in stars is not the only way that one can convert gas into other
material and release electromagnetic radiation along the way. Accretion onto a black
hole in the centres of galaxies (the Active Galactic Nuclei, or AGN phenomenon) is
another way and is about 400 times more efficient. This phenomenon is however
quite rare since one requires lots of gas in a small region, and this usually only happens
in the centres of galaxies.
In its most extreme phenomenon, AGNs can be QSOs or quasars, which are more
luminous than the most luminous galaxies (up to absolute blue magnitudes of - 28).
These are probably quite shortlived, as they require enormous gas supplies. More
common weaker AGNs like Seyfert galaxies, etc. are also found. Many of the most
luminous AGNs are dust-enshrouded, particularly when they are very young and have
just formed.
AGNs have non-thermal spectra and so emit quite a lot of energy outside visible
wavebands. They are much brighter than stars at X-ray and radio wavelengths, for a
given optical luminosity.
AGNs vary considerably in their radio properties. Optically luminous QSOs can be
either radio-loud quasars, or radio quiet. Quasars may be radio galaxies that happened
to be observed down the jet.
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The entire theoretical framework on which AGNs are based is
somewhat less secure than for stars. This is in part due to the extreme
conditions near these very massive black holes of 106 to 109 solar masses,
which is quite unlike anything we can test in laboratories on Earth (we are in
the strong field limit of general relativity). On the other hand, atomic
spectroscopy and nuclear physics (the physics on which stellar astrophysics is
based) is much more thoroughly tested.
The black-hole models for AGNs predict that when the AGN has run
out of gaseous fuel, one should still find very massive (now dark) objects in
the centres of nearby galaxies. These can be found by virtue of their
dynamical effects on stars in the centres of galaxies. Recent observations
strongly suggest that these massive dark objects do in fact exist. Interestingly,
there is a very tight relationship between the mass of the black hole and the
mass (or velocity dispersion) of the stars in the spheroid population of the
host galaxy: MSMBH ~ 0.0015 M* (spheroid)
This ties together black-hole formation and star formation together in some
(presumably complex) way.
7. Components of galaxies 3. Gas
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The space between the stars is occupied by gas that is not very dense (about 1 atom
per cc, a vacuum more perfect than we can get on Earth in laboratories). However,
the galaxies are so big that the total mass in this gas is an appreciable (though usually
less than a percent) fraction of the mass of the galaxy.
The gas is about 70% H and 25% He by mass. Other elements are present in trace
amounts (mostly CNO), and have been made in stars. These are of astronomical
interest as they offer useful probes of conditions, such as the integrated chemical
evolution history of the galaxies.
Gas may be ionized (hot), atomic (cold), or molecular (very cold, less than 50 K). In
elliptical galaxies most gas is hot. In spiral in irregular galaxies, most gas is cold, 50%
or less of which is molecular. The molecular gas is very clumpy, the others are more
evenly spread.
It is in the molecular gas clumps that stars form. Often associated with these cold
molecular gas clumps are substantial amounts of dust (about 1% of the cloud mass).
It is this dust that obscures the light from young stars.
The gas in galaxies, called the interstellar medium, is much denser than the gas
between galaxies, called the intergalactic medium (1 atom/cc in the interstellar medium
compared to 10-8 atom/cc in the intergalactic medium).
8. Components of galaxies 4. Dark matter
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This occupies about 90% (at least) of the mass of
galaxies. It is distributed in a smooth halo that
envelopes the stars and gas.
Spatially the dark matter halo occupies the same region
as a number of small (< 106 Msun) dense old star
clusters, the globular clusters. There about 150 globular
clusters in the Milky Way, more in bigger galaxies.
There are also about 109 Msun of individual stars in the
Milky Way field halo.
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The existence of dark halos around galaxies comes from dynamical measurements, X-ray profiles
of elliptical galaxies and measurements of gravitational lensing by individual galaxies.
The existence of dark matter in galaxy clusters, comes from X-ray, velocity dispersion and
gravitational lensing (both weak and strong) measurements.
The existence of dark matter in a cosmological context comes from the consideration of a large
number of datasets in conjunction with each other.for example, information comes from
measurements of cosmic shear and the Lyman forest.
Cosmological simulations, like the Millennium simulation, show that the three are the same
material. We require a universe with about 30% of the critical density in normal matter, of which
about 15% (about 4% of the total) is in baryons. By “matter”, we mean material that obeys a
pressureless equation of state. This is what distinguishes it from dark energy, which makes up the
other 70% or so. This dark matter must be cold in order to form galaxies, since hot dark matter
(like neutrinos) will free-stream out of perturbations in the cosmological fluid at early times. By
“cold”, we mean that the material has low thermal velocity. That all observations point towards
one consistent picture is another example of a successful match between theory and observation
in astrophysics.
HI and Ha rotation curves are both flat
for many spiral galaxies.
These galaxies
are all at about
5000 km/s,
where 1 arcmin
corresponds to
about 30 kpc.
Science (2003) 301, 1696
ACS image of a Abell 1689 (z=0.18) from Broadhurst et al.
2005 ApJ, 621, 53
The ACS is the optical camera on board the
HST. It has a field of view 202 X 202
arcsec.
At z=0.18, 1 kpc = 0.3 arcseconds, so the
cluster core radius 300 kpc = 1.5
arcminutes
This is one of large number of clusters
for which measurements like this have
been made. Clusters like Abell 1689
and Abell 2218 are particularly good,
because they had gravitational arcs near
the center. So the results can be
calibrated by strong gravitational
lensing (the green points in the figure).
The dark matter often has structure,
sometimes with lumps of dark matter
that are quite massive but have no
optical galaxies (for example Abell
1942; Erben et al. 2000, A&A, 355, 23)
Dark matter masses via X-ray halos
This equation can be applied to either galaxies or clusters but T(r) is more straightforward to measure in
clusters. The main complication is lack of spherical symmetry.
For a review of the applications of these techniques to clusters, see the earlier paper by Buote.
Title: The ESO Nearby Abell Cluster Survey. XII.
The mass and mass-to-light-ratio profiles of rich
clusters
Authors: Peter Katgert (Sterrewacht Leiden),
Andrea Biviano (INAF/OAT, Trieste), Alain
Mazure (OAMP/LAM, Marseille)
Journal-ref: Astrophys.J. 600 (2004) 657-669
If perturbations in the microwave background arise due to baryons falling within
dark matter fluctuations, then galaxies (and clusters) will grow out of the
perturbations with the observed clustering properties. They will then have dark
matter halos around them. This requires the dark matter to be cold, meaning that
it does not free-stream of fluctuations.
This is a fairly robust prediction of simulations. Since dark matter particles
interact only by gravitational forces, we can have some confidence in the result.
This phenomenon is implicit in the results of most simulation papers. For
example, Springel et al., Nature, 2005, 435, 629.
An early reference for clusters is Croft & Efstathiou, 1994, NN RAS, 267, 390
Read & Trentham (2005)
CDM theory also predicts a galaxy dark matter (halo) mass function for galaxies that
is steeper than the baryonic mass function at both the bright and faint ends. The
former is probably due to AGN feedback preventing arbitrarily large numbers of
atoms from falling into galaxies at late times. The latter is probably due to feedback
from supernovae in small galaxies and maybe reionization.
Most simulations show that the dark matter obeys an NFW
profile down to the resolution limit…………..
Trentham et al. 2001, MNRAS, 322, 658
…………….but there is increasing evidence for deviations on
small scales, particularly near galaxy centres.
A core has a=0 and a cusp has a<0.
Astrophys.J. 583 (2003) 732-751
The dwarf spheroidal galaxy Ursa Minor, which is composed
almost entirely of dark matter, also shows evidence for
substructure.
Astrophys.J. 588 (2003) L21-L24
Lower luminosity galaxies are increasingly dark-matter dominated.
astro-ph/0407321
•Much about the global properties of dark matter is known, specifically that it is cold and that
of the four fundamental physics forces it only responds to gravity (not electroweak for example,
as it emits no radiation).
•Nothing about the detailed nature of dark matter (like what particle it is) is known. Figuring it
out is one major current area of study in astrophysics. It is probably NOT baryonic (big-bang
nucleosynthesis + dynamical constraints), neutrinos (phase-space constraints) or black-holes
that result from stellar evolution (chemical constraints).
•Possibilities include primordial black-holes, axions (QCD predicts a <10^-5eV cold noninteracting particle), or some supersymmetric entity (beyond the standard theory of particle
physics or even GUTs), or something else. If it is either the first or second, there are hopes of
progress as far as figuring it out. If not, it will be difficult, at least for the foreseeable future,
despite the fact that there are about 70 orders of magnitude difference in mass between the
candidates.
•Dark matter is important in understanding galaxy formation since it is dark matter
perturbations in the early universe that grow gravitationally and drag the baryons with them
(meaning the gas that later forms stars). So it's worth repeating: its global properties are wellstudied without knowing what it is!
9. Local galaxies
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The Milky Way is one of two big galaxies in the Local Group, which is a
region of the local Universe about 1 Mpc across. Andromeda (M31) is the
other and is about twice as big. On the blue absolute magnitude scale, these
are at about -20.
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The two big galaxies are separated by 0.7 Mpc. Both have a number of
smaller satellites. The Milky Way has two well-known ones, the Magellanic
Clouds. The largest satellite of M31 is M33, a small spiral galaxy. There are a
few other small galaxies between and around the two large galaxies.
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M31, and the Magellanic Clouds can be seen with the naked eye. The LMC
and SMC are obvious, but we are too far north to see them here. You can see
M31 at the moment at the beginning of the night, but it is quite faint (it is
about as big as the moon).
Beyond the Local Group:
Over the past few years, Karachentsev and collaborators have been compiling a list of all galaxies within 10 Mpc,
the Local Volume sample. This includes all galaxies in the nearby Sculptor and M81 Groups. The program is
essentially a two-stage project. Firstly candidate galaxies need to be identified, usually from photographic all-sky
surveys. Secondly, distances to the galaxies need to be established; any one of a variety of methods may be used,
the best being the TRGB method. The first results from this program were published in 2004.
10. Distribution of galaxies
Galaxies tend to cluster. This means that the
probability of finding a galaxy at some point
P is highest when P is known to be close to
another galaxy. We saw a hint of this in the
Local Group because there are 2 big galaxies,
not one.
On much larger scales, the clustering is more
obvious. Most big galaxies exist in small
groups of 2, 3, or 4 like the Local Group
(these are called groups).
Garcia 1993, A&AS, 100, 47
This kind of study can be performed in much more detail with the new redshift surveys. An example this kind of study
is Eke et al., 2004, MNRAS, 348, 866, which uses the 2dfGRS.
Some big galaxies exist in much bigger aggregations called galaxy clusters. In a galaxy
cluster there are hundreds or even thousands of galaxies within a few megaparsecs radius.
Group tend to cluster too. So do galaxy clusters. The result is large-scale structure.
AJ 114, 2205
Large-scale structure can be mathematically quantified by the power spectrum of fluctuations. Redshifts surveys
provide three-dimensional positions. Two recent papers are:
Tegmark et al. 2004, ApJ, 606, 702 (SDSS) and Percival et al. 2004, MNRAS, 353, 1201 (2dF)
Large-scale structure is commonly seen in simulations of galaxy formation like the Millennium Simulation. This
is the natural result of the dark matter fluctuations that we see imprinted in the microwave background. The dark
matter grows by gravity and each dark matter condensation is accompanied by baryons, which may turn into a
galaxy according to some prescription. The natural result is a galaxy distribution with considerable large-scale
structure. The picture about is about 100 Mpc on the side and looks rather like the picture in the previous
viewgraph.
Elliptical galaxies are more commonly found in denser environments that spiral galaxies.
This is quantified in the morphology-density relation.
Dwarf ellipticals tend to be found in denser
environments than dwarf irregulars. There
found either within groups for clusters or in
close proximity to a giant galaxy (we saw that
in the Local Group).
The galaxy correlation function is a convenient mathematical way to express clustering properties. It is the
Fourier transform of the power spectrum. Much of its popularity as a mathematical tool follows from its
convenience as a way to represent nonlinear dynamical phenomena.
Historically, people used the angular correlation function
w(q) to derive the spatial correlation function above,
using what is known in Limber’s equation. This is
because the angular correlation function was so easy to
measure, before we had many redshifts. In the age of
the major galaxy redshift surveys like SDSS and 2dF, this
kind of approach is less common.
What is shown in the figure is the galaxy-galaxy correlation function, or autocorrelation function. It is also
possible to derive correlation functions between different populations. For example, we have seen that the dwarf
spheroidal – giant galaxy correlation function is large.
Different kinds of galaxies are clustered by different amounts. Most significantly, red elliptical galaxies are clustered
much more than blue spiral galaxies and therefore have higher correlation functions.
Budavari et al., 2003,
ApJ, 595, 59.
Later-type and bluer
galaxies have higher
values of t
Quasars are clustered more than galaxies. Galaxy clusters are clustered more than galaxies as well.
Clustering properties allow us to relate galaxies at different redshifts to each other.
Galaxies are more clustered than the underlying dark matter distribution. The theoretical reason for this is that galaxies
represent high-s peaks in the mass distribution. Clusters represent even higher-s peaks. The difference in clustering
properties of the galaxies in the dark matter, is quantified by the bias parameter b.
In the largest accumulations of galaxies, rich galaxy clusters, the dark matter, hot gas and galaxies are all mixed together
in roughly cosmological proportions. The ratio by mass of these three components in the richest clusters is about 70:8:1.
The dark matter masses come from gravitational lensing measurements, measurements of velocity dispersions, and X-ray
gas tracer measurements. The gas masses come from volume-weighted X-ray emission measures. Galaxy clusters are
characterized by their richness on the Abell scale. The Virgo Cluster would have a richness of about 1, the Coma Cluster
has a richness of 3, and the richest cluster known is Abell 665 (z = 0.18), which has a richness of 5.
Abell 665 (top to bottom is about four arcminutes)
In rich galaxy clusters, at the centre there is normally a luminous elliptical galaxy with a very large extended halo of
light. M87 in the Virgo cluster is an example. These galaxies probably come from the cannibalism of several smaller
cluster galaxies. In extreme cases, these are called cD galaxies and can be several hundred kiloparsecs in diameter. For
example, the nearest cD galaxy NGC 6166 (z = 0.03) would extend beyond Andromeda were it centred on the
Galactic Centre.
NGC 6166 in Abell 2199
in rich galaxy clusters, there is also intracluster light between galaxies. This probably accounts for a few percent of the
total mass in stars. It is probably the result of tidal stripping from all the galaxies in the cluster.
Zibetti et al., 2005, MNRAS, 358, 949
11. Spectral energy distributions
The spectrum of a galaxy normally consists of a smooth continuum emission plus
various absorption and emission lines at specific wavelengths. The main emission
mechanisms are:
RADIO --- free-free electron + synchroton continuum, 21 cm line from HI
SUBMM ---thermal emission from cold dust, CO and other molecular rotational lines
from molecular gas
INFRARED --- thermal emission from warm dust
VISIBLE --- stellar photospheric continuum emission plus photospheric absorption
lines, emission lines from gas
ULTRAVIOLET --- stellar photospheric continuum emission plus photospheric
absorption from very young stars
X-RAY --- thermal bremstraalung from free-free proton-electron scattering
Young stars and spiral/irregular galaxies have a blackbody spectrum peaked in the blue. Old stars and elliptical
galaxies have a blackbody spectrum peaked in the red (we saw this from the HR diagram).
Spiral and late-type galaxies have spectra with many emission lines from the gas associated with star-forming
regions. Elliptical and early-type galaxies have spectra dominated by photospheric absorption lines.
Dust-enshrouded young stars (or AGNs) have blackbody spectra peaked in the infrared between 10 and 1000 microns.
The example below is IRAS P09104+4109 (z=0.442), a dust-enshrouded quasar, where the dust is very hot (about 200
K).
Deane & Trentham, 2001, MNRAS, 326, 1467
Optically-bright AGNs like quasars have non-thermal spectra that are not blackbodies.
Sanders et al. 1989, ApJ, 347, 29
In terms of bolometric luminosity, the most
luminous galaxies in the universe are
ultraluminous infrared galaxies. These have
total luminosities of about 1012 Lsun and emit
most of their radiation at about 100 mm (3 x
1014 Hz), in the far-infrared. These are violent
starbursts, or maybe active galactic nuclei are,
that are enshrouded by dust. which is heated by
the photons from the young stars or AGN. The
dust then reradiates then energy in the farinfrared.
Sanders et al. 1988, ApJ, 325, 74
At optical wavelengths, the ultraluminous galaxies look like peculiar interacting galaxies. All the energy comes
out of a small area near the centre. This is quite unlike what happens in optically-luminous star forming galaxies.
The star formation happening in the centres of these of the galaxies is probably quite unlike the kind of star
formation we know about from observations of star forming regions within the Milky Way. Alternatively, these
galaxies may be powered by dusty AGNs, and may be quasars in the process of formation.
Ramirez-Ruiz et al., 2002, 329,
465
Ramirez-Ruiz et al., 2002, MNRAS, 329, 465
Below some threshold infrared luminosity L60 = 6 x 1010 Lsun, the optical luminosity of a galaxy tracks the
infrared luminosity. Above that luminosity, this is true for some galaxies, but there are other galaxies with
far greater infrared luminosity than is predicted given the scaling for the lower luminosity galaxies. In
these galaxies the infrared luminosity is optiically thick. The extreme case is the ultraluminous galaxies.
For example, there are about 30 magnitudes of visual extinction towards the core of Arp 220.
Rieke & Lebofsky, 1986, ApJ, 304, 326
12. Luminosity functions
These luminosity function describes how many galaxies exist per
luminosity interval. The functions look different when plotted for
different wavelength bands, as we would expect from the last section.
One generic feature of the luminosity function in any waveband is
that very luminous objects are rare.
The luminosity function F(L) dL is defined where F(L) dL
is the density of galaxies with luminosiities between L and
L+dL
A common analytic form for the total (summed over all galaxy types) optical galaxy luminosity function is the
Schechter function: F(L) ~ (L/L*)a exp (- L/L*)
This reproduces the general shape, but not the finer details.
Trentham et al., 2005, MNRAS, 357, 783
It is surprising how similar the field and cluster luminosity functions are, given the morphology-density relation.
The most significant difference is a steepening of the luminosity function at absolute magnitudes of about M B = 15 in clusters but not in the field. This is due to a substantial population of dwarf elliptical galaxies in clusters that
do not exist in the field. Following this rise, the luminosity function in clusters flattens again faintward of about
MB = -13.
The Schechter function is useful for a number of analytical approximations:
f(L) = f* (L/L*)a exp (- L/L*)
The number density of galaxies whose luminosity exceeds L is f* G(a+1, L/L*).
The luminosity density of galaxies whose luminosity exceeds L is f* L* G(a+2, L/L*).
The total luminosity density of the Universe is f* L* G(a+2), which is about 1 x 108 Lsun
Mpc-3. About half of this is in galaxies with luminosities above L*.
The median luminosity in an apparent magnitude limited sample is about L*. The number
counts peak at about ¼ L*.
In a cluster, cD galaxies have luminosities greater than 5 L*. They are not consistent with a
Schechter function fit to the other galaxies and are presumably formed by a special cluster
process.
No turnover in the galaxy luminosity function has yet been seen, though I suspect that we are close to observing
it. On the other hand, the turnover in the globular cluster luminosity function is highly significant.
Chandar et al., 2004, ApJ, 611, 220
Recall that a single O supergiant has a V-band absolute magnitude of about -7!
The radio luminosity function is dominated by the contribution from giant elliptical galaxies at the bright end.
Toffolatti et al., 1987, A&A, 184, 7
The bolometric luminosity function is similar to the far-infrared luminosity function. This was measured for
the first time by IRAS but has since been refined by future generations of infrared satellites like Spitzer.
The dark matter mass spectrum comes from N-body simulations of the growth of dark matter halos, with initial
conditions given by the CDM power spectrum, normalized by the microwave background
An approximate expression can be derived analytically
from Press-Schechter (1974, ApJ, 187, 425) theory.
The dark matter mass function is predicted from simulations and is not straightforward to measure. The baryonic mass
function, on the other hand, can be determined. The low all the baryonic mass functions for stars, atomic gas, molecular
gas, and the total baryonic mass function of galaxies (Read & Trentham, 2005, astro-ph/0502517). As we saw earlier, the
baryonic mass function is very different from the dark matter halo mass function, for a variety of astrophysical reasons.
13. Light profiles and surface brightnesses
In so far as galaxies are regular and have smooth light distributions, they are always brighter in the centre and
fainter in the outer parts, following a brightness profile that is approximately exponential (brightness is defined as
luminosity per unit projected area on the sky, as opposed to total luminosity). Most elliptical galaxies and bulges
have brightness profiles slightly more centrally peaked than an exponential and are fit accordingly (the de
Vaucouleurs function).
If we want to know the surface brightness at the very center of a galaxy, we can't usually measure it directly due to
atmospheric blurring (seeing) so we derive it from a fit to the rest of the galaxy.
An interesting set of correlations is
seen when one plots the derived central
surface-brightness against total luminosity
0for all galaxies. These are summarized in
the adjacent plot, which was shown earlier
in this course
Elliptical galaxes have a brightness profile that is fit by a de Vaucouleurs or r1/4 law.
Here re is the effective, or half-light, radius and Ie is the brightness at this radius. Often, the brightness is quoted
as a surface brightness [units mag arcsec-2] me = -2.5 log10 Ie + constant. The total luminosity is the intergral
over 2pr of the profile and equals 22.67 Iere2.
This profile is a description of the shape of a galaxy in two dimensions. Analytical deprojection to three
dimensions is given by Mellier & Mathez, 1987, A&A, 175, 1
Tidal effects can lead to a truncation of this profile. For example, this probably happened to M32 (King,
1952, AJ, 67, 471).
The three-dimensional shapes of elliptical galaxies are inferred from minor axis rotation and from
photometric twists (Kormendy, 1982, SAAS-FEE lectures)
Elliptical galaxies can have isophtes that are either boxy (a4 < 0) or disky (a4 > 0).
Kormendy & Djorgovski, 1989, ARAA,
27, 235
Bender et al., 1988, A&AS, 74, 385
Disk (lenticular and spiral) galaxes have a brightness profile that is fit by an exponential law.
Here h is the scale length and I0 is the brightness at this radius. The total luminosity is 2 p Ie h2.
In the vertical direction, disk galaxies have a surface brightness profile I(z) = I0 sech2(z/z0). Typically z0 is between 0.5
and 1.0 kpc for luminous galaxies. The 3D light distribution is then I(r,z) = I0 sech2(z/z0)exp(-r/h).
The face-on projected profile is then I(r) = 2 I0 z0 exp(-r/h).
The edge-on projected profile is then I(r,z) = 2 I0 z0 sech2(z/z0) K1(-r/h). The situation is complicated by internal
obscuration from dust within the disk. Inclination corrections to galaxy magnitudes due to internal extinction are given
by Tully et al. 1998 (AJ, 115, 2264).
The light from many galaxies can be decomposed into a red bulge/spheroidal component and a blue disk
component.
This scatter in bulge-to-disk ratio among galaxies of a given
Hubble type is large.
Globular clusters have light profiles that are well fit by King (1966, AJ, 71, 64) models. These are motivated by dynamics
but look quite similar to r1/4 models. Different models are specified by different values of a core radius rc and a tidal radius
r t.
Dwarf elliptical and dwarf irregular galaxies both have exponential profiles, and have similar scaling relations.
Galaxies have dark matter and gas profiles that are very different fro their stellar profiles. The dark matter probably has
an NFW profile, maybe with a discrete core. Associated with this is a hot ionized gas component, from the
warm/intergalactic medium (WHIM). Within the optical galaxy, most ionized hydrogen is in HII regions. These have a
similar radial distribution to the molecular gas; in the Milky Way, a ring-like structure is seen. The atomic HI gas is more
widely distributed.
Navarro, Frenk & White, 1996, ApJ, 462, 563
Clemens et al., 1988, ApJ, 327, 139
14. Stellar and gas dynamics
Stars and gas atoms in galaxies move around: the exact details of how they do
this are complicated.
Stellar dynamics
This is a complex subject because the physics is basically gravitational but always
global, meaning that the combined effect on the motion of any particular star from
stars on the opposite side of the galaxy has as much effect as the combined effect
from nearby stars (the increased number of distant stars compensates exactly for the
inverse-square fall-off in the gravitation law). Although fundamentally we only need
Newton's law, since there are 100 billion stars, this is effectively an N body problem
where N is huge and the global nature of the problem makes it hard to break it down
into smaller problems. Various approximations can be made, however:
Stellar motions are generally decoupled into hot (thermal, where the stars follow a Maxwellian distribution
function) and cold (where the stars rotate in almost-circular orbits) components. In elliptical galaxies the hot
component dominates (also in the bulges of spiral galaxies). In the outer parts of spiral galaxies, rotation
dominates.
Maller et al., 2000, ApJ, 533, 194, for B1600+434, an edge-on
spiral galaxy lens at z=0.41.
In different galaxies, the halos , disks, and bulges
contribute different amounts to the rotation occurred at
different radii.
Fuchs 1997, A&A, 328, 43, for NGC 488 at a
heliocentric velocity of 2272 km/s.
In ellipticals the thermal motions of the stars are not isotropic - hence they are not spheres.
In spiral galaxies, the flatness of the galaxy is a direct result of most stars being cold. The detailed motion of the
spiral arms has been well studied (density wave theory).
Toomre, 1969,
ApJ, 158, 899
Many spirals show other features, like bars and rings, and these can be explained in terms of stellar-dynamical
theories based on Newton's laws applied to complex systems.
Bar
NGC 1365
Ring
ESO 269-57
Gas dynamics
Gas dynamics is even more complicated since gas atoms are affected by non-gravitational forces too. They
can for example, dissipate energy and clump - this is how star forming regions presumably form in the outer
parts of spiral galaxies.
Much current research effort is spent in
trying to simulate the collective behavior
of gas atoms. Since we can't simulate
individual atoms, we need to work out
recipes for the motions and properties of
whole parcels of gas. Since gas dynamics
is important in predicting how starforming regions (and ultimately stars)
form, it is a crucial element in models of
galaxy formation.
The formation of stars in galaxies is
complex and is the subject of a number of
hydrodynamic simulations. This paper is
an example of a study investigating the
match between the properties of galaxies
(in this case, the stellar initial mass
function) to the results of the simulations.
15. Galaxy formation 1. Dark matter and cosmology
• In order to understand how galaxies formed, it is instructive to think of the dark matter and baryonic
(gas+stars) components separately. The dark matter is non-interacting and the two therefore only affect
each other gravitationally, and the dark matter so much dominates the mass that the effect of the baryonic
matter on it is small.
• The basic idea is: dark matter perturbations in the early universe grow gravitationally. Eventually little bits
become bound which end up as the galaxy dark matter halos. These bits then accrete more dark matter
from the surroundings and become more massive. The scale is such that the mass of these bits today is
about 1011 solar masses, the size of galaxies. How all this happens can be worked out from gravitational
physics as applied to an expanding universe (the growth of the fluctuations is slower because the Universe
is expanding).
• As the dark matter fluctuations grow, they drag the baryons (a few percent by mass) with them from the
intergalactic medium.
•The baryons then cool, clump, fragment, and form stars, which in turn causes feedback (both negative
and positive through heating of gas, and compression) which affects further cooling and star formation in
the galaxies. The remaining gas, and the stars that form, are the tracers.
So the ingredients of a galaxy formation model are: a description of the initial dark matter fluctuations shortly after the
big bang, and a recipe for their evolution, a recipe for the behavior of the baryons once they get dragged into the halos.
Both of these are complex, and much of current research in the subject concentrates on finding ways to do this which
match all the observations. The largerst simulation of galaxy formation to date is the Millennium run by the Virgo
Consortium. They normalize the power spectrum of fluctuations population using the microwave background, and
uses a semi-analytic prescription to describe star formation and feedback within galaxies.
Springel et al., 2005, Nature, 435, 629
16.
Galaxy formation 2. The high redshift Universe
Between the microwave background at z=1100 and z=7, no objects are known. We hypothesize
Population III stars to lie somewhere around z=30.
Between z=7 and z=6, we are discovering quite a few objects. The nature of these objects is
strongly influenced by the selection techniques used to find them.
Between z=6 and z=3, we are beginning to get quite a complete picture of the Universe. A variety of
observations the relevant.
Here is a list of the highest-redshift objects known as of today.
Galaxies:
z=10.0
Abell 1835 background lensing candidate
Pello et al., 2004, A&A, 416, L35
but see Weatherley et al., 2004, A&A, 428, L29
z =6.9
A2218 background lensing candidate
Kneib et al., 2004, ApJ, 607, 697
6.5 <z <6.6
9 Subaru Deep Field sources Taniguchi et al., 2005, PASJ, 57, 165
z =6.56
A370 background lensing source
Hu et al., 2002, ApJ, 368, L75
z =6.43
SDSS J1148+5251
Fan et al., 2003, AJ, 125, 1649
z =6.28
SDSS J1030+0524
Fan et al., 2001, AJ, 122, 2833
z =6.22
SDSS J1623+3112
Fan et al., 2004, AJ, 128, 515
Quasars:
QSO absorption-line systems
Wolfe et al., 2005, ARAA, 43, 861
Prochaska et al., 2005, astro-ph/0508361
Lyman Break Galaxies
The break technique has been pioneered by Steidel and
collaborators and has revealed a population of starforming galaxies at z>2.. Some of the main properties of
these galaxies are given below:
Stellar masses 1010 – 1011 Msuu
Star formation rates inferred from UV luminosity are
generally 1 – 100 Msuu yr-1
Gas metallicities are typically 0.1 – 1 solar.
The stellar IMF is Saltpeter
They are highly clustered, as much as elliptical galaxies are
at z=0.
Aelberger & Steidel, 2000, ApJ, 544, 218:
We describe the characteristic luminosities and dust obscurations of galaxies at
z~0, z~1, and z~3. After discussing the relationship between the high-redshift
populations selected in surveys at different wavelengths, we calculate the
contribution to the 850 mm background from each and argue that these known
galaxy populations can together have produced the entire observed background.
The available data show that a correlation between star formation rate and dust
obscuration Lbol,dust/LUV exists at low and high redshift alike. The existence of this
correlation plays a central role in the major conclusion of this paper: most star
formation at high redshift occurred in galaxies with moderate dust obscurations
1<~Lbol,dust/LUV<~100 similar to those that host the majority of star formation in
the local universe and to those that are detected in UV-selected surveys.
Dickinson 1988, astro-ph/9802064
Recently break techniques have been use to obtain a sample of galaxies in the redshift desert.
2004, ApJ, 604,534
Break techniques at very high redshifts
Eyles et al., 2005, astro-ph/0502385
Incredibly, the new objects lie below the relevant constant-star-formation diagonal line; these are for z=0,1,2,3,4,5,6
moving upwards on the diagram. Also shown are the Hubble sequence, the Madau plot for an average 1Mpc3, the
Milky Way, M31, the LMC, three nearby luminous infrared galaxies, Lyman break galaxies (the cyan points from
Shapley et al. 2005, ApJ, 626, 698), the average dead red galaxy with 2 < z < 3 from the sample of van Dokkum et
al. 2004, ApJ, 611, 703, the average SCUBA galaxy from the sample of Smail et al. 2004, ApJ, 616, 71, and the
average z=1.8 ERO from Cimatti et al.2004, Nature, 430, 184
Ly-a emitters
These do not contribute significantly to the cosmic
star formation history for z<4.
2004, AJ, 127, 563
http://www.ast.cam.ac.uk/~optics/dazle/
DAZLE is intended to be the first imaging instrument optimised to detect faint emission lines between the intense lines of the
OH airglow spectrum that hinders current ground-based observations. In conjunction with the improved image quality now
demonstrated with new 6.5-10 m telescopes, DAZLE will be the only instrument well suited to searching for early star-forming
systems located beyond the redshift range probed by current instruments for at least the next 5 years. The predicted flux limit
for detecting un-reddened Lyman-alpha emission at redshifts of 10 corresponds to a star formation rate of only 1 solar mass
per year. The large format detector we have available in the CIRPASS camera makes it ideal for wide field survey work.
GRB 050904
GCN notice #3937
N. Kawai (Tokyo Tech), T. Yamada (NAOJ), G. Kosugi, T. Hattori, and K. Aoki (Subaru/NAOJ) report on
behalf of Subaru GRB team:
"We observed the field of GRB 050904 (GCN 3910) with Faint Object Camera And Spectrograph on the
Subaru 8.2m telescope atop Mauna Kea on the night of September 6, approximately 3.5 days after the burst. We
obtained spectra of the afterglow candidate (Haislip et al. GCN 3913, 3922, D'Avanzo et al. GCN 3921).
Based on the absorption features we measure the redshift to be z=6.29 +- 0.01, confirming the photometoric
redshift reported earlier (Haislip et al. GCN 3914, 3919, Antonelli et al. GCN 3924)."
To get to the very highest redshifts (z>15), prompt afterglows (which may arise from reverse shocks) from GRBs
is probably the best hope. The prompt afterglow of GRB 990123 at z=1.6 was very bright and reached 9th
magnitude in the V-band about one minute after the burst. Time dilation will slow the whole thing down at high
redshift. Equivalent events from Population III stars could be detected with rapid response near-infrared
technology on relatively small telescopes.
GRB 990123: Akerlof et al., 1999, Nature, 398, 400
The detection limits are appropriate for minute-long
exposures using NSFCAM on the 3.0 m Telescope.
17. Galaxy Formation 3. The Formation of Stars in Galaxies
The Madau or Madau-Lilly Plot was first presented in 1996 and describes the star formation rate of the Universe within a
comovng volume element as a function of redshift.
Madau et al. 1996, MNRAS, 283, 1388.
Note that heavy element production tracks the star
formation rate.
Star formation rate densities are computed from optical surveys where the galaxies are selected using methods like
the Lyman break technique. Summing over the ultraviolet luminosities of the galaxies, we then require a
correction for the the presence of faint galaxies using the luminosity function, and also for dust extinction. The
correction for dust extinction can be factors of several. In the example below, a Calzetti extinction law is used,
with the assumption that most of the dust in the galaxies in the optically selected sample is optically thin so that
measurements that are made at different optical wavelengths can be scaled to a global E(B-V) for the galaxy
population.
Steidel et al. 1999, ApJ, 519, 1
A quite different possibility is that most of the automation happened in infrared galaxies where the dust is optically
thick. Very substantial amounts of star formation could then be hidden; we observed this happening locally in
ultraluminous infrared galaxies like Arp 220. This kind of star formation would not be accounted for in optical
surveys. It would even be possible that very extreme star-forming galaxies are missing altogether from optical surveys,
if all their star formation is hidden by optically thick dust. If this kind of star formation is important, then the optical
Madau Plot is a poor representation of the true Madau Plot. This possibility has been investigated by studies of
infrared and submillimetre galaxy counts and backgrounds. One model is presented in the plot below.
Ramirez-Ruiz et al., 2002, MNRAS, 329, 465
We might expect a significant amount of cosmic star formation to have been dust-enshrouded, because the infrared
background is so high.
Spitzer has mostly resolved the background at 24 mm.
Chary et al., 2004, ApJS, 154, 80
The SCUBA submillimetre galaxies probably contain a great deal of optically thick star formation at high
redshift. These galaxies have a high space density and luminosities and spectral energy distributions similar to
ultraluminous galaxies locally. Individually, these have high star formation rates: > 100 M sun/yr, compared with
typical values of 10 Msun/yr for Lyman Break galaxies.
However, the luminosities and star formation rates of SCUBA galaxies depend sensitivity on the detailed shape
of the spectral energy distribution. For example, the luminosity depends on the 5th or 6th power of the
temperature.
Trentham et al., 1999, and MNRAS, 305, 61
An additional complication is that SCUBA galaxy populations, particularly at the highest luminosities, may be
powered by active galactic nuclei and not starbursts. Most current evidence suggests that this is not this serious
concern, else the local supermassive black hole density would be overproduced.
Recent observations suggest that the SCUBA sources (at least the radio-loud ones) have a median redshift z=2.5,
similar to optical and radio quasars.
This does not necessarily mean that the galaxies are powered by dust-embedded AGNs, because of the constraint
of the local supermassive black hole density – unless the black holes release a very substantial amount of radiation
per unit mass accreted onto them. My current guess is that the power source is an extreme high-mass biassed burst
of star formation that happens as gas infalls close to the central black hole. As these stars and their remnants are
probably consumed ultimately by the black hole, this star formation should not be included in the Madau Plot.
Long-duration GRBs seem to be linked with the deaths of massive stars, so the GRB redshift distribution,
which is easy to observe because the GRBs are so bright, may perhaps be used to derive the total Madau Plot.
This assertion is based on the following lines of reasoning:
•Concordance between GRB 030329 at z=0.16 and a supernova (Hjorth et al., 2003, Nature, 423, 847).
•GRBs tend to happen in galaxies that are currently forming large numbers of stars. Often these are distant
blue star-forming galaxies, perhaps similar to local HII galaxies (van Paradijs et al., 2000, ARA&A, 38, 379). A
few times they have been even been observed in infrared galaxies with huge star formation rates (Berger et al.,
2003, ApJ, 588, 99).
•On theoretical grounds, a natural way of producing a long-duration (lasting longer than a second) burst of
gamma rays is the cataclysmic collapse of a massive star leading to a hypernova explosion (MacFadyen et al.,
2001, ApJ, 550, 210).
•Iron edge and line features have been seen in the spectra of GRBs, suggesting the presence of considerable
amounts of iron, as would be expected from the collapse of a massive star (for example, Amati et al., 2000,
Science, 290, 953 and Piro et al., 2000, Science, 290, 955).
Most analyses of the GRB redshift distribution suggest a Madau Plot that is rising as high redshift, but with poor
statistics.
Ramirez-Ruiz et al., 2001, astro-ph/0010588
This.formation is happening predominantly in compact blue emission-line galaxies.
Conselice et al., 2005, ApJ, 633, 29
There may, however, be significant biases. GRBs are thought to come from stars with high mass and low
metallicity, so would come preferentially from galaxies with a high-mass biassed IMF and those that are metal-poor.
The former might explain the preponderance of GRBs in ultraluminous infrared galaxies at redshifts near to one,
and the latter might explain their preponderance in Lyman alpha emitters. GRB 030323 is the extreme example of
a GRB happening in a low-metallicity system.
Berger et al., 2003, ApJ, 588, 99
Fynbo et al., 2003, A&A,
406, L63
Vreeswijk et al., 2004, A&A, 419, 927
A recent measurement of the total (optical + infrared) Madau Plot is provided by the GOODS collaboration, who
use infrared Spitzer data. They make corrections for optically thick star formation, using the models of Adelberger
& Steidel (2000, ApJ, 544, 218), which are based on multiwavelength observations of Lyman break galaxies.
Trentham 2005, astro-ph/0411542
At high redshift, the Madau Plot is poorly constrained, and there is a lot of uncertaintyin translating
measurements of galaxies in the Hubble Deep Field into a cosmic star formation rate.
The GOODS Madau Plot on the previous
slide results in about 6% of the stars in the
Universe having formed by a redshift z=6.
Bunker et al., 2004, MNRAS, 355, 374
Stiavelli et al., 2004,
ApJL, 610, 1
Probably the main aim of contemporary extragalactic astrophysics is to describe the mapping between the
Madau Plot and the galaxy luminosity function function. This is described by the following equation:
Integration of the optical Madau Plot gives
Most evidence suggests that the cosmological density in stars is W* = 0.0045 or thereabouts,
which implies that the fraction of star formation happening in optically thick sources, fIR, is
quite small. The P values are the corrections made to star formation in optically-detected
galaxies due to internal extinctio.
Stellar mass-to-light ratios can be obtained either from population synthesis models or from dynamics. The two
do not always give concordant answers. Note the following discussion from Read & Trentham, 2005, astroph/0502517.
Here are some numerical values, along with some bulge in-to-disk ratios.
Metalicity is an important factor in determining the mass-to-light ratio of a stellar population. This is in the sense that
increased metalicity leads to a higher mass-to-light ratio because increased line blanketing from metals pushes more
flux out of the optical into the near-infrared. This in turn results in higher optical mass-to-light ratios.
Bruzual & Charlot, 2003,
MNRAS, 344, 1000
Another important factor is the stellar IMF. The problem is that we observe the red giants in stellar
populations (these observations determine the constraints on the stellar population models), but the masses
are determined by how many low-mass stars there are. The mass-to-light ratio depends on the stellar IMF
through the following mass-integral:
A commonly used stellar IMF comes from the study of local regions of the Milky Way by Kroupa
(2001, MNRAS, 322, 231).
Here the stellar mass m is in units of the solar mass, and the stellar IMF h(m) = x(m) is the number of stars per
unit mass interval. Brown dwarfs with m < 0.08 contribute a few percent the stellar mass. The contributions to
the mass integral of the three components are 0.04:0.27:0.69.
Unfortunately, the different parameters like metalicity and stellar IMF are degenerate in computing stellar
mass-to-lightroute from ratios.
Lyman Break galaxies like cB58 (z=2.7) must form stars with a Salpeter IMF (index -2.35) in order to
simultaneously reproduce the properties of the stellar continuum and the interstellar CIV 1549 emission feature.
Pettini et al., 2000, ApJ, 528, 96
Galaxies whose star-forming regions exhibit a Salpeter IMF will evolve into galaxies that exhibit a Kroupa IMF
when the bulk of their star formation is completed. This provides an attractive link between the previous two
slides.
This follows from the observation that higher mass star-forming regions have an IMF that has a
higher upper mass cutoff and that the mass function of star-forming regionsis a power law with
index -2.
2005, ApJ, 598, 1076
When material is converted into young stars, much of this material is ultimately returned to the interstellar
medium via stellar winds. This material can end up in future generations of stars. We need to correct for this
effect when matching the galaxy luminosity function to the cosmic star formation rate. It is premature to model
this in detail (despite what is said below), so it is conventional to just use a single scaling factor. About 30% or
40% of the mass that goes into young stars is probably ejected back into the interstellar medium. This is a very
crude estimate, but it is probably reasonable.
Cole et al., 2001, MNRAS,326, 255
Before continuing, it is useful to note how the luminosity function and stellar mass is partitioned between galaxies
of different Hubble types.
Wb=W*+Wgas
Read & Trentham, 2005, astro-ph/0502517
Taking all this information into account, the equation relating the cosmic star formation rate to the local luminosity
function is now
The sum on the LHS gives W* = 0.0028 assuming an IMF in all galaxies derived from dynamic measurements.
The integral on the RHS gives W*=0.0063 assuming a Salpeter IMF during star formation and an infrared
fraction from GOODS. These numbers are comparable and could be consistent with each other given the
rather large uncertainties, which are mostly systematic. The fact that the second number is so much higher
leads me to suspect that the infrared fractions are lower than we think.
In the rest of the course, we will consider constraints on the match between the luminosity function and
the Madau Plot.
1. Constraints from the Evolution of the Cosmic Stellar Mass Density
From optically or near-infrared selected samples, we can assign a star formation history to each galaxy if
multicolour imaging is available. Integrating over time and summing over all galaxies gives the total mass density
in stars. Corrections due to faint galaxies missing from the survey are small because the luminosity function is
flat at the faint end.
Dickinson et al., 2003, ApJ, 587, 25
Two things are apparent from this figure.
Firstly, the boxes are large, so that improved multicolour
data and stellar population modeling are very important.
The decrease in this plot between z=1 and z=2 is greater
than that in the conventional Madau Plot. Perhaps this is
the signature of an infrared star-forming population.
2. Population Synthesis Modeling and Archaeoastronomy
These models are based on stellar evolution theory and describe the spectrophotometric evolution of galaxies. They
can then be applied to large samples of nearby galaxies to work out star formation histories in a statistical sense.
MNRAS, 344, 1000
Heavens et al., 2004, Nature, 428, 625
3.
Chemical and Gas Content Evolution
As galaxies evolve on for more stars, their gas content decreases in a stellar content and metal content increases.
Stars made out of material that has been enriched for many generations will be more metal-rich. Some of the metals
that are produced will be ejected out of the galaxy into the intergalactic medium.
The most metal-rich galaxies are probably luminous elliptical galaxies. This indicates that internal recycling can be
very efficient.
Gas metalicities are derived from emission-line
properties:
Stellar metalicities are derived from
Lick indices:
Shapley et al., 2004, ApJ, 612, 108
Faber, 1973, ApJ, 179, 731.
5. Mergers
The following observations will be very important in this context, and should become considerably more
detailed over the next few years:
1) Higher resolution images of high redshift mergers
2) Multiwavelength images of low redshift mergers, in particular gas velocity maps
3) Higher signal-to-noise observations of the extragalactic background light at optical wavelengths.
More detailed computer simulations of mergers should be available as well in the future. In the long term, we
hope to generate atlases of simulated mergers that can be compared to optical imaging surveys like SDSS.
We can then assign merger probabilities to each event and measure the merger history of Universe.
6. Joint Magorrian Relation Considerations
Identical analyses can be performed for the formation of stars and for the formation of supermassive black
holes in the centres of galaxies. These two mechanisms must happen in such a way so as to reproduce the
tight relationship between stellar mass and black hole mass in local galaxies.
The following appear to be secure observational facts. There are a very large number of references in the
literature.
1. The Magorrian relation between bulge stellar mass and central black hole mass is very tight, with a
proportionality constant of about 0.015. An even tighter relationship exists between velocity
dispersion and black hole mass.
2. The space density of optical quasars is strongly peaked at about z=2.5. The space density of radio
quasars behaves similarly.
3. All quasars have luminous hosts. At low redshift the most luminous quasars and all the radio-loud quasars
are in elliptical galaxies. At higher redshifts, they can lie in irregular systems. All radio-quiet Seyfert
galaxies are in spirals.
4. About 1/10 of quasars are radio-loud. This fraction is slightly higher for the most luminous quasars.
5. Radio galaxies have the same space density and redshift evolution as radio-loud quasars.
5. X-ray AG N tend to have lower redshifts than optical quasars.
This leads to the following conjectures, which are all probably true with some level.
Quasars form from the mergers of massive galaxies which have already formed their stars.
Optical quasars form along an evolutionary sequence: cold ultraluminous galaxies ->warm ultraluminous
galaxies ->infrared quasars ->optical quasars
Precisely tuned feedback during star formation leaves exactly 0.0015 mass fraction of gas left over. This is
the material that eventually winds up in a black hole.
Most mass buildup happened in the optically luminous phase, as described by Yu & Tremaine (2002,
MNRAS, 335, 965).
Radio-loud quasars are probably the most massive quasars near the end of their life.
Many local quasars in elliptical galaxies are probably secondary accretion events.
Seed black holes are probably required to initiate supermassive black hole growth.
Radio-loud quasars are probably the same objects as radio galaxies seen down the jet.
X-ray AGN are smaller than optical quasars and represent the late stages of evolution of small black holes.
Quantifying all this will be an important exercise in the next few years. Better simulations of AGN
physics and black hole simulations by Hawley, Krolik and collaborators are in progress and these will
provide an important framework to compare the observations to. Host galaxy studies are going to
improve, particularly multiwavelength ones, partly due to higher resolution and partly due to better
algorithms and subtracting out bright nuclei. This will be particularly relevent in the context of the
current discussion. We can see what galaxies look like when the black holes are building up.
7. Number Counts
Galaxy counts will be measured more precisely and to fainter limits over a wide range of wavelengths in
the next few years.
8. The Milky Way Galaxy
My guess is that the final solution will look something
like this.
Bunker et al.
2004
Trentham et al. 2005
Elliptical
Spiral
Dwarf irregular
Dwarf elliptical