1. Distance to Galaxies – The Hubble Law
In the 1920s, Hubble determined the distance to the Andromeda galaxy by locating a Cepheid variable star there.
Hubble and collaborators began a systematic study of nearby galaxies which included measuring both their distance (Cepheids etc) and radial velocity.
They soon noticed a remarkable trend: virtually all the galaxies they observed were moving away from our galaxy (redshifted) and the recession speed increased with distance.
Hubble's first dataset included only a few dozen galaxies which were < 2 Mpc away but his basic conclusion has not changed as more and more galaxies at larger distances have been observed.
We live in an expanding Universe. Due to the Big Bang, the Universe is expanding.
Hubble found that there was a direct linear relation between distance and redshift: the further a galaxy was from us, the faster its recession velocity. This relation, which has come to be known as Hubble's Law, is written
v = Ho D
where v is the recession velocity, D is the distance to the galaxy, and Ho is the constant of proportionality known as Hubble's constant
Hubble found H0 ~ 500 km/s/Mpc !! Hubble had confused two different kinds of Cepheid variable stars used for calibrating distances and also that what Hubble thought were bright stars in distant galaxies were actually H II regions.
Throughout the 20th century we found evidence for H in the range 50 -100 km/s/Mpc, depending on the method employed.
So, we took h = H/100 km/s/Mpc in all our formula to parameterize our ignorance
WMAP: These results are consistent with a combination of results from CMB anisotropy, supenovae scaling, and the accelerating expansion of the Universe which now give 71 +/- 3.5 km/sec/Mpc.
With this value for Ho, the "age" 1/Ho is 14 Gyr while the actual age from a fully consistent model is 13.7+/-0.2 Gyr.
Figure: A redshift versus magnitude plot reveals a linear relationship between recession velocity and distance. (Type Ia supernova).
The Hubble law defines a special frame of reference at any point in the Universe. An observer with a large motion with respect to the Hubble flow would measure blueshifts in front and large redshifts behind, instead of the same redshifts proportional to distance in all directions (Universe is isotropic).
Thus we can measure our motion relative to the Hubble flow, which is also our motion relative to the observable Universe. A comoving observer is at rest in this special frame of reference.
Our Solar System is not quite comoving: we have a velocity of 370 km/sec relative to the observable Universe.
The Local Group of galaxies, which includes the Milky Way, appears to be moving at 600 km/sec relative to the observable Universe.
For relatively nearby objects, Hubble's law itself becomes a way to determine distances. Suppose you had a galaxy in which you found an emission line of sodium, which has a rest wavelength of 590 nm, shifted to 620 nm. What is the distance to that galaxy using Hubble's Law?
First, compute the redshift:
z = o) /o = (620 - 590) / 590 = 0.05
For speeds much less than the speed of light, z = v/c. Hence this galaxy is receding at a speed that is 5 percent the speed of light, or 0.05 x 3 x 105 = 1.5 x 104 km s-1.
Using a value of the Hubble constant of 70 km s-1 Mpc-1 we can now solve for the distance in Megaparsecs:
1.5 x 104 / 70 = 214 Mpc.
The Doppler formula we have been using to relate the redshift z to the velocity v is appropriate only for velocities much less than the speed of light (i.e., nearby galaxies).
The formula z = v / c implies that you can't have redshifts greater than one because that would give you a velocity greater than the speed of light, something not permitted by the laws of physics.
In fact, redshifts larger than 1 are possible, and are observed. For example, if an object has a velocity near the speed of light we have to use the "relativistic Doppler shift formula"
which is derived from special relativity. As v gets close to c the redshift becomes increasingly large. (v = c would yield an infinite redshift).
This means the Hubble law at high redshift becomes
Hubble Length and Time
Two galaxies have been moving apart for something like 13 Gyr (assuming that they were one time very close together – such as at the moment of the Big Bang). Another way of looking at this is to see that:
and Ho is essentially an inverse Hubble time.
Can define a Hubble length:
c / H0 ~ 4000 Mpc
at which this expression for the recession velocity extrapolates
to the speed of light - more detailed relativistic treatment is
needed for distances of this order.
Can also define a Hubble time:
1 / H0 ~ 1010 years
…this is to order of magnitude the age of the Universe.
But there is sufficient mass in the Universe which has slowed down the expansion - so our assumption that, for example, M87 and the Galaxy have been moving apart at a constant speed since the expansion began is false.
2. Clusters of Galaxies:
Clusters are systems a few Mpc across, typically containing at least 50-100 luminous galaxies within the central 1 Mpc
Clusters are filled with hot X-ray gas
Only ~20% of galaxies live in clusters, most live in groups or in the “field”
But it is hard to draw the line between group and cluster, ~50% of galaxies live in clusters or groups
Clusters have higher densities than groups, contain a majority of E’s and S0’s while groups are dominated by spirals
Nearby clusters cataloged by Abell (1958), extended to southern hemisphere by Abell et al (1989). cataloged 4073 rich clusters
Abell also classified clusters as:
Regular: ~circularly symmetrical with a central concentration, members are predominantly E/S0’s (e.g., Coma)
Irregular: ~ less well defined structure, more spirals (e.g., Hercules, Virgo)
Bautz-Morgan classification scheme (1970), based on brightest galaxy in cluster
I: cluster has centrally located cD galaxy
II: central galaxy is somewhere between a cD and a giant elliptical galaxy (e.g., Coma)
III: cluster has no dominant central galaxy
Oemler (1974) classified clusters by galaxy content
cD clusters: 1 or two dominant cD galaxies, E:S0:S ~3:4:2
Spiral rich: E:SO:S~1:2:3 (similar to the field)
Spiral poor: no dominant cD, E:S0:S~1:2:1
Regular, cD clusters have had time to “relax” and reach dynamic equilibrium
Intermediate and Irregular clusters are still in the process of coming together, have not yet reached dynamic equilibrium
cD galaxies have probably formed by merging in the central regions.
cD galaxy with multiple (6!) nuclei
The percentages of various galaxy types in rich and poor clusters and in the "field", a clear distinction emerges:
Large-scale structure: These frequently show intricate structure - clouds, superclusters, filaments, sheets, voids... as shown in the famous CfA "Slice of the Universe"
A redshift survey (a 6 degree wedge, 1065 galaxies, distance expressed in velocity – suggests sheets; Coma cluster is the ‘torso’)
The 2DF survey seems to have finally found a limit to structure sizes at a fraction of a Gpc (shown below)
Note the Bubbles and Voids! (100 Mpc in size). This is beyond the size of superclusters. Galaxies lie on 2D sheets that form the walls of bubble-shaped regions
On smaller scales clusters and superclusters may drift along through the Hubble flow, as we do towards the Great Attractor ( 2 x 1016Msun) 42 h-1 Mpc away
Galaxy evolution: the Butcher-Oemler Effect
In 1978, Butcher & Oemler found that the fraction of blue galaxies in two clusters at z=0.4 was significantly higher than in Coma
This was later extended to larger samples of clusters, and to higher redshifts
Star formation is decreasing rapidly in clusters as an inverse function of redshift (why??)
HST allowed us to push to higher redshifts and to study the morphologies of these high-redshift clusters
On the larger scale we have galaxy clusters such as the Virgo Cluster, about 50 million light years away, that is the nearest regular cluster of galaxies. Our Local Group is an outlying member of a "supercluster" of galaxies of which the Virgo Cluster is the dominant member.
The Virgo Cluster
The Virgo Cluster (3Mpc at 16 Mpc, 2000 members, mostly dEs, M87 – a cD galaxy at the centre) with its some 2000 member galaxies dominates our intergalactic neighbourhood, as it represents the physical centre of our Local Supercluster (also called Virgo or Coma-Virgo Supercluster), and influences all the galaxies and galaxy groups by the gravitational attraction of its enormous mass.
The Virgo Cluster has slowed down the escape velocities (due to cosmic expansion, the `Hubble effect') of all the galaxies and galaxy groups around it, causing an effective matter flow towards itself (the so-called Virgo-centric flow).
Eventually many of these galaxies have fallen, or will fall in the future, into this giant cluster which will increase in size due to this effect. Our Local Group has experienced a speed-up of 100--400 km/sec towards the Virgo cluster.
The Coma Cluster
Nearest, rich cluster of galaxies
Distance = 90 Mpc
Diameter = 4-5° on the sky, 6-8 Mpc
Of the bright galaxies, <10% spirals, rest are ellipticals or lenticulars (E/S0s)
Roughly spherical in shape, probably virialized, 2 cD galaxies in the center
The Hercules Cluster (below), about 200 Mpc distant.
This cluster is loaded with gas and dust rich, star forming, spiral galaxies but has relatively few elliptical galaxies, which lack gas and dust and the associated newborn stars.
Colours in the composite image show the star forming galaxies with a blue tint and ellipticals with a slightly yellowish cast.
IMany galaxies seem to be colliding or merging while others seem distorted - clear evidence that cluster galaxies commonly interact.
Over time, the galaxy interactions are likely to affect the content of the cluster itself. Researchers believe that the Hercules Cluster is significantly similar to young galaxy clusters in the distant, early Universe.
The Hercules Cluster
Distant Clusters. The Hubble Space Telescope has provided the first opportunity to look back into the early universe at clusters. Billions of years ago, clusters contained many more spiral galaxies than they do today.
CL 0024+1654 is a large cluster of galaxies located 5 billion light-years from Earth. It is distinctive because of its richness (large number of member galaxies), and its magnificent gravitational lens. The blue loops in the foreground are lensed images of a spiral galaxy located behind the cluster.
The CL 0024+1654 Cluster – note the gravitational lensing
The rich galaxy cluster, Abell 2218, is a spectacular example of gravitational lensing. The arc-like pattern spread across the picture like a spider web is an illusion caused by the gravitational field of the cluster. The cluster is so massive and compact that light rays passing through it are deflected by its enormous gravitational field.
Hubble Deep Field: Probably the deepest image ever taken was by the HST over about 150 consecutive orbits (about 10 days) from December 18 through 30, 1995 on a single piece of sky located at 12h 36m 49.4000s +62d 12' 58.000" (near the Big Dipper).
3. Galaxy Evolution
The number of irregular galaxies increases with redshift (e.g., the Hubble Deep Field)
The rate of merging as a function of cosmic time (redshift) can be estimated by counting the number of close pairs (the merger fraction) in redshift surveys
Parameterize merger fraction f(z) ~ (1+z)m and find values for m ranging from 0 (no evolution) to 4 (lots of evolution)
Evolution of the star formation rate as a function of lookback time, Pettini (2003) Springel & Hernquist (2003), Perez-Gonzales et al 2005. Star Formation tracers:
UV (but dust obscured)
H-alpha / optical line
Far IR continuum
Hopkins and Beacom 2006, ApJ
Galactic Nuclei: Many (all?) ellipticals (& bulges) have black holes.
Can measure BH masses for galaxies without central disks via their velocity dispersion
Currently there are observations of at least 40 BH masses in nearby ellipticals and spiral bulges
There is a strong correlation between black hole mass and galaxy luminosity and velocity dispersion. Kormendy (2003):
Observations imply BH mass directly tied to the formation of bulges and ellipticals
For Mbulge = 5 × 1010 Msun the median black hole mass is 0.14% ± 0.04% of the bulge mass
All proto-galaxy clumps harboured an equal sized (relative to total mass) BH, and BH merged as galaxy formed
BH started out small and grew as galaxy formed – e.g., central BH is fed during process of formation and is the seed of the formation process (all galaxies have BHs?)
Galaxy Formation: Monolithic? Hierarchical? Downsizing?
Do massive galaxies form from scratch, or by chunking together smaller galaxies?
Monolithic: This hypothesis posits that giant galaxies form all at once, with the bulk of star formation happening at the same time as the galaxy gains the bulk of its mass. Collapse and dissipation of energy occurs together.
Ellipticals formed in a monolithic collapse, which induced violent relaxation of the stars, stars have since reached an equilibrium state.
In the monolithic theory, the gas is lost in the initial phases through the burst of star formation.
Physical Origin of the Luminosity Function
Why does the galaxy luminosity function have the form that it does? A complete understanding of this is not yet possible, but here are the ingredients:
Making galaxies involves at least two things
• dark matter halos must form (relatively straightforward)
• baryons must fall in and make stars (complex physics)
Large-scale simulations predict: too many huge and dwarf halos without huge and dwarf galaxies:
To understand why, we need to look at what prevents baryons from making stars within halos of different size (see figure).
a Gas falling into huge halos is too hot to cool.
This becomes the intercluster medium in galaxy clusters.
b Gas falling into less massive halos is kept hot by AGN jets
c Gas falling into small halos can be easily blown out by supernovae and star winds
d Gas cannot fall into tiny halos -- it is prevented by its own pressure.
These processes are added to the cosmological dark matter simulations using simple prescriptive formulae, to generate so-called: "semi-analytic models" (see figure).
These nicely reproduce many galaxy demographic results, including a galaxy mass function that is a much better match to the observed galaxy luminosity function.
Hierarchical: Evidence is building for this theory. Using an array of both ground-based and space telescopes, including ESO's Very Large Telescope in Chile and the Hubble Space Telescope, a team of astronomers recently observed groups of huge galaxies in the process of merging, showing that large, established galaxies can still grow bigger.
In this version, galaxies would form most of their stars early on as small galaxies, but accumulate most of their mass later through mergers.
A study, published in 2005 by Pieter van Dokkum of Yale University, found a large number of established galaxies with old stars that displayed signs of having recently merged with other galaxies to add on to their mass.
Though many astronomers agree that hierarchical formation seems to be occurring, there are still some wrinkles to the theory.
For example, the very most massive galaxies don't seem to be growing at as high a rate as middle-mass galaxies. When astronomers look at the brightest galaxies now compared to the brightest galaxies at an earlier), they don't seem to have gained much mass.
It suggests that there might be an upper ceiling to how large a galaxy can grow. Perhaps when a galaxy gets to be very large, its gravity is so strong that it rips up smaller galaxies that pass nearby before they can join it.
Another question is why, if all galaxies are mergers of smaller ones, many of them don't look it. Beautiful spiral galaxies, for instance, appear neat and symmetrical, not as though they were formed from violent collisions of multiple smaller galaxies.
Merging galaxies look like train wrecks. Maybe they only look like train wrecks for a relatively short amount of time. Perhaps there are stabilizing forces, such as the galaxies' angular momentum and the large halos of dark matter that surround them, that help galaxies regain their orderly spiral structure after a merger.
Downsizing. A comprehensive survey of more than 4,000 elliptical and lenticular galaxies in 93 nearby galaxy clusters has found a curious case of galactic "downsizing."
Contrary to expectations, the largest, brightest galaxies in the census consist almost exclusively of very old stars, with much of their stellar populations having formed as long ago as 13 billion years.
There appears to be very little recent star formation in these galaxies, nor is there strong evidence for recent ingestion of smaller, younger galaxies.
By contrast, the smaller, fainter galaxies are significantly younger -- their stars were formed as little as four billion years ago.
The results of the survey contrast sharply with conventional hierarchical model of galaxy formation, where large elliptical galaxies in the nearby universe formed by swallowing smaller galaxies with young stars; this theory predicts that, on average, the stars in the largest elliptical galaxies should be no older than those in the smallest ones.
The stars in the biggest, oldest galaxies formed early in the history of the Universe. On average, the smaller galaxies have one-tenth the mass of the larger ones, and are only about half their age.
The term 'downsizing' essentially means that when the Universe was young, the star formation activity occurred in large galaxies, but as the Universe aged, the 'action' stopped in the larger galaxies, even as it continued in smaller galaxies.
Formation of the Milky Way Galaxy
There are many theories on how the MW galaxy formed. Some astronomers believe that the halo formed first. In this theory, as gravity pulled the spherical halo material inward, the material formed a disk to conserve its angular momentum.
During the collapse, stars in the halo continued to evolve, producing metals (elements other than hydrogen and helium) through the process of fusion. These metals were spewed into the galactic medium through stellar winds and supernova explosions and became part of the disk. This means that the stars in the disk formed out of metal rich material. This process is known as the "Outside-In" theory.
Some galaxies, or their nuclei, show evidence of a recent and transient increase in SFR by as much as a factor of 50.
Much of the star formation in starburst systems has been found to occur in very luminous, compact star clusters (up to 108 solar luminosities, dimensions of a few parsecs), which occur in bursting dwarfs, interacting galaxies, and mergers
Both direct mergers and more indirect interactions can trigger star formation in galaxies
Caused by gas compression/accumulation, causing shocks which trigger star formation
Gas which loses enough angular momentum will fall into the centre (especially true if a bar is formed)
These can lead to strong nuclear starbursts
M82 is currently forming a few M¤/year of stars (similar to a large spiral) in a nuclear area only 100 pc across!
Starburst phases are short.
Powerful starbursts surrounded by dust will be very bright in the infrared
We observe numerous ultraluminous infrared galaxies (ULIRGs), first discovered by the IRAS satellite, with L > 1012L¤
These galaxies are merging too!