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The Structure of the Universe
1. Distance to Galaxies – The Hubble Law
Redshifts.
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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.
Original data:
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.
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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
 These results are consistent with a combination of results from
CMB anisotropy 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.
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
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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 slows 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 probably false.
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 gravitationally bound
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
Interpretation:
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:
cD
Rich clusters 93
Poor clusters 6
Field"
<6
E+S0
56
20
< 24
S+I
38
14
48
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)
106688 galaxies
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
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 =90Mpc
Diameter = 4-5 on the sky, 6-8 Mpc
>10,000 galaxies!!
 Mostly dE’s
 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
X-ray contours:
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. In this cosmic vista
many 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 and that exploring
galaxy types and their interactions in nearby Hercules will help unravel the threads of galaxy
and cluster evolution.
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).
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
Galactic Nuclei:
Many (all?) ellipticals (& bulges) have
black holes.
Can measure BH masses for galaxies without central disks via their
velocity dispersion
E.g. M32:
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
Either
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?)
Starburst activity
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
 M81 group
Gas which loses enough angular momentum will fall into the
center (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!