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6. The Structure of the Universe
6.1. Distance to Galaxies – The Hubble Law
Redshifts.
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:
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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.
).
Comoving Coordinates
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
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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.
Distances
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.
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Figure: A redshift versus magnitude plot reveals a linear relationship
between recession velocity and distance. (Type Ia supernova
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"
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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.
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6.2 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 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
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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
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Large-scale structure: These frequently show intricate structure clouds, superclusters, filaments, sheets, voids... as shown in
the famous CfA "Slice of the Universe"
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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)
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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
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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 16 megaparsecs 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.
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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.
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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.
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The Coma Cluster
Nearest, rich cluster of galaxies
Distance = 90 Mpc
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:
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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.
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.
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.
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CL 0024+1654 is a large cluster of galaxies located 1.6 Gpc ( z =
0.4) 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.
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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).
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