Key Concepts: Lecture 32: Towards Cosmology
The Distribution of Galaxies: towards a large scale view of the cosmos
Why is the sky dark? Implications for the cosmos
The Expanding Universe
The Age of the Universe since the Big Bang
Clusters of Galaxies
• Some galaxies are found
in dense groups of 100 to
10000 galaxies
• Few spiral galaxies in
clusters
• Typical sizes 10 million
LY across
• Galaxy collisions are
frequent: note galaxies
can be changed in a
collision, but the existing
stars are not affected
(stars do not collide).
Nearest Galaxy Cluster: Virgo
Distance = 50 million LY
The Distribution of Galaxies
• Galaxies tend to group together on many scales
• Gravity is the glue that tries to bind all galaxies together
Groups: “The Local Group”
• The group of galaxies of
which the Milky Way is a
part.
• 3 million LY across
• 30 total members
• Three large spirals
– M31 (Andromeda), M33 &
Milky Way
• Total mass 5x1012 Msun
The Rich Cluster Abell 2218
Gravitational
Lensing
C
L
0
0
2
4
+
1
6
5
4
or cluster of
galaxies
Images of distant
galaxy
Light from distant galaxies is deflected
by the gravitational influence of the
intervening cluster of galaxies,
analogous to light being deflected by a
lens. The amount of deflection tells us
about the mass of the cluster
Cluster of Galaxies
Einstein Ring
The Masses of Galaxy Clusters
• Clusters are bound together by gravity
– Using the Doppler shift we can measure the
orbital velocities of the galaxies
– We can the apply Newton’s version of Kepler’s
law to find the mass
– They typically have 300x more mass than can be
seen in the stars
• Other evidence for high mass
– 10,000,000K X-ray emitting gas is bound in
cluster
– Gravitational lensing of background galaxies
The high gravitational masses of clusters of galaxies compared to the
mass seen in stars and gas is more evidence for DARK MATTER.
Walls and Filaments
Super Clusters
• Galaxy groups tend to
form larger walls and
filaments 100’s of MLY
long
• The Great Wall
• Clusters of galaxies tend to group
together into super clusters
• Typically span 100 Million LY
• Typically contain 1015 Msun
• Most of space is empty of
galaxies
– clusters fill only 5% of volume
100x100MLY around the sun
– 500 Million LY long
– 15 Million LY thick
– 2x1016 Msun
• The filaments tend to be
separated by voids with
few galaxies
800 Million LY
The Cosmological Principle
• If you look at larger & larger chunks of
the universe it will eventually look
Homogeneous and Isotropic
• Simply stated this means that there is no
special or preferred place in the universe
of galaxies
– All parts of the universe will behave the
same
– This must be true if we ever wish to
understand the universe as a whole
Cosmology: the whole Universe
How Big? How Old? What is its Future?
• Olbers’ Paradox: why is the night sky dark?
–If the Universe is infinite in size and age, and
uniformly filled with stars (on average), then every
line of sight should intersect a star, producing a
Bright Sky!
Like looking
through a forest.
This appears to be true on the largest
scales, ~100Mpc
Movie of Large Scale Galaxy Distribution
Possible solutions:
(each is very profound)
• Universe has a finite size
• Universe has an infinite size, but few or no
stars far away
• Universe has a finite age: light from most stars
hasn’t reached us (Edgar Allan Poe)
It turns out that the 3rd one of these solutions is the main reason
the sky is dark at night!
In every direction the Galaxies are receding from us: the
Universe is EXPANDING!
The Receding Galaxies
Measure velocity using the Doppler effect:
• Does this mean we are in a special
place? - the center of the Universe?
• NO! There is no center of
expansion. Every galaxy sees the
same thing: more distant galaxies
recede more quickly
• Analogies discussed in class: the
expanding raisin cake (3D); dots on
surface of a balloon (2D); knots in a
rubber band (1D)
• 1912 - Vesto Slipher of Lowell Observatory
– all the galaxies he observed were moving away
– some as fast 1800 km/sec
• 1929-1953 - Edwin Hubble & Milton
Humason
– More distant galaxies were moving away faster
– The speed increases with the distance
The Receding Galaxies
The Raisin Bread Analogy
Hubble’s 1929 data
Velocity is proportional to the distance: v ∝ d
v = Constant × d = H0 d
Hubble’s
Constant
H0 = 70 km/s/Mpc
Raisin Bread (1):
Data from ~2003
Redshift = Δλ / λ = v/c
Note that this formula for the Doppler effect is only accurate for
v much smaller than c; redshifts greater than 1 are possible, but
correspond to v just less than c
This first picture shows a ball of raisin bread dough.
Did you know raisin bread is a really good example
of an expanding universe? Let's assume that this ball
of dough is our universe, and each raisin represents a
galaxy cluster. The raisins are distributed fairly
uniformly throughout the dough, just like the galaxy
clusters in our universe.
Raisin Bread (2):
But what happens if we let the raisin bread dough sit
out to rise for awhile? As you can see in the picture,
as the dough rises and expands, the raisins start to
move away from each other. The raisins closer to the
edges of the dough move away from the center
faster than the one that are closer to the center. Now
imagine our galaxy cluster as one of the raisins near
the center of the dough. The farther the other raisins
are from us, the faster they are moving away from
us.
What Hubble’s Law is Not!!
• The universe is not expanding into space
• Space itself is expanding
Expansion implies there was a beginning
• If the universe is expanding we can follow the expansion back into
time: the universe must have been denser and denser in the past
• At some finite time in the past all of the galaxies must have been in
the same place and the Universe would have had an infinite density:
the Big Bang!
• Define a measure of the size of the Universe: e.g. the average
separation between galaxies.
Size
T=0,Size=0
e.g. if a galaxy 1 Mpc away is moving away from
us at 70 km/s, then if this speed was constant, 14
Gyr ago the galaxy would have been 0 Mpc away.
Hubble’s Law implies this is true for all galaxies WHY?
T=now
Time
Hubble’s Law Explained
• All of space is expanding
• All points in space get spread further
apart
• The rate at which points move apart is
proportional to their separation
v = Ho d