Mini Review:

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• Mini Review
• Ocams Razor Start out with simplest
  assumptions
• Hot Big Bang, Expanding Universe
• Only baryonic matter gt
• CMB existence, universe old and large and
  expanding

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• CMB too smooth
• Add non-baryonic matter
• Galaxies seen early (high 1z) gt CDM
• First Peak in CMB indicates universe flat IF we
  put in model of initial fluctuations as
  adiabatic.
• Wt 1, k 0
• Second and Third peaks of CMB fit nicely with
  First peak and adiabatic model, but need MAP data
  to be sure

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• SNe says from a measure of the geometry of the
  universe versus time gt
• Accelerating Universe gt Dark Energy
• Clusters of galaxies say Wm lt 0.4 gt
• With CMB Wt1, gt WL gt 0.6, gt Dark Energy
• Dark Energy is the dark side of physics

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• Ways to overcome dark side
• Assume SNe wrong
• Assume Clusters wrong
• Assume other new physics (e.g. iso-curvature) in
  early about 10-30 sec after BB rather than
  adiabatic fluctuations gt
• In this case First peak doesnt require Wt 1, k
  0 flat in this case.
• First Peak in CMB looks so solid need new
  interpretation for a model with no Dark Energy.
• Cluster and SNe observations alone are less
  solid.

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• In early Universe, any goes so to a few,
  iso-curvature more appealing than adiabatic
• First, Second and Third peaks are likely to be
  verified by MAP
• A very neat confirmation of adiabatic initial
  fluctuations
• Status quo is very likely to be upheld gt
• Our final answer is Dark Energy, CDM, the
  Universe is flat but the expansion rate of the
  Universe is increasing

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CMB peak plot
CMB smoothness map
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End mini-Review, back to clusters
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• Some of missing mass was found, but not enough
  gt confirmation of non-baryonic dark matter

• Second method

• Use hot (100 million K) gas.
• Most light comes out in X-rays.

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X-ray
Optical
No color
False color
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Concept of escape velocity
If an object is moving fast enough the object
will escape the pull of gravity of that system. gt

• (1/2)mv2 gt GMm/R
• m mass of escaping object
• v velocity of escaping object
• M mass of retaining object,
• R distance from center to center

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• Atom mass is m (assumed)
• Cluster mass is M
• gt Measure T of gas
• Relate T to v (simple theory)
• Derive M!
• Derived M agrees with galaxy velocity method

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Bottom Line from first 2 methods

• Gas mass 3-5 times total galaxy mass
• Total directly detected baryonic matter
  (galaxies plus hot gas) mass still about 10
  (closer to 8) times too low! gt
• Wouldnt hurt to check another way

OK check one more way! gt Gravitational lensing
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Gravitational Lensing
Magnifies and distorts images
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Gravitational Lensing

• 4-d surface is distorted by local mass
  concentration
• light travels on the surface
• light path is deflected when traveling close to
  the body

Black hole
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Gravitational Lensing Cont.
Gives rise to beautiful effects
Core of the Cluster called A2218
Arc-like structures caused by grav. lensing of
the mass in the cluster
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Grav. Lensing

• Derive a cluster mass again!
• Agrees with other methods

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• Number of clusters there are per unit volume
• lower bound on the Wm! about 0.1- 0.2 !
• We will assume 0.1

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Models of how clusters form and evolve yield
total Wm
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Model of Cluster formation and Wm

• Universe is expanding
• Density falls
• gt Total mass in a cluster radius is less than
  cluster mass. gt
• Cant form any more clusters then.

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• Prediction
• If we see a steep (factor of 2) in number of
  clusters per unit volume as go from z 0.1 to z
  1, then Wm gt 0.7
• See shallow change (less than factor of 1.2),
  then Wm lt 0.4
• See shallow change gt
• Wm lt 0.4, all fits!

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Clusters are no longer able to form as the
universe is not dense enough
High Wm
Low Wm
No. of clusters per unit volume
z
Age of universe
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Clusters have problems also
Just measuring the mass is difficultgt
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Velocity of galaxy measurement assumes you know
all the galaxies are in the clusters and how
they are moving.

And, where do clusters end (in radius), anyway?
Gas mass measurements based on possibly false
assumption of stable situation.

• Our cluster counts could be wrong
• Our model for relating Wm to number of clusters
  per unit volume with age of universe could be
  wrong