Cosmology and Dark Matter III: The Formation of Galaxies

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Cosmology and Dark Matter III The Formation of
Galaxies

• Jerry Sellwood

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The story so far

• Four serious problems with the hot big bang model
  were solved in one attractive stroke
• What caused inflation? How does it work?
• Questions still without clear answers
• But the idea is very appealing
• We can test two key predictions
• universe really should be flat i.e. ? 1
• power spectrum of density fluctuations

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Is the universe flat?

• Astronomers could not find enough matter
• Expressed as fractions of ?crit, we find
• stars in galaxies 0.5
• all normal atoms 4 (from BBN)
• dark matter not more than 20 30
• Increasing confidence that the mass density was
  less than critical
• Crisis for inflation

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Accelerating Universe

• Gravity attracts and slows expansion of the
  universe
• Should see more rapid expansion in the past
• i.e. at large distances or high redshift
• Type Ia supernovae seem to be standard candles
  more distant ones are fainter
• Slowing expansion apparent brightness should
  decrease less rapidly with redshift
• data showed the opposite!

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Dark Energy

• Supernovae data alone not all that convincing
  (e.g. possible systematic errors)
• But CMB measurements (and theoretical prejudice)
  suggest universe is in fact flat
• Can save inflation if 70 of the critical density
  is a new component Dark Energy
• Gravitationally repulsive to cause acceleration
• We have resurrected Einsteins cosmological
  constant with ?? 0.7 so ?M ?? 1

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Cosmic microwave background

• NASAs WMAP measured temperature differences in
  CMB from point to point
• Blue is cooler than mean, red is hotter
• ?T/T ? ?10-5 (i.e. measurements arent easy!)

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Origin of fluctuations

• Curvature fluctuations laid down during inflation
• Slight density differences affect the expansion
  rate relative to the mean
• Differences amplify since they were created
• Overdense regions are slightly warmer
• Underdense regions are slightly cooler
• Two-thirds counteracted by gravitational redshift

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Fluctuation power spectrum

• Want to quantify the fluctuations on different
  angular scales
• Expand in surface harmonics, Ylm (or multipoles)
• Compute the total power at each l
• Points with error bars are data (scatter with m)
• Red line is a fitted theoretical model

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Acoustic oscillations

• Fluctuations are superpositions of many waves of
  different scales
• Each wave begins to oscillate once ? is inside
  the horizon
• We get peaks in the power at max compression and
  rarefaction

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Standard ruler

• For the first peak at about 1?, we know
• the oscillation period and thus the time since
  waves entered the horizon
• the expansion rate, and can therefore calculate
  the linear scale of these waves
• We also measure the angular scale
• So we can determine the curvature of the
  universe!
• Find that it must be flat within the errors

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Growth of structure

• The universe was very smooth at z?1100
• Not today stars planets, galaxies, and
  clusters of galaxies formed somehow
• Computer simulations needed
• start from reasonable initial conditions
• treat baryons and dark matter in same way as a
  1st approximation
• choose a box size and make it periodic
• fill it with particles almost uniformly
• compute forces on particles and step forward in
  time

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• Kravtsov et al
• Expansion is not shown positions are in
  co-moving coordinates

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Appear successful

• Dark matter forms dense clumps
• connected by a cosmic web of filaments
• Resembles observed galaxy distribution
• Comparison requires a rule to assign galaxies
  within mass clumps

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Power specturm

• Data points with error bars are from 2dFGRS
• Line is the average power spectrum from 35
  simulations with a (physically reasonable) rule
  for assigning galaxies
• Agreement is impressive

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Dark Matter halos

• Dark matter clumps are called halos
• Every halo has many sub-halos
• Examine the mass profiles of the halos

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Universal halo density profile

• Spherically averaged density of dark matter seems
  to approximate the form
• ?(r) ?s rs3 / r?(rrs)3-?
• i.e. a broken power law, with 1 lt ? lt 1.5
• ? 1 ??
• is NFW

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Concentration

• The cosmology papers do not use ?s directly, but
  define a new parameter c
• They define , r200, within which the average
  density is 200?crit
• halo approximately settled
• and then set c r200/rs
• Furthermore, c correlates mass halos are
  predicted to be a 1-parameter family

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Clear and testable predictions

• If only we could measure DM halos directly
• we see only baryons, which are distributed
  differently
• Gas cools in DM halos
• Settles into a rotationally supported disk
• Compresses the halo as it cools
• Forms stars etc.

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More simulation needed

• Governato et al
• Dark matter gas stars
• Promising disk bulge
• embedded in a DM halo