Dark Matter Halos and the Galaxy Luminosity Function

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Dark Matter Halos and the Galaxy Luminosity
Function

• Dark Matter Halos
• Formation of a halo
• The mass function of halos
• Virial radius and velocity
• Infall, shocking and cooling of baryons
• Galaxy luminosity function
• Simple predictions for the luminosity function
• Comparison with observations
• The need for feedback

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Some basic definitions

• On the largest scales, the Universe is
  homogeneous (uniform density). The density
  perturbation is given by
• We tend to think of this in terms of its Fourier
  components
• The power-spectrum of density perturbations is
  then given by

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• Inflation predicts the initial spectrum of
  perturbations P(k)?k
• These perturbations then grow (or decay) due to
  the action of gravity (or other forces)
• Provided perturbations are small, ?(x)ltlt1, can
  use linear theory to deduce behaviour. Find
  that
• Today, leq?130Mpc and corresponds to the
  particle horizon at decoupling, expanded by the
  normal cosmic expansion well discuss this in
  class

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LogP(k)
Fluctuations were able to grow even before
decoupling
Fluctuations were not able to grow before
decoupling
1/leq
log(k)
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IV.5 Dark Matter Halos

• For small enough scales, perturbations are not
  small. On these scales, the dark matter
  collapses to form well defined bound objects
  (halos!)
• Dark Matter in the halos is in virial
  equilibrium
• In order to settle down to this state, the Dark
  Matter has to dissipate excess energy.

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Jenkins et al. (2001)
Galaxies
Groups and clusters of galaxies
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• One more definition let ?(r) be the average
  density within radius r of a dark matter halo in
  units where the overall cosmological density is
  unity.
• It turns out that the virial radius rv of a DM
  halo corresponds to a pretty universal value of ?
  , often assume ?v200.
• Suppose that a DM halo has a mass Mv with the
  virial radius. If ? is velocity of an average DM
  particle, Virial theorem gives

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• By definition we have
• Combining with the virial theorem
• Putting numbers into a slightly more detailed
  calculation gives

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What about the baryonic matter?

• The baryonic matter falls into the
  gravitational potential wells of the DM halos
• Infall heats baryonic matter until it reaches the
  virial temperature. Roughly,

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What then?

• The shocked gas cools via e/m radiation
• Define the Cooling time as

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• Put in expression for T evaluate for ?200
• So, for all galaxy sized objects, we might expect
  the baryons to cool. What happens then?
• The cooled gas falls to the bottom of the
  gravitational potential well
• Eventually, the cold gas turns into stars
  (through small scale gravitational collapse)
• Bottom line significant fraction of baryons
  should end up as stars!

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IV.6 The Galaxy Luminosity Function

• Galaxy luminosity function ?(L) the number of
  galaxies per unit volume with luminosity in the
  range L?LdL
• Using arguments just given
• The galaxy luminosity (stars) should be
  proportional to the DM halo mass
• Hence the the galaxy luminosity function should
  follow the DM mass distribution

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Benson et al. (2003)
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• Simple model fails to explain ?(L)
• Deficit of galaxies at low-L and high-L
• Something is suppressing star formation
  selectively in low-mass and high-mass halos
• Star formation suppressed itself in low-mass
  halos!
• Initial phase of star formation proceeds
• Subsequent supernovae propel gas out of the DM
  halo removes fuel for the star formation!

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M82