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Class 23 : Dark Matter Halos

n  This class l  Dark matter halos; the “skeleton” of a galaxy l  Halo over-density factor ΔV

l  Applications of Virial Theorem

O : Recap

n  Last class : Linear theory of structure formation l  Gravitational Instability l  Evolution of perturbations, from big bang to

present day l  Find “preferred scale” corresponding to the

particle horizon at matter-radiation equality l  Beautiful agreement between observed and

predicted power-spectrum

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I : Dark Matter Halos

n  On small scales, the dark matter collapses to form well defined bound objects (halos!)

n  Dark Matter in the halos obeys the virial theorem (i.e. the system is in virial equilibrium)…

n  In order to settle down to this state, the Dark Matter has to dissipate excess energy.

n  How does collisionless dark matter dissipate energy???

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Galaxies

Groups and clusters of galaxies

Jenkins et al. (2001)

Properties of a DM halo

n  Definition… let Δ(r) be average density within radius r of a dark matter halo in units where the overall cosmological density is unity.

n  It turns out that the “virial radius” rv of a DM halo corresponds to a pretty universal value of Δ , often assume Δv=200.

n  Suppose that a DM halo has a mass Mv with the virial radius. If σ is velocity of an average DM particle, Virial theorem gives

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n  By definition we have

n  Combining with the virial theorem…

n  For illustrative purposes, evaluating at z=1…