Halos Below the FreeStreaming Scale

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Halos Below the Free-Streaming Scale
Neal Dalal CITA with Hugh Merz, Alex Shirokov
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Halo mass function

• Lots of interest in using halo counts as a
  cosmological probe.
• mass function can be computed precisely (5) and
  robustly for standard cosmology
• dn/dm appears universal i.e. f(s) for
  standard cosmologies
• abundance of rare objects is exponentially
  sensitive to cosmological parameters, power
  spectrum, etc.

Lukic et al. (2007) astro-ph/0702360
e.g. cluster surveys as a probe of dark energy
(Holder Haiman)
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Dark matter free-streaming scale
WIMPs typically have rfs1 pc (M10-6 Msun) warm
dark matter models have rfs 0.1-1 Mpc. e.g.
light gravitinos, sterile ?s. possible
observational evidence low DM density in centers
of galaxies, dearth of faint dwarfs. observationa
l constraints exist, but no theoretical mass
function has been calculated!
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WDM sims are hard
random dist
glass
grid
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Wang White (2007)
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first halos for WIMP-like power spectrum
Diemand et al. (2006)
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mass function
location of upturn scales like N-1/3
HDM simulation Wang White (2007)
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Possible solutions?

• brute force (i.e. higher resolution)?
• just increases like N-1/3! not practical (but
  more later)
• turning off gravity on small scales

3843 particles on 1923 grid
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wash out grid coherence with thermal velocities
since velocities decay, start sim at high enough
z that particles travel distance r ?v dt gt dx
(grid spacing)
shot noise
grid units
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back to brute force
its not practical to increase the mass
resolution everywhere, so you have to use an
adaptive refinement scheme. as with AMR for
hydro, its OK to refine adaptively because there
is a filtering scale below which there is little
power. for hydro, this is the Jeans scale here
its the free-streaming scale.
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results
mass function is NOT universal!
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a single FOF group!
the high density in filaments causes unvirialized
particles to be grouped together
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a halo with no cutoff in P(k)
anisotropy in the velocity dispersion
3 s12/stot2
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FOF halo below rfs
3 s12/stot2
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SO halo below rfs
3 s12/stot2
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density vs. virialization
For halo mass, we want virialized mass.
Normally, using r200 etc. is OK because dynamical
time is 10x smaller than Hubble time, so regions
presumably have virialized. Here this fails
however. One (simple) criterion for
virialization is no net infall, ltvrgt 0
vr
r
specifically, require vr/sr lt 1 in annulus
containing outer 10 of mass.
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virialized mass function
Mfof 2563 5123 2563 x 2 refinement 2563 x 4
refinement 2563 x 6 refinement Mvir 2563 x 6
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dependence on P(k) slope...
n-1
n-2
n-2.5
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summary

• WDM sims are hard (but not impossible)!
• virialized mass function well below analytic
  fitting formulae (e.g. Jenkins, Sheth-Tormen),
  but non-zero.
• dn/d(log M) const for r rfs.
• not much dependence on shape of P(k) above rfs.

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future

• who needs halos? LOTS of high density material
  in filaments!
• ?, T seem high enough that tcool lt tHubble. Can
  form stars galaxies without halos?
• also cannot estimate matter P(k) from halos
  alone.
• individual halos profiles, substructure
• comparison with observations (e.g. lensing)