Transcript Self-Consistent Theory of Halo Mergers

Self-Consistent Theory of
Halo Mergers
Andrew Benson (Caltech/Oxford)
Marc Kamionkowski (Caltech)
Steven Hassani (Caltech/Princeton)
astro-ph/0407136 (MNRAS, in press)
and Steven Furlanetto (in progress)
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Hierarchical clustering
early
late
Halo Theory: Press-Schechter abundance
 Mn(M)dM  
0
log n
Normalization:
log M
Extended Press-Schechter (Lacey-Cole ‘93):
Rate for halo of mass M1 to run into halo of mass M2
Rate/volume for halo 1 to merge with halo 2:
n(M1)(d p /dM2 )  n(M2 )(d p /dM1) !!!!!
2
2
Rate/volume must be
n(M1)n(M2)Q(M1,M2)
rate coefficient (units of
cross section x velocity)
Must satisfy Smoluchowski coagulation eqn:
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Problem 1: Correct merger kernel
Q(M1,M2) must satisfy coagulation
equation. ePS does not. Can we find
correct Q(M1,M2) ??
Problem 2: Inversion of coagulation eqn
not unique; several Q(M1,M2) give same
n(M1).
Benson, MK, Hassani (2004): For given
n(M1), find Q(M1,M2) that provides closest
fit (in least-squares sense) to coagulation
equation, subject to constraint that demands
Q(M1,M2) varies smoothly with M1 and M2
For n=0 (white noise) power spectrum(only!),
 analytic solution for n(M1): i.e.,
Q(M1,M2) M1+M2
Evolution of mass function evolved over
small time step
n=-1 power-law power spectrum
n=-2 power-law power spectrum
n=-2
n=-1
n=2 power-law power spectrum
n=3 power-law power spectrum
n=1 power-law power spectrum
n=2
n=3
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Preliminary results for CDM power spectrum!!
(Press-Schechter mass function at z=0)
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Benson, Furlanetto, MK, in preparation
Same, but for Sheth-Tormen mass function
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PS mass function at z=3
ST mass function at z=3
Effective spectral index
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Still left to do:
• Check dependence of result on alternative
smoothing constraints
• Implement improved discretization
• Compare formation-z distribution and distribution
of most massive progenitors with simulations
• Understand better mathematics of coagulation
equation
• Produce CDM results and provide in easily
accessible form