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). Hierarchical clustering. early. late. Halo Theory: Press-Schechter abundance.
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Andrew Benson (Caltech/Oxford)
Marc Kamionkowski (Caltech)
Steven Hassani (Caltech/Princeton)
astro-ph/0407136 (MNRAS, in press)
and Steven Furlanetto (in progress)
Rate for halo of mass M1 to run into halo of mass M2
Rate/volume for halo 1 to merge with halo 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:
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).
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.,
small time step
n=-1 power-law power spectrum
n=-2 power-law power spectrum
n=3 power-law power spectrum
n=1 power-law power spectrum
(Press-Schechter mass function at z=0)
Benson, Furlanetto, MK, in preparation