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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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Self consistent theory of halo mergers l.jpg

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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Halo Theory: Press-Schechter abundance

Normalization:

log n

log M


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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:

!!!!!


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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).


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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


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For n=0 (white noise) power spectrum(only!),

 analytic solution for n(M1): i.e.,

Q(M1,M2) M1+M2



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n=-1 power-law power spectrum


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n=-2 power-law power spectrum


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n=-2

n=-1



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n=3 power-law power spectrum


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n=1 power-law power spectrum


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n=3

n=2


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Preliminary results for CDM power spectrum!!

(Press-Schechter mass function at z=0)

Benson, Furlanetto, MK, in preparation






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Still left to do:

  • Check dependence of result on alternativesmoothing 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