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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). Hierarchical clustering. early. late. Halo Theory: Press-Schechter abundance.

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Self-Consistent Theory of Halo Mergers

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  1. 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)

  2. Hierarchical clustering early late

  3. Halo Theory: Press-Schechter abundance Normalization: log n log M

  4. 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: !!!!!

  5. Rate/volume must be n(M1)n(M2)Q(M1,M2) rate coefficient (units of cross section x velocity) Must satisfy Smoluchowski coagulation eqn:

  6. 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).

  7. 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

  8. For n=0 (white noise) power spectrum(only!),  analytic solution for n(M1): i.e., Q(M1,M2) M1+M2

  9. Evolution of mass function evolved over small time step

  10. n=-1 power-law power spectrum

  11. n=-2 power-law power spectrum

  12. n=-2 n=-1

  13. n=2 power-law power spectrum

  14. n=3 power-law power spectrum

  15. n=1 power-law power spectrum

  16. n=3 n=2

  17. Preliminary results for CDM power spectrum!! (Press-Schechter mass function at z=0) Benson, Furlanetto, MK, in preparation

  18. Same, but for Sheth-Tormen mass function

  19. PS mass function at z=3

  20. ST mass function at z=3

  21. Effective spectral index

  22. 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

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