Assumption1: dark matter particles have no strong self interaction


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Assumption1: dark matter particles have NO strong self interaction

  • Assumption1: dark matter particles have NO strong self interaction

  • Assumption2: MAHs are well simulated with pure dark matter



1. MARs depend on power index of the initial density fluctuation power spectrum — since structure forms form initial density fluctuation

  • 1. MARs depend on power index of the initial density fluctuation power spectrum — since structure forms form initial density fluctuation

  • MARs depend on halo mass (acctually on fluctuation amplitude)



2. MARs depend on cosmology — since cosmology determines gravity in the expanding background universe

  • 2. MARs depend on cosmology — since cosmology determines gravity in the expanding background universe

  • MARs depend on redshift



















Statistically

  • Statistically

    • NFW 1997
    • Bullock 2001
    • Eke 2001
    • Zhao 2003b
    • Salvador-Solé 2007
    • Neto 2007 (MS)
    • Maccio 2008
    • Gao 2008 (MS)










It can also predict the evolution of halo structural properties along the main branch of merger trees, thus, one can plot its NFW density profile at any point of its history and then obtain density evolution at any fixed radius.

  • It can also predict the evolution of halo structural properties along the main branch of merger trees, thus, one can plot its NFW density profile at any point of its history and then obtain density evolution at any fixed radius.















Van den Bosch 2001 argues that his formula is universal, but the formula is based on MAHs constructed from EPS formalism, which are not consistent with those from simulations as already noticed by himself. Furthermore, actually it’s not universal even for EPS MAHs.

    • Van den Bosch 2001 argues that his formula is universal, but the formula is based on MAHs constructed from EPS formalism, which are not consistent with those from simulations as already noticed by himself. Furthermore, actually it’s not universal even for EPS MAHs.















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