Halo substructure and the power spectrum

We present a semianalytic model to investigate the merger history, destruction rate, and survival probability of substructure in hierarchically formed dark matter halos and use it to study the substructure content of halos as a function of input primordial power spectrum. For a standard cold dark matter "concordance" cosmology (LambdaCDM; n = 1, sigma(8) = 0.95) we successfully reproduce the subhalo velocity function and radial distribution pro. le seen in N-body simulations and determine that the rate of merging and disruption peaks similar to10-12 Gyr in the past for Milky Way-like halos, while surviving substructures are typically accreted within the last similar to0-8 Gyr. We explore power spectra with normalizations and spectral "tilts" spanning the ranges sigma(8) similar or equal to 1-0.65 and n similar or equal to 1-0.8, and include a "running-index" model with dn/d ln k = -0.03 similar to the best-fit model discussed in the first-year Wilkinson Microwave Anisotropy Probe (WMAP) report. We investigate spectra with truncated small-scale power, including a broken-scale inflation model and three warm dark matter cases with m(W) = 0.75-3.0 keV. We find that the mass fraction in substructure is relatively insensitive to the tilt and overall normalization of the primordial power spectrum. All of the CDM-type models yield projected substructure mass fractions that are consistent with, but on the low side, of published estimates from strong lens systems: f(9) = 0.4%-1.5% (64th percentile) for subhalos smaller than 10(9) M-circle dot within projected cylinders of radius r < 10 kpc. Truncated models produce significantly smaller fractions, f(9) = 0.02%-0.2% for m(W) similar or equal to 1 keV, and are disfavored by lensing estimates. This suggests that lensing and similar probes can provide a robust test of the CDM paradigm and a powerful constraint on broken-scale inflation/warm particle masses, including masses larger than the similar to 1 keV upper limits of previous studies. We compare our predicted subhalo velocity functions with the dwarf satellite population of the Milky Way. Assuming that dwarfs have isotropic velocity dispersions, we find that the standard n = 1 model overpredicts the number of Milky Way satellites at V-max less than or similar to 35 km s(-1\), as expected. Models with less small-scale power do better because subhalos are less concentrated and the mapping between observed velocity dispersion and halo Vmax is significantly altered. The running-index model, or a fixed tilt with sigma(8) similar to 0.75, can account for the local dwarfs without the need for differential feedback (for V-max greater than or similar to 20 km s(-1)); however, these comparisons depend sensitively on the assumption of isotropic velocities in satellite galaxies.