Halo Substructure and the Power Spectrum

In this proceeding, we present the results of a semi-analytic study of CDM substructure as a function of the primordial power spectrum. We apply our method to several “tilted ” models in the ΛCDM framework, with n ≃ 1.1−0.8, or σ 8 ≃ 1.2−0.65 when normalized to COBE. We also study a more extreme, warm dark matter-like spectrum that is sharply truncated below a scale of ∼ 0.3 h −1 Mpc ( ∼ 10 10 h −1 M ⊙). Contrary to some expectations, we show that the mass fraction of halo substructure is not a strong function of spectral slope, so it likely will be difficult to constrain tilt using flux ratios of gravitationally lensed quasars. On the positive side, all of our CDM-type models yield projected mass fractions that are in good agreement with strong lensing estimates: f ≈ 1.5 % at M ∼ 10 8 M ⊙. The truncated model produces a significantly smaller fraction, f ≈ 0.3%, suggesting that warm dark matter-like spectra are disfavored and potentially may be distinguished from CDM spectra using lensing. We also discuss the issue of dwarf satellite abundances, with emphasis on the cosmological dependence of the map between the observed central velocity dispersions of Milky Way satellites and the maximum circular velocities of their host halos. In agreement with earlier work, we find that standard ΛCDM over-predicts the estimated count of Milky Way satellites at fixed Vmax by an order of magnitude, but tilted models do better because subhalos are less concentrated. Interestingly, under the assumption that dwarfs have isotropic velocity dispersion tensors, models with significantly tilted primordial power spectra (e.g., n ∼ 0.85, σ8 ∼ 0.7) may underpredict the number of large Milky Way satellites with Vmax ∼ 40 km s−1. 1.