Halo Substructure And The Power Spectrum

TL;DR

Zentner and Bullock develop a fast semi-analytic framework to predict dark matter subhalo populations in galaxy halos under varied power spectra. The model combines EPS-based merger histories, NFW density profiles with formation-epoch–dependent concentrations, and orbit integration including dynamical friction and tidal stripping to derive accretion histories, subhalo mass/velocity functions, and projected substructure fractions relevant for lensing. They find that the overall substructure mass fraction $f$ for CDM-like models is largely insensitive to tilt and normalization, but sharp small-scale power cuts such as BSI and warm dark matter can reduce $f$ by a factor of a few; in these cases, the velocity function is more affected due to changes in $V_{max}$ mappings. Gravitational lensing constraints and Local Group dwarfs depend sensitively on inner halo structure and the mapping from stellar velocity dispersions to halo $V_{max}$, implying that lensing and dwarf counts can jointly constrain the small-scale power spectrum and dark matter physics. Overall, the work demonstrates the utility of semi-analytic modeling to guide simulations and interpret lensing signals and dwarf galaxy demographics in the context of a broad range of cosmologies.

Abstract

(ABRIDGED) We present a semi-analytic model to explore merger histories, destruction rates, and survival probabilities of substructure in dark matter halos and use it to study the substructure populations of galaxy-sized halos as a function of the power spectrum. We successfully reproduce the subhalo velocity function and radial distribution seen in N-body simulations for standard LCDM. We explore the implications of spectra with normalizations and tilts spanning sigma_8 = 0.65-1 and n = 0.8-1. We also study a running index (RI) model with dn/dlnk=-0.03, as discussed in the first year WMAP report, and several WDM models with masses m_W = 0.75, 1.5, 3.0 keV. The substructure mass fraction is relatively insensitive to the tilt and overall normalization of the power spectrum. All CDM-type models yield projected substructure mass fractions that are consistent with, but on the low side of, estimates from strong lens systems: f = 0.4-1.5% (64 percentile) in systems M_sub < 10^9 Msun. Truncated models produce significantly smaller fractions and are disfavored by lensing results. We compare our predicted subhalo velocity functions to the dwarf satellite population of the Milky Way. Assuming isotropic velocity dispersions, we find the standard n=1 model overpredicts the number of MW satellites as expected. Models with less small-scale power are more successful because there are fewer subhalos of a given circular velocity and the mapping between observed velocity dispersion and halo circular velocity is markedly altered. The RI model, or a fixed tilt with sigma_8=0.75, can account for the MW dwarfs without the need for differential feedback; however, these comparisons depend sensitively on the assumption of isotropic velocities in satellite galaxies.

Figures (22)

• Figure 1: Galaxy central densities. The symbols show the mean density (relative to the critical density) within the radius where each rotation curve falls to half of its maximum value, inferred from the measured rotation curves of several dark matter-dominated dwarf and low surface brightness galaxies (see ZB02 for details). The data are taken from de Blok, McGaugh, & Rubin (2001; triangles and hexagons), de Blok and Bosma (2002; squares), and Swaters (1999; pentagons). The lines show the theoretical expectation for several of the power spectra we describe in § \ref{['sec:ps']} and Table \ref{['table:spectra']}. The points with error bars in the upper right corner reflect the expected theoretical scatter in the density as inferred by Bullock et al. (2001, larger range) and Jing (2000, smaller range).
• Figure 2: Input orbital circularity distribution of initially in-falling substructure (dashed) shown along with the circularity distribution of the final surviving population of ($n=1$) LCDM subhalos at $z=0$ (solid). For reference, the thin dotted line shows the circularity distribution of surviving substructure measured by Ghigna et al. (1998) in their N-body simulations.
• Figure 3: The velocity functions of progenitor and surviving subhalo populations derived using our fiducial ($n=1$, $\sigma_8=0.95$) $\Lambda$CDM cosmology and a 200-halo ensemble of $1.4\times10^{12}$ M$_{\odot}$ systems at $z=0$. Shown are all accreted halos (dashed), and the fraction of those that are tidally destroyed (short-dashed) and centrally merged (dotted). The solid line shows the surviving population of subhalos at $z=0$ and, for comparison, the thin dashed line shows the surviving population derived by K99 using N-body simulations. The error bars represent the sample variance.
• Figure 4: The radial number density profile of substructure derived from 200 model realizations of a $M_{\rm vir}=1.4\times10^{12}$ M$_{\odot}$ host halo at $z=0$ in our fiducial ($n=1$, $\sigma_8= 0.95$) $\Lambda$CDM cosmology. The open circles show the number density of subhalos with $M_{\rm sat} > 10^{6}$ M$_{\odot}$ divided by the average number density of systems meeting this mass threshold within the virial radius of the host system. The points reflect the radial profile averaged over all realizations, and the error bars reflect the sample variance. Solid pentagons show the same result for $M_{\rm sat} > 6\times 10^{8}$ M$_{\odot}$ subhalos. The variance (not shown) is significantly larger for the higher mass threshold because there are significantly fewer such systems in each host. For reference, the solid line shows the NFW density profile of the host at $z=0$. The virial radius for a host halo of this size is $R_{\rm vir} \simeq 285$ kpc and the typical NFW scale radius is $r_{\rm s} \simeq 20$ kpc. We do not plot predictions beyond $r = 0.75 R_{\rm vir} \simeq 215$ kpc because this is the maximum circular radius we assign to in-falling, bound systems.
• Figure 5: Fraction of final host mass accreted in subhalos of mass $M_{\rm sat}$ as a function of $M_{\rm sat}$. The final host mass is $1.4\times10^{12}$ M$_{\odot}$. The results for several input power spectra are shown.