The Tully-Fisher and mass-size relations from halo abundance matching

The Tully-Fisher relation (TFR) expresses the connection between rotating galaxies and the dark matter haloes they inhabit, and therefore contains a wealth of information about galaxy formation. We construct a general framework to investigate whether models based on halo abundance matching are able to reproduce the observed stellar mass TFR and mass-size relation (MSR), and use the data to constrain galaxy formation parameters. Our model tests a range of plausible scenarios, differing in the response of haloes to disc formation, the relative angular momentum of baryons and dark matter, the impact of selection effects, and the abundance matching parameters. We show that agreement with the observed TFR puts an upper limit on the scatter between galaxy and halo properties, requires weak or reversed halo contraction, and favours selection effects that preferentially eliminate fast-rotating galaxies. The MSR constrains the ratio of the disc to halo specific angular momentum to be approximately in the range 0.6-1.2. We identify and quantify two problems that models of this nature face. (1) They predict too large an intrinsic scatter for the MSR, and (2) they predict too strong an anticorrelation between the TFR and MSR residuals. We argue that resolving these problems requires introducing a correlation between stellar surface density and enclosed dark matter mass. Finally, we explore the expected difference between the TFRs of central and satellite galaxies, finding that in the favoured models this difference should be detectable in a sample of ~700 galaxies.Comment: 27 pages, 10 figures; revised to match published MNRAS versio

A Comprehensive Analysis of Uncertainties Affecting the Stellar Mass - Halo Mass Relation for 0<z<4

We conduct a comprehensive analysis of the relationship between central galaxies and their host dark matter halos, as characterized by the stellar mass-halo mass (SM-HM) relation, with rigorous consideration of uncertainties. Our analysis focuses on results from the abundance matching technique, which assumes that every dark matter halo or subhalo above a specific mass threshold hosts one galaxy. We discuss the quantitative effects of uncertainties in observed galaxy stellar mass functions (GSMFs) (including stellar mass estimates and counting uncertainties), halo mass functions (including cosmology and uncertainties from substructure), and the abundance matching technique used to link galaxies to halos (including scatter in this connection). Our analysis results in a robust estimate of the SM-HM relation and its evolution from z=0 to z=4. The shape and evolution are well constrained for z < 1. The largest uncertainties at these redshifts are due to stellar mass estimates; however, failure to account for scatter in stellar masses at fixed halo mass can lead to errors of similar magnitude in the SM-HM relation for central galaxies in massive halos. We also investigate the SM-HM relation to z=4, although the shape of the relation at higher redshifts remains fairly unconstrained when uncertainties are taken into account. These results will provide a powerful tool to inform galaxy evolution models. [Abridged]Comment: 27 pages, 12 figures, updated to match ApJ accepted version

Cosmological Constraints from Galaxy Clustering and the Mass-to-Number Ratio of Galaxy Clusters: Marginalizing over the Physics of Galaxy Formation

Many approaches to obtaining cosmological constraints rely on the connection between galaxies and dark matter. However, the distribution of galaxies is dependent on their formation and evolution as well as the cosmological model, and galaxy formation is still not a well-constrained process. Thus, methods that probe cosmology using galaxies as a tracer for dark matter must be able to accurately estimate the cosmological parameters without knowing the details of galaxy formation a priori. We apply this reasoning to the method of obtaining $\Omega_m$ and $\sigma_8$ from galaxy clustering combined with the mass-to-number ratio of galaxy clusters. To test the sensitivity of this method to variations due to galaxy formation, we consider several different models applied to the same cosmological dark matter simulation. The cosmological parameters are then estimated using the observables in each model, marginalizing over the parameters of the Halo Occupation Distribution (HOD). We find that for models where the galaxies can be well represented by a parameterized HOD, this method can successfully extract the desired cosmological parameters for a wide range of galaxy formation prescriptions.Comment: 10 pages, 7 figures, Submitted to Ap

The Rockstar Phase-Space Temporal Halo Finder and the Velocity Offsets of Cluster Cores

We present a new algorithm for identifying dark matter halos, substructure, and tidal features. The approach is based on adaptive hierarchical refinement of friends-of-friends groups in six phase-space dimensions and one time dimension, which allows for robust (grid-independent, shape-independent, and noise-resilient) tracking of substructure; as such, it is named Rockstar (Robust Overdensity Calculation using K-Space Topologically Adaptive Refinement). Our method is massively parallel (up to 10^5 CPUs) and runs on the largest current simulations (>10^10 particles) with high efficiency (10 CPU hours and 60 gigabytes of memory required per billion particles analyzed). A previous paper (Knebe et al 2011) has shown Rockstar to have class-leading recovery of halo properties; we expand on these comparisons with more tests and higher-resolution simulations. We show a significant improvement in substructure recovery as compared to several other halo finders and discuss the theoretical and practical limits of simulations in this regard. Finally, we present results which demonstrate conclusively that dark matter halo cores are not at rest relative to the halo bulk or satellite average velocities and have coherent velocity offsets across a wide range of halo masses and redshifts. For massive clusters, these offsets can be up to 350 km/s at z=0 and even higher at high redshifts. Our implementation is publicly available at http://code.google.com/p/rockstar .Comment: 20 pages, 14 figures. Minor revisions to match accepted versio