We present new results on the relationship between central galaxies and dark matter haloes inferred from observations of satellite kinematics in the Sloan Digital Sky Survey (SDSS) DR7. We employ an updated analysis framework that includes detailed mock catalogues to model observational effects in SDSS. Our results constrain the colour-dependent conditional luminosity function (CLF) of dark matter haloes, as well as the radial profile of satellite galaxies. Confirming previous results, we find that red central galaxies live in more massive haloes than blue galaxies at fixed luminosity. Additionally, our results suggest that satellite galaxies have a radial profile less centrally concentrated than dark matter but not as cored as resolved subhaloes in dark matter-only simulations. Compared to previous works using satellite kinematics by More et al., we find much more competitive constraints on the galaxy-halo connection, on par with those derived from a combination of galaxy clustering and galaxy-galaxy lensing. We compare our results on the galaxy-halo connection to other studies using galaxy clustering and group catalogues, showing very good agreement between these different techniques. We discuss future applications of satellite kinematics in the context of constraining cosmology and the relationship between galaxies and dark matter haloes.

Dark matter halo clustering depends not only on halo mass, but also on other properties such as concentration and shape. This phenomenon is known broadly as assembly bias. We explore the dependence of assembly bias on halo definition, parametrized by spherical overdensity parameter, ∆. We summarize the strength of concentration-, shape-, and spin-dependent halo clustering as a function of halo mass and halo definition. Concentration-dependent clustering depends strongly on mass at all ∆. For conventional halo definitions (∆ ∼ 200m − 600m), concentration-dependent clustering at low mass is driven by a population of haloes that is altered through interactions with neighbouring haloes. Concentration-dependent clustering can be greatly reduced through a mass-dependent halo definition with ∆ ∼ 20m − 40m for haloes with M 200m 10 12 h −1 M . Smaller ∆ implies larger radii and mitigates assembly bias at low mass by subsuming altered, so-called backsplash haloes into now larger host haloes. At higher masses (M 200m 10 13 h −1 M ) larger overdensities, ∆ 600m, are necessary. Shapeand spin-dependent clustering are significant for all halo definitions that we explore and exhibit a relatively weaker mass dependence. Generally, both the strength and the sense of assembly bias depend on halo definition, varying significantly even among common definitions. We identify no halo definition that mitigates all manifestations of assembly bias. A halo definition that mitigates assembly bias based on one halo property (e.g., concentration) must be mass dependent. The halo definitions that best mitigate concentration-dependent halo clustering do not coincide with the expected average splashback radii at fixed halo mass.

The concentration parameter is a key characteristic of a dark matter halo that conveniently connects the halo’s present-day structure with its assembly history. Using ‘Dark Sky’, a suite of cosmological N-body simulations, we investigate how halo concentration evolves with time and emerges from the mass assembly history. We also explore the origin of the scatter in the relation between concentration and assembly history. We show that the evolution of halo concentration has two primary modes: (1) smooth increase due to pseudo-evolution; and (2) intense responses to physical merger events. Merger events induce lasting and substantial changes in halo structures, and we observe a universal response in the concentration parameter. We argue that merger events are a major contributor to the uncertainty in halo concentration at fixed halo mass and formation time. In fact, even haloes that are typically classified as having quiescent formation histories experience multiple minor mergers. These minor mergers drive small deviations from pseudo-evolution, which cause fluctuations in the concentration parameters and result in effectively irreducible scatter in the relation between concentration and assembly history. Hence, caution should be taken when using present-day halo concentration parameter as a proxy for the halo assembly history, especially if the recent merger history is unknown.

Extracting accurate cosmological information from galaxy-galaxy and galaxy-matter correlation functions on non-linear scales ( < ∼ 10 h −1 Mpc) requires cosmological simulations. Additionally, one has to marginalise over several nuisance parameters of the galaxy-halo connection. However, the computational cost of such simulations prohibits naive implementations of stochastic posterior sampling methods like Markov chain Monte Carlo (MCMC) that would require of order O(10 6 ) samples in cosmological parameter space. Several groups have proposed surrogate models as a solution: a so-called emulator is trained to reproduce observables for a limited number of realisations in parameter space. Afterwards, this emulator is used as a surrogate model in an MCMC analysis. Here, we demonstrate a different method called Cosmological Evidence Modelling (CEM). First, for each simulation, we calculate the Bayesian evidence marginalised over the galaxy-halo connection by repeatedly populating the simulation with galaxies. We show that this Bayesian evidence is directly related to the posterior probability of cosmological parameters. Finally, we build a physically motivated model for how the evidence depends on cosmological parameters as sampled by the simulations. We demonstrate the feasibility of CEM by using simulations from the Aemulus simulation suite and forecasting cosmological constraints from BOSS CMASS measurements of redshift-space distortions. Our analysis includes an exploration of how galaxy assembly bias affects cosmological inference. Overall, CEM has several potential advantages over the more common approach of emulating summary statistics, including the ability to easily marginalise over highly complex models of the galaxy-halo connection and greater accuracy, thereby reducing the number of simulations required.

Most models for the statistical connection between galaxies and their haloes ignore the possibility that galaxy properties may be correlated with halo properties other than halo mass, a phenomenon known as galaxy assembly bias. And yet, it is known that such correlations can lead to systematic errors in the interpretation of survey data that are analyzed using traditional halo occupation models. At present, the degree to which galaxy assembly bias may be present in the real Universe, and the best strategies for constraining it remain uncertain. We study the ability of several observables to constrain galaxy assembly bias from redshift survey data using the decorated halo occupation distribution (dHOD), an empirical model of the galaxyhalo connection that incorporates assembly bias. We cover an expansive set of observables, including the projected two-point correlation function w p (r p ), the galaxy-galaxy lensing signal ∆Σ(r p ), the void probability function VPF(r), the distributions of counts-in-cylinders P(N CIC ), and counts-in-annuli P(N CIA ), and the distribution of the ratio of counts in cylinders of different sizes P(N 2 /N 5 ). We find that despite the frequent use of the combination w p (r p ) + ∆Σ(r p ) in interpreting galaxy data, the count statistics, P(N CIC ) and P(N CIA ), are generally more efficient in constraining galaxy assembly bias when combined with w p (r p ). Constraints based upon w p (r p ) and ∆Σ(r p ) share common degeneracy directions in the parameter space, while combinations of w p (r p ) with the count statistics are more complementary. Therefore, we strongly suggest that count statistics should be used to complement the canonical observables in future studies of the galaxy-halo connection.