How to optimally constrain galaxy assembly bias: supplement projected correlation functions with count-in-cells statistics

Abstract

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.

Differentiable Predictions for Large Scale Structure with SHAMNet

“…In some cases, virtually no adaptation of the computations detailed in §4 would be required. For example, both the under-density probability function (UPF) and counts-incells (CIC) summary statistics have been shown to be sensitive probes of galaxy-halo information that is not contained in galaxy clustering or lensing (Tinker et al 2008;Wang et al 2019). Both of these summary statistics are defined in terms of number counts of galaxies residing within some enclosing volume.…”

CLIMBER: Galaxy-Halo Connection Constraints from Next-Generation Surveys

“…By tuning the radius of the cylinder and inner annulus, CIC can effectively separate the signal of centrals from satellites, without requiring full group catalog reconstruction. Wang et al (2019) demonstrate that CIC + w p (r p ) may be sufficient to constrain assembly bias as well. However, further testing is required for samples affected by fiber collisions like PFS and MOONS.…”

“…The two-point correlation function, ξ(r), is a canonical constraint on the HOD because it measures the clustering strength of the galaxy population, which is indicative of the clustering strength of the underlying halo population. Since halo clustering is a strong function of halo mass, the two-point correlation function is very sensitive to the typical mass of the halo population (Zehavi et al 2005;Reddick 2013;Wang et al 2019). We adopt the projected correlation function, which is defined as…”

“…First of all, it is possible to partially break the degeneracy between central and satellite clustering by measuring the two-point correlation function to smaller scales (sub-Mpc) using fiber collision corrections. Additionally, alternative statistics like counts-in-cylinders tend to be more sensitive to certain galaxy populations, and therefore provide excellent complementary information to the two-point correlation function (Wang et al 2019). This will be important for analyzing the real data, but will come at a greater computational cost, particularly because this increases the size of the covariance matrix, and will likely require many more mock realizations to calculate accurately.…”

“…Methods such as the halo occupation distribution (HOD; e.g., Berlind & Weinberg 2002;Zheng et al 2007;Hearin et al 2016) or abundance-matching (e.g., Kravtsov et al 2004;Hearin & Watson 2013) are most commonly used to statistically match the stellar masses of galaxies to the masses of their host halos. Since the number density and clustering of halos are strongly dependent on halo mass (Press & Schechter 1974;Kaiser 1984;Bond et al 1991;Mo & White 1996;Zentner 2007), these models are informed through observations of the stellar mass function and the two-point correlation function (Zehavi et al 2005;Reddick 2013; Wang et al 2019).…”