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Most models for the connection between galaxies and their haloes ignore the possibility that galaxy properties may be correlated with halo properties other than mass, a phenomenon known as galaxy assembly bias. Yet, it is known that such correlations can lead to systematic errors in the interpretation of survey data. 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 galaxy--halo connection that incorporates assembly bias. We cover an expansive set of observables, including the projected two-point correlation function $w_{mathrm{p}}(r_{mathrm{p}})$, the galaxy--galaxy lensing signal $Delta Sigma(r_{mathrm{p}})$, the void probability function $mathrm{VPF}(r)$, the distributions of counts-in-cylinders $P(N_{mathrm{CIC}})$, and counts-in-annuli $P(N_{mathrm{CIA}})$, 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 $w_{mathrm{p}}(r_{mathrm{p}})+Delta Sigma(r_{mathrm{p}})$ in interpreting galaxy data, the count statistics, $P(N_{mathrm{CIC}})$ and $P(N_{mathrm{CIA}})$, are generally more efficient in constraining galaxy assembly bias when combined with $w_{mathrm{p}}(r_{mathrm{p}})$. Constraints based upon $w_{mathrm{p}}(r_{mathrm{p}})$ and $Delta Sigma(r_{mathrm{p}})$ share common degeneracy directions in the parameter space, while combinations of $w_{mathrm{p}}(r_{mathrm{p}})$ 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.
We investigate the level of galaxy assembly bias in the Sloan Digital Sky Survey (SDSS) main galaxy redshift survey using ELUCID, a state-of-the-art constrained simulation that accurately reconstructed the initial density perturbations within the SDS
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Understanding the impact of halo properties beyond halo mass on the clustering of galaxies (namely galaxy assembly bias) remains a challenge for contemporary models of galaxy clustering. We explore the use of machine learning to predict the halo occu