Concentrations of Dark Haloes Emerge from Their Merger Histories

The concentration parameter is a key characteristic of a dark matter halo that conveniently connects the halos 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.

How to Optimally Constrain Galaxy Assembly Bias: Supplement Projected Correlation Functions with Count-in-cells Statistics

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.