Halo Profiles and the Concentration-Mass Relation for a {\Lambda}CDM Universe

Abstract

Profiles of dark matter-dominated halos at the group and cluster scales play an important role in modern cosmology. Using results from two very large cosmological $N$-body simulations, which increase the available volume at their mass resolution by roughly two orders of magnitude, we robustly determine the halo concentration-mass $(c-M)$ relation over a wide range of masses, employing multiple methods of concentration measurement. We characterize individual halo profiles, as well as stacked profiles, relevant for galaxy-galaxy lensing and next-generation cluster surveys; the redshift range covered is $0\leq z \leq 4$, with a minimum halo mass of $M_{200c}\sim2\times10^{11} M_\odot$. Despite the complexity of a proper description of a halo (environmental effects, merger history, nonsphericity, relaxation state), when the mass is scaled by the nonlinear mass scale $M_\star(z)$, we find that a simple non-power-law form for the $c-M/M_\star$ relation provides an excellent description of our simulation results across eight decades in $M/M_{\star}$ and for $0\leq z \leq 4$. Over the mass range covered, the $c-M$ relation has two asymptotic forms: an approximate power law below a mass threshold $M/M_\star\sim 500-1000$, transitioning to a constant value, $c_0\sim 3$ at higher masses. The relaxed halo fraction decreases with mass, transitioning to a constant value of $\sim 0.5$ above the same mass threshold. We compare Navarro-Frenk-White (NFW) and Einasto fits to stacked profiles in narrow mass bins at different redshifts; as expected, the Einasto profile provides a better description of the simulation results. At cluster scales at low redshift, however, both NFW and Einasto profiles are in very good agreement with the simulation results, consistent with recent weak lensing observations.