An efficient and robust method to estimate halo concentration based on the method of moments

Abstract

ABSTRACT We propose an efficient and robust method to estimate the halo concentration based on the first moment of the density distribution, which is $R_1\equiv \int _0^{r_{\rm vir}}4\pi r^3\rho (r)\mathrm{ d}r/M_{\rm vir}/r_{\rm vir}$. We find that R1 has a monotonic relation with the concentration parameter of the Navarro–Frenk–White (NFW) profile, and that a cubic polynomial function can fit the relation with an error $\lesssim 3~{{\ \rm per\ cent}}$. Tests on ideal NFW haloes show that the conventional NFW profile fitting method and the Vmax/Vvir method produce biased halo concentration estimation by $\approx 10~{{\ \rm per\ cent}}$ and $\approx 30~{{\ \rm per\ cent}}$, respectively, for haloes with 100 particles. In contrast, the systematic error for our R1 method is smaller than 0.5  per cent even for haloes containing only 100 particles. Convergence tests on realistic haloes in N-body simulations show that the NFW profile fitting method underestimates the concentration parameter for haloes with ≲300 particles by $\gtrsim 20~{{\ \rm per\ cent}}$, while the error for the R1 method is $\lesssim 8~{{\ \rm per\ cent}}$. We also show other applications of R1, including estimating Vmax and the Einasto concentration ce ≡ rvir/r−2. The calculation of R1 is efficient and robust, and we recommend including it as one of the halo properties in halo catalogues of cosmological simulations.