We propose an efficient and robust method to estimate the halo concentration based on the first moment of the density distribution, which is $R_1\equiv \int_0^{ r_{ \rm vir}}4\pi r^3\rho(r)dr/M_{ \rm vir}/r_{ \rm vir}$. We find that $R_1$ has a monotonic relation with the concentration parameter of the NFW profile, and that a cubic polynomial function can fit the relation with an error $\lesssim 3\%$. Tests on ideal NFW halos show that the conventional NFW profile fitting method and the $V_{ \rm max}/V_{ \rm vir}$ method produce biased halo concentration estimation by $\approx 10\%$ and $\approx 30\%$, respectively, for halos with 100 particles. In contrast, the systematic error for our $R_1$ method is smaller than $0.5\%$ even for halos containing only 100 particles. Convergence tests on realistic halos in $N$-body simulations show that the NFW profile fitting method underestimates the concentration parameter for halos with $\lesssim 300$ particles by $\gtrsim 20\%$, while the error for the $R_1$ method is $\lesssim 8\%$. We also show other applications of $R_1$, including estimating $V_{ \rm max}$ and the Einasto concentration $c_{ \rm e}\equiv r_{ \rm vir}/r_{ -2}$. The calculation of $R_1$ is efficient and robust, and we recommend including it as one of the halo properties in halo catalogs of cosmological simulations.
Categories: astro-ph.CO astro-ph.GA