An efficient and robust method to estimate halo concentration

Kai Wang; H. J. Mo; Yangyao Chen; Joop Schaye

doi:10.1093/mnras/stad3927

paper

An efficient and robust method to estimate halo concentration

arXiv:2310.00200 · doi:10.1093/mnras/stad3927

Abstract

We propose an efficient and robust method to estimate the halo concentration based on the first moment of the density distribution, which is $R_{1} \equiv \int_{0}^{r_{vir}} 4 π r^{3} ρ (r) d r / M_{vir} / r_{vir}$ . 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 $≲ 3%$ . Tests on ideal NFW halos show that the conventional NFW profile fitting method and the $V_{max} / V_{vir}$ 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 $≲ 300$ particles by $≳ 20%$ , while the error for the $R_{1}$ method is $≲ 8%$ . We also show other applications of $R_{1}$ , including estimating $V_{max}$ and the Einasto concentration $c_{e} \equiv r_{vir} / r_{- 2}$ . 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.

arXiv comment17 pages, 9 + 9 figures. Main figure: Fig. 3. MNRAS accepted

An efficient and robust method to estimate halo concentration

Abstract

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