Abundance and phase-space distribution of subhalos in cosmological N-body simulations: testing numerical convergence and correction methods

TL;DR

This study tackles the numerical convergence of subhalo populations in the nonlinear regime by comparing two ultra-high-resolution $6144^3$ N-body simulations with differing mass resolutions and an advanced time-domain halo finder. It demonstrates that the Surviving subhalo Peak Mass Function converges only when $m_{ m peak}$ exceeds about $5{,}000$ particles, but can be accurately recovered by including orphan subhalos using the merger-time model of Jiang et al., which outperforms alternatives. Incorporating orphans enables real-space spatial and velocity distributions to be recovered at the $5$–$10\%$ level down to $0.1$–$0.2\,h^{-1}{\rm Mpc}$, though convergence below $0.1\,h^{-1}{\rm Mpc}$ remains difficult and likely requires more sophisticated orphan modeling. Redshift-space multipoles remain especially sensitive to small-scale pairs due to elongated Fingers-of-God, suggesting the use of modified or alternative statistics to mitigate small-projection-separation effects in subhalo-based analyses.

Abstract

Subhalos play a crucial role in accurately modeling galaxy formation and galaxy-based cosmological probes within the highly nonlinear, virialized regime. However, numerical convergence of subhalo evolution is difficult to achieve, especially in the inner regions of host halos where tidal forces are strongest. I investigate the numerical convergence and correction methods for the abundance, spatial, and velocity distributions of subhalos using two $6144^3$-particle cosmological N-body simulations with different mass resolutions -- Jiutian-300 ($1.0 \times 10^{7}\,h^{-1}M_{\odot}$) and Jiutian-1G ($3.7 \times 10^{8}\,h^{-1}M_{\odot}$) -- with subhalos identified by HBT+. My study shows that the Surviving subhalo Peak Mass Function (SPMF) converges only for subhalos with $m_{\mathrm{peak}}$ above $5000$ particles but can be accurately recovered by including orphan subhalos that survive according to the merger timescale model of Jiang et al., which outperforms other models. Including orphan subhalos also enables recovery of the real-space spatial and velocity distributions to $5$--$10\%$ accuracy down to scales of $0.1$--$0.2\,h^{-1}\mathrm{Mpc}$. The remaining differences are likely due to cosmic variance and finite-box effects in the smaller Jiutian-300 simulation. Convergence below $0.1\,h^{-1}\mathrm{Mpc}$ remains challenging and requires more sophisticated modeling of orphan subhalos. I further highlight that redshift-space multipoles are more difficult to recover even at larger scales because unreliable small-scale pairs at $r_{\mathrm{p}} < 0.1\,h^{-1}\mathrm{Mpc}$ in real space affect scales of tens of $\mathrm{Mpc}$ in redshift space due to elongated Fingers-of-God effects. Therefore, for redshift-space statistics, I recommend using modified or alternative measures that reduce sensitivity to small projected separations in subhalo-based studies.

Figures (15)

• Figure 1: Subhalo peak mass functions of surviving subhalos (squares) and all infall subhalos (triangles) in Jiutian-300 (orange) and Jiutian-1G (blue) within $R_{\rm vir}$ at $z=0$, shown for host halos in different mass bins. Black solid lines indicate the universal IPMFs from Han et al. 2018MNRAS.474..604H. The orange and blue solid lines show the SPMFs predicted by applying the merger timescale model of Jiang et al. 2008ApJ...675.1095J to all infall subhalos in Jiutian-300 and Jiutian-1G, regardless of their present-day status. Dashed vertical lines indicate the subhalo mass corresponding to 5000 particles.
• Figure 2: Infall redshift distributions of resolved subhalos with peak masses in the range $10^{10.7} < m_{\rm peak} < 10^{12.3}\,h^{-1}M_{\odot}$. In this range, subhalos are fully resolved in Jiutian-300 but are affected by numerical effects in Jiutian-1G. Results are shown for different host halo mass bins. The Jiutian-1G distributions are normalized using the subhalo counts from Jiutian-300, scaled by the simulation volumes. As a result, the histogram area for Jiutian-300 is 1, while that for Jiutian-1G is less than 1.
• Figure 3: Comparison of SPMFs within $R_{\rm vir}$ from the combination of Jiutian-300 and Jiutian-1G at $z=0$ with predictions obtained by checking whether each infall subhalo should have merged according to the merger timescale $T_{\rm merger}$ from four different models. Results are shown for three host halo mass bins. The blue dashed vertical lines indicate the subhalo mass corresponding to 5000 particles in Jiutian-300. The universal IPMF from Han et al. 2018MNRAS.474..604H is shown as black solid lines for comparison.
• Figure 4: Host halo mass dependence and redshift evolution of the SPMF within $R_{\rm vir}$. Dots represent results from simulations, while solid lines show the fitting formula. The universal IPMF from Han et al. 2018MNRAS.474..604H is shown as black dashed lines for comparison. Dashed horizontal lines in the ratio panels indicate the $\pm10\%$ deviation range. Poisson noise is shown as error bars.
• Figure 5: Same as figure \ref{['fig:evo_rvir']}, but counting all subhalos within the FOF groups instead of only those inside $R_{\rm vir}$.