# Group galaxy number density profiles far out: is the 'one-halo' term NFW out to $>10$ virial radii?

## TL;DR

This study investigates whether the NFW profile accurately describes galaxy number density profiles far beyond the virial radius, revealing that the NFW model can fit observations out to 10-13 times the virial radius when using an optimal galaxy assignment scheme.

## Contribution

The paper demonstrates that the NFW profile applies to galaxy number densities out to large radii beyond the virial radius, challenging the notion that it only describes inner halo regions.

## Key findings

- NFW profiles fit galaxy distributions out to 13 virial radii with optimal mass assignment.
- SDSS observations show similar long-range NFW surface profiles.
- Populating haloes with galaxies requires extending models beyond traditional radii.

## Abstract

While the density profiles (DPs) of $\Lambda$CDM haloes obey the NFW law out to roughly one virial radius, $r_{\rm vir}$, the structure of their outer parts is still poorly understood, since the 1-halo term describing the halo itself is dominated by the 2-halo term representing the other haloes picked up. Using a semi-analytical model, we measure the real-space `1-halo' number DP of groups out to $20\,r_{\rm vir}$ by assigning each galaxy to its nearest group with mass above $M_{\rm a}$, in units of the group $r_{\rm vir}$. If $M_{\rm a}$ is small (large), the outer DP of groups falls rapidly (slowly). We find that there is an optimal $M_{\rm a}$ for which the stacked DP resembles the NFW model to $0.1$ dex accuracy out to $\simeq 13\,r_{\rm vir}$. We find similar long-range NFW surface DPs (out to $\simeq 10\,r_{\rm vir}$) in the SDSS observations using a galaxy assignment scheme that combines the non-linear virialized regions of groups with their linear outer parts. The optimal $M_{\rm a}$ scales as the minimum mass of the groups that are stacked to the power $0.25-0.3$. Our results suggest that the NFW model does not solely originate from violent relaxation. Moreover, populating haloes with galaxies using HOD models must proceed out to larger radii than usually done.