# Why does Einasto profile index $n\sim 6$ occur so frequently?

## TL;DR

This paper investigates why the Einasto profile with index around 6 is common in dark matter halos, proposing that it is a natural attractor solution of Fokker-Planck diffusion processes, which questions standard N-body simulation convergence criteria.

## Contribution

It demonstrates that the Einasto index ~6 is a stationary and likely attractor solution of the Fokker-Planck equation, providing a new explanation for its frequent occurrence in simulations.

## Key findings

- Einasto profile with n≈6 is a stationary solution in the halo center.
- Fokker-Planck diffusion tends to produce profiles with n≈6.
- This explains the frequent appearance of n≈6 in N-body simulations.

## Abstract

We consider the behavior of spherically symmetric Einasto halos composed of gravitating particles in the Fokker-Planck approximation. This approach allows us to consider the undesirable influence of close encounters in the N-body simulations more adequately than the generally accepted criteria. The Einasto profile with index $n \approx 6$ is a stationary solution of the Fokker-Planck equation in the halo center. There are some reasons to believe that the solution is an attractor. Then the Fokker-Planck diffusion tends to transform a density profile to the equilibrium one with the Einasto index $n \approx 6$. We suggest this effect as a possible reason why the Einasto index $n \approx 6$ occurs so frequently in the interpretation of N-body simulation results. The results obtained cast doubt on generally accepted criteria of N-body simulation convergence.