A Short Research Note on Calculating Exact Distribution Functions and Random Sampling for the 3D NFW Profile

TL;DR

This paper provides an analytic quantile function for the NFW profile, enabling faster and more accurate sampling of particle positions in astrophysical simulations, improving efficiency in modeling galaxy distributions.

Contribution

It introduces an exact analytic quantile function for the 3D NFW profile, replacing approximate methods for sampling in astrophysical modeling.

Findings

Analytic quantile function for NFW profile provided

Code implementations in R and Python released

Sampling process significantly faster and more accurate

Abstract

In this short note we publish the analytic quantile function for the Navarro, Frenk & White (NFW) profile. All known published and coded methods for sampling from the 3D NFW PDF use either accept-reject, or numeric interpolation (sometimes via a lookup table) for projecting random Uniform samples through the quantile distribution function to produce samples of the radius. This is a common requirement in N-body initial condition (IC), halo occupation distribution (HOD), and semi-analytic modelling (SAM) work for correctly assigning particles or galaxies to positions given an assumed concentration for the NFW profile. Using this analytic description allows for much faster and cleaner code to solve a common numeric problem in modern astronomy. We release R and Python versions of simple code that achieves this sampling, which we note is trivial to reproduce in any modern programming language.