Constraining dark matter halo profiles with symbolic regression

TL;DR

This paper introduces a novel method using Exhaustive Symbolic Regression to directly constrain dark matter halo density profiles from observational data, effectively testing and identifying the most supported models.

Contribution

The authors develop and demonstrate a new, simulation-independent approach to determine halo density profiles directly from observations using symbolic regression.

Findings

ESR recovers NFW profiles from small samples with 5% errors.

At higher uncertainties, simpler functions are preferred over NFW.

The method is robust and effective for testing mass models and data constraints.

Abstract

Dark matter haloes are typically characterised by radial density profiles with fixed forms motivated by simulations (e.g. NFW). However, simulation predictions depend on uncertain dark matter physics and baryonic modelling. Here, we present a method to constrain halo density profiles directly from observations using Exhaustive Symbolic Regression (ESR), a technique that searches the space of analytic expressions for the function that best balances accuracy and simplicity for a given dataset. We test the approach on mock weak lensing excess surface density (ESD) data of synthetic clusters with NFW profiles. Motivated by real data, we assign each ESD data point a constant fractional uncertainty and vary this uncertainty and the number of clusters to probe how data precision and sample size affect model selection. For fractional errors around 5%, ESR recovers the NFW profile even from samples as small as 20 clusters. At higher uncertainties representative of current surveys, simpler functions are favoured over NFW, though it remains competitive. This preference arises because weak lensing errors are smallest in the outskirts, causing the fits to be dominated by the outer profile. ESR therefore provides a robust, simulation-independent framework both for testing mass models and determining which features of a halo's density profile are genuinely constrained by the data.