Constraining dark matter halo profiles with symbolic regression
This provides a simulation-independent framework for testing mass models in astrophysics, though it is incremental as it applies an existing symbolic regression method to a new domain-specific problem.
The authors tackled the problem of constraining dark matter halo density profiles from observational data by using Exhaustive Symbolic Regression (ESR) to search for analytic expressions that balance accuracy and simplicity. They found that with 5% fractional errors, ESR recovers the NFW profile from as few as 20 clusters, but at higher uncertainties representative of current surveys, simpler functions are favored.
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.