Constraining dark matter halo profiles with symbolic regression

Area of Science:

• Astrophysics
• Cosmology
• Computational Physics

Background:

• Dark matter halo density profiles are typically modeled using simulation-derived forms like the Navarro-Frenk-White (NFW) profile.
• Simulation predictions are subject to uncertainties in dark matter physics and baryonic matter modeling.
• Observational constraints on halo profiles often rely on these potentially uncertain simulations.

Purpose of the Study:

• To develop and test a simulation-independent method for constraining dark matter halo density profiles directly from observational data.
• To assess the impact of data precision and sample size on the selection of halo density profile models.
• To determine which aspects of halo density profiles are robustly constrained by observational data.

Main Methods:

• Utilized Exhaustive Symbolic Regression (ESR), a technique that searches for analytic expressions balancing accuracy and simplicity.
• Applied ESR to mock weak lensing excess surface density (ESD) data from synthetic galaxy clusters with NFW profiles.
• Investigated the influence of varying fractional uncertainties and the number of clusters on model selection.

Main Results:

• ESR successfully recovered the NFW profile from mock data with ~5% fractional errors using as few as ~20 clusters.
• With higher uncertainties, characteristic of current surveys, simpler profiles were favored over NFW, though NFW remained competitive.
• The preference for simpler models at higher uncertainties is linked to weak lensing errors being smallest in the outer regions of halos.

Conclusions:

• ESR offers a robust, simulation-independent framework for testing dark matter halo mass models using observational data.
• The method helps identify which features of a halo's density profile are genuinely constrained by the available data.
• This approach provides a powerful tool for advancing our understanding of dark matter distribution in the universe.