Augmenting astrophysical scaling relations with machine learning: Application to reducing the Sunyaev-Zeldovich flux-mass scatter.

Complex astrophysical systems often exhibit low-scatter relations between observable properties (e.g., luminosity, velocity dispersion, oscillation period). These scaling relations illuminate the underlying physics, and can provide observational tools for estimating masses and distances. Machine learning can provide a fast and systematic way to search for new scaling relations (or for simple extensions to existing relations) in abstract high-dimensional parameter spaces. We use a machine learning tool called symbolic regression (SR), which models patterns in a dataset in the form of analytic equations. We focus on the Sunyaev-Zeldovich flux-cluster mass relation ( Y _SZ - M ), the scatter in which affects inference of cosmological parameters from cluster abundance data. Using SR on the data from the IllustrisTNG hydrodynamical simulation, we find a new proxy for cluster mass which combines Y _SZ and concentration of ionized gas ( c _gas ): M ∝ Y _conc ^3/5 ≡ Y _SZ ^3/5 (1 - A c _gas ). Y _conc reduces the scatter in the predicted M by ∼20 - 30% for large clusters ( M ≳ 10 ¹⁴ h ^-1 M _⊙ ), as compared to using just Y _SZ . We show that the dependence on c _gas is linked to cores of clusters exhibiting larger scatter than their outskirts. Finally, we test Y _conc on clusters from CAMELS simulations and show that Y _conc is robust against variations in cosmology, subgrid physics, and cosmic variance. Our results and methodology can be useful for accurate multiwavelength cluster mass estimation from upcoming CMB and X-ray surveys like ACT, SO, eROSITA and CMB-S4.