The SZ flux-mass (Y-M) relation at low-halo masses: improvements with symbolic regression and strong constraints on baryonic feedback

Feedback from active galactic nuclei (AGNs) and supernovae can affect measurements of integrated Sunyaev-Zeldovich (SZ) flux of haloes (Y_SZ) from cosmic microwave background (CMB) surveys, and cause its relation with the halo mass (Y_SZ-M) to deviate from the self-similar power-law prediction of the virial theorem. We perform a comprehensive study of such deviations using CAMELS, a suite of hydrodynamic simulations with extensive variations in feedback prescriptions. We use a combination of two machine learning tools (random forest and symbolic regression) to search for analogues of the Y-M relation which are more robust to feedback processes for low masses ($M\lesssim 10^{14}\, \mathrm{ h}^{-1} \, \mathrm{ M}_\odot$); we find that simply replacing Y → Y(1 + M_*/M_gas) in the relation makes it remarkably self-similar. This could serve as a robust multiwavelength mass proxy for low-mass clusters and galaxy groups. Our methodology can also be generally useful to improve the domain of validity of other astrophysical scaling relations. We also forecast that measurements of the Y-M relation could provide per cent level constraints on certain combinations of feedback parameters and/or rule out a major part of the parameter space of supernova and AGN feedback models used in current state-of-the-art hydrodynamic simulations. Our results can be useful for using upcoming SZ surveys (e.g. SO, CMB-S4) and galaxy surveys (e.g. DESI and Rubin) to constrain the nature of baryonic feedback. Finally, we find that the alternative relation, Y-M_*, provides complementary information on feedback than Y-M.