Feedback from active galactic nuclei (AGN) and supernovae can affect measurements of integrated SZ flux of halos ($Y_\mathrm{SZ}$) from CMB surveys, and cause its relation with the halo mass ($Y_\mathrm{SZ}-M$) 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 ($M\lesssim 10^{14}\, h^{-1} \, M_\odot$); we find that simply replacing $Y\rightarrow Y(1+M_*/M_\mathrm{gas})$ 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 percent-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 an alternative relation, $Y-M_*$, provides complementary information on feedback than $Y-M$

翻译：摘要：活动星系核（AGN）和超新星的反馈会干扰CMB巡天中晕的积分SZ通量（$Y_\mathrm{SZ}$）测量，并导致其与晕质量（$Y_\mathrm{SZ}-M$）的关系偏离维里定理的自相似幂律预言。我们利用CAMELS——一组反馈机制广泛变化的流体动力学模拟套件——对此类偏离进行了全面研究。结合随机森林与符号回归两种机器学习工具，我们寻找低质量（$M\lesssim 10^{14}\, h^{-1} \, M_\odot$）下对反馈过程更稳健的$Y-M$关系类似形式；发现简单地将关系式中的$Y$替换为$Y(1+M_*/M_\mathrm{gas})$后，该关系显著恢复自相似性。这可为低质量星系团和星系群提供稳健的多波段质量代理。我们的方法学也可广泛用于改善其他天体物理标度关系的有效域。我们还预测，对$Y-M$关系的测量能以百分之一精度约束反馈参数的特定组合，或排除当前最先进流体动力学模拟中使用的超新星与AGN反馈模型的主要参数空间。研究结果有助于利用即将开展的SZ巡天（如SO、CMB-S4）与星系巡天（如DESI和Rubin）约束重子反馈的本质。最后，我们发现另一种关系$Y-M_*$能提供与$Y-M$互补的反馈信息。