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

arXiv: https://arxiv.org/abs/2209.02075 · HTML: https://mlsanity.com/paper/2209.02075/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 71 references that are in the map.
- First posted on arXiv 5 Sep 2022.

## Builds on (most cited first, 1 of 1)

- [Augmenting astrophysical scaling relations with machine learning: application to reducing the Sunyaev-Zeldovich flux-mass scatter](https://mlsanity.com/paper/2201.01305/) (2022)

## Built on by (most cited first, 5 of 5)

- [Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl](https://mlsanity.com/paper/2305.01582/) (2023)
- [Exhaustive Symbolic Regression](https://mlsanity.com/paper/2211.11461/) (2022)
- [SymbolNet: Neural Symbolic Regression with Adaptive Dynamic Pruning for Compression](https://mlsanity.com/paper/2401.09949/) (2024)
- [The CAMELS project: Expanding the galaxy formation model space with new ASTRID and 28-parameter TNG and SIMBA suites](https://mlsanity.com/paper/2304.02096/) (2023)
- [SymbolFit: Automatic Parametric Modeling with Symbolic Regression](https://mlsanity.com/paper/2411.09851/) (2024)

## Abstract (arXiv)

Feedback from active galactic nuclei (AGN) and supernovae can affect measurements of integrated SZ flux of halos (YSZ) from CMB surveys, and cause its relation with the halo mass (YSZ-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 (Mlesssim 1014, h-1 , M_odot); we find that simply replacing Yrightarrow Y(1+M_*/Mgas) 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