Baryonification IV: Constraining baryonic feedback with X-ray gas fractions

Abstract

Baryonic feedback redistributes gas around dark matter halos, suppressing the matter power spectrum at scales now probed by weak lensing surveys. X-ray observations directly trace this hot gas, and are one of the main probes of its distribution and properties. We present a forward-modelling framework, built on the baryonification model, linking the three-dimensional gas density and temperature profiles of groups and clusters to observed X-ray surface brightness and luminosity profiles on one side, and to matter power spectrum suppression on the other. We validate the model against independent three-dimensional density reconstructions from the literature, and examine our temperature and metallicity treatment in the group-scale regime. Applying this framework to the SZ-selected CHEX-MATE and X-ray-selected eFEDs samples, we measure gas fractions across the group-to-cluster mass range while accounting for X-ray selection effects, with the first published gas fractions based on CHEX-MATE data. Combining both samples, we derive a joint constraint on the hot gas fraction retained by groups and clusters as a function of mass and on the baryonic suppression of the matter power spectrum. We find $f_{\rm gas} = 0.029 \pm 0.006$ at $M_{500c} = 3\times 10^{13}M_\odot$, $f_{\rm gas} = 0.078 \pm 0.004$ at $M_{500c} = 3\times 10^{14}M_\odot$, and suppression of 6% at $k=1\,h/\rm Mpc$ and 23% at $k=5\,h/\rm Mpc$. Our findings are consistent with recent kinematic Sunyaev-Zel'dovich results, hinting at strong feedback. We also show that the $L_X$-$M$ relation is degenerate with feedback strength, and that different feedback scenarios produce distinct X-ray profile shapes that map onto the same $L_X$-$M$ point. This work is a first step toward extending the framework to forward-model diffuse X-ray emission at the map level for simulation-based inference in upcoming wide-area X-ray surveys such as eROSITA.