Accurate connected modeling of gas thermodynamics and matter distribution

We introduce gas thermodynamics and matter distribution using jax (godmax), a novel code designed to calculate correlations between the cosmological matter distribution and various gas thermodynamic quantities. Utilizing the extensive antilles suite of 200 hydrodynamical simulations with a diverse range of baryonic feedback strengths, we jointly fit the 3D profiles of total matter distribution, electron density, and electron pressure across various halo masses and redshifts. By accommodating significant variations in gas profiles expected due to baryonic feedback, solving exact hydrostatic equilibrium equation, and offering flexible modeling of nonthermal pressure support, godmax has the capability to jointly fit all these profiles within the measurement uncertainties. This advancement provides consistent profiles to enable, for the first time, robust joint halo-model-based modeling of multiple cosmic probes, including the kinetic and thermal Sunyaev-Zel'dovich (tSZ) effect, weak lensing, and x-ray observations. Furthermore, the model accurately captures correlations between the total matter power suppression due to baryonic feedback and local average thermodynamic quantities, such as the baryon fraction and integrated tSZ effect, in high-mass halos, aligning with observations from hydrodynamical simulations. Looking ahead, we forecast the expected constraints on cosmological and baryonic parameters from upcoming weak lensing catalogs from the Legacy Survey of Space and Time and tSZ maps from the Simons Observatory. This analysis underscores the importance of cross-correlations between weak lensing and tSZ signal in enhancing parameter constraints by resolving major systematic uncertainties due to baryonic physics. The godmax code leverages the jax library, resulting in a fully differentiable halo model with native GPU compilation support.