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MESA-QUEST: Tracing the formation of direct collapse black hole seeds via quasi-stars

The origin of the first supermassive black holes (SMBHs) observed at redshifts $z\geq 9$ remains one of the most challenging open questions in astrophysics. Their rapid emergence suggests that massive ``heavy seeds'' must have formed early, possibly through the direct collapse of pristine gas clouds in the first galaxies. We present MESA-QUEST, a new framework built upon the Modules for Experiments in Stellar Astrophysics (MESA) code, designed to model the structure and evolution of quasi-stars -- massive, radiation-supported envelopes hosting accreting black holes at their cores -- believed to be the progenitors of direct-collapse black hole (DCBH) seeds. Our implementation introduces flexible boundary conditions representing both Bondi accretion and saturated-convection regimes, and explores the impact of several stellar wind and mass-loss prescriptions, including Reimers, Dutch, and super-Eddington radiation-driven winds. We find that quasi-stars can grow central black holes to $\geq 10^3\,M_{\odot}$ under favorable conditions, with saturated-convection models yielding BH-to-total mass ratios up to 0.55$M_*$ -- five times higher than Bondi-limited cases. However, strong radiation-driven winds can dramatically curtail growth, potentially quenching heavy-seed formation unless balanced by sustained envelope accretion. Our results delineate the physical limits under which quasi-stars can remain stable and produce heavy seeds capable of evolving into the earliest SMBHs detected by JWST and Chandra. Future extensions will incorporate rotation, magnetic fields, and GR-radiation hydrodynamics to refine accretion physics and constrain the viability of the quasi-star pathway for early SMBH formation.