Fate of Stars Embedded in the AGN Disks is Determined by an Internal-Mixing Threshold

Stars can form and evolve within gaseous disks around active galactic nuclei (AGN). In the sub-parsec region of disks around ~ 10⁸ M_ black holes, stars accrete rapidly, reaching 200\,M_ and settling into a quasi-steady state in which accretion balances wind-driven mass loss. Within this environment, their ultimate fate depends critically on the radiative-zone diffusion coefficient (Dₘᵢₓ), which encapsulates various mixing processes and governs chemical transport between surface and core. Using the MESA stellar evolution code, we simulate AGN stars across a range of mixing efficiencies. We find a critical threshold floor value Dmix,min ≈ 10¹⁰\,cm²\,s⁻¹ that separates two distinct fates: 1. Immortal stars — when mixing is over-efficient (Dmix,min 10¹⁰\,cm²\,s⁻¹), rapid hydrogen replenishment sustains core hydrogen burning, maintains main-sequence equilibrium, rendering the star effectively ``immortal''. 2. Metamorphic stars — when mixing is merely efficient (Dmix,min < 10¹⁰\,cm²\,s⁻¹), stars exhaust core hydrogen, evolve off-main-sequence, shed mass to ≈15\,M_, and produce super-solar α-abundances consistent with AGN observations. We conclude that maintaining a mixing floor below this threshold is sufficient to avoid immortality, as flux-induced extra mixing can be effectively modeled via constant floor values. Our estimates provide a foundation for future work on disk enrichment and stellar evolution.