Implications of Inelastic Dark Matter for Primordial Dark-Star Evolution: Kinematic Thresholds and Nonthermal Capture

Abstract

The recent 248-keV nuclear recoil candidate reported by LUX-ZEPLIN has renewed interest in endothermic inelastic dark matter, motivating us to examine its capture in primordial dark stars. Relative to the conventional elastic-capture picture in dark star evolution, endothermic capture adds two qualitative features. First, it opens only after the growing star crosses a compactness threshold, expressed as a kinematic radius $R_{\rm kin}\proptoμ_χM_\star/δ$ set by the stellar mass, the dark-matter--nucleus reduced mass and the mass splitting. The accreting growth carries the star through the threshold, and the capture rate turns on quadratically above it. Second, although newly captured particles generically begin on nonthermal bound orbits, endothermic kinematics can keep this normally transient population spatially extended, turning it into a persistent reservoir rather than an intermediate step toward a thermal core. Following complete chains of state-changing collisions, we find that the reservoir compacts sharply and then stalls, because a ground state particle below a compactness-dependent orbital energy has no allowed up-scatter anywhere in the star. A percent-level radius contraction reopens the relaxation. These kinematic results do not depend on whether the excited state decays promptly or is long-lived. As a result, inelastic capture does not replenish a thermal annihilation core. The captured population forms an evolving orbital distribution that sets up the co-evolutionary dynamics between the star and the dark matter in the core and the reservoir, which we develop in a companion paper.