Revising Indirect Dark Matter Constraints with Updated Astrophysical $J$-Factor Priors

Abstract

Indirect searches for particle dark matter with gamma-ray experiments have produced a large number of constraints on the annihilation cross section (or decay lifetime) over a wide range of dark matter masses. These constraints depend critically on the assumed astrophysical $J$ factor and its uncertainty, which encodes the dark matter distribution in the target and represents the dominant source of systematic uncertainty. As improved observational data and dynamical modeling are expected to revise current $J$-factor determinations, many published limits risk becoming obsolete unless the full experimental analyses are repeated. In this work we present a general and statistically consistent framework for updating published dark matter limits when revised $J$-factor estimates become available, without requiring access to the full experimental likelihood. We derive an analytical expression that quantifies the impact of astrophysical uncertainties on dark matter limits, treating both Gaussian and log-normal priors on the $J$ factor. The formalism is validated through toy Monte Carlo simulations, including dedicated studies of its numerical stability under successive reinterpretations, and demonstrate their accuracy by reproducing published limits. Lastly, we further show that the formalism naturally extends to the combination of multiple targets through a simple numerical procedure, allowing limits to be combined and updated using only publicly available information. The proposed method is intended as a complementary reinterpretation tool for situations in which a complete experimental reanalysis is impractical, offering a practical means to preserve and extend the scientific relevance of published dark matter constraints across present and future experiments.