A Unified Model for Radioactive Signatures and Source Identifiability in Neutron Star Mergers

Abstract

Late light curves of neutron star mergers can contain substantial fission power while remaining compatible with different radioactive inventories. We develop a unified source attribution model in which a common bounded response formulation links nuclear heating, radiation transport and isotope identification. Within particle dependent deposition and gray photon escape, matched luminosity comparisons show how long alpha and fission responses become aligned. Explicit competing inventories then reproduce a light curve with a substantial $^{254}$Cf contribution, with smooth evolution of the beta luminosity response providing an important source of compensation. We derive optimization certificates and collective likelihood bounds that quantify the resulting limits on identification under specified source and ejecta constraints. We also introduce an energy conserving model with two radiation frequency groups to resolve the information carried by color at fixed total luminosity precision. Its exact response modes identify the source adjustments that absorb color contrast, while a residual color floor characterizes the contrast retained by the permitted family. Late observations of AT~2023vfi with the James Webb and Hubble Space Telescopes provide an observational benchmark: the reference and retained alternatives predict bolometric declines about 1.5 quoted uncertainties shallower than the reconstruction, while differences between inventories containing and excluding $^{254}$Cf remain within the reported decline uncertainty. The unified model provides a quantitative basis for connecting nucleosynthesis predictions, gravitational wave constraints and the temporal and spectral information in merger observations to radioactive source attribution.