Relativistic Dynamical Evolution of Kilonova Spectral Emission

Abstract

We develop a relativistic dynamical model for the thermal evolution of expanding kilonova ejecta, in which the effective temperature is determined by the ejecta mass, opacity, velocity, and radioactive heating rate. The resulting thermal evolution follows a broken power law as the ejecta transition from the optically thick to the optically thin regime. We incorporate this thermal history into a relativistic spectral calculation that accounts for the equal-arrival-time surface geometry and Doppler boosting, enabling us to model the observed kilonova spectrum and constrain the underlying ejecta properties. We investigate the effects of the model parameters and relativistic corrections on the observed temperature and spectral shape, and find that light-travel-time delays and Doppler shifts can produce significant spectral distortions at high ejecta velocities. We apply the model to the early-time X-shooter spectrum of the kilonova AT2017gfo and infer the ejecta mass, opacity, and velocity through Markov chain Monte Carlo (MCMC) fitting with a Student's $t$ likelihood. We find that relativistic effects become increasingly important for fast ejecta ($v \gtrsim 0.5c$), particularly at large viewing angles, where the observed temperature can differ substantially from the rest-frame effective temperature. These results highlight the importance of incorporating relativistic and equal-arrival-time effects when interpreting early-time kilonova spectra, especially for rapidly expanding ejecta.