Radioactive Heating and Late Time Kilonova Light Curves

Compact object mergers can produce a thermal electromagnetic counterpart (a kilonova) powered by the decay of freshly synthesized radioactive isotopes. The luminosity of kilonova light curves depends on the efficiency with which beta-decay electrons are thermalized in the ejecta. Here we derive a simple analytic solution for thermalization by calculating how accumulate electrons lose energy adiabatically and via plasma interactions. The thermalization efficiency is well described by f (t) approximate to (1 + t/t(e))(-n) where the timescale t(e) is a function of the ejecta mass and velocity and the exponent n approximate to 1.0-1.5 depends on the electron energies and the thermalization cross-sections. For a statistical distribution of r-process isotopes with radioactive power (Q)over dot(beta) proportional to t(-4/3) and n = 1, the late time kilonova luminosity asymptotes to L = f (t) (Q)over dot(beta) proportional to t(-7/3) and depends super-linearly on the ejecta mass, L proportional to M-5/3. If a kilonova is instead powered by a single dominate isotope, we show that the late time luminosity can deviate substantially from the underlying exponential decay and the heating from the accumulation of trapped electrons eventually exceeds the instantaneous radioactivity. Applied to the kilonova associated with the gravitational wave source GW170817, these results imply that a possible steepening of the light curve at greater than or similar to 7 days is unrelated to thermalization effects and instead could mark the onset of translucency in a high opacity component of ejecta. The analytic results should be convenient for estimating the properties of observed kilonovae and assessing the potential late time detectability of future events.