  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 electrons accumulate in
the ejecta and lose energy adiabatically and via plasma losses. We find that
the time-dependent thermalization efficiency is well described by $f(t) \approx
(1 + t/t_e)^{-n}$ where $n \approx 1$ and the timescale $t_e$ is a function of
the ejecta mass and velocity. For a statistical distribution of r-process
isotopes with radioactive power $\dot{Q} \propto t^{-4/3}$, the late time
kilonova luminosity asymptotes to $L \propto t^{-7/3}$ and depends
super-linearly on the ejecta mass, $L \propto M^{5/3}$. 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
eventually become brighter than the instantaneous radioactivity due to the
accumulation of trapped electrons. Applied to the kilonova associated with the
gravitational wave source GW170817, these results imply that a possible
steepening of the observed light curve at $\gtrsim 7$ 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.
