Title: Analytic heating rate of neutron star merger ejecta derived from Fermi's theory of beta decay,
Abstract: Macronovae (kilonovae) that arise in binary neutron star mergers are powered
by radioactive beta decay of hundreds of $r$-process nuclides. We derive, using
Fermi's theory of beta decay, an analytic estimate of the nuclear heating rate.
We show that the heating rate evolves as a power law ranging between $t^{-6/5}$
to $t^{-4/3}$. The overall magnitude of the heating rate is determined by the
mean values of nuclear quantities, e.g., the nuclear matrix elements of beta
decay. These values are specified by using nuclear experimental data. We
discuss the role of higher order beta transitions and the robustness of the
power law. The robust and simple form of the heating rate suggests that
observations of the late-time bolometric light curve $\propto t^{-\frac{4}{3}}$
would be a direct evidence of a $r$-process driven macronova. Such observations
could also enable us to estimate the total amount of $r$-process nuclei
produced in the merger.