Abstract
Abstract 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 where the timescale is a function of the ejecta mass and velocity and the exponent depends on the electron energies and the thermalization cross-sections. For a statistical distribution of r-process isotopes with radioactive power and n = 1, the late time kilonova luminosity asymptotes to and depends super-linearly on the ejecta mass, . 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 ≳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.
Highlights
The violent merger of two neutron stars can eject neutron-rich matter that, upon decompression, will assemble into heavy nuclei via rapid neutron capture (Lattimer & Schramm 1976; Eichler et al 1989; Meyer 1989; Rosswog et al 1999; Freiburghaus et al 1999)
We find that the time-dependent thermalization efficiency is well described by f (t) ≈ (1 + t/te)−n where n ≈ 1 and the timescale te is a function of the ejecta mass and velocity
Applied to the kilonova associated with the gravitational wave source GW170817, these results imply that a possible steepening of the observed light curve at 7 days is unrelated to thermalization effects and instead could mark the onset of translucency in a high opacity component of ejecta
Summary
The violent merger of two neutron stars (or a neutron star and a black hole) can eject neutron-rich matter that, upon decompression, will assemble into heavy nuclei via rapid neutron capture (the r -process) (Lattimer & Schramm 1976; Eichler et al 1989; Meyer 1989; Rosswog et al 1999; Freiburghaus et al 1999). At later times ( days to weeks), the ejecta become optically thin and the bolometric light curve directly tracks the instantaneous deposition of radioactive energy. Barnes et al (2016) carried out detailed numerical calculations of thermalization efficiency for all r -process decay products, including electrons, alpha particles and fission fragments. The kilonova luminosity is not a function of the instantaneous decay rate, but rather depends on the accumulated store of electrons emitted from prior epochs We determine this cumulative heating by calculating how electrons deposit energy in the plasma while simultaneously losing energy due to adiabatic expansion. Because plasma losses roughly follow the Bethe formula (dE/dt ∝ E−1/2 ln E), electrons deposit energy more effectively as they adiabatically degrade to lower energy E We account for this energy dependence, along with the fact that in beta decay the longer lived nuclei on average emit lower energy electrons.
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