Isospin equilibration in neutron star mergers

Abstract

We analyze the isospin equilibration properties of neutrinoless nuclear ($npe$) matter in the temperature and density range that is relevant to neutron star mergers. Our analysis incorporates neutrino-transparency corrections to the isospin (``beta'') equilibrium condition which become noticeable at $T\ensuremath{\gtrsim}1\phantom{\rule{0.16em}{0ex}}\text{MeV}$. We find that the isospin relaxation rate rises rapidly as temperature rises, and at $T\ensuremath{\approx}5\phantom{\rule{0.16em}{0ex}}\text{MeV}$ it is comparable to the timescale of the density oscillations that occur immediately after the merger. This produces a resonant peak in the bulk viscosity at $T\ensuremath{\approx}5\phantom{\rule{0.16em}{0ex}}\text{MeV}$, which causes density oscillations to be damped on the timescale of the merger. Our calculations suggest that isospin relaxation dynamics may also be relevant when neutrinos are treated more accurately via neutrino transport schemes.