Electroweak decay of quark matter within dense astrophysical combustion flames

We study the weak interaction processes taking place within a combustion flame that converts dense hadronic matter into quark matter in a compact star. Using the Boltzmann equation we follow the evolution of a small element of just deconfined quark matter all along the flame interior until it reaches chemical equilibrium at the back boundary of the flame. We obtain the reaction rates and neutrino emissivities of all the relevant weak interaction processes without making any assumption about the neutrino degeneracy. We analyse systematically the role the initial conditions of unburnt hadronic matter, such as density, temperature, neutrino trapping and composition, focusing on typical astrophysical scenarios such as cold neutron stars, protoneutron stars, and post merger compact objects. We find that the temperature within the flame rises significantly in a timescale of 1 nanosecond. The increase in $T$ strongly depends on the initial strangeness of hadronic matter and tends to be more drastic at larger densities. Typical final values range between $20$ and $60 \, \mathrm{MeV}$. The nonleptonic process $u + d \rightarrow u + s$ is always dominant in cold stars, but in hot object the process $u + e^{-} \leftrightarrow d + {\nu_e}$ becomes relevant, and in some cases dominant, near chemical equilibrium. The rates for the other processes are orders of magnitude smaller. We find that the neutrino emissivity per baryon is very large, leading to a total energy release per baryon of $2-64 \, \mathrm{MeV}$ in the form of neutrinos along the flame. We discuss some astrophysical consequences of the results.