Numerical Simulation of the Hydrodynamical Combustion to Strange Quark Matter in the Trapped Neutrino Regime

We simulate and study the microphysics of combustion (flame burning) of two flavored quark matter (u, d) to three flavoured quark matter (u,d,s) in a trapped neutrino regime applicable to conditions prevailing in a hot proto-neutron star. The reaction-diffusion-advection equations for (u,d) to (u,d,s) combustion are coupled with neutrino transport, which is modelled through a flux-limited diffusion scheme. The flame speed is proportional to initial lepton fraction because of the release of electron chemical potential as heat, and reaches a steady-state burning speed of (0.001-0.008)c. We find that the burning speed is ultimately driven by the neutrino pressure gradient, given that the pressure gradient induced by quarks is opposed by the pressure gradients induced by electrons. This suggests, somewhat counter-intuitively, that the pressure gradients that drive the interface are controlled primarily by leptonic weak decays rather than by the quark Equation of State (EOS). In other words, the effects of the leptonic weak interaction, including the corresponding weak decay rates and the EOS of electrons and neutrinos, are at least as important as the uncertainties related to the EOS of high density matter. We find that for baryon number densities nB <= 0.35 fm-3, strong pressure gradients induced by leptonic weak decays drastically slow down the burning speed, which is thereafter controlled by the much slower burning process driven by backflowing downstream matter. We discuss the implications of our findings to proto-neutron stars.