Influence of the direct Urca on the r-mode spin-down features of newborn neutron stars pulsars

We perform a study on the time duration, final frequency, and exit temperature of the r-mode instability in newborn neutron stars of normal fluid composition under the assumption that the r-mode is the dominating spin-down mechanism. It is found that these spin-down features will vary widely depending on the star mass when direct Urca becomes operative. The occurrence of direct Urca is decided from the stiffness of the symmetry energy of the underlying equation of state, which is still uncertain. The change in the spin-down features in stars of different masses has been studied by computing the magnitude of the bulk viscosity due to the extent of direct Urca coverage in the core. The range for the variation of the symmetry energy stiffness, characterized by the slope parameter L, is decided from the tidal deformability data of the GW170817 event and the maximum mass constraint. The study is done by applying a family of equation of states obtained with the finite range simple effective interaction, constrained at low and intermediate densities by nuclear data and the flow analysis in heavy-ion collisions and at high densities by causality.