Stellar electron capture rates on neutron-rich nuclei and their impact on core-collapse

During the late stages of gravitational core-collapse of massive stars, extreme isospin asymmetries are reached within the core. Due to the lack of microscopic calculations of electron capture (EC) rates for all relevant nuclei, in general simple analytic parameterizations are employed. We study here several extensions of these parameterizations, allowing for a temperature, electron density and isospin dependence as well as for odd-even effects. The latter extra degrees of freedom considerably improve the agreement with large scale microscopic rate calculations. We find, in particular, that the isospin dependence leads to a significant reduction of the global EC rates during core collapse with respect to fiducial results, where rates optimized on calculations of stable $fp$-shell nuclei are used. Our results indicate that systematic microscopic calculations and experimental measurements in the $N\approx 50$ neutron rich region are desirable for realistic simulations of the core-collapse.