Nuclear pasta in hot neutron-star matter and proto-neutron stars

Abstract

We investigate nuclear pasta phases appearing in hot neutron-star matter based on the compressible liquid-drop model, where the matter consists of a dense liquid phase and a dilute gas phase separated by a sharp interface. The surface tension is calculated self-consistently from the Thomas-Fermi approximation, and it depends on temperature and isospin asymmetry. We employ relativistic mean-field models with different symmetry energy slopes to describe nuclear interactions. It is found that the TM1e model with a small symmetry energy slope of $L=40$ MeV predicts various pasta shapes at low temperatures, while the TM1 model with $L=110.8$ MeV yields only the droplet configuration up to the crust-core transition density. We examine the occurrence and influence of pasta phases in proto-neutron stars with a constant entropy per baryon. These pasta phases may occur in the inner crust with a thickness of about $1.2$ km, playing an important role in the thermal evolution of the star.