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.

Figures (14)

• Figure 1: Energy per baryon $E/A$ of symmetric nuclear matter and pure neutron matter as a function of the baryon number density $n_b$ in the TM1e and TM1 models.
• Figure 2: Symmetry energy $E_{\rm sym}$ as a function of the baryon number density $n_b$ in the TM1e and TM1 models.
• Figure 3: Phase diagrams in the $n_b$--$T$ plane obtained in the CLD method using the TM1e and TM1 models. Different colors indicate the regions for different pasta shapes. The black dot-dashed lines indicate the boundary of nonuniform matter obtained from a bulk calculation without finite-size effects. The blue solid lines correspond to isentropic trajectories with entropy per baryon $S=0.5,\, 1,\, 2$.
• Figure 4: Average proton fraction $Y_p$ as a function of the baryon density $n_b$ in the matter under the conditions of charge neutrality and $\beta$-equilibrium. The results for the TM1e and TM1 models are shown in the left and right panels, respectively. The dashed lines indicate the proton fraction of uniform matter.
• Figure 5: Density profiles of nucleons and electrons within the Wigner-Seitz cell for a droplet configuration at $n_b=0.02 \, {\rm fm^{-3}}$. The results obtained with the TM1e and TM1 models are shown in the left and right panels, respectively. The cell boundary and the sharp interface between the liquid and gas phases are indicated by the vertical dashed lines.