Thermodynamically adaptive piecewise polytropic equation of state for neutron stars

The equation of state (EoS) governing high-density matter inside neutron stars can exhibit phase transitions (PTs), which have the potential to induce anomalous wave structures in hydrodynamics and alterations in star stability. However, existing analytic models that are employed to replace realistic tabulated EoS in simulations often fall short in accurately capturing the intricate thermodynamics associated with these PT. Modeling PTs poses a challenge as they occur in thin density regions yet significantly impact the description of matter, rendering the EoS nonconvex and leading to a distinct hydrodynamic behavior. In this paper, we present a new analytic model for tabulated EoS with special focus on the modeling of PTs by means of a thermodynamically adaptive slope piecewise polytropic (T-ASPP) approximation, able to replicate nonconvex EoS and therefore triggering anomalous wave dynamics. In addition, we present a comprehensive analysis of the stellar properties (mass, radius, and tidal deformability) obtained from our model and compare them with those derived from the tabulated EoS. The results demonstrate that our T-ASPP EoS model provides a fair approximation to the neutron star properties. Furthermore, we investigate the hydrodynamic discrepancies between including and excluding the proper thermodynamics of PTs by examining two Riemann problems. This analysis sheds light on the significant impact of incorporating the accurate thermodynamics of PTs on the hydrodynamic behavior.

Figure 1

Region around the PT, marked in black vertical lines, for PS EoS. Tabulated data in points, fit by PP model in dashed line, T-ASPP model in continuous line. From top to bottom: pressure, fluid sound speed, and fundamental derivative.

Figure 2

Region around the PT, marked in black vertical lines, for ALF1 EoS. Tabulated data in points, fit by PP model in dashed line, T-ASPP model in continuous line. From top to bottom: pressure, fluid sound speed, and fundamental derivative.

Figure 3

Numerical solution of cold blast wave 1 at time $t=0.2$ using ALF1 EoS. In dots, there is the solution using the PP model for the EoS. In crosses, there is the solution using the T-ASPP model.

Figure 4

Numerical solution of cold blast wave 2 at time $t=0.2$ using ALF1 EoS. In dots, there is the solution using the PP model for the EoS. In crosses, there is the solution using the T-ASPP model.