Causal representations of neutron-star equations of state

Parametrized representations of the equation of state play an important role in efforts to measure the properties of the matter in the cores of neutron stars using astronomical observations. New representations are presented here that are capable of representing any equation of state to any desired level of accuracy, while automatically imposing causality and thermodynamic stability constraints. Numerical tests are presented that measure how accurately and efficiently these new parameterizations represent a collection of causal nuclear-theory model equations of state.

Figure 1

Curves illustrate 34 nuclear-theory models of the neutron-star equation of state, $\epsilon =\epsilon (p)$. The density $\epsilon$ and pressure $p$ (divided by the speed of light squared) are displayed here in cgs units, ${\mathrm{g}/\mathrm{cm}}^3$.

Figure 2

Curves illustrate the adiabatic index $\mathrm{\Gamma }(p)$ for the 27 causal nuclear-theory model equations of state used to test the accuracy and efficiency of various parametric representations.

Figure 3

Curves illustrate the sound speed function $\mathrm{\Upsilon }(p)=[c^2-v^2(p)]/v^2(p)$ for 27 nuclear-theory model equations of state that satisfy the causality condition, $\mathrm{\Upsilon }(p)\ge 0$, in the pressure domain of interest to neutron-star interiors.

Figure 4

Curves illustrate the sound speed function $\mathrm{\Upsilon }(h)$ for 27 nuclear-theory model equations of state that satisfy the causality condition, $\mathrm{\Upsilon }(h)\ge 0$, in the enthalpy domain of interest to neutron-star interiors.

Figure 5

Residuals ${\mathrm{\Delta }}_n$ are illustrated as functions of $n$ (the number of parameters ${\upsilon }_k$ used) for the pressure-based causal piecewise-analytical (PB-C-PA) representations of 27 causal nuclear-theory model equations of state.

Figure 6

Residuals ${\mathrm{\Delta }}_n$ are illustrated as functions of $n$ (the number of parameters ${\upsilon }_k$ used) for the pressure-based causal spectral (PB-C-S) representations of 27 causal nuclear-theory model equations of state.

Figure 7

Residuals ${\mathrm{\Delta }}_n$ are illustrated as functions of $n$ (the number of parameters ${\upsilon }_k$ used) for the enthalpy-based causal spectral (HB-C-S) representations of 27 causal nuclear-theory model equations of state.

Figure 8

Convergence of the average residuals ${\mathrm{\Delta }}_n$ is illustrated for the seven different representations studied here. Piecewise-analytical representations are shown with square data points (and colored red), while the spectral representations are shown with round data points (and colored blue).