Hot and dense homogeneous nucleonic matter constrained by observations, experiment, and theory

We construct a new class of phenomenological equations of state for homogeneous matter for use in simulations of hot and dense matter in local thermodynamic equilibrium. We construct a functional form which respects experimental, observational, and theoretical constraints on the nature of matter in various density and temperature regimes. Our equation of state (EOS) matches (i) the virial coefficients expected from nucleon-nucleon scattering phase shifts, (ii) experimental measurements of nuclear masses and charge radii, (iii) observations of neutron star radii, (iv) theory results on the equation of state of neutron matter near the saturation density, and (v) theory results on the evolution of the EOS at finite temperatures near the saturation density. Our analytical model allows one to compute the variation in the thermodynamic quantities based on the uncertainties in the nature of the nucleon-nucleon interaction. Finally, we perform a correction to ensure the equation of state is causal at all densities, temperatures, and electron fractions.

Figure 1

Fit of virial coefficients to data. The points at $T=0.1$ MeV are computed through effective range expansion.

Figure 2

Three figures which show how the full EOS compares to the limiting forms. The top panel compares the full free energy to the result from the virial expansion and shows that they match at lower densities where the fugacities are much smaller than 1. The middle panel shows that the result for neutron matter matches the QMC free energy at low densities, the neutron star free energy at densities reached in the neutron star interiors, and is softened at high densities to ensure a speed of sound less than the speed of light. The bottom panel shows that free energy starts to deviate from the Skyrme interaction at higher temperatures as the corrections from the chiral EOS begin to contribute. These panels show the result from one of many EOSs generated in this work.

Figure 3

The probability distribution for the free energy per baryon at $n_B=0.004{\mathrm{fm}}^{-3},Y_e=0.5$, and $T=10\mathrm{MeV}$.

Figure 4

The probability distribution for the free energy per baryon at $n_B=0.16{\mathrm{fm}}^{-3},Y_e=0.01$, and $T=0.1\mathrm{MeV}$.

Figure 5

The probability distribution for the free energy per baryon at $n_B=0.16{\mathrm{fm}}^{-3},Y_e=0.01$, and $T=10\mathrm{MeV}$.

Figure 6

The probability distribution for the free energy per baryon at $n_B=0.48{\mathrm{fm}}^{-3},Y_e=0.10$, and $T=0.1\mathrm{MeV}$.

Figure 7

The probability distribution for the free energy per baryon at $n_B=0.48{\mathrm{fm}}^{-3},Y_e=0.5$, and $T=0.1\mathrm{MeV}$.

Figure 8

Density plots showing the free energy per baryon for matter at $Y_e=0.1$ and $Y_e=0.4$ over the full range of densities and temperatures considered in this work for one parametrization. Points with a free energy per baryon less than $-1000\mathrm{MeV}$ are set equal to $-1000\mathrm{MeV}$ to make the high-density behavior more clear. The main variation in the free energy per baryon from the lower-right region to the upper-left region in these plots is dominated by the virial contribution to the EOS. The degenerate part of the EOS is clear in the large increase in the free energy per baryon on the right-hand boundary (at large baryon densities).

Figure 9

Values of $n_B$ and $c_s^2$ explored by the EOS at $Y_e=0.1$ and $\tilde{s}=0.5$. The different curves represent models which differ only by a different value of the parameter $\varphi$.

Figure 10

Values of $n_B$ and $c_s^2$ explored by the EOS at $Y_e=0.4$ and $\tilde{s}=0.5$. The different curves represent randomly selected models. Most of them have two kinks. The first one (often very slight) is the residual impact of fixing the speed of sound in neutron matter at high densities to $\varphi$ as shown in Fig. 9. The second kink between $1.3<n_B^{*}<1.8{\mathrm{fm}}^{-3}$ is due to the use of the C&P prescription to decrease the speed of sound above $n_B=n_B^{*}$.

Figure 11

Contour plot of $ds/dT$ as a function of $n_B$ and $T$ explored by the EOS for one of our EOS parametrizations. The speed of sound correction from the C&P prescription has not yet been applied. The blue line indicates the value $n_B=n_B^{*}$. The region above this line is replaced with the C&P EOS (including the region where $ds/dT<0)$.

Figure 12

Values of $n_B$ and $s$ explored by the EOS. The dots represent boundaries where $c_s^2=0.9$ and the C&P solution starts to take effect.