Hot and dense matter equation of state probability distributions for astrophysical simulations

We add an ensemble of nuclei to the equation of state for homogeneous nucleonic matter to generate a new set of models suitable for astrophysical simulations of core-collapse supernovae and neutron star mergers. We implement empirical constraints from (i) nuclear mass measurements, (ii) proton-proton scattering phase shifts, and (iii) neutron star observations. Our model is also guided by microscopic many-body theory calculations based on realistic nuclear forces, including the zero-temperature neutron matter equation of state from quantum Monte Carlo simulations and thermal contributions to the free energy from finite-temperature many-body perturbation theory. We ensure that the parameters of our model can be varied while preserving thermodynamic consistency and the connection to experimental or observational data, thus providing a probability distribution of the astrophysical hot and dense matter equation of state. We compare our results with those obtained from other available equations of state. While our probability distributions indeed represent a large number of possible equations of state, we cannot yet claim to have fully explored all of the uncertainties, especially with regard to the structure of nuclei in the hot and dense medium.

Figure 1

Baryon number fractions $X_i$ for protons, light nuclei, and a sum over heavy nuclei, as a function of density for $Y_e=0.1$ and $Y_e=0.5$ for four temperatures. In the top four panels, the neutron baryon number fraction is omitted to help make the heavy nuclei more visible. In the bottom four panels, the neutron mass fraction is hidden behind the proton mass fraction at low densities where these two quantities coincide. The right edge of the plots is chosen to be $n_B=n_0$ and nuclei always disappear at a baryon density below $n_0$ (independent of electron fraction or temperature).

Figure 2

Baryon number fractions $X_n$ and $X_p$ as a function of baryon density and temperature for $Y_e=0.01$, 0.1, 0.3, 0.5, respectively. The right edge of the plots is chosen to be $n_B=n_0$ where nuclei disappear (independent of electron fraction or temperature).

Figure 3

Baryon number fractions $X_{\alpha }$ and $X_{\mathrm{nuclei}}$ as a function of baryon density and temperature for $Y_e=0.01$, 0.1, 0.3, 0.5, respectively. The right edge of the plots is chosen to be $n_B=n_0$ where nuclei disappear (independent of electron fraction or temperature).

Figure 4

Average mass(top)/proton(bottom) number for $Y_e=0.01$, 0.1, 0.3, 0.5, respectively.

Figure 5

Average mass (top four panels) and proton (bottom four panels) number for $T=1$, 3, 5, $7\mathrm{MeV}$, respectively.

Figure 6

Average mass number for $T=1$, 3, 5, and $7\mathrm{MeV}$, for the LS220, SFHO, FSU21, NRAPR, STOS, and FYSS EOSs.

Figure 7

Mass fraction of nuclei in the nuclear chart for matter at four selected points, comparable with Ref. [19].

Figure 8

Isotopic distribution for the same four points shown in Fig. 7.

Figure 9

Probability distribution for the average nuclear mass number for equations of state generated by our code at four points.