Sensitivity of nuclear statistical equilibrium to nuclear uncertainties during stellar core collapse

I have systematically investigated the equations of state (EOSs) in nuclear statistical equilibrium under thermodynamic conditions relevant for core collapse of massive stars by varying the bulk properties of nuclear matter, the mass data for neutron-rich nuclei, and the finite-temperature modifications of the nuclear model. It is found that the temperature dependence of the nuclear free energies has a significant impact on the entropy and nuclear composition, which affect the dynamics of core-collapse supernovae. There is a little influence from the bulk properties and the mass data. For all models, common nuclei that are likely to contribute to core-deleptonization are those near $Z\approx 30$ and $N\approx 50$. A model with a semi-empirical expression for internal degrees of freedom, however, overestimates the number densities of magic nuclei with $N\approx 50$ and 82, while a model in which nuclear shell effects are not considered underestimates the number densities of heavy nuclei, and especially of the magic nuclei. Other models, which include the temperature dependence of shell effects in the internal degrees of freedom and/or in the nuclear internal free energy, indicate that the difference in population between magic nuclei and non-magic nuclei disappears as the temperature increases. The construction of complete statistical EOS will require further theoretical and experimental studies of medium-mass, neutron-rich nuclei with proton numbers 25–45 and neutron numbers 40–85.

Figure 1

Nuclear species for which experimental nuclear mass data AME12 [51] (green crosses) have been adopted. Theoretical mass data are available in extended regions in the (N, Z) plane inside the following contours: FRDM [52] (blue solid line), HFB24 [53] (magenta dotted line), KTUY [29] (orange dashed line), and WS4 [54] (cyan double-dotted line). The red circles indicate nuclei for which the data are obtained from Rauscher's partition function [39]. The black dashed lines denote the neutron- and proton-magic numbers.

Figure 2

Free energy per baryon for symmetric nuclear matter (left panel, $x=0.5$) and for asymmetric nuclear matter (right panel, $x=0.1$) for parameter sets B (black solid lines), D (magenta dashed-dotted line), and E (cyan double-dotted dashed line) at $T=0$ MeV (thick lines), 5 MeV (medium lines), and 10 MeV (thin lines).

Figure 3

Critical temperatures for bulk nuclear matter, above which the bulk pressure has no local minimum, as a function of charge fraction for parameter sets B (black solid lines), D (magenta dashed-dotted line), and E (cyan double-dotted dashed line).

Figure 4

Shell energies per baryon for models 2FD (top-left panel), 2FE (top-right panel), 2KE (bottom-left panel), and 2WE (bottom-right panel) at $T=0$ MeV (black crosses), 1 MeV (cyan pluses), and 3 MeV (magenta circles).

Figure 5

Effective internal degrees of freedom for all nuclei for models 1E (black dashed lines) and 2FE (blue crosses), as calculated from Eq. (17); semi-empirical expression for internal degrees of freedom as functions of mass number, as given by Eq. (16) and provided by Fai and Randrup [36] (green dashed lines); and internal partition functions in tabular form of Raucher [39] (red circle dots) at $T=1$ MeV (top-left panel), 3 MeV (top-right panel), 5 MeV (bottom-left panel) and 10 MeV (bottom-right panel).

Figure 6

Temperatures (red solid lines) and charge fractions (blue dashed lines) as a function of density at the centers of the collapsing cores of supernova progenitors of $15M_{\odot }$ (thick lines) and $25M_{\odot }$ (thin lines) [58].

Figure 7

Mass fractions $X_{AZ}$ in the $(N,Z)$ plane at $({\rho }_B,T,Y_p)=(1.9\times {10}^{11}\mathrm{g}/{\mathrm{cm}}^3$, 1.3 MeV, 0.36) for the collapsing core of a $25M_{\odot }$ supernova progenitor for models 1E (top-left panel), 2FE (top-right panel), 3FE (bottom-left panel), and 4FE (bottom-right panel).

Figure 8

Mass fractions $X_{AZ}$ in the $(N,Z)$ plane at $({\rho }_B,T,Y_p)=(2.0\times {10}^{12}\mathrm{g}/{\mathrm{cm}}^3$, 1.8 MeV, 0.28) for the collapsing core of a $15M_{\odot }$ supernova progenitor for models 1E (top-left panel), 2FE (top-right panel), 3FE (bottom-left panel), and 4FE (bottom-right panel).

Figure 9

Average mass numbers (thick lines) and proton numbers (thin lines) at the centers of the collapsing cores of supernova progenitors of $15M_{\odot }$ (left panel) and $25M_{\odot }$ (right panel) for models 1B (black dashed-dotted lines), 1D (black double-dotted dashed lines), 1E (black solid lines), 2FB (blue dashed-dotted lines), 2FE (blue solid lines), 2KE (blue dashed lines), 3FE (green solid lines), 3KE (green dashed lines), 3HE (green dotted lines), 3WE (green double-dotted lines), and 4FE (red solid lines).

Figure 10

Total mass fractions of heavy nuclei at the centers of the collapsing cores of supernova progenitors of $15M_{\odot }$ (left panel) and $25M_{\odot }$ (right panel) for models 1B (black dashed-dotted lines), 1D (black double-dotted dashed lines), 1E (black solid lines), 2FB (blue dashed-dotted lines), 2FE (blue solid lines), 2KE (blue dashed lines), 3FE (green solid lines), 3KE (green dashed lines), 3HE (green dotted lines), 3WE (green double-dotted lines), and 4FE (red solid lines).

Figure 11

Baryonic entropies per baryon at the centers of the collapsing cores of supernova progenitors of $15M_{\odot }$ (left panel) and $25M_{\odot }$ (right panel) for models 1B (black dashed-dotted lines), 1D (black double-dotted dashed lines), 1E (black solid lines), 2FB (blue dashed-dotted lines), 2FE (blue solid lines), 2KE (blue dashed lines), 3FE (green solid lines), 3KE (green dashed lines), 3HE (green dotted lines), 3WE (green double-dotted lines), and 4FE (red solid lines).