Medium modifications for light and heavy nuclear clusters in simulations of core collapse supernovae: Impact on equation of state and weak interactions

The present article investigates the role of heavy nuclear clusters and weakly bound light nuclear clusters based on a newly developed equation of state for core collapse supernova studies. A novel approach is brought forward for the description of nuclear clusters, taking into account the quasiparticle approach and continuum correlations. It demonstrates that the commonly employed nuclear statistical equilibrium approach, based on noninteracting particles, for the description of light and heavy clusters becomes invalid for warm nuclear matter near the saturation density. This has important consequences for studies of core collapse supernovae. To this end, we implement this nuclear equation of state provided for arbitrary temperature, baryon density, and isospin asymmetry, to spherically symmetric core collapse supernova simulations to study the impact on the dynamics as well as on the neutrino emission. For the inclusion of a set of weak processes involving light clusters the rate expressions are derived, including medium modifications at the mean-field level. A substantial impact from the inclusion of a variety of weak reactions involving light clusters on the post bounce dynamics and on the neutrino emission could not be found.

Figure 1

Effective nuclear binding energy for selected hydrogen isotopes in graphs (a), (c), and (e), and helium isotopes in graphs (b), (d), and (f), for two representative conditions, with $T=5$ MeV and $Y_e=0.1$ (solid lines) as well as $T=10$ MeV and $Y_e=0.2$ (dashed lines), comparing the gRDF approach including a shift due to Pauli blocking (blue lines) and the QS approach of Ref. [17] (gray lines).

Figure 2

Nuclear composition; mass fractions for neutrons and protons in graph (a), hydrogen isotopes in graph (b), helium isotopes in graph (c), and for heavy nuclei averaging over all species with $Z>2$ in graph (d), as well as their average atomic mass $A$ and charge $Z$ in graph (e), and furthermore including the nucleon effective mass $m_N^{*}$ in graph (f), and the mean-field potential difference $U_n-U_p$ in graph (g), as a function of the restmass density $\rho$ in units of the saturation density ${\rho }_0$, comparing the HS(DD2) modified NSE model (black lines) of Ref. [9] and the gRDF(DD2) model (blue lines) for selected condition, $T=5$ MeV and $Y_e=0.1$.

Figure 3

The same quantities are shown in graphs (a)–(g) as in Fig. 2 but for different conditions, $T=10$ MeV and $Y_e=0.2$.

Figure 4

Radial profiles of selected quantities; velocity $u$ in graph (a), restmass density $\rho$ in graph (b), electron fraction $Y_e$ in graph (c), temperature $T$ and entropy per baryon $s$ in graph (d), as well as various mass fraction $X_i$ in graphs (e), (g), and (h), and the heavy nuclei in graph (f) as well as the composition characterised by the average atomic mass $\langle A\rangle$ and charge $\langle Z\rangle$, as a function of the enclosed baryon mass $M$ at about 0.5 ms before core bounce, comparing two SN simulations with the HS(DD2) EOS of Ref. [9] (black lines) and the newly developed gRDF(DD2) EOS (blue lines).

Figure 5

The same quantities are shown in graphs (a)–(h) as in Fig. 4 but at core bounce.

Figure 6

The same quantities are shown in graphs (a)–(h) as in Fig. 4 but with respect to the radius $R$ at 10 ms after core bounce.

Figure 7

The same quantities are shown in graphs (a)–(h) as in Fig. 4 but with respect to the radius $R$ at 100 ms after core bounce.

Figure 8

The same quantities are shown in graphs (a)–(h) as in Fig. 4 but with respect to the radius $R$ at 300 ms after core bounce.

Figure 9

Post bounce evolution of the shock radii, $R_{\mathrm{shock}}$, in graphs (a) and of the neutrinospheres, $R_{\nu }$, for ${\nu }_e$ in graph (b) and ${\overline{\nu }}_e$ in graph (c) as well as muon- and tau-(anti)neutrinos collectively denoted as ${\nu }_{\mu /\tau }$ in graph (d) and the corresponding densities, ${\rho }_{\nu }$, for ${\nu }_e$ in graph (e) and ${\overline{\nu }}_e$ in graph (f) as well as muon- and tau-(anti)neutrinos ${\nu }_{\mu /\tau }$ in graph (g), comparing the SN simulations based on the HS(DD2) EOS (black lines) and the generalized relativistic density-functional approach gDRF(DD2) without (blue lines) and with weak processes involving light clusters (red lines). Note that the latter two lay indistinguishably on top of each other (see text for details).

Figure 10

Post bounce evolution of the neutrino luminosities, $L_{\nu }$, for (${\nu }_e,{\nu }_{\mu /\tau }$) in graph (a) and (${\overline{\nu }}_e,{\overline{\nu }}_{\mu /\tau }$) in graph (c), and average energies, $\langle E_{\nu }\rangle$, for (${\nu }_e,{\overline{\nu }}_e$) in graph (d) and (${\nu }_{\mu /\tau },{\overline{\nu }}_{\mu /\tau }$) in graph (e), comparing the SN simulations based on the HS(DD2) EOS (black lines) and the generalized relativistic density-functional approach gDRF(DD2) without (blue lines) and with weak processes involving light clusters (red lines). Note that the latter two lay indistinguishably on top of each other (see text for details). The inlay graph (b) shows a zoom in the ${\nu }_e$ deleptonization burst.

Figure 11

Charged current neutrino (top panels) and antineutrino opacity (bottom panels) comparing the processes with the unbound nucleons (green dash-dotted lines) including the inverse neutron decay (green solid lines) for ${\overline{\nu }}_e$, and (anti)neutrino absorption on ${}^2\mathrm{H}$ (solid dark red lines) as well as the inverse $e^{\pm }$ captures on ${}^2\mathrm{H}$ (dark red dashed lines), (anti)neutrino absorption on ${}^3\mathrm{H}$ and ${}^3\mathrm{He}$ (gray dash-dotted lines), and (anti)neutrino absorption on ${}^4\mathrm{H}$ and ${}^4\mathrm{He}$ (yellow dashed lines), for the two selected conditions (A) in graph (a) and (B) in graph (b) as listed in Table 3 in the left and right panels, respectively. Thick lines include all medium modifications, see therefore the rate expressions in Appendix pp3, while thin lines omit them.

Figure 12

SN simulation profiles with respect to the restmass density at 100 ms post bounce. Graph (a): mass fractions, $X_i$, for selected nuclear species. Graph (b): net neutrino heating rate, ${\dot{Q}}_{\nu }$, comparing gRDF(DD2) with (red dashed lines) and without (solid light blue lines) weak reactions involving light nuclei for ${\nu }_e$ (left panel) and ${\overline{\nu }}_e$ (right panel), as well as the inverse neutrino mean-free path, $1/\lambda$, for selected weak processes corresponding to the simulations with the gRDF(DD2) EOS including weak reactions with light clusters, also for ${\nu }_e$ (left panel) and ${\overline{\nu }}_e$ (right panel), distinguishing neutral current neutrino-nucleon scattering (solid blue lines), charged current neutrino absorption with unbound nucleons (dark green dash-dotted lines), ${}^2\mathrm{H}$ (thick solid dark red lines), inverse $e^{\pm }$ captures on ${}^2\mathrm{H}$ (thin dashed dark red lines), involving ${}^3\mathrm{H}$ and ${}^3\mathrm{He}$ (thick gray dash-dotted lines) as well as ${}^4\mathrm{H}$ and ${}^4\mathrm{He}$ (thick dashed dark yellow lines). The vertical black lines mark the locations of the neutrinospheres (dotted lines) and the shock position (solid lines).

Figure 13

Neutrino absorption cross section for reactions involving ${}^3\mathrm{H}$ and ${}^3\mathrm{He}$ (grey dash-dotted lines) as well as ${}^4\mathrm{H}$ and ${}^4\mathrm{He}$ (yellow dashed lines), in comparison to those for the charged current reactions (1)–(3) in Table 1, for ${\nu }_e$ in graph (a) and ${\overline{\nu }}_e$ in graph (b).