Impact of electron capture rates for nuclei far from stability on core-collapse supernovae

The impact of electron-capture (EC) cross sections for neutron-rich nuclei on the dynamics of core collapse during infall and early post-bounce is studied by performing spherically symmetric simulations in general relativity using a multigroup scheme for neutrino transport and full nuclear distributions in extended nuclear statistical equilibrium models. We thereby vary the prescription for EC rates on individual nuclei, the nuclear interaction for the equation of state, the mass model for the nuclear statistical equilibrium distribution, and the progenitor model. In agreement with previous works, we show that the individual EC rates are the most important source of uncertainty in the simulations, while the other inputs only marginally influence the results. A recently proposed analytic formula to extrapolate microscopic results on stable nuclei for EC rates to the high densities and temperatures and the neutron-rich region, with a functional form motivated by nuclear-structure data and parameters fitted from large scale shell-model calculations, is shown to lead to a sizable (16%) reduction of the electron fraction at bounce compared to more primitive prescriptions for the rates, leading to smaller inner core masses and slower shock propagation. We show that the EC process involves $\approx 170$ different nuclear species around ${}^{86}\mathrm{Kr}$, mainly in the $N=50$ shell closure region, and establish a list of the most important nuclei to be studied in order to constrain the global rates.

Figure 1

EC rate evolution (labeled by baryon density) in the central grid cell during infall using different prescriptions for the EC rate on nuclei; see text for details. The vertical dashed lines show the density above which $\beta$ equilibrium sets in.

Figure 2

Time evolution of the electron fraction $Y_e(r=0)$ for the central element of the numerical grid for all three EC models during the late prebounce phase.

Figure 3

Radial profiles of the electron fraction at bounce employing the three different EC rate prescriptions.

Figure 4

Comparison of shock propagation at different instants during the early post-bounce phase with the three different EC rate prescriptions.

Figure 5

Time evolution of electron neutrino luminosity around bounce, for the three different EC rate prescriptions.

Figure 6

Neutrino inverse mean free path as functions of baryon density in the central numerical cell with reactions computed either on a single mean nucleus (SNA) or on a statistical ensemble of nuclei (NSE): contribution of electron capture effects only (left panel) and scattering effects only (central panel). Electron fraction time evolution for both models (right panel).

Figure 7

Baryonic number of the most probable nucleus in the central element during infall as a function of time (labeled by the baryon number density). Three different mass models are considered.

Figure 8

Radial profile at the time of bounce of the baryonic number of the most probable nucleus (left), the entropy (central), and the electron fraction (right), using three different mass models.

Figure 9

Distribution of nuclei $(N,Z)$ for a chosen thermodynamic condition during the collapse before trapping: $k_{B}T=1$ MeV, ${\rho }_B=6.02\times {10}^{11}$ g ${\mathrm{cm}}^{-3}$, $Y_e=0.27$. Contour lines correspond to the cluster normalized probabilities (red to blue, more to less probable) for the original LS model (oval-shaped contour) and for the HFB-24 nuclear mass model. See text for details.

Figure 10

Upper panel: the instantaneous capture rate evaluated on a limited number $k$ of nuclei, normalized to the rate obtained taking the 200 most probable ones, as a function of the size of the sample. Nuclei are ordered according to their abundance. The labels give the instantaneous rate on the whole distribution, with lower rates corresponding to earlier times. Lower panel: the number of nuclei accounting for 50% of the total instantaneous rate is plotted as a function of the EC rate (dashed line). The number of species which are not included in the tabulated microscopic EC rates [21, 22, 24, 25] is plotted with a solid line.

Figure 11

Time integrated relative deleptonization rate (color scale) associated to the different nuclear species identified by their proton $Z$ and neutron $N$ number. The black contour indicates the most relevant nuclei for EC identified by Sullivan et al. [12] and Titus et al. [18]. The red, blue, and green contours indicate the nuclei for which microscopic rates are available from Langanke and Martinez-Pinedo [22], Oda et al. [24], and Pruet and Fuller [25], respectively. Nuclei with experimentally known masses are situated between the gray lines.