Impact of late-time neutrino emission on the diffuse supernova neutrino background

In the absence of high-statistics supernova neutrino measurements, estimates of the diffuse supernova neutrino background (DSNB) hinge on the precision of simulations of core-collapse supernovae. Understanding the cooling phase of protoneutron star (PNS) evolution ($\gtrsim 1\mathrm{s}$ after core bounce) is crucial, since approximately 50% of the energy liberated by neutrinos is emitted during the cooling phase. We model the cooling phase with a hybrid method by combining the neutrino emission predicted by 3D hydrodynamic simulations with several cooling-phase estimates, including a novel two-parameter correlation depending on the final baryonic PNS mass and the time of shock revival. We find that the predicted DSNB event rate at Super-Kamiokande can vary by a factor of $\sim 2–3$ depending on the cooling-phase treatment. We also find that except for one cooling estimate, the range in predicted DSNB events is largely driven by the uncertainty in the neutrino mean energy. With a good understanding of the late-time neutrino emission, more precise DSNB estimates can be made for the next generation of DSNB searches.

Figure 1

Comparison of the time-integrated ${\overline{\nu }}_e$ spectral parameters in the cooling phase of PNS evolution shown against the final baryon mass of the PNS. Here we compare those quantities of the Hüdepohl [74], Nakazato [73], Bollig [60], and Sumiyoshi [78] (integrated from shock revival time to the end of simulation time: $\sim 10$, 20, $\sim 7$, and $\sim 60\mathrm{s}$, respectively). Their EOSs are the Shen/LS220, Shen, SFHo, and TM1/TM1e, respectively. See text and Table 1 for details. There are other differences not mentioned here, but these serve to show some dependence of neutrino emission on final PNS mass and hint at systematic differences due to e.g., EOS. More simulation details can be found in Table 1.

Figure 2

The functional form from Ref. [85] (red) using the effective density correction $g$, and opacity boosting factor $\beta$, compared to the hydrodynamic neutrino data for the $9M_{\odot }$ progenitor (black). These parameters are chosen to best agree with the mean energy data and then are used in the luminosity function. Around the end of the simulation time, the functional form underpredicts the neutrino luminosity and mean energy. Later comparisons show that integrating these functions still gives reasonable results, but ideally would be applied to longer-duration ($\gtrsim 10\mathrm{s}$) data.

Figure 3

Time-integrated (from shock revival time to 20 s) neutrino spectral parameters (top panel, ${\overline{\nu }}_e$ energy liberated; bottom panel, ${\overline{\nu }}_e$ mean energy) from the Supernova Neutrino Database [73]. Approximately linear trends are visible with respect to the PNS final baryon mass (x-axis) and shock revival time (100, 200, and 300 ms as labeled); see Eqs. (1) and (2). With these linear trends, we can estimate the late-phase neutrino emission for combinations of shock revival and final PNS mass.

Figure 4

To properly compare these neutrino spectral parameters, we time integrate the liberated and mean energies from shock revival time to $\sim 10\mathrm{s}$. We then renormalize the $\sim 10\mathrm{s}$ revival-time–final-mass correlations using a sum-of-least-squares method to best fit the four Hüdepohl progenitors. This is performed for the Shen and LS220 EOSs to capture some EOS and simulation dependence on the integrated neutrino spectral parameters.

Figure 5

Time-integrated (represents integration from 0 to $\sim 20\mathrm{s}$ postbounce) neutrino spectral parameters using the Burrows simulation set for the hydrodynamic phase and five estimates, as labeled, for adding the cooling phase. In energy liberated, Corr is systematically lower than the other four estimates. In mean energy, there is a fairly clear hierarchy where Const is always highest and Corr lowest. For each method, the early-phase neutrino emission is calculated using the SFHo EOS, but in the Corr and RenormShen methods the late-phase neutrino emission is dependent on the Shen EOS and the RenormLS method is dependent on the LS220 EOS.

Figure 6

Energy spectra for the $\text{early}+\text{five}$ late-phase neutrino emission estimates. These spectra include the contributions from an ONeMg progenitor and $\sim 8\%$ failed supernovae for progenitors with initial masses $>40M_{\odot }$. The BH neutrino signal in this figure assumes the representative s40 model, but choosing s40s7b2 gives qualitatively similar results. Note that Analyt and RenormLS overlap.

Figure 7

Same as Fig. 3 but for ${\nu }_e$.

Figure 8

Same as Fig. 3 but for ${\nu }_x$.

Figure 9

Same as Fig. 4 but for ${\nu }_e$.

Figure 10

Same as Fig. 4 but for ${\nu }_x$. In the bottom panel, the renormalization constant for mean energy is equal to 1 between Corr and RenormShen.