Exciting prospects for detecting late-time neutrinos from core-collapse supernovae

The importance of detecting neutrinos from a Milky Way core-collapse supernova is well known. An understudied phase is proto-neutron star cooling. For SN 1987A, this seemingly began at about 2 s and is thus probed by only 6 of the 19 events (and only the ${\overline{\nu }}_e$ flavor) in the Kamiokande-II and IMB detectors. With the higher statistics expected for present and near-future detectors, it should be possible to measure detailed neutrino signals out to very late times. We present the first comprehensive study of neutrino detection during the proto-neutron star cooling phase, considering a variety of outcomes, using all flavors, and employing detailed detector physics. For our nominal model, the event yields (at 10 kpc) after 10 s—the approximate duration of the SN 1987A signal—far exceed the entire SN 1987A yield, with $\simeq 250$ ${\overline{\nu }}_e$ events (to 50 s) in Super-Kamiokande, $\simeq 110$ ${\nu }_e$ events (40 s) in the Deep Underground Neutrino Experiment (DUNE), and $\simeq 10$ ${\nu }_{\mu },{\nu }_{\tau },{\overline{\nu }}_{\mu },{\overline{\nu }}_{\tau }$ events (to 20 s) in the Jiangmen Underground Neutrino Observatory. These data would allow unprecedented probes of the proto-neutron star, including the onset of neutrino transparency and hence its transition to a neutron star. If a black hole forms, even at very late times, this can be clearly identified. But will the detectors fulfill their potential for this perhaps once-ever opportunity for an all-flavor, high-statistics detection of a core collapse? Maybe. Further work is urgently needed, especially for DUNE to thoroughly investigate and improve its MeV capabilities.

Figure 1

Schematic illustration of the ${\overline{\nu }}_e$ emission profile from a successful core-collapse supernova. The time axis is linear before 0 s, linear from 0 to ${10}^{-1}\mathrm{s}$ with a different scale, and logarithmic after ${10}^{-1}\mathrm{s}$. The different physical phases—pre-SN (red), accretion/pre-explosion (blue), and cooling (green)—are shaded, with key periods noted. The labels on the top axis show common—but not physically motivated—descriptions.

Figure 2

Example total neutrino luminosities for three cases: PNS cooling, BH formation due to a failed supernova [28], and BH formation due to a soft nuclear equation of state [42].

Figure 3

Evolution of the internal structure of the PNS. The panels show the total luminosity carried by neutrinos (upper left), total lepton number luminosity carried by neutrinos (upper right), entropy (lower left), and lepton fraction (lower right). All quantities are plotted as a function of enclosed baryonic mass. The colors of the lines encode the post-bounce time, which can be read off the color bar at the top of the plot. The propagation of the SN shock is clearly visible until it is excised from the grid, as described in Sec. 3. After this, the cooling and deleptonization of the PNS occur on a time scale of tens of seconds.

Figure 4

Evolution of the luminosities (left panel) and average energies (right panel) of each flavor of neutrinos, as well as selected ratios. The thin gray line is the functional fit in Eq. (2).

Figure 5

Left: evolution of the number fluxes and the electron-flavors difference. Right: cumulative fractions of total emitted energy and lepton number (note that the $x$-axis does not start at zero).

Figure 6

Left: event rate (more precisely, the counts in each log-time bin) of ${\overline{\nu }}_e$ in Super-K due to the inverse-beta interaction (with a detector threshold of 3.5 MeV). The vertical error bars show the Poisson uncertainties on the counts and the horizontal error bars show the bin widths. Cumulative counts remaining beyond selected times (1, 3, 10, and 30 s) are shown on the top axis. At late times (green shading), PNS cooling is the dominant emission mechanism and our PNS model is at its most reliable. At early times (blue shading, with an uncertain boundary), these assumptions are less valid. Right: spectra of positron kinetic energy in Super-K in selected time ranges, as marked. The spectra are individually normalized to facilitate comparison of their shapes. The vertical dotted line at 3.5 MeV indicates the assumed Super-K threshold.

Figure 7

Similar to Fig. 6, but for ${\nu }_e$ events in DUNE due to neutrino-argon interactions (first case, based on primary-electron energy). Left: event rate for a threshold of 6 MeV in electron kinetic energy. In addition to the signal rate, we show the background rate using the same bins (equal steps in ${\log }_{10}t$). Because the background rate $dN/dt$ is constant, the number of background counts per bin, $\mathrm{\Delta }N=2.3(tdN/dt)\mathrm{\Delta }{\log }_{10}t$, rises linearly with $t$. Right: for the spectra, the vertical dotted line at 6 MeV indicates the assumed DUNE threshold.

Figure 8

Similar to Fig. 7 for DUNE, but for the second case, based on neutrino energy. Left: event rate for a threshold of 10 MeV in neutrino energy. Right: solid and dashed lines show the smeared and true neutrino energy spectra. The vertical dotted line at 10 MeV indicates the assumed DUNE threshold.

Figure 9

Similar to Fig. 6, but for the neutral-current events in JUNO due to neutrino-proton elastic scattering. Left: event rate for two cases: a solid line for a detection threshold of 0.2 MeV (nominal design) and a dashed line for a detection threshold of 0.1 MeV (optimistic). The counts on the top axis and the background rate are both for the 0.2 MeV case. The thin solid line shows the ${\nu }_x$ contribution for the 0.2 MeV case. Right: for the spectra, we plot $EdN/dE=dN/d\ln E=(2.3{)}^{-1}dN/d\log E$ to match our log-$E$ axis. The vertical dotted lines at 0.2 and 0.1 MeV indicate the possible thresholds.

Figure 10

Prospects for detecting BH formation in Super-K, showing the parameter dependence on $t_{\mathrm{BH}}$. The left $y$-axis shows the number of events after the BH formation time, $t_{\mathrm{BH}}$, that would have been expected in our nominal PNS model. The right $y$-axis shows the corresponding significance level for identifying BH formation. The vertical lines mark the times corresponding to detection significances of 40, 10, 5, and $3\sigma$.

Figure 11

Expected measurement precision for the transition time. For Case 1 (NS formation), this is the transparency time, $t_{\mathrm{NS}}$, when there is a superexponential drop relative to the $1/t$ trend. For Case 2 (early BH formation), this is the BH formation time, $t_{\mathrm{BH}}$, where we assume the sharp truncation occurs relative to the $1/t$ trend. For Case 3 (late BH formation), we assume the sharp truncation occurs relative to the superexponential drop of the NS-forming case.