Supernova implications

A Type II supernova is due to the collapse of the iron core of a star with mass exceeding $\sim 8 M_\odot$. The core collapses into a neutron star or black hole. The initial collapse leads to a ms neutronization pulse of $\nu_e$ from $e^- p \mbox{$\rightarrow$}\mbox{$\nu_e$}n$. The collapsing core eventually bounces, with an expanding shock, leaving behind a dense hot core and neutrinosphere. The latter radiates neutrinos of all types over a period of $\sim$ 10 s. The characteristic temperature of the $\nu_\mu, \bar{\nu}_\mu, \nu_\tau, \bar{\nu}_\tau$ is $\sim$ 8 MeV. The $\nu_e$ and $\bar{\nu}_e$ stay in equilibrium longer due to charged current interactions with matter, implying smaller temperatures, e.g., $T_{\nu_e} \sim 3.5$ MeV, $T_{\bar{\nu}_e} \sim 4.5$ MeV [62]. Neutrinos are relevant because:

• Almost all (99%) of the energy ( ergs) is radiated in neutrinos. The spectacular optical effects are a perturbation.
• Observation of a neutrino burst may give an early warning of a supernova, with the Solar $\nu$ Early Warning System (SNEWS) network under organization [47].
• Neutrinos are important for the dynamics. Scattering of neutrinos radiated from the neutrinospere may revive a stalled shock, leading to the observed explosion.
• The $\nu$-heated supernova ejecta is a favored candidate for the site of the $r$-process, which refers to the synthesis of nuclei heavier than iron by the rapid capture of neutrons on a heavy core in a neutron-rich environment. However, some estimates [63] suggest that $\mbox{$\nu_e$}n \mbox{$\rightarrow$}e^- p$, with the $p$ immediately incorporated into an $\alpha$, will be too efficient at destroying neutrons, preventing the $r$-process. The situation can be worsened or improved in the presence of neutrino mixing.
• The kinematic effects of neutrino mass can distort the time and energy spectrum of the neutrinos. The observed Kamiokande and IMB events from SN 1987A, which were sensitive to $\bar{\nu}_e$ from the neutrinosphere, allowed a limit of around eV. This limit, as well as many other constraints, depended on the theoretical modelling of the supernova.
• A future supernova within our galaxy should yield large numbers of events in large detectors if they are running. This should allow much more stringent direct limits on $m_{\nu_\mu, \nu_\tau}$ than by any laboratory method [47]. For example, SNO should be sensitive to 30 eV, and Super K to 50 eV neutrinos [64]. A collapse into a black hole would provide a sharp cutoff in time for the neutrino signal, allowing even more precise constraints (in the few eV range) for all neutrino types [65]. With large numbers of events it will be possible to study the supernova dynamics in detail and to constrain other neutrino properties. SNO should be especially useful because it can separately observe $\nu_e$ , $\bar{\nu}_e$, and the neutral current scattering of all neutrinos.
• Neutrino mixing can lead to a variety of oscillation and MSW resonance effects. Because the densities are higher than in the Sun, there may be resonant conversions for higher $\Delta m^2$ than the solar neutrinos. In particular,
  • $\nu_e \leftrightarrow \nu_{\mu, \tau}$ conversions can increase the final $\nu_e$ energy because of the harder initial $\nu_{\mu, \tau}$ spectrum. This makes $\nu_e$ scattering more efficient in reviving the stalled shock. On the other hand, it aggravates the problem of destroying neutrons before they can participate in the $r$-process, excluding $\mbox{$\Delta m^2$}>$ few eV$^2$ escept for very small mixing [63].
  • For the LMA solar neutrino solution, there may have been a partial conversion of $\bar{\nu}_e$ and $\bar{\nu}_\mu$, in contrast with the observed SN 1987A spectrum [66,67]. However, it has recently been argued that matter effects may reduce this difficulty, or even help reconcile the observed Kamiokande and IMB spectra [68].
  • Minakata [21] argued that the observed spectra would be very different for an inverted spectrum, e.g., with the the dominant $\nu_e$ mass eigenstate heavier than $\nu_\tau$. This could lead to a determination of the sign of $\Delta m^2_{23}$.
  • It has been argued that active-sterile conversions could solve the $r$-process problem [69] by the sequence of $\mbox{$\nu_\mu$}\mbox{$\rightarrow$}\mbox{$\nu_s$}$ followed by $\mbox{$\nu_e$}\mbox{$\rightarrow$}\mbox{$\nu_\mu$}$.
• One expects a supernova in our galaxy on average every 30-100 years. This is an unfortunate mismatch with the practical human time scale for carrying out experiments, but we should make an attempt. Large neutrino detectors should be designed to run for a minimum of 10-20 yr, and preferably longer.