Supernova neutrino challenges

A principal `supernova neutrino challenge' is the computational difficulty of six-dimensional neutrino radiation hydrodynamics. The variety of resulting approximations has provoked a long history of uncertainty in the core-collapse supernova explosion mechanism, but recent work highlighting low-mode convection and a newly-recognized instability in spherical accretion shocks may signal (yet another) resolution. As part of its goal of elucidating the explosion mechanism, the Terascale Supernova Initiative is committed to meeting the full complexity of the computational challenge. The understanding of supernova neutrino emission gained in detailed simulations provides a potential basis for learning about two major remaining unknowns in neutrino flavor mixing: the value of the mixing angle $\theta_{13}$, and distinguishing between ``normal'' and ``inverted'' mass hierarchies.Comment: 6 pages. Contribution to the proceedings of NOW2004, Conca Specchiulla (Otranto, Italy), September 11-17, 2004, to be published by Nucl. Phys. B (Proc. Suppl.), ed. P. Bernardini, G.L. Fogli, and E. Lis

Neutrino absortion cross sections in supernova environment

We study charged-current neutrino cross sections on neutronrich nuclei in the mass $A\sim60$ region. Special attention is paid to environmental effects, i.e. finite temperature and density, on the cross sections. As these effects are largest for small neutrino energies, it is sufficient to study only the Gamow-Teller (GT) contributions to the cross sections. The relevant GT strength distributions are derived from large-scale shell model calculations. We find that the low-energy cross sections are enhanced at finite temperatures. However, for $(\nu_e,e^-)$ reactions Pauli blocking of the electrons in the final state makes the cross sections for low-energy neutrinos much smaller than for the competing inelastic scattering on electrons at moderate and large densities. Absorption cross sections for low-energy antineutrinos are strongly enhanced at finite temperatures.Comment: 11 pages, 4 figure

Evidence for two neutrino mass eigenstates from SN 1987A and the possibility of superluminal neutrinos

This paper reports a new phenomenological analysis of the neutrino burst detected from SN 1987 A, and it reveals the presence of two mass eigenstates. The heavier mass eigenstate has $m_H=21.4 \pm 1.2 eV/c^2$, while the lighter one has $m_L=4.0 \pm0.5 eV/c^2$. It is not the first paper to make such a claim, but it expands on a 1988 conditional analysis by Cowsik, and it attempts to make the evidence more robust through an improved statistical analysis, and through providing reasons why alternative explanations are unlikely. It also shows how the result can be made consistent with existing smaller electron neutrino mass limits with the existence of a third tachyonic (superluminal) mass eigenstate.Comment: 11 pages, 2 figure

Conditions for Shock Revival by Neutrino Heating in Core-Collapse Supernovae

Energy deposition by neutrinos can rejuvenate the stalled bounce shock and can provide the energy for the supernova explosion of a massive star. This neutrino-heating mechanism, however, is not finally accepted or proven as the trigger of the explosion. Part of the problem is that the complexity of the hydrodynamic models often hampers a clear and simple interpretation of the results. This demands a deeper theoretical understanding of the requirements of a successful shock revival. A toy model is presented here for discussing the neutrino heating phase analytically by a time-dependent treatment, which allows one to calculate the radius and velocity of the supernova shock from global properties of the gain layer as solutions of an initial value problem. A criterion is derived for the requirements of shock revival. It confirms the existence of a minimum neutrino luminosity needed for shock expansion, but also demonstrates the importance of a sufficiently large mass infall rate to the shock. The possibility of very energetic neutrino-driven explosions seems excluded because the total specific energy transferred to nucleons is limited by about 1e52 ergs per solar mass (about 5 MeV per nucleon) and the total mass in the gain layer is typically only around 0.1 solar masses. Energy transport by convection from the region of maximum heating to radii closer behind the shock is found to support the explosion by reducing the energy loss associated with the inward advection of neutrino-heated matter through the gain radius. (abridged)Comment: 36 pages, A&A LaTeX, 14 eps figures, major extensions due to referee comments; accepted by Astronomy & Astrophysic

Anisotropic convection in rotating proto-neutron stars

We study the conditions for convective instability in rotating, non-magnetic proto--neutron stars. The criteria that determine stability of nascent neutron stars are analogous to the Solberg--Hoiland conditions but including the presence of lepton gradients. Our results show that, for standard angular velocity profiles, convectively unstable modes with wave-vectors parallel to the rotation axis are suppressed by a stable angular momentum profile, while unstable modes with wave-vectors perpendicular to the axis remain unaltered. Since the wave-vector is perpendicular to the velocity perturbation, the directional selection of the unstable modes may result in fluid motions along the direction of the rotation axis. This occurs in rigidly rotating stars as well as in the inner core of differentially rotating stars. Our results provide a natural source of asymmetry for proto--neutron stars with the only requirement that angular velocities be of the order of the convective characteristic frequency.Comment: 5 pages, 4 figures, final version to appear in A&

Approaching the dynamics of hot nucleons in supernovae

All recent numerical simulations agree that stars in the main sequence mass range of 9-40 solar masses do not produce a prompt hydrodynamic ejection of the outer layers after core collapse and bounce. Rather they suggest that stellar core collapse and supernova explosion are dynamically distinct astrophysical events, separated by an unspectacular accretion phase of at least ~40 ms duration. As long as the neutrinospheres remain convectively stable, the explosion dynamics is determined by the neutrons, protons, electrons and neutrinos in the layer of impact-heated matter piling up on the protoneutron star. The crucial role of neutrino transport in this regime has been emphasized in many previous investigations. Here, we search for efficient means to address the role of magnetic fields and fluid instabilities in stellar core collapse and the postbounce phase.Comment: 4 pages, contribution to Nuclei in the Cosmos VIII, Jul. 19-23, submitted to Nucl. Phys.

Properties of a relativistic equation of state for collapse-driven supernovae

We study characteristics of the relativistic equation of state (EOS) for collapse-driven supernovae, which is derived by relativistic nuclear many body theory. Recently the relativistic EOS table has become available as a new complete set of physical EOS for numerical simulations of supernova explosion. We examine this EOS table by using general relativistic hydrodynamics of the gravitational collapse and bounce of supernova cores. In order to study dense matter in dynamical situation, we perform simplified calculations of core collapse and bounce by following adiabatic collapse with the fixed electron fraction for a series of progenitor models. This is intended to give us ``approximate models'' of prompt explosion. We investigate the profiles of thermodynamical quantities and the compositions during collapse and bounce. We also perform the calculations with the Lattimer-Swesty EOS to compare the properties of dense matter. As a measure of the stiffness of the EOS, we examine the explosion energy of the prompt explosion with electron capture totally suppressed. We study the derivative of the thermodynamical quantities obtained by the relativistic EOS to discuss the convective condition in neutron-rich environment, which may be important in the delayed explosion.Comment: 42 pages, 13 figures, Nucl. Phys. A. accepte

Adiabatic Perturbations in Homologous Conventional Polytropic Core Collapses of a Spherical Star

We perform a non-radial adiabatic perturbation analysis on homologous conventional polytropic stellar core collapses. The core collapse features a polytropic exponent $\Gamma=4/3$ relativistic gas under self-gravity of spherical symmetry while three-dimensional perturbations involve an adiabatic exponent $\gamma$ with $\gamma\neq\Gamma$ such that the Brunt-V$\ddot{\rm a}$is$\ddot{\rm a}$l$\ddot{\rm a}$ buoyancy frequency ${\cal N}$ does not vanish. With proper boundary conditions, we derive eigenvalues and eigenfunctions for different modes of oscillations. In reference to stellar oscillations and earlier results, we examine behaviours of different modes and the criterion for instabilities. The acoustic p$-$modes and surface f$-$modes remain stable. For $\gamma<\Gamma$, convective instabilities appear as unstable internal gravity g$^{-}-$modes. For $\gamma>\Gamma$, sufficiently low-order internal gravity g$^{+}-$modes are stable, whereas sufficiently high-order g$^{+}-$modes, which would have been stable in a static star, become unstable during self-similar core collapses. For supernova explosions, physical consequences of such inevitable g$-$mode instabilities are speculated.Comment: 5 pages, 4 figures, accepted for publication in MNRA