H.-Thomas Janka

Radiation hydrodynamics with neutrinos - Variable Eddington factor method for core-collapse supernova simulations

Neutrino transport and neutrino interactions in dense matter play a crucial role in stellar core collapse, supernova explosions and neutron star formation. Here we present a detailed description of a new numerical code for treating the time and energy dependent neutrino transport in hydrodynamical simulations of such events. The code is based on a variable Eddington factor method to deal with the integro-differential character of the Boltzmann equation. The moments of the neutrino distribution function and the energy and lepton number exchange with the stellar medium are determined by iteratively solving the zeroth and first order moment equations in combination with a model Boltzmann equation. The latter is discretized on a grid of tangent rays. The integration of the transport equations and the neutrino source terms is performed in a time-implicit way. In the present version of the program, the transport part is coupled to an explicit hydrodynamics code which follows the evolution of the stellar plasma by a finite-volume method with piecewise parabolic interpolation, using a Riemann solver to calculate the hydrodynamic states. The neutrino source terms are implemented in an operator-split step. Neutrino transport and hydrodynamics can be calculated with different spatial grids and different time steps. The structure of the described code is modular and offers a high degree of flexibility for an application to relativistic and multi-dimensional problems at different levels of refinement and accuracy. We critically evaluate results for a number of test cases, including neutrino transport in rapidly moving stellar media and approximate relativistic core collapse, and suggest a path for generalizing the code to be used in multi-dimensional simulations of convection in neutron stars and supernovae.

Spherically Symmetric Simulation with Boltzmann Neutrino Transport of Core Collapse and Postbounce Evolution of a 15 M☉ Star

We present a spherically symmetric, Newtonian core collapse simulation of a 15 M☉ star with a 1.28 M☉ iron core. The time-, energy-, and angle-dependent transport of electron neutrinos (νe) and antineutrinos (e) was treated with a new code that iteratively solves the Boltzmann equation and the equations for neutrino number, energy, and momentum to order O(v/c) in the velocity v of the stellar medium. The supernova shock expands to a maximum radius of 350 km instead of only ~240 km as in a comparable calculation with multigroup flux-limited diffusion (MGFLD) by Bruenn, Mezzacappa, & Dineva. This may be explained by stronger neutrino heating due to the more accurate transport in our model. Nevertheless, after 180 ms of expansion the shock finally recedes to a radius around 250 km (compared to ~170 km in the MGFLD run). The effect of an accurate neutrino transport is helpful but not large enough to cause an explosion of the considered 15 M☉ star. Therefore, postshock convection and/or an enhancement of the core neutrino luminosity by convection or reduced neutrino opacities in the neutron star seem necessary for neutrino-driven explosions of such stars. We find an electron fraction Ye > 0.5 in the neutrino-heated matter, which suggests that the overproduction problem of neutron-rich nuclei with mass numbers A ≈ 90 in exploding models may be absent when a Boltzmann solver is used for the νe and e transport.

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, though investigated by numerical simulations and analytic studies, is not finally accepted or proven as the trigger of the explosion. Part of the problem is that different groups have obtained seemingly discrepant results, and 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 developed here for discussing the neutrino heating phase analytically. The neutron star atmosphere between the neutrinosphere and the supernova shock can well be considered to be in hydrostatic equilibrium, with a layer of net neutrino cooling below the gain radius and a layer of net neutrino heating above. Since the mass infall rate to the shock is in general different from the rate at which gas is advected into the neutron star, the mass in the gain layer varies with time. Moreover, the gain layer receives additional energy input by neutrinos emitted from the neutrinosphere and the cooling layer. Therefore the determination of the shock evolution requires a time-dependent treatment. To this end the hydrodynamical equations of continuity and energy are integrated over the volume of the gain layer to obtain conservation laws for the total mass and energy in this layer. The radius and velocity of the supernova shock can then be calculated from global properties of the gain layer as solutions of an initial value problem, which expresses the fact that the behavior of the shock is controlled by the cumulative effects of neutrino heating and mass accumulation in the gain layer. The described toy model produces steady-state accretion and mass outflow from the nascent neutron star as special cases. The approach is useful to illuminate the conditions that can lead to delayed explosions and in this sense supplements detailed numerical simulations. On grounds of the model developed here, a criterion is derived for the requirements of shock revival. It confirms the existence of a minimum neutrino luminosity that is needed for shock expansion, but also demonstrates the importance of a sufficiently large mass infall rate to the shock. If the neutrinospheric luminosity or accretion rate by the shock are too low, the shock is weakened because the gain layer loses more mass than is resupplied by inflow. On the other hand, very high infall rates damp the shock expansion and above some threshold, the development of positive total energy in the neutrino-heating layer is prevented. Time-dependent solutions for the evolution of the gain layer show that the total specific energy transferred to nucleons by neutrinos is limited by about 10 52 erg

Toward gravitational wave signals from realistic core-collapse supernova models

M_{\odot}^{-1}

Gravitational wave burst signal from core collapse of rotating stars

(~5 MeV per nucleon). This excludes the possibility of very energetic explosions by the neutrino-heating mechanism, because the typical mass in the gain layer is about 0.1

Three-dimensional simulations of core-collapse supernovae: from shock revival to shock breakout

M_{\odot}

Electron-, mu-, and tau-number conservation in a supernova core

and does not exceed a few tenths of a solar mass. The toy model also allows for a crude discussion of the global effects of convective energy transport in the neutrino-heating layer. Transfer of energy from the region of maximum heating to radii closer behind the shock mainly reduces the loss of energy by the inward flow of neutrino-heated matter through the gain radius.

Supernova explosions and the birth of neutron stars

Hydrodynamic simulations of the merger of stellar mass black hole-neutron star binaries are compared with mergers of binary neutron stars. The simulations are Newtonian but take into account the emission and back-reaction of gravitational waves. The use of a physical nuclear equation of state allows us to include the effects of neutrino emission. For low neutron star-to-black hole mass ratios, the neutron star transfers mass to the black hole during a few cycles of orbital decay and subsequent widening before finally being disrupted, whereas for ratios near unity the neutron star is destroyed during its first approach. A gas mass between approximately 0.3 and approximately 0.7 M middle dot in circle is left in an accretion torus around the black hole and radiates neutrinos at a luminosity of several times 1053 ergs s-1 during an estimated accretion timescale of about 0.1 s. The emitted neutrinos and antineutrinos annihilate into e+/- pairs with efficiencies of 1%-3% and rates of up to approximately 2x1052 ergs s-1, thus depositing an energy Enunu&d1; less, similar1051 ergs above the poles of the black hole in a region that contains less than 10-5 M middle dot in circle of baryonic matter. This could allow for relativistic expansion with Lorentz factors around 100 and is sufficient to explain apparent burst luminosities Lgamma approximately Enunu&d1;&solm0;&parl0;fOmegatgamma&parr0; up to several times 1053 ergs s-1 for burst durations tgamma approximately 0.1-1 s, if the gamma emission is collimated in two moderately focused jets in a fraction fOmega=2deltaOmega&solm0;&parl0;4pi&parr0; approximately 1&solm0;100-(1/10) of the sky.