AN INVESTIGATION OF NEUTRINO-DRIVEN CONVECTION AND THE CORE COLLAPSE SUPERNOVA MECHANISM USING MULTIGROUP NEUTRINO TRANSPORT

We investigate neutrino-driven convection in core collapse supernovae and its ramifications for the explosion mechanism. We begin with a pos tbounce model that is optimistic in two important respects: (1) we beg in with a 15 M. precollapse model, which is representative of the clas s of stars with compact iron cores; (2) we implement Newtonian gravity . Our precollapse model is evolved through core collapse and bounce in one dimension using multigroup (neutrino energy-dependent) flux-limit ed diffusion (MGFLD) neutrino transport and Newtonian Lagrangian hydro dynamics, providing realistic initial conditions for the postbounce co nvection and evolution. Our two-dimensional simulation begins at 12 ms after bounce and proceeds for 500 ms. We couple two-dimensional piece wise parabolic method (PPM) hydrodynamics to precalculated one-dimensi onal MGFLD neutrino transport. (The neutrino distributions used for ma tter heating and deleptonization in our two-dimensional run are obtain ed from an accompanying one-dimensional simulation. The accuracy of th is approximation is assessed.) For the moment, we sacrifice dimensiona lity for realism in other aspects of our neutrino transport. MGFLD is an implementation of neutrino transport that simultaneously (1) is mul tigroup and (2) simulates with sufficient realism the transport of neu trinos in opaque, semitransparent, and transparent regions. Both are c rucial to the accurate determination of postshock neutrino heating, wh ich sensitively depends on the luminosities, spectra, and flux factors of the electron neutrinos and antineutrinos emerging from their respe ctive neutrinospheres. By 137 ms after bounce, we see neutrino-driven convection rapidly developing beneath the shock. By 212 ms after bounc e, this convection becomes large scale, characterized by higher entrop y, expanding upflows and lower entropy, denser, finger-like downflows. The upflows reach the shock and distort it from sphericity. The radia l convection velocities at this time become supersonic just below the shock, reaching magnitudes in excess of 10(9) cm s(-1). Eventually, ho wever, the shock recedes to smaller radii, and at similar to 500 ms af ter bounce there is no evidence in our simulation of an explosion or o f a developing explosion. Our angle-averaged density, entropy, electro n fraction, and radial velocity profiles in our two-dimensional model agree well with their counterparts in our accompanying one-dimensional MGFLD run above and below the neutrino-driven convection region. In t he convection region, the one-dimensional and angle-averaged profiles differ somewhat because (1) convection tends to flatten the density, e ntropy, and electron fraction profiles, and (2) the shock radius is bo osted somewhat by convection. However, the differences are not signifi cant, indicating that, while vigorous, neutrino-driven convection in o ur model does not have a significant impact on the overall shock dynam ics. The differences between our results and those of other groups are considered. These most likely result from differences in (1) numerica l hydrodynamics methods; (2) initial postbounce models, and, most impo rtant; (3) neutrino transport approximations. We have compared our neu trino luminosities, rms energies, and inverse flux factors with those from the exploding models of other groups. Above all, we find that the neutrino rms energies computed by our multigroup (MGFLD) transport ar e significantly lower than the values obtained by Burrows and coworker s, who specified their neutrino spectra by tying the neutrino temperat ure to the matter temperature at the neutrinosphere and by choosing th e neutrino degeneracy parameter arbitrarily, and by Herant and coworke rs in their transport scheme, which (1) is gray and (2) patches togeth er optically thick and thin regions. The most dramatic difference betw een our results and those of Janka and Muller is exhibited by the diff erence in the net cooling rate below the gain radii: Our rate is 2-3 t imes greater during the critical 50-100 ms after bounce. We have compu ted the mass and internal energy in the gain region as a function of t ime. Up to similar to 150 ms after bounce, we find that both increase as a result of the increasing gain region volume, as the gain and shoc k radii diverge. However, at all subsequent times, we find that the ma ss and internal energy in the gain region decrease with time in accord ance with the density falloff in the preshock region and with the how of matter into the gain region at the shock and out of the gain region at the gain radius. Therefore, we see no evidence in the simulations presented here that neutrino-driven convection leads to mass and energ y accumulation in the gain region. We have compared our one-and two-di mensional densities, temperatures, and electron fractions in the regio n below the electron neutrino and antineutrino gain radii, above which the neutrino luminosities are essentially constant (i.e., the neutrin o sources are entirely enclosed), in an effort to assess how spherical ly symmetric our neutrino sources remain during our two-dimensional ev olution, and therefore, in an effort to assess our use of precalculate d one-dimensional MGFLD neutrino distributions in calculating the matt er heating and deleptonization. We find no difference below the neutri nosphere radii. Between the neutrinosphere and gain radii we find no d ifferences with obvious ramifications for the supernova outcome. We no te that the interplay between neutrino transport and convection below the neutrinospheres is a delicate matter and is discussed at greater l ength in another paper (Mezzacappa and coworkers). However, the result s presented therein do support our use of precalculated one-dimensiona l MGFLD in the present context. Failure in our ''optimistic'' 15 M. Ne wtonian model leads us to conclude that it is unlikely, at least in ou r approximation, that neutrino-driven convection will lead to explosio ns for more massive stars with fatter iron cores or in cases in which general relativity is included.