We investigate neutrino-driven convection in core collapse supernovae and its ramifications for the explosion mechanism. We begin with an "optimistic" postbounce model in two important respects: (1) we begin with a 15 M ⊙ precollapse model, which is representative of the class 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-limited diffusion (MGFLD) neutrino transport and Newtonian Lagrangian hydrodynamics, providing realistic initial conditions for the postbounce convection and evolution.Our two-dimensional simulation began at 12 ms after bounce and proceeded for 500 ms.We couple two-dimensional (PPM) hydrodynamics to precalculated one-dimensional MGFLD neutrino transport. (The neutrino distributions used for matter heating and deleptonization in our 2D run are obtained from an accompanying 1D simulation. The accuracy of this approximation is assessed.) For the moment we sacrifice dimensionality for realism in other aspects of our neutrino transport. MGFLD is an implementation of neutrino transport that simultaneously (a) is multigroup and (b) simulates with sufficient realism the transport of neutrinos in opaque, semitransparent, and transparent regions. Both are crucial to the accurate determination of postshock neutrino heating, which sensitively depends on the luminosities, spectra, and flux factors of the electron neutrinos and antineutrinos emerging from their respective neutrinospheres.By 137 ms after bounce, we see neutrino-driven convection rapidly developing beneath the shock. By 212 ms after bounce, this convection becomes large-scale, characterized by higher-entropy, expanding upflows and denser, lower-entropy, finger-like downflows. The upflows reach the shock and distort it from sphericity. The radial convection velocities at this time become supersonic just below the shock, reaching magnitudes in excess of 10 9 cm/sec. Eventually, however, the shock recedes to smaller radii, and at ∼500 ms after bounce there is no evidence in our simulation of an explosion or of a developing explosion.Our angle-averaged density, entropy, electron fraction, and radial velocity profiles in our below the electron neutrino and antineutrino gain radii, above which the neutrino luminosities are essentially constant (i.e., the neutrino sources are entirely enclosed), in an effort to assess how spherically symmetric our neutrino sources remain during our 2D evolution, and therefore, to assess our use of precalculated 1D MGFLD neutrino distributions in calculating the matter heating and deleptonization. We find no differences below the neutrinosphere radii, and between the neutrinosphere and gain radii, no differences with obvious ramifications for the supernova outcome.We note that the interplay between neutrino transport and convection below the neutrinospheres is a delicate matter, and is discussed at greater length in another paper (Mezzacappa et al. 1997a).However, ...

We couple two-dimensional hydrodynamics to realistic one-dimensional multigroup Ñux-limited di †u-sion neutrino transport to investigate protoÈneutron star convection in core-collapse supernovae, and more speciÐcally, the interplay between its development and neutrino transport. Our initial conditions, time-dependent boundary conditions, and neutrino distributions for computing neutrino heating, cooling, and deleptonization rates are obtained from one-dimensional simulations that implement multigroup Ñux-limited di †usion and one-dimensional hydrodynamics.The development and evolution of protoÈneutron star convection are investigated for both 15 and 25 models, representative of the two classes of stars with compact and extended iron cores, respectively. M _ For both models, in the absence of neutrino transport, the angle-averaged radial and angular convection velocities in the initial Ledoux unstable region below the shock after bounce achieve their peak values in D20 ms, after which they decrease as the convection in this region dissipates. The dissipation occurs as the gradients are smoothed out by convection. This initial protoÈneutron star convection episode seeds additional convectively unstable regions farther out beneath the shock. The additional protoÈneutron star convection is driven by successive negative entropy gradients that develop as the shock, in propagating out after core bounce, is successively strengthened and weakened by the oscillating inner core. The convection beneath the shock distorts its sphericity, but on the average the shock radius is not boosted signiÐcantly relative to its radius in our corresponding one-dimensional models.In the presence of neutrino transport, protoÈneutron star convection velocities are too small relative to bulk inÑow velocities to result in any signiÐcant convective transport of entropy and leptons. This is evident in our two-dimensional entropy snapshots, which in this case appear spherically symmetric. The peak angle-averaged radial and angular convection velocities are orders of magnitude smaller than they are in the corresponding "" hydrodynamics-only ÏÏ models.A simple analytical model supports our numerical results, indicating that the inclusion of neutrino transport reduces the entropy-driven (lepton-driven) convection growth rates and asymptotic velocities by a factor D3 (50) at the neutrinosphere and a factor D250 (1000) at o \ 1012 g cm~3, for both our 15 and 25 models. Moreover, when transport is included, the initial postbounce entropy gradient is M _ smoothed out by neutrino di †usion, whereas the initial lepton gradient is maintained by electron capture and neutrino escape near the neutrinosphere. Despite the maintenance of the lepton gradient, protoÈ neutron star convection does not develop over the 100 ms duration typical of all our simulations, except in the instance where "" low-test ÏÏ intial conditions are used, which are generated by core-collapse and bounce simulations that neglect neutrinoÈelectron scattering and ionÈion screening...