We present an extensive study of the inception of supernova explosions by following the evolution of the cores of two massive stars (15 M ⊙ and 25 M ⊙ ) in multidimension. Our calculations begin at the onset of core collapse and stop several hundred milliseconds after the bounce, at which time successful explosions of the appropriate magnitude have been obtained. Similar to the classical delayed explosion mechanism of Wilson (1985), the explosion is powered by the heating of the envelope due to neutrinos emitted by the protoneutron star as it radiates the gravitational energy liberated by the collapse. However, as was shown by Herant, Benz & Colgate (1992), this heating generates strong convection outside the neutrinosphere, which we demonstrate to be critical to the explosion. By breaking a purely stratified hydrostatic equilibrium, convection moves the nascent supernova away from a delicate radiative equilibrium between neutrino emission and absorption. Thus, unlike what has been observed in one-dimensional calculations, explosions are rendered quite insensitive to the details of the physical input parameters such as neutrino cross-sections or nuclear

We Ðnd a linear instability of nonaxisymmetric Rossby waves in a thin nonmagnetized Keplerian disk when there is a local maximum in the radial proÐle of a key function L(r) 4 F(r)S2@!(r), where F~1 \ is the potential vorticity, S \ P/&! is the entropy, & is the surface mass density, P is the zü AE ($ Â ¿)/& vertically integrated pressure, and ! is the adiabatic index. We consider in detail the special case where there is a local maximum in the disk entropy proÐle S(r). This maximum acts to trap the waves in its vicinity if its height-to-width ratio max(S)/*r is larger than a threshold value. The pressure gradient derived from this entropy variation provides the restoring force for the wave growth. We show that the trapped waves act to transport angular momentum outward. A plausible way to produce an entropy variation is when an accretion disk is starting from negligible mass and temperature, therefore, negligible entropy. As mass accumulates by either tidal torquing, magnetic torquing, or Roche-lobe overÑow, conÐnement of heat will lead to an entropy maximum at the outer boundary of the disk. Possible nonlinear developments from this instability include the formation of Rossby vortices and the formation of spiral shocks. What remains to be determined from hydrodynamic simulations is whether or not Rossby wave packets (or vortices) "" hold together ÏÏ as they propagate radially inward.

No abstract

In earlier work we identified a global, non-axisymmetric instability associated with the presence of an extreme in the radial profile of the key function L(r) ≡ (ΣΩ/κ 2 )S 2/Γ in a thin, inviscid, nonmagnetized accretion disk. Here, Σ(r) is the surface mass density of the disk, Ω(r) the angular rotation rate, S(r) the specific entropy, Γ the adiabatic index, and κ(r) the radial epicyclic frequency. The dispersion relation of the instability was shown to be similar to that of Rossby waves in planetary atmospheres. In this paper, we present the detailed linear theory of this Rossby wave instability and show that it exists for a wider range of conditions, specifically, for the case where there is a "jump" over some range of r in Σ(r) or in the pressure P (r). We elucidate the physical mechanism of this instability and its dependence on various parameters, including the magnitude of the "bump" or "jump," the azimuthal mode number, and the sound speed in the disk. We find large parameter range where the disk is stable to axisymmetric perturbations, but unstable to the non-axisymmetric Rossby waves. We find that growth rates of the Rossby wave instability can be high, ∼ 0.2Ω K for relative small "jumps" or "bumps". We discuss possible conditions which can lead to this instability and the consequences of the instability.

No abstract