Inside the supernova: A powerful convective engine

Abstract

We present an extensive study of the inception of supernova explosions by following the evolution of the cores of two massive stars (15 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, 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, 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 equation of state parameters. As a confirmation, our comparative one-dimensional calculations with identical microphysics, but in which convection cannot occur, lead to dramatic failures. Guided by our numerical results, we have developed a paradigm for the supernova explosion mechanism. We view a supernova as an open cycle thermodynamic engine in which a reservoir of low-entropy matter (the envelope) is thermally coupled and physically connected to a hot bath (the protoneutron star) by a neutrino flux, and by hydrodynamic instabilities. Neutrino heating raises the entropy of matter in the vicinity of the protoneutron star until buoyancy carries it to low-density, low-temperature regions at larger radii. This matter is replaced by low-entropy downflows with negative buoyancy. In essence, a Carnot cycle is established in which convection allows out-of-equilibrium heat transfer mediated by neutrinos to drive low-entropy matter to higher entropy and therefore extracts mechanical energy from the heat generated by gravitational collapse. We argue that supernova explosions are nearly guaranteed and self-regulated by the high efficiency of the thermodynamical engine. The mechanical efficiency is high because mixing during the heat exchange is limited by the rapid rise and shape-preserving expansion of the bubbles in a p ∝ r-3 atmosphere. In addition, the ideal Carnot efficiency is high due to the large temperature contrast between the surface of the protoneutron star and the material being convected down from large radii (this contrast remains large in spite of compression and shock heating which is relatively small). By direct P dV integration over the convective cycle, we estimate the energy deposition to be ∼4 foes per M⊙ involved. Further, convection, by keeping the temperature low in rising neutrino-heated high-entropy bubbles, allows the storage of internal energy while minimizing the losses due to neutrino emission. Thus convection continues to accumulate energy exterior to the neutron star until a successful explosion has occurred. At this time, the envelope is expelled and therefore uncoupled from the heat source (the neutron star) and the energy input ceases. This paradigm does not invoke new or modified physics over previous treatments, but relies on compellingly straightforward thermodynamic arguments. It provides a robust and self-regulated explosion mechanism to power supernovae that is effective under a wide range of physical parameters.