Nonlinear Astrophysical Fluid Dynamics [antikvár]

The Hot Bubble and Supernova Calculations" STIRLING A. COLGATE Los Alamos National Laboratory Los Alamos, New Mexico 87545 The recent calculations of James Wilson and Ronald Mayle' showed that the mechanism of supernova explosions caused by collapse to a neutron star now appears to be both understood conceptually and modeled convincingly up to 3.4 s following collapse. In particular they show the formation of a hot, high-entropy bubble (Fig. 1) that continues to push on the shocked matter for a long time, enough that the subsequent history is not in significant doubt. The hot bubble is formed primarily due to mu, tau neutrino antineutrino annihilation as first proposed by Goodman, Dar, and Nussinov.^ The hot bubble that separates the neutron star from the ejected matter has high entropy, 10' to 10\ measured in units of the Boltzmann constant, k, per free nucleón. This high entropy means that for every nucleón there are many photons and electrons (pairs), and so the molecular weight is small and the scale height is large even at modest temperatures, < 1 MeV. Such a photon gas can "push" simultaneously on both the neutron star surface as well as on the expanding matter. It extends to a radius of 10" cm, so that no fallback or reimplosion of any significant fraction of the ejected matter will take place. The kinetic and internal energy minus the gravitational energy of matter, whose total energy is positive, is 0.35 X 10" ergs at 3.4 s. Wilson and Mayle expect this to increase to 1 to 1.5 x 10^' ergs by the end of the calculation, typical of Type II supernovas. It has long been my major concern (Colgate^) that despite a very strong shock wave, a significant fraction of the ejected matter would subsequently fall back onto the neutron star. This fraction, several solar masses or more, would fall back in a time of about a half an hour despite an initial large positive velocity (greater than escape) but ultimately leading to a black hole. The reason for the large fallback mass is twofold. First, normal matter falling onto a neutron star will be cooled by neutrino emission in a few tens of seconds from the high temperature, 1 to 2 MeV, that is created when this matter is shocked and compressed at the neutron star surface. Hence, the pressure that might ordinarily extend from the neutron star surface to the shocked matter, forming a piston to maintain the shock, disappears. The neutron star then acts like a black hole. Second, the internal energy in shocked material is always equal to the kinetic energy of motion of the same matter (behind a strong shock). Hence, despite the radially outward velocity that exists behind a strong ejection shock, there is always enough heat to allow for an expansion inwards or backwards (in one dimension) at a velocity equal to the shock-created outward velocity. The radially inward velocity of the rarefaction wave overcomes the original outward radial velocity of the shocked "This work was performed under the auspices of the U.S. Department of Energy. 1