Physics
Scientific paper
Aug 1991
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991phr...206...99p&link_type=abstract
Physics Reports, Volume 206, Issue 3, p. 99-141.
Physics
3
Scientific paper
We present an analytical study of the relations between the softness of the nuclear equation of state (EOS) which describes the dense matter in the core of a supernova, the structure of such a core under hydrostatic conditions and the initial strength of the shock wave which forms after bounce and eventually, if not stalled by energy losses, disrupts the whole star.
We start by developing a first-order perturbation theory for Newtonian polytropes around the n = 1 exact solution, and obtain explicit expressions for the various physical parameters of the polytrope. We then point out that a dense pack of cold nuclear matter obeying a BCK-like EOS plus pressure from degenerate relativistic electrons and neutrinos can be described as an effective polytrope with index close to unity. Thence we can deduce analytical expressions for the structure of the dense pack as a function of the softness of the nuclear EOS.
Finally, we outline a phenomenological Newtonian model to describe the formation of the shock wave and its early propagation before it reaches the neutrinosphere; we are thus able to calculate the pressure and temperature profiles in the region behind the shock, corresponding to different nuclear EOS. Although very schematic, the model still retains the main physical features of the actual problem; indeed it reproduces within a satisfactory approximation the magnitudes of pressure and temperature obtained in Newtonian computer simulations as the softness of the nuclear EOS is changed. In particular, it shows explicitly that a softer EOS gives an initially stronger shock, and that this follows directly from the larger central density reached by the core at ``maximum scrunch''. Such behaviour, which is crucial in helping the subsequent propagation of the shock after the neutrinosphere, is well known from numerical calculations, but so far it had not been reproduced analytically in terms of a simple dynamical model.
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