The Dynamics of Supernova Explosions

We have calculated the dynamical implosion of a supernova star 10 Mo using an equation of state that includes the thermal decomposition of iron to helium (Burbidge, E. M., Burbidge, G. K., Fowler, W. A., and Hoyle, F., Revs. Modern Phys. 29, 547,1957) and helium to neutrons and protons. Starting from an initial equilibrium star of a polytrope of index 3, a mock-quasistatic evolution evolves the star by 2 % total change in energy until a dynamical collapse takes place. The validity of the calculation is limited to p <3 X 1011 gcc corresponding to a compression of the central zones of 10 at which point the transformation to a neutron star by inverse beta decay occurs within the dynamic time of the implosion. The pressure at this time is one-half that required for mechanical support of the star, so that further collapse to a neutron star is expected, provided the fractional energy in rotation or magnetic fields is small. The "bounce" of a neutron star due to adiabatic compression will occur at very much higher densities. We created a "bounce" artificially after 103-fold compression, assuming that the initial rotational energy of the core was 10- of the internal energy. The bounce forms a shock wave which ejects approximately 1 solar mass with a specific energy (2 x 1018 ergs7g) equal to its gravitational potential. This potential at the ejection mass-cut depends in turn on the dynamical energy of the core implosion, but excluding the inverse beta decay, the shock strength heats the ejected mass to 4.0 X 108 deg and compresses it to 10 gcc. The temperature and density time history of the subsequent expansion determines the nuclear composition of the ejected material and this is independent of the initial state because the fractional thermonuclear energy addition is small compared to the shock energy. The characteristic expansion time starts at 0.07 sec increasing to 0.4 sec at 10 density while the temperature falls ~` as fast. This work was done under the auspices of the U.S. Atomic Energy Commission. % total change in energy until a dynamical collapse takes place. The validity of the calculation is limited to p <3 X 1011 gcc corresponding to a compression of the central zones of 10 at which point the transformation to a neutron star by inverse beta decay occurs within the dynamic time of the implosion. The pressure at this time is one-half that required for mechanical support of the star, so that further collapse to a neutron star is expected, provided the fractional energy in rotation or magnetic fields is small. The "bounce" of a neutron star due to adiabatic compression will occur at very much higher densities. We created a "bounce" artificially after 103-fold compression, assuming that the initial rotational energy of the core was 10- of the internal energy. The bounce forms a shock wave which ejects approximately 1 solar mass with a specific energy (2 x 1018 ergs7g) equal to its gravitational potential. This potential at the ejection mass-cut depends in turn on the dynamical energy of the core implosion, but excluding the inverse beta decay, the shock strength heats the ejected mass to 4.0 X 108 deg and compresses it to 10 gcc. The temperature and density time history of the subsequent expansion determines the nuclear composition of the ejected material and this is independent of the initial state because the fractional thermonuclear energy addition is small compared to the shock energy. The characteristic expansion time starts at 0.07 sec increasing to 0.4 sec at 10 density while the temperature falls ~` as fast. This work was done under the auspices of the U.S. Atomic Energy Commission. % total change in energy until a dynamical collapse takes place. The validity of the calculation is limited to p <3 X 1011 gcc corresponding to a compression of the central zones of 10 at which point the transformation to a neutron star by inverse beta decay occurs within the dynamic time of the implosion. The pressure at this time is one-half that required for mechanical support of the star, so that further collapse to a neutron star is expected, provided the fractional energy in rotation or magnetic fields is small. The "bounce" of a neutron star due to adiabatic compression will occur at very much higher densities. We created a "bounce" artificially after 103-fold compression, assuming that the initial rotational energy of the core was 10- of the internal energy. The bounce forms a shock wave which ejects approximately 1 solar mass with a specific energy (2 x 1018 ergs7g) equal to its gravitational potential. This potential at the ejection mass-cut depends in turn on the dynamical energy of the core implosion, but excluding the inverse beta decay, the shock strength heats the ejected mass to 4.0 X 108 deg and compresses it to 10 gcc. The temperature and density time history of the subsequent expansion determines the nuclear composition of the ejected material and this is independent of the initial state because the fractional thermonuclear energy addition is small compared to the shock energy. The characteristic expansion time starts at 0.07 sec increasing to 0.4 sec at 10 density while the temperature falls ~` as fast. This work was done under the auspices of the U.S. Atomic Energy Commission.