A 2-DIMENSIONAL HYDRODYNAMIC MODEL FOR ASYMMETRIC EXPLOSIONS OF COLLAPSING SUPERNOVAE WITH RAPID INITIAL ROTATION

In accordance with the rotational model of the explosions of collapsin g supernovae, the main energy release (similar to 10(51) erg) arises f rom the hydrodynamic transformation of a low-mass neutron star of crit ical mass approximate to 0.1M. into a hydrodynamically expanding ''iro n'' star. We consider a two-dimensional, axially symmetric hydrodynami c model for the explosion of such a low-mass neutron star. This star i s assumed to move in a circular orbit in a binary system, together wit h a more massive neutron star, which turns into a pulsar (or a black h ole?). The binary system of neutron stars is embedded in a relatively rarified gas (the outer shell of the iron core of the presupernova) of total mass 0.1M. with initial density that is uniformly distributed i n space. The numerical calculation of the axisymmetric explosion is pe rformed by two independent finite-difference methods: (1) by the Lagra ngian method (LM) developed by Godunov et al. (1976), which singles ou t both the contact boundary between the region of energy release and t he surrounding medium and the front of an outgoing shock wave; and (2) by the Eulerian parabolic piecewise method (PPM) (Colella and Woodwor d, 1984; Colella and Glas, 1985) that has been previously applied by A ksenov and Imshennik (1994) to a similar problem. The results obtained by the two methods for the shock front configuration and for the high -temperature gas behind it are in good agreement. The equation of stat e was taken in the simplest but adequate form for the problem under co nsideration-an ideal gas with blackbody radiation. The numerical model has one essential parameter-the kick velocity of the pulsar (or the b lack hole?) v(p). The main result of the calculations is that for a hi gh kick velocity of the pulsar (v(p) approximate to 1000 km s(-1)) tha t is typical of the rotational mechanism there is a strong asymmetry o f the explosion, which turns out to be concentrated in a cone with an opening angle approximate to 120 degrees (the solid angle approximate to pi) whose direction is opposite to that of the velocity vector of t he pulsar, Such an explosion is capable of producing a jet of radioact ive Ni-56 of mass similar to 0.1M., in qualitative and quantitative ag reement with the observations of SN 1987A. An appreciable asymmetry of the explosion is also retained for more moderate kick velocities of t he pulsar-down to the mean observed velocity similar to 500 km s(-1) ( Lyne and Lorimer, 1994).