PULSAR NEBULAE IN SUPERNOVAE

Pulsars are expected to be born inside Type II supernovae, and the nebulae generated by their spin-down power thus initially interact with the expanding supernova gas. The hydrodynamic interaction can be described analytically while the pulsar is in a constant power output phase if the surrounding density profile is a power law in radius. The power generated by the shock front driven into the supernova gas is about 1.5% of the pulsar power, and, for typical parameters, the shock wave remains in a radiative phase for at least hundreds of years. The stability of the accelerating shell can be analyzed on the thin shell approximation, and we find that linear spherical harmonic perturbations with l greater-than-or-equal-to 4 are unstable to Rayleigh-Taylor instability growth. The growth is exponential in time for large wavenumbers. If the pulsar bubble produces ionizing radiation, the radiation is trapped close to the shocked shell throughout the initial evolution and may be able to break out of the supernova gas only after tens of years. By allowing for the evolution of the pulsar power on the assumption of constant braking index, the model is applied to the young pulsars PSR 0531 + 21 (Crab), PSR 0540 - 69, and PSR 1509 - 58, and their associated nebulae. There is general agreement between the predicted and observed properties of the shell nebulae, and the models make predictions for future observations. If pulsars "turn-on" rapidly after the supernova explosion, our model has implications for observations of supernovae at an age,of years. We present detailed results for the possible photoionization in a supernova at ages of 4 and 10 yr. The upper limit on the total power of a pulsar in SN 1987A is approximately 5 X 10(38) ergs s-1, or lower if the pulsar nebula has a high radiative efficiency. A general prediction of the pulsar model is broadening of the lines with time because of the acceleration by the pulsar bubble.