Mass-Energy Relation for SN 1987A from Observations

We derive a relation between mass and kinetic energy for the hydrogen envelope of SN 1987A, using direct observations of the luminosities and photospheric velocities of the supernova. With a schematic but realistic treatment of the radiative transfer problem, which allows us to follow the position in mass of the photosphere as a function of time, we find that the observations determine uniquely the kinetic energy of the envelope once its mass is known. We do not use any input from the existing computer calculations of supernova explosions: therefore, our results are independent from any model assumed for the explosion mechanism and can actually constrain such models. Although the mass of the envelope has not so far been determined from observations, from different studies of the progenitor star there seems to be evidence for a quite large value, in the range Menv > 7 M ⊙. Corresponding to this, our approach gives for SN 1987 A a kinetic energy of the ejecta > 1 foe (=1051 ergs), the energy scaling roughly linearly with Menv.