Heating from Free-Free Absorption and the Mass-loss Rate of the Progenitor Stars to Supernovae

An accurate determination of the mass-loss rate of the progenitor stars to core-collapse supernovae is often limited by uncertainties pertaining to various model assumptions. It is shown that under conditions when the temperature of the circumstellar medium is set by heating due to free-free absorption, observations of the accompanying free-free optical depth allow a direct determination of the mass-loss rate from observed quantities in a rather model-independent way. The temperature is determined self-consistently, which results in a characteristic time dependence of the free-free optical depth. This can be used to distinguish free-free heating from other heating mechanisms. Since the importance of free-free heating is quite model dependent, this also makes possible several consistency checks of the deduced mass-loss rate. It is argued that the free-free absorption observed in SN 1993J is consistent with heating from free-free absorption. The deduced mass-loss rate of the progenitor star is, approximately, 10^-5 M _⊙ yr^-1 for a wind velocity of 10 km s^-1.