Photospheric Radius Evolution of Homologous Explosions

Recent wide-field surveys discovered new types of peculiar optical transients that showed diverse behaviors of the evolution of photospheric properties. We develop a general theory of homologous explosions with constant opacity, paying special attention to the evolution of the photospheric radius Rph. We find that regardless of the density distribution profile, Rph always increases early on and decreases at late times. This result does not depend on the radiation and cooling processes inside the ejecta. The general rising/falling behavior of Rph can be used to quickly diagnose whether the source originates from a supernova-like explosion. The shape of the Rph evolution curve depends on the density profile, so the observations may be used to directly diagnose the density profile as well as the temperature profile of the ejecta. All of the well-monitored supernovae show such a Rph rising/falling behavior, which is consistent with our theory. The recently discovered peculiar transient AT 2018cow showed a continuous decay of Rph, for which a supernova-like explosion origin is disfavored. Our result therefore supports the interpretation of this transient as a tidal disruption event.