On the size distribution of supernova remnants in the Magellanic Clouds

The physical sizes of supernova remnants (SNRs) in a number of nearby galaxies follow an approximately linear cumulative distribution, contrary to what is expected for decelerating shock fronts. This phenomenon has been variously attributed to observational selection effects, or to a majority of SNRs being in 'free expansion', with shocks propagating at a constant velocity into a tenuous ambient medium. We compile multi-wavelength observations of the 77 known SNRs in the Magellanic Clouds, and argue that they provide a fairly complete record of the SNe that have exploded over the last similar to 20 kyr, with most of them now in the adiabatic, Sedov phase of their expansions. The roughly linear cumulative distribution of sizes (roughly uniform in a differential distribution) can be understood to result from the combination of the deceleration during this phase, a transition to a radiation-loss-dominated phase at a radius that depends on the local gas density and a probability distribution of densities in the interstellar medium varying approximately as -1. This explanation is supported by the observed power-law distributions, with index similar to -1, of three independent tracers of density: neutral hydrogen column density, H alpha surface brightness and star formation rate based on resolved stellar populations. In this picture, the observed cut-off at a radius of 30 pc in the SNR size distribution is due to a minimum in the mean ambient gas density in the regions where supernovae (SNe) explode. We show that M33 has an SNR size distribution very similar to that of the Magellanic Clouds, suggesting these features, and their explanation, may be universal. In a companion paper, we use our sample of SNRs as an effective 'SN survey' to calculate the SN rate and delay time distribution in the Magellanic Clouds. The hypothesis that most SNRs are in free expansion, rather than in the Sedov phase of their evolution, would result in SN rates that are in strong conflict with independent measurements, and with basic stellar evolution theory.