A statistical approach to radio emission from shell-type SNRs

Abstract

Context. Shell-type supernova remnants (SNRs) exhibit correlations between radio surface brightness, SNR diameter, and ambient medium density, that between the first two quantities being the well known Σ-D relation. Aims: We investigate these correlations, to extract useful information about the typical evolutionary stage of radio SNRs, as well as to obtain insight into the origin of the relativistic electrons and magnetic fields responsible for the synchrotron emission observed in radio. Methods: We propose a scenario, according to which the observed correlations are the combined effect of SNRs evolving in a wide range of ambient conditions, rather than the evolutionary track of a “typical” SNR. We then develop a parametric approach to interpret the statistical data, and apply it to the data sample previously published by Berkhuijsen, as well as to a sample of SNRs in the galaxy M 33. Results: We find that SNRs cease to emit effectively in radio at a stage near the end of their Sedov evolution, and that models of synchrotron emission with constant efficiencies in particle acceleration and magnetic field amplification do not provide a close match to the data. We discuss the problem of the cumulative distribution in size, showing that the slope of this distribution does not relate to the expansion law of SNRs, as usually assumed, but only to the ambient density distribution. This solves a long-standing paradox: the almost linear cumulative distribution of SNRs led several authors to conclude that these SNRs are still in free expansion, which also implies very low ambient densities. Within this framework, we discuss the case of the starburst galaxy M 82. Conclusions: Statistical properties of SNR samples may be used to shed light on both the physics of electron acceleration and the evolution of SNRs. More precise results could be obtained by combining data of several surveys of SNRs in nearby galaxies.