The Radio Luminosity-Risetime Function of Core-Collapse Supernovae

We assemble a large set of 2-10 GHz radio flux density measurements and upper limits of 294 different supernovae (SNe), from the literature and our own and archival data. Only 31% of the SNe were detected. We characterize the SN lightcurves near the peak using a two-parameter model, with $t_{\rm pk}$ being the time to rise to a peak and $L_{\rm pk}$ the spectral luminosity at that peak. Over all SNe in our sample at $D<100$ Mpc, we find that $t_{\rm pk} = 10^{1.7\pm0.9}$ d, and that $L_{\rm pk} = 10^{25.5\pm1.6}$ erg s$^{-1}$ Hz$^{-1}$, and therefore that generally, 50% of SNe will have $L_{\rm pk} < 10^{25.5}$ erg s$^{-1}$ Hz$^{-1}$. These $L_{\rm pk}$ values are ~30 times lower than those for only detected SNe. Types I b/c and II (excluding IIn's) have similar mean values of $L_{\rm pk}$ but the former have a wider range, whereas Type IIn SNe have ~10 times higher values with $L_{\rm pk} = 10^{26.5\pm1.1}$ erg s$^{-1}$ Hz$^{-1}$. As for $t_{\rm pk}$, Type I b/c have $t_{\rm pk}$ of only $10^{1.1\pm0.5}$ d while Type II have $t_{\rm pk} = 10^{1.6\pm1.0}$ and Type IIn the longest timescales with $t_{\rm pk} = 10^{3.1\pm0.7}$ d. We also estimate the distribution of progenitor mass-loss rates, $\dot M$, and find the mean and standard deviation of log$_{10}(\dot M/$Msol) yr$^{-1}$ are $-5.4\pm1.2$ (assuming $v_{\rm wind}=1000$ km s$^{-1}$) for Type I~b/c SNe, and $-6.9\pm1.4$ (assuming $v_{\rm wind} = 10$ km s$^{-1}$ for Type II SNe excluding Type IIn.