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 $t_{\mathrm{p}\mathrm{k}}$ being the time to rise to a peak and $L_{\mathrm{p}\mathrm{k}}$ 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,andthat$L_{\rm pk} = 10^{25.5\pm1.6}$ergs$^{-1}$Hz$^{-1}$,andthereforethatgenerally,50$L_{\rm pk} < 10^{25.5}$ergs$^{-1}$Hz$^{-1}$\mathrm{.}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 $L_{\mathrm{p}\mathrm{k}}$ but the former have a wider range, whereas Type IIn SNe have ~10 times higher values with $L_{\rm pk} = 10^{26.5\pm1.1}$ergs$^{-1}$Hz$^{-1}$\mathrm{.}Asfor$t_{\rm pk}$,TypeIb\mathrm{/}chave$t_{\rm pk}$ofonly$10^{1.1\pm0.5}$dwhileTypeIIhave$t_{\rm pk} = 10^{1.6\pm1.0}$andTypeIInthelongesttimescaleswith$t_{\rm pk} = 10^{3.1\pm0.7}$ 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$v{\rm wind}=1000$kms$^{-1}$) for Type I~b/c SNe, and $-6.9\pm 1.4$ (assuming $v_{\mathrm{w}\mathrm{i}\mathrm{n}\mathrm{d}}=10$ km s${}^{-1}$ for Type II SNe excluding Type IIn.