The Radio Luminosity-Risetime Function of Core-Collapse Supernovae

Abstract

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 $t_{\mathrm{pk}}$ being the time to rise to a peak and $L_{\mathrm{pk}}$ the spectral luminosity at that peak. Over all SNe in our sample at $D<100$ Mpc, we find that $t_{\mathrm{pk}}=10^{1.7\pm 0.9}$ d, and that $L_{\mathrm{pk}}=10^{25.5\pm 1.6}$ erg s${}^{-1}$ Hz${}^{-1}$, and therefore that generally, 50% of SNe will have $L_{\mathrm{pk}}<10^{25.5}$ erg s${}^{-1}$ Hz${}^{-1}$. These $L_{\mathrm{pk}}$ 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 $L_{\mathrm{pk}}$ but the former have a wider range, whereas Type IIn SNe have ~10 times higher values with $L_{\mathrm{pk}}=10^{26.5\pm 1.1}$ erg s${}^{-1}$ Hz${}^{-1}$. As for $t_{\mathrm{pk}}$, Type I b/c have $t_{\mathrm{pk}}$ of only $10^{1.1\pm 0.5}$ d while Type II have $t_{\mathrm{pk}}=10^{1.6\pm 1.0}$ and Type IIn the longest timescales with $t_{\mathrm{pk}}=10^{3.1\pm 0.7}$ 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 $-5.4\pm 1.2$ (assuming $v_{\mathrm{wind}}=1000$ km s${}^{-1}$) for Type I~b/c SNe, and $-6.9\pm 1.4$ (assuming $v_{\mathrm{wind}}=10$ km s${}^{-1}$ for Type II SNe excluding Type IIn.

Accepted for publication in the Astrophysical Journal 15 Figures, 4 Tables; Full version of Table 1 in ancillary files. Minor revisions only from version 1

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