From core collapse to superluminous: The rates of massive stellar explosions from the Palomar Transient Factory

We present measurements of the local core collapse supernova (SN) rate using SN discoveries from the Palomar Transient Factory (PTF). We use a Monte Carlo simulation of hundreds of millions of SN light curve realizations coupled with the detailed PTF survey detection efficiencies to forward-model the SN rates in PTF. Using a sample of 86 core collapse SNe, including 26 stripped-envelope SNe (SESNe), we show that the overall core collapse SN volumetric rate is $r^\mathrm{CC}_v=9.10_{-1.27}^{+1.56}\times10^{-5}\,\text{SNe yr}^{-1}\,\text{Mpc}^{-3}\, h_{70}^{3}$ at $ \langle z \rangle = 0.028$, and the SESN volumetric rate is $r^\mathrm{SE}_v=2.41_{-0.64}^{+0.81}\times10^{-5}\, \text{SNe yr}^{-1}\,\text{Mpc}^{-3}\, h_{70}^{3}$. We further measure a volumetric rate for hydrogen-free superluminous SNe (SLSNe-I) using 8 events at $z{\le}0.2$ of $r^\mathrm{SLSN-I}_v=35_{-13}^{+25}\, \text{SNe yr}^{-1}\text{Gpc}^{-3}\, h_{70}^{3}$, which represents the most precise SLSN-I rate measurement to date. Using a simple cosmic star-formation history to adjust these volumetric rate measurements to the same redshift, we measure a local ratio of SLSN-I to SESN of $\sim1/810^{+1500}_{-94}$, and of SLSN-I to all CCSN types of $\sim 1/3500^{+2800}_{-720}$. However, using host galaxy stellar mass as a proxy for metallicity, we also show that this ratio is strongly metallicity dependent: in low-mass ($\mathrm{log} M_{*} < 9.5 \mathrm{M}_\odot$) galaxies, which are the only environments that host SLSN-I in our sample, we measure a SLSN-I to SESN fraction of $1/300^{+380}_{-170}$ and $1/1700^{+1800}_{-720}$ for all CCSN. We further investigate the SN rates a function of host galaxy stellar mass and show that the specific rates of all core collapse SNe decrease with increasing stellar mass.