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 (CCSN) 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 CCSNe, including 26 stripped-envelope SNe (SESNe), we show that the overall CCSN volumetric rate is rCC v = 9.10 ^+1.56 _−1.27 × 10⁻⁵ SNe yr⁻¹ Mpc⁻³ h³ ₇₀ at z = 0.028, and the SESN volumetric rate is r ^SE _v = 2.41 ^+0.81 _−0.64 × 10⁻⁵ SNe yr⁻¹ Mpc⁻³ h³ ₇₀. We further measure a volumetric rate for hydrogen-free superluminous SNe (SLSNe-I) using eight events at z ≤ 0.2 of r^SLSN−I _v = 35 ⁺²⁵ ₋₁₃ SNe yr⁻¹ Gpc⁻³ h³ ₇₀, 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 ∼1/810+1500 −94 , and of SLSN-I to all CCSN types of ∼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 (logM_∗ < 9.5 M_⊙) galaxies, which are the only environments that host SLSN-I in our sample, we measure an 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 CCSNe decrease with increasing stellar mass.