Type II supernova energetics and comparison of light curves to shock-cooling models

During the first few days after explosion, Type II supernovae (SNe) are dominated by relatively simple physics. Theoretical predictions regarding early-time SN light curves in the ultraviolet (UV) and optical bands are thus quite robust. We present, for the first time, a sample of $57$ $R$-band Type II SN light curves that are well monitored during their rise, having $>5$ detections during the first 10 days after discovery, and a well-constrained time of explosion to within $1-3$ days. We show that the energy per unit mass ($E/M$) can be deduced to roughly a factor of five by comparing early-time optical data to the model of Rabinak & Waxman (2011), while the progenitor radius cannot be determined based on $R$-band data alone. We find that Type II SN explosion energies span a range of $E/M=(0.2-20)\times 10^{51} \; \rm{erg/(10 M}_\odot$), and have a mean energy per unit mass of $\left\langle E/M \right\rangle = 0.85\times 10^{51} \; \rm{erg/(10 M}_\odot$), corrected for Malmquist bias. Assuming a small spread in progenitor masses, this indicates a large intrinsic diversity in explosion energy. Moreover, $E/M$ is positively correlated with the amount of $^{56}\rm{Ni}$ produced in the explosion, as predicted by some recent models of core-collapse SNe. We further present several empirical correlations. The peak magnitude is correlated with the decline rate ($\Delta m_{15}$), the decline rate is weakly correlated with the rise time, and the rise time is not significantly correlated with the peak magnitude. Faster declining SNe are more luminous and have longer rise times. This limits the possible power sources for such events.