If the neutrino luminosity from the proto-neutron star formed during a massive star core collapse exceeds a critical threshold , a supernova ( SN ) results .
Using spherical quasi-static evolutionary sequences for hundreds of progenitors over a range of metallicities , we study how the explosion threshold maps onto observables , including the fraction of successful explosions , the neutron star ( NS ) and black hole ( BH ) mass functions , the explosion energies ( E _ { SN } ) and nickel yields ( M _ { Ni } ) , and their mutual correlations .
Successful explosions are intertwined with failures in a complex pattern that is not simply related to initial progenitor mass or compactness .
We predict that progenitors with initial masses of 15 \pm 1 , 19 \pm 1 , and \sim 21 - 26 M _ { \odot } are most likely to form BHs , that the BH formation probability is non-zero at solar-metallicity and increases significantly at low metallicity , and that low luminosity , low Ni-yield SNe come from progenitors close to success/failure interfaces .
We qualitatively reproduce the observed E _ { SN } - M _ { Ni } correlation , we predict a correlation between the mean and width of the NS mass and E _ { SN } distributions , and that the means of the NS and BH mass distributions are correlated .
We show that the observed mean NS mass of \simeq 1.33 M _ { \odot } implies that the successful explosion fraction is higher than 0.35 .
Overall , we show that the neutrino mechanism can in principle explain the observed properties of SNe and their compact objects .
We argue that the rugged landscape of progenitors and outcomes mandates that SN theory should focus on reproducing the wide ranging distributions of observed SN properties .