The uncertain masses of progenitors of core-collapse supernovae and direct-collapse black holes

We show that it is not possible to determine the final mass M-fin of a red supergiant (RSG) at the pre-supernova (SN) stage from its luminosity L and effective temperature T-eff alone. Using a grid of stellar models, we demonstrate that for a given value of L and T-eff, an RSG can have a range of M-fin as wide as 3 to 45 M-circle dot. While the probability distribution within these limits is not flat, any individual determination of M-fin for an RSG will be degenerate. This makes it difficult to determine its evolutionary history and to map M-fin to an initial mass. Single stars produce a narrower range that is difficult to accurately determine without making strong assumptions about mass-loss, convection, and rotation. Binaries would produce a wider range of RSG M-fin. However, the final Helium core mass MHe-core is well determined by the final luminosity and we find log(MHe-core/M-circle dot) = 0.659 log(L/L-circle dot) - 2.630. Using this relationship, we derive MHe-core for directly imaged SN progenitors and one failed SN candidate. The value of M-fin for stripped star progenitors of SNe IIb is better constrained by L and T-eff due to the dependence of T-eff on the envelope mass M-env for M-env less than or similar to 1 M-circle dot. Given the initial mass function, our results apply to the majority of progenitors of core-collapse SNe, failed SNe, and direct-collapse black holes.