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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 $M_{\rm fin}$ of a red supergiant (RSG) at the pre-supernova (SN) stage from its luminosity $L$ and effective temperature $T_{\rm eff}$ alone. Using a grid of stellar models, we demonstrate that for a given value of $L$ and $T_{\rm eff}$, a RSG can have a range of $M_{\rm fin}$ as wide as 3 to $45~\mathrm{M}_{\odot}$. While the probability distribution within these limits is not flat, any individual determination of $M_{\rm fin}$ for a RSG will be degenerate. This makes it difficult to determine its evolutionary history and to map $M_{\rm fin}$ 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 $M_{\rm fin}$. However, the final Helium core mass M$_{\rm He-core}$ is well determined by the final luminosity and we find $\log (\mathrm{M}_{\rm He-core}/M_{\odot}) = 0.659 \log (L/\mathrm{L}_{\odot}) -2.630$ Using this relationship, we derive M$_{\rm He-core}$ for directly imaged SN progenitors and one failed SN candidate. The value of $M_{\rm fin}$ for stripped star progenitors of SNe IIb is better constrained by $L$ and $T_{\rm eff}$ due to the dependence of $T_{\rm eff}$ on the envelope mass $M_{\rm env}$ for $M_{\rm env} \lesssim 1~$M$_{\odot}$. Given the initial mass function, our results apply to the majority of progenitors of core collapse SNe, failed SNe and direct collapse black holes.