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