The Uncertain Masses of Progenitors of Core Collapse Supernovae and Direct Collapse Black Holes

Abstract

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

Re-submitted to MNRAS Letters after referee comments

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