On `On the Red Supergiant Problem': a rebuttal, and a consensus on the upper mass cutoff for II-P progenitors

The `Red Supergiant Problem' describes the claim that the brightest Red Supergiant (RSG) progenitors to type II-P supernovae are significantly fainter than RSGs in the field. This mismatch has been interpreted by several authors as being a manifestation of the mass threshold for the production of black holes (BHs), such that stars with initial masses above a cutoff of $M_{\rm hi}=17$M$_\odot$ and below 25$M_\odot$ will die as RSGs, but with no visible SN explosion as the BH is formed. However, we have previously cautioned that this cutoff is more likely to be higher and has large uncertainties ($M_{\rm hi}=19^{+4}_{-2}M_{\odot}$), meaning that the statistical significance of the RSG Problem is less than $2\sigma$. Recently, Kochanek (2020) has claimed that our work is statistically flawed, and with their analysis has argued that the upper mass cutoff is as low as $M_{\rm hi} = 15.7 \pm 0.8M_\odot$, giving the RSG Problem a significance of $>10\sigma$. In this letter, we show that Kochanek's low cutoff is caused by a statistical misinterpretation, and the associated fit to the progenitor mass spectrum can be ruled out at the 99.6\% confidence level. Once this problem is remedied, Kochanek's best fit becomes $M_{\rm hi} =19^{+4}_{-2}M_{\odot}$, in excellent agreement with our work. Finally, we argue that, in the search for a RSG `vanishing' as it collapses directly to a BH, any such survey would have to operate for decades before the absence of any such detection became statistically significant.