'On the red supergiant problem': a rebuttal, and a consensus on the upper mass cut-off for II-P progenitors

The 'red supergiant (RSG) problem' describes the claim that the brightest RSG progenitors to Type II-P supernovae (SNe) 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 cut-off of M_hi = 17 M_⊙ and below 25 M_⊙ will die as RSGs, but with no visible SN explosion as the BH is formed. However, we have previously cautioned that this cut-off is more likely to be higher and has large uncertainties ( $M_{\rm hi}=19^{+4}_{-2}\,\mathrm{ M}_{\odot }$ ), meaning that the statistical significance of the RSG problem is less than 2σ. Recently, Kochanek has claimed that our work is statistically flawed, and with his analysis has argued that the upper mass cut-off is as low as M_hi = 15.7 ± 0.8 M_⊙, giving the RSG problem a significance of >10σ. In this letter, we show that Kochanek's low cut-off is caused by a statistical misinterpretation, and the associated fit to the progenitor mass spectrum can be ruled out at the 99.6 per cent confidence level. Once this problem is remedied, Kochanek's best fit becomes $M_{\rm hi} =19^{+4}_{-2}\,\mathrm{ M}_{\odot }$ , in excellent agreement with our work. Finally, we argue that, in the search for an 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.