The `Red Supergiant Problem': the upper luminosity boundary of type-II
  supernova progenitors
  By comparing the properties of Red Supergiant (RSG) supernova progenitors to
those of field RSGs, it has been claimed that there is an absence of
progenitors with luminosities $L$ above $\log(L/L_\odot) > 5.2$. This is in
tension with the empirical upper luminosity limit of RSGs at $\log(L/L_\odot) =
5.5$, a result known as the `Red Supergiant Problem'. This has been interpreted
as evidence for an upper mass threshold for the formation of black-holes. In
this paper, we compare the observed luminosities of RSG SN progenitors with the
observed RSG $L$-distribution in the Magellanic Clouds. Our results indicate
that the absence of bright SN II-P/L progenitors in the current sample can be
explained at least in part by the steepness of the $L$-distribution and a small
sample size, and that the statistical significance of the Red Supergiant
Problem is between 1-2$\sigma$ . Secondly, we model the luminosity distribution
of II-P/L progenitors as a simple power-law with an upper and lower cutoff, and
find an upper luminosity limit of $\log(L_{\rm hi}/L_\odot) =
5.20^{+0.17}_{-0.11}$ (68\% confidence), though this increases to $\sim$5.3 if
one fixes the power-law slope to be that expected from theoretical arguments.
Again, the results point to the significance of the RSG Problem being within
$\sim 2 \sigma$. Under the assumption that all progenitors are the result of
single-star evolution, this corresponds to an upper mass limit for the parent
distribution of $M_{\rm hi} = 19.2{\rm M_\odot}$, $\pm1.3 {\rm M_\odot
(systematic)}$, $^{+4.5}_{-2.3} {\rm M_\odot}$ (random) (68\% confidence
limits).
