  (Abridged) We present evidence that the HII regions of high luminosity in
disk galaxies may be density bounded, so that a significant fraction of the
ionizing photons emitted by their exciting OB stars escape from the regions.
The key piece of evidence is the presence, in the H\alpha luminosity functions
(LFs) of the populations of HII regions, of glitches, local sharp peaks at an
apparently invariant luminosity, defined as the Stromgren luminosity (L_ Str),
L_H\alpha = L_Str = 10^38.6 (\pm 10^0.1) erg/s (no other peaks are found in any
of the LFs) accompanying a steepening of slope for L_H\alpha> L_Str. This
behavior is readily explicable via a physical model whose basic premises are:
(a) the transition at L_H\alpha = L_Str marks a change from essentially
ionization bounding at low luminosities to density bounding at higher values,
(b) for this to occur the law relating stellar mass in massive star-forming
clouds to the mass of the placental cloud must be such that the ionizing photon
flux produced within the cloud is a function which rises more steeply than the
mass of the cloud. Supporting evidence for the hypothesis of this transition is
presented. If confirmed, the density-bounding hypothesis would imply that the
density-bounded regions were the main sources of the photons which ionize the
diffuse gas in disk galaxies. We estimate that these regions emit sufficient
Lyman continuum not only to ionize the diffuse medium, but to cause a typical
spiral to emit significant ionizing flux into the intergalactic medium. The low
scatter observed in L_Str, less than 0.1 mag rms in the still quite small
sample measured to date, is an invitation to widen the data base, and to
calibrate against primary standards, with the aim of obtaining a precise
standard candle.
