  The measurement of electron temperatures and metallicities in H ii regions
and Planetary Nebulae (PNe) has-for several decades-presented a problem:
results obtained using different techniques disagree. What it worse, they
disagree consistently. There have been numerous attempts to explain these
discrepancies, but none has provided a satisfactory solution to the problem. In
this paper, we explore the possibility that electrons in H ii regions and PNe
depart from a Maxwell-Boltzmann equilibrium energy distribution. We adopt a
"kappa-distribution" for the electron energies. Such distributions are widely
found in Solar System plasmas, where they can be directly measured. This simple
assumption is able to explain the temperature and metallicity discrepancies in
H ii regions and PNe arising from the different measurement techniques. We find
that the energy distribution does not need to depart dramatically from an
equilibrium distribution. From an examination of data from Hii regions and PNe
it appears that kappa ~ 10 is sufficient to encompass nearly all objects. We
argue that the kappa-distribution offers an important new insight into the
physics of gaseous nebulae, both in the Milky Way and elsewhere, and one that
promises significantly more accurate estimates of temperature and metallicity
in these regions.
