Analytic Estimates of the Effect of Plasma Density Fluctuations on HII
  Region Density Diagnostics
  An analytic calculation is made of the effect of plasma density fluctuations
on some spectroscopic diagnostics commonly used in the study of HII regions and
planetary nebulae. To permit an analytic treatment, attention is restricted to
the case of density fluctuations possessing an exponential probability
distribution function (pdf). The present investigation is made in support of a
completely numerical and more extensive study of nebular diagnostics by
Bergerud et al (2019). Results from this paper are presented in terms of graphs
of the observed quantity (spectroscopic line ratio) versus mean nebular
density. Our results yield a higher density estimate, given the same observed
line ratio, for the case of a nebula with density fluctuations than for the
case of a nebula with uniform density. This is qualitatively consistent with
the typically observed case, in which the observations lead to the inference of
a filling factor < 1. Our results are in quantitative agreement with those of
Bergerud et al (2019), and thus corroborate those calculations for the case of
an exponential pdf.
