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An analytic calculation is made of the effect of plasma density fluctuationson some spectroscopic diagnostics commonly used in the study of HII regions andplanetary nebulae. To permit an analytic treatment, attention is restricted tothe case of density fluctuations possessing an exponential probabilitydistribution function (pdf). The present investigation is made in support of acompletely numerical and more extensive study of nebular diagnostics byBergerud et al (2019). Results from this paper are presented in terms of graphsof the observed quantity (spectroscopic line ratio) versus mean nebulardensity. Our results yield a higher density estimate, given the same observedline ratio, for the case of a nebula with density fluctuations than for thecase of a nebula with uniform density. This is qualitatively consistent withthe typically observed case, in which the observations lead to the inference ofa filling factor < 1. Our results are in quantitative agreement with those ofBergerud et al (2019), and thus corroborate those calculations for the case ofan exponential pdf.

Analytic Estimates of the Effect of Plasma Density Fluctuations on HII Region Density Diagnostics