HII Region Density Distributions

Class providing models for the distribution of hydrogen number density \(n_\mathrm{H}\) within H**ii** regions—the probability distribution of gas density within the photoionized nebula. The cumulative density distribution is returned between specified minimum and maximum \(n_\mathrm{H}\) values, and is used to model the density-dependent emission line ratios and ionization structure of the nebula. Different implementations (e.g.log-normal) capture the clumpy, inhomogeneous nature of real H**ii** regions, which affects nebular line luminosities and the ionizing photon budget.

Default implementation: hiiRegionDensityDistributionLogNormal

Methods

cumulativeDensityDistribution → double precision

Return the cumulative distribution of HII region hydrogen density between a minimum and maximum \(n_\mathrm{H}\).

  • double precision, intent(in ) :: densityHydrogenMinimum, densityHydrogenMaximum

hiiRegionDensityDistributionDeltaFunction

A class for the distribution of hydrogen density in a HII region in which the distribution is a delta function. Specifically:

\[p(n_\mathrm{H}) = \delta(n_\mathrm{H} - n_\mathrm{H,0}),\]

where \(n_\mathrm{H,0}=\)[densityHydrogen].

Parameters

  • [densityHydrogen] (default 100.0d0) — The density of hydrogen, \(n_\mathrm{H}\), in HII regions (in units of cm\(^{-3}\)).

  • [spin] (default 0.03687d0) — The fixed value of spin in a \(\delta\)-function spin distribution.

hiiRegionDensityDistributionLogNormal

A class for the distribution of hydrogen density in a HII region in which the distribution is a lognormal, specifically:

\[\begin{split}p(n_\mathrm{H}) = \left\{ \begin{array}{ll} \frac{1}{\sqrt{2\pi} n_\mathrm{H} \sigma} \exp\left(-\frac{1}{2}\left[\frac{\log(n_\mathrm{H})-\log(n_\mathrm{H,0})}{\sigma}\right]^2\right) & \hbox{ if } n_\mathrm{H,min} < n_\mathrm{H} < n_\mathrm{H,max}, \\ 0 & \hbox{ otherwise.} \end{array} \right.\end{split}\]

(Default implementation)

Parameters

  • [densityHydrogenReference] (default 250.0d0) — The parameter \(n_\mathrm{H,0}\) in the log normal distribution of HII region densities.

  • [sigma] (default 1.8d0) — The parameter \(\sigma\) in the log normal distribution of HII region densities.

  • [densityHydrogenMinimum] (default 1.0d1) — Minimum value of hydrogen density in HII regions.

  • [densityHydrogenMaximum] (default 1.0d5) — Maximum value of hydrogen density in HII regions.