HII Region Luminosity Functions

Class providing models of the H**ii** region luminosity function—the distribution of ionizing photon rates \(Q_\mathrm{H}\) (photons s\(^{-1}\)) among H**ii** regions within a galaxy, characterizing the population of star-forming nebulae. Methods return the cumulative distribution and cumulative luminosity of regions between specified minimum and maximum ionizing photon rates, allowing the total nebular emission and its variation with galaxy star formation rate to be computed for emission-line luminosity function predictions.

Default implementation: hiiRegionLuminosityFunctionPowerLaw

Methods

cumulativeDistributionFunction → double precision

Returns the cumulative distribution of the HII region luminosity function between a minimum and maximum \(Q_\mathrm{H}\).

  • double precision, intent(in ) :: rateHydrogenIonizingPhotonsMinimum, rateHydrogenIonizingPhotonsMaximum

cumulativeLuminosity → double precision

Returns the cumulative luminosity from the HII region luminosity function between a minimum and maximum \(Q_\mathrm{H}\).

  • double precision, intent(in ) :: rateHydrogenIonizingPhotonsMinimum, rateHydrogenIonizingPhotonsMaximum

hiiRegionLuminosityFunctionPowerLaw

An HII region luminosity function class in which the luminosity function is given by:

\[\begin{split}\phi(Q_H) \propto \left\{ \begin{array}{ll} Q_\mathrm{H}^{-\alpha} & \hbox{ if } Q_\mathrm{H,min} < Q_\mathrm{H} < Q_\mathrm{H,max} \\ 0 & \hbox{ otherwise} \end{array} \right. ,\end{split}\]

Where \(Q_H\) is the rate of photon production rate, \(Q_\mathrm{H,min}=\)[rateHydrogenIonizingPhotonsMinimum] and \(Q_\mathrm{H,max}=\)[rateHydrogenIonizingPhotonsMaximum] and the minimum and maximum HII region luminosities respectively, and \(\alpha=\)[exponent].

(Default implementation)

Parameters

  • [exponent] (default 1.73d0) — Exponent of the differential luminosity function.

  • [rateHydrogenIonizingPhotonsMinimum] (default 1.0d48) — The minimum ionizing photon production rate (\(Q_\mathrm{H,min}\), in photons/s) below which the power-law HII region luminosity function is truncated to zero.

  • [rateHydrogenIonizingPhotonsMaximum] (default huge(0.0d0)) — The maximum ionizing photon production rate (\(Q_\mathrm{H,max}\), in photons/s) above which the power-law HII region luminosity function is truncated to zero.

  • [exponent] (default 1.0d0) — Halo masses will be (pseudo-)uniformly distributed in \([\log(M)]^{1/(1+\alpha)}\) where \(\alpha=\)exponent.

  • [wavelengthMinimum] — The minimum wavelength (in units of AA) for the power-law spectrum.

  • [wavelengthMaximum] — The maximum wavelength (in units of AA) for the power-law spectrum.

  • [exponent] — The exponent of the power-law spectrum.

  • [normalization] — The normalization (in units of \(L_\odot / \AA\)) of the power-law spectrum.

  • [normalization] — Parameter \(\sigma_{12}\) appearing in model for random errors in the halo mass function.

  • [fractionalErrorHighMass] — Parameter \(\sigma_\infty\) appearing in model for random errors in the halo mass function.

  • [exponent] — Parameter \(\gamma\) appearing in model for random errors in the halo mass function. Specifically, the fractional error is given by \(\sigma(M) = \left[ \sigma^2_{12} \left({M_\mathrm{halo} \over 10^{12}\mathrm{M}_\odot}\right)^{2\gamma} + \sigma^2_\infty \right]^{1/2}\), where \(\sigma_{12}=\)[normalization] and \(\gamma=\)[exponent].

  • [correlationModelTrivial] (default .true.) — If true, the correlation between mass errors of pairs of halos is unity for halos with identical mass and time, and zero otherwise. If false, a power-law correlation model in mass ratio and expansion factor ratio is used instead.

  • [correlationNormalization] (default 0.0d0) — Variable \(C_0\) in the model for the correlation between halo mass errors: \(C_{12} = C_0 [M_2/M_1]^\alpha [(1+z_2)/(1+z_1)]^\beta\).

  • [correlationMassExponent] (default 0.0d0) — Variable \(\alpha\) in the model for the correlation between halo mass errors: \(C_{12} = C_0 [M_2/M_1]^\alpha [(1+z_2)/(1+z_1)]^\beta\).

  • [correlationRedshiftExponent] (default 0.0d0) — Variable \(\beta\) in the model for the correlation between halo mass errors: \(C_{12} = C_0 [M_2/M_1]^\alpha [(1+z_2)/(1+z_1)]^\beta\).

  • [radiusLow] (default +0.0154d0) — The low-mass limit of the characteristic scale radius \(r_0\) (in Mpc) in the power-law scale radius model, giving the scale radius normalization for low-mass halos as a function of peak height and expansion factor.

  • [radiusHigh] (default +0.0962d0) — The high-mass limit of the characteristic scale radius \(r_1\) (in Mpc) in the power-law scale radius model, giving the scale radius normalization for high-mass halos.

  • [radiusTransition] (default +1.2137d0) — The peak height \(\nu\) at which the characteristic scale radius transitions between its low-mass and high-mass limiting values in the power-law scale radius model.

  • [radiusWidth] (default +0.5482d0) — The parameter \(\Delta r\) in the power-law scale radius model.

  • [massLow] (default +0.3895d0) — The parameter \(\alpha_0\) in the power-law scale radius model.

  • [massHigh] (default +0.2984d0) — The parameter \(\alpha_1\) in the power-law scale radius model.

  • [massTransition] (default -0.2583d0) — The parameter \(\alpha_\nu\) in the power-law scale radius model.

  • [massWidth] (default +16.6050d0) — The parameter \(\Delta \alpha\) in the power-law scale radius model.

  • [expansionFactorLow] (default -0.6977d0) — The parameter \(\beta_0\) in the power-law scale radius model.

  • [expansionFactorHigh] (default +0.7972d0) — The parameter \(\beta_1\) in the power-law scale radius model.

  • [expansionFactorTransition] (default +0.5395d0) — The parameter \(\beta_\nu\) in the power-law scale radius model.

  • [expansionFactorWidth] (default +0.4282d0) — The parameter \(\Delta \beta\) in the power-law scale radius model.

  • [scatter] (default +0.1513d0) — The scatter (in dex) in the scale radius at fixed halo mass and redshift in the power-law scale radius model, representing the intrinsic halo-to-halo variation in concentration.

  • [index] (default 0.9649d0) — The index of the power-law primordial power spectrum.

  • [running] (default 0.0d0) — The running, \(\d n_\mathrm{s} / \d \ln k\), of the power spectrum index.

  • [runningRunning] (default 0.0d0) — The running-of-the-running, \(\d^2 n_\mathrm{s} / \d \ln k^2\), of the power spectrum index.

  • [wavenumberReference] (default 1.0d0) — When a running power spectrum index is used, this is the wavenumber, \(k_\mathrm{ref}\), at which the index is equal to [index].

  • [runningSmallScalesOnly] (default .false.) — If true then the index runs only for \(k > k_\mathrm{ref}\), for smaller \(k\) the index is constant.