.. _physics-hiiRegionLuminosityFunction:

HII Region Luminosity Functions
===============================

Class providing models of the H**ii** region luminosity function---the distribution of ionizing photon rates :math:`Q_\mathrm{H}` (photons s\ :math:`^{-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 :math:`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 :math:`Q_\mathrm{H}`.

   * ``double precision, intent(in ) :: rateHydrogenIonizingPhotonsMinimum, rateHydrogenIonizingPhotonsMaximum``

.. _physics-hiiRegionLuminosityFunctionPowerLaw:

``hiiRegionLuminosityFunctionPowerLaw``
---------------------------------------

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

.. math::

   \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. ,

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

**(Default implementation)**

**Parameters**

* ``[exponent]`` (real; default ``1.73d0``) — Parameter :math:`\gamma` appearing in model for random errors in the halo mass function. Specifically, the fractional error is given by :math:`\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 :math:`\sigma_{12}=`\ ``[normalization]`` and :math:`\gamma=`\ ``[exponent]``.
* ``[rateHydrogenIonizingPhotonsMinimum]`` (real; default ``1.0d48``) — The minimum ionizing photon production rate (:math:`Q_\mathrm{H,min}`, in photons/s) below which the power-law HII region luminosity function is truncated to zero.
* ``[rateHydrogenIonizingPhotonsMaximum]`` (real; default ``huge(0.0d0)``) — The maximum ionizing photon production rate (:math:`Q_\mathrm{H,max}`, in photons/s) above which the power-law HII region luminosity function is truncated to zero.