.. _physics-massFunctionIncompleteness:

Mass Function Incompletenesses
==============================

Class providing models of the survey completeness fraction for observed mass functions---the probability that an object of a given mass is included in an observational sample. Incompleteness arises from flux limits, surface brightness thresholds, or volume corrections, and causes the observed number counts to fall below the true underlying mass function at low masses. The ``completeness`` method returns the fraction (between 0 and 1) of objects at a given mass that are expected to appear in the sample, allowing model predictions to be corrected before comparison with data.

**Default implementation:** ``massFunctionIncompletenessComplete``

Methods
-------

``completeness`` → ``double precision``
   Return the completeness of the observational sample at the given mass.

   * ``double precision, intent(in ) :: mass``

.. _physics-massFunctionIncompletenessComplete:

``massFunctionIncompletenessComplete``
--------------------------------------

A mass function incompleteness class that assumes the observational sample is fully complete at all masses---i.e., the completeness fraction is identically 1 for every object regardless of mass. This is the appropriate choice when no observational selection effects need to be modelled, and serves as the trivial (no-op) implementation of the :galacticus-class:`massFunctionIncompletenessClass` interface.

**(Default implementation)**

.. _physics-massFunctionIncompletenessSurfaceBrightness:

``massFunctionIncompletenessSurfaceBrightness``
-----------------------------------------------

A mass function incompleteness class which models the surface brightness distribution of galaxies as a normal distribution with mean :math:`\langle \mu \rangle (M) = \alpha \log_{10}(M/M_0)+\beta`, with root-variance :math:`\sigma`, where :math:`\alpha=`\ ``[slope]``, :math:`\beta=`\ ``[zeroPoint]``, and :math:`\sigma=`\ ``[scatter]``. The completeness is the fraction of this distribution above the surface brightness limit given by ``[limit]``.

**Parameters**

* ``[limit]`` — Limiting surface brightness for mass function incompleteness calculations.
* ``[zeroPoint]`` — Mass zero point for the mass function incompleteness surface brightness model, i.e. :math:`M_0` in :math:`\mu(M) = \alpha \log_{10}(M/M_0)+\beta`.
* ``[slope]`` — Slope of mass function incompleteness surface brightness model, i.e. :math:`\alpha` in :math:`\mu(M) = \alpha \log_{10}(M/M_0)+\beta`.
* ``[offset]`` — Offset in the mass function incompleteness surface brightness model, i.e. :math:`beta` in :math:`\mu(M) = \alpha \log_{10}(M/M_0)+\beta`.
* ``[scatter]`` — Scatter in the mass function incompleteness surface brightness model.