.. _physics-darkMatterHaloBias:

Dark Matter Halo Biases
=======================

Class providing models of the linear bias factor :math:`b(M, t)` of dark matter halos---the ratio of halo-to-matter overdensity on large scales, describing how strongly halos cluster relative to the underlying dark matter distribution. More massive halos form in rarer, higher-:math:`\nu` peaks and are therefore more strongly biased. The bias enters the two-halo term of the halo model power spectrum, void-galaxy cross-correlations, and galaxy clustering predictions. Implementations typically follow analytic fitting functions (e.g.\ :cite:author:`tinker_large_2010` :cite:year:`tinker_large_2010`) calibrated to N-body simulations as a function of halo mass and redshift.

**Default implementation:** ``darkMatterHaloBiasTinker2010``

Methods
-------

``biasByMass`` → ``double precision``
   Returns the bias of a halo specified by a mass (in :math:`\mathrm{M}_\odot`) and time (in Gyr).

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

   * ``double precision, intent(in ), optional :: radius``

``biasByNode`` → ``double precision``
   Returns the large-scale linear bias factor :math:`b` of the dark matter halo represented by the supplied :term:`node`, extracted from the node's basic component for its mass and formation time.

   * ``type (treeNode), intent(inout) :: node``

   * ``double precision , intent(in ), optional :: radius``

.. _physics-darkMatterHaloBiasPressSchechter:

``darkMatterHaloBiasPressSchechter``
------------------------------------

A dark matter halo mass bias class consistent with the halo mass function of :cite:t:`press_formation_1974` (see :cite:p:`mo_analytic_1996`).

.. _physics-darkMatterHaloBiasSheth2001:

``darkMatterHaloBiasSheth2001``
-------------------------------

A dark matter halo mass bias class utilizing the algorithm of :cite:t:`sheth_ellipsoidal_2001`.

.. _physics-darkMatterHaloBiasTinker2005:

``darkMatterHaloBiasTinker2005``
--------------------------------

A dark matter halo bias class which applies the radial dependence fitting function of :cite:p:`tinker_mass--light_2005` to another bias class.

.. _physics-darkMatterHaloBiasTinker2010:

``darkMatterHaloBiasTinker2010``
--------------------------------

A dark matter halo mass bias class utilizing the algorithm of :cite:t:`tinker_large_2010`. The bias is computed at the appropriate virial overdensity (see :galacticus-class:`virialDensityContrast`).

**(Default implementation)**