.. _physics-starFormationRateNuclearStarClusters:

Star Formation Rates in Nuclear Star Clusters
=============================================

Class providing models of the star formation rate (in :math:`\mathrm{M}_\odot \, \mathrm{Gyr}^{-1}`) in the nuclear star cluster component of a galaxy---the compact, dense stellar system residing at the galactic center. Nuclear star cluster star formation is fuelled by gas inflows driven by disk instabilities and dynamical processes, and is governed by local gas conditions analogous to, but more extreme than, those in the main disk. Implementations may apply the same star formation prescription as the disk but evaluated at the nuclear cluster's characteristic density and dynamical time.

**Default implementation:** ``starFormationRateNuclearStarClustersKrumholz2009``

Methods
-------

``rate`` → ``double precision``
   Returns the rate (in units of :math:`\mathrm{M}_\odot` Gyr\ :math:`^{-1}`) for star formation in the nuclear star cluster component of ``node``.

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

.. _physics-starFormationRateNuclearStarClustersKrumholz2009:

``starFormationRateNuclearStarClustersKrumholz2009``
----------------------------------------------------

A star formation rate implementing the model of :cite:p:`antonini_coevolution_2015` for galactic :term:`NSC`. This model uses the :cite:p:`krumholz_star_2009` star formation rule:

.. math::

   \dot{M}_\star^\mathrm{NSC} = f_c\frac{M_\mathrm{gas}^\mathrm{gas}}{t_{SF}},

where :math:`f_c` is the fraction of cold gas available for star formation given by

.. math::

   f_c = 1 - \left( 1 + \left[ { 3 s \over 4 (1+\delta)} \right]^{-5} \right)^{-1/5},

if :math:`f_c > 0.02` and :math:`f_c = 0.02` otherwise, with

.. math::

   \delta = 0.0712 \left[ 0.1 s^{-1} + 0.675 \right]^{-2.8},

and

.. math::

   s = {\ln(1+0.6\chi+0.01\chi) \over 0.04 \Sigma_1 Z^\prime},

with

.. math::

   \chi = 0.77 \left[ 1 + 3.1 Z^{\prime 0.365} \right],

and :math:`\Sigma_1= \Sigma_\mathrm{gas}^\mathrm{NSC}/\mathrm{M}_\odot \hbox{pc}^{-2}` where :math:`\Sigma_\mathrm{gas}^\mathrm{NSC}=\frac{M_\mathrm{gas}^{NSC}}{4\pi r^\mathrm{NSC}}` is the surface density of the NSC gas reservoir. The timescale is given by

.. math::

   t_\mathrm{SF}^{-1} = (2.36~\mathrm{Gyr})^{-1}\times \left\{ \begin{array}{cc} \left(\frac{\Sigma_\mathrm{res}}{\Sigma_\mathrm{th}} \right) ^{-0.33}, &
   \Sigma_\mathrm{res} \le \Sigma_\mathrm{th} \\  \left(\frac{\Sigma_\mathrm{res}}{\Sigma_\mathrm{th}} \right) ^{0.33}, & \Sigma_\mathrm{res} > \Sigma_\mathrm{th} \end{array}  \right. ,

with :math:`\Sigma_\mathrm{th}=85\mathrm{M}_\odot\,\hbox{pc}^{-2}`

**(Default implementation)**

**Methods**

* ``calculationReset`` — Reset memoized calculations.
* ``computeFactors`` — Compute constant factors required.
* ``surfaceDensityFactors`` — Compute surface density factors required.
* ``molecularFraction`` — Compute the molecular fraction.

**Parameters**

* ``[frequencyStarFormation]`` (default ``2.36d0``) — The characteristic timescale for star formation in nuclear star clusters (in units of Gyr), corresponding to the normalization factor :math:`(2.36~\mathrm{Gyr})^{-1}` in the :cite:t:`krumholz_star_2009` star formation rate law.
* ``[frequencyStarFormation]`` (default ``0.385d0``) — The star formation frequency (in units of Gyr\ :math:`^{-1}`) in the "Krumholz-McKee-Tumlinson" star formation timescale calculation.
* ``[clumpingFactorMolecularComplex]`` (default ``5.0d0``) — The density enhancement (relative to mean disk density) for molecular complexes in the "Krumholz-McKee-Tumlinson" star formation timescale calculation.
* ``[molecularFractionFast]`` (default ``.false.``) — Selects whether the fast (but less accurate) fitting formula for molecular hydrogen should be used in the "Krumholz-McKee-Tumlinson" star formation timescale calculation.
* ``[assumeMonotonicSurfaceDensity]`` (default ``.false.``) — If true, assume that the surface density in disks is always monotonically decreasing.