.. _physics-satelliteTidalHeatingRate:

Satellite Halo Tidal Heating Rates
==================================

Class providing models of tidal heating rates in satellite halos. Specifically, the integrated, normalized (i.e. the energy divided by radius squared) tidal heating energy, :math:`Q_\mathrm{tidal}`.

**Default implementation:** ``satelliteTidalHeatingRateZero``

Methods
-------

``heatingRate`` → ``double precision``
   Return the satellite tidal heating rate for ``node`` (in units of (km/s/Mpc)\ :math:`^2`/Gyr).

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

.. _physics-satelliteTidalHeatingRateGnedin1999:

``satelliteTidalHeatingRateGnedin1999``
---------------------------------------

A satellite tidal heating rate class which uses the formalism of :cite:t:`gnedin_tidal_1999` to compute the heating rate:

.. math::

   \dot{Q}_\mathrm{tidal}=\frac{1}{3}\epsilon\left[1+\left(\frac{T_\mathrm{shock}}{T_\mathrm{orb}}\right)^2\right]^{-\gamma}
   g_{ij} G^{ij}

where :math:`T_\mathrm{orb}` and :math:`T_\mathrm{shock}` are the orbital period and shock duration, respectively, of the satellite, :math:`\epsilon=`\ ``[epsilon]`` and :math:`\gamma=`\ ``[gamma]`` are model parameters, :math:`g_{ij}` is the tidal tensor, and :math:`G_{ij}` is the integral with respect to time of :math:`g_{ij}` along the orbit of the satellite.  Upon tidal heating, a mass element at radius :math:`r_\mathrm{i}` expands to radius :math:`r_\mathrm{f}`, according to the equation

.. math::

   \frac{1}{r_\mathrm{f}}=\frac{1}{r_\mathrm{i}}-\frac{2r_\mathrm{i}^3Q_\mathrm{tidal}}{\mathrm{G}M_\mathrm{sat}(<r_\mathrm{i})}.

**Parameters**

* ``[epsilon]`` (default ``3.0d0``) — Parameter, :math:`\epsilon`, controlling the tidal heating rate of satellites in the ``Gnedin1999`` method.
* ``[gamma]`` (default ``2.5d0``) — Parameter, :math:`\gamma`, controlling the tidal heating rate of satellites in the ``Gnedin1999`` method.

.. _physics-satelliteTidalHeatingRateZero:

``satelliteTidalHeatingRateZero``
---------------------------------

A satellite tidal heating rate class which implements a tidal heating rate model in which the heating rate is always zero.

**(Default implementation)**