.. _physics-satelliteTidalField:

Satellite Tidal Fields
======================

Class providing models of tidal fields experienced by satellite halos---the second-order spatial derivatives of the gravitational potential that characterize the differential force stretching or compressing the satellite. The key quantity returned is the radial component :math:`\Phi_\mathrm{rr}` of the tidal tensor :math:`\Phi_\mathrm{ab} = \partial^2\Phi/\partial x_a \partial x_b`, evaluated at the satellite's orbital position. This tidal field drives tidal heating and mass loss, and is used by tidal stripping rate calculations to determine how rapidly material is removed from the satellite.

**Default implementation:** ``satelliteTidalFieldStandard``

Methods
-------

``tidalTensor`` → ``type(tensorRank2Dimension3Symmetric)``
   Returns the tidal tensor, :math:`\Phi_\mathrm{ab}`.

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

   * ``type (treeNode), intent(inout), optional, target :: nodeHost``

   * ``logical , intent(in ), optional :: atPericenter, includeCentrifugalAcceleration``

``tidalTensorRadial`` → ``double precision``
   Returns the radial component, :math:`\Phi_\mathrm{rr}`, of the tidal tensor, :math:`\Phi_\mathrm{ab}`.

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

   * ``type (treeNode), intent(inout), optional, target :: nodeHost``

   * ``logical , intent(in ), optional :: atPericenter, includeCentrifugalAcceleration``

``tidalTensorDominant`` → ``double precision``
   Returns the dominant eigenvalue of the tidal tensor, :math:`\Phi_\mathrm{ab}`.

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

   * ``type (treeNode), intent(inout), optional, target :: nodeHost``

   * ``logical , intent(in ), optional :: atPericenter, includeCentrifugalAcceleration``

.. _physics-satelliteTidalFieldNull:

``satelliteTidalFieldNull``
---------------------------

A satellite tidal field class which assumes a zero tidal field always.

.. _physics-satelliteTidalFieldSphericalSymmetry:

``satelliteTidalFieldSphericalSymmetry``
----------------------------------------

A satellite tidal field class which assumes a spherically-symmetric host halo, and computes the tidal field accordingly using:

.. math::

   \mathcal{F} = f_\mathrm{boost} \left[ {\mathrm{G} M_\mathrm{host}(<r_\mathrm{p}) \over r_\mathrm{p}^3} - 4 \pi \mathrm{G}
   \rho_\mathrm{host}(r_\mathrm{p}) + \omega_\mathrm{p}^2 \right],

where :math:`r_\mathrm{p}` is the pericentric radius. :math:`M_\mathrm{host}(<r)` is the mass of the host halo enclosed within a sphere of radius :math:`r`, :math:`\rho_\mathrm{host}(r)` is the host density at radius :math:`r`, and :math:`\omega_\mathrm{p}` is the orbital angular velocity at pericenter. The term :math:`f_\mathrm{boost}=`\ ``[factorBoost]`` scales the overall tidal field. Note that the centrifugal term, :math:`\omega_\mathrm{p}^2`, is included only if the ``includeCentrifugalAcceleration`` argument is set to true. The tidal field is evaluated at the current orbital position of the satellite by default, but can be evaluated at the orbital pericenter if the ``atPericenter`` argument is set to true.

**Methods**

* ``factors`` — Compute factors needed for tidal tensor calculation.

**Parameters**

* ``[factorBoost]`` (real; default ``1.0d0``) — The factor by which to boost satellite tidal fields in the ``sphericalSymmetry`` tidal field class.

.. _physics-satelliteTidalFieldStandard:

``satelliteTidalFieldStandard``
-------------------------------

A satellite tidal field class that computes the tidal field in arbitrary geometry. Note that the centrifugal term, :math:`\omega_\mathrm{p}^2`, is included only if the ``includeCentrifugalAcceleration`` argument is set to true. The tidal field is evaluated at the current orbital position of the satellite by default, but can be evaluated at the orbital pericenter if the ``atPericenter`` argument is set to true.

**(Default implementation)**

**Methods**

* ``factors`` — Compute factors needed for tidal tensor calculation.
* ``tidalTensorGet`` — Get the tidal tensor.