.. _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.

**Parameters**

* ``[dimensionless]`` (default ``.true.``) — If true the null profile is considered to be dimensionless.

.. _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]`` (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.

**Parameters**

* ``[stellarDensityChangeBinaryMotion]`` (default ``.true.``) — If true, account for the change in stellar density caused by the black hole binary's motion through the stellar background when computing the hardening rate of the binary via stellar scattering.
* ``[computeVelocityDispersion]`` (default ``.false.``) — Specifies whether or not the velocity dispersion of dark matter and stars should be computed using Jeans equation in black hole binary hardening calculations. If ``false``, then the velocity dispersions are assumed to equal the characteristic velocity of dark matter and spheroid.
* ``[bondiHoyleAccretionEnhancementSpheroid]`` (default ``5.0d0``) — The factor by which the Bondi-Hoyle accretion rate of spheroid gas onto black holes is enhanced.
* ``[bondiHoyleAccretionEnhancementHotHalo]`` (default ``6.0d0``) — The factor by which the Bondi-Hoyle accretion rate of hot halo gas onto black holes is enhanced.
* ``[bondiHoyleAccretionEnhancementNuclearStarCluster]`` (default ``5.0d0``) — The factor by which the Bondi-Hoyle accretion rate of :term:`NSC` gas onto black holes is enhanced.
* ``[bondiHoyleAccretionHotModeOnly]`` (default ``.true.``) — Determines whether accretion from the hot halo should only occur if the halo is in the hot accretion mode.
* ``[bondiHoyleAccretionTemperatureSpheroid]`` (default ``1.0d2``) — The assumed temperature (in Kelvin) of gas in the spheroid when computing Bondi-Hoyle accretion rates onto black holes.
* ``[bondiHoyleAccretionTemperatureNuclearStarCluster]`` (default ``1.0d2``) — The assumed temperature (in Kelvin) of gas in the :term:`NSC` when computing Bondi-Hoyle accretion rates onto black holes.
* ``[instantaneousRecyclingApproximation]`` (default ``.false.``) — If true, then use an instantaneous recycling approximation when computing recycling rates.
* ``[instantaneousYieldApproximation]`` (default ``.false.``) — If true, then use an instantaneous recycling approximation when computing yield rates.
* ``[instantaneousEnergyInputApproximation]`` (default ``.false.``) — If true, then use an instantaneous recycling approximation when computing energy input rates.
* ``[massLongLived]`` (default ``1.0d0``) — The mass below which stars are assumed to be infinitely long-lived in the instantaneous approximation for stellar evolution.
* ``[ageEffective]`` (default ``13.8d0``) — The effective age to use for computing SNeIa yield when using the instantaneous stellar evolution approximation.
* ``[recycledFraction]`` (default ``0.0d0``) — The recycled fraction to use in the instantaneous stellar evolution approximation. (If not specified it will be computed internally.)
* ``[metalYield]`` (default ``0.0d0``) — The metal yield to use in the instantaneous stellar evolution approximation. (If not specified it will be computed internally.)
* ``[integrationToleranceRelative]`` (default ``4.0d-3``) — The relative tolerance used when integrating the flux of stellar populations through filters.
* ``[integrationToleranceDegrade]`` (default ``.false.``) — If ``true``, automatically degrade the relative tolerance used when integrating the flux of stellar populations through filters to ensure convergence.
* ``[storeToFile]`` (default ``.true.``) — Specifies whether or not stellar populations luminosities (integrated under a filter) should be stored to file for rapid reuse.
* ``[storeDirectory]`` (default ``inputPath(pathTypeDataDynamic)//'stellarPopulations'``) — Specifies the directory to which stellar populations luminosities (integrated under a filter) should be stored to file for rapid reuse.
* ``[maximumAgeExceededIsFatal]`` (default ``.true.``) — Specifies whether or not exceeding the maximum available age of the stellar population is fatal.
* ``[inactiveBoundMass]`` (default ``.false.``) — Specifies whether or not the bound mass variable of the standard satellite component is inactive (i.e. does not appear in any ODE being solved).
* ``[odeToleranceAbsolute]`` (default ``0.01d0``) — The absolute tolerance used in solving differential equations for node evolution.
* ``[odeToleranceRelative]`` (default ``1.0d-2``) — The relative tolerance used in solving differential equations for node evolution.
* ``[odeJacobianStepSizeRelative]`` (default ``0.01d0``) — The relative step size to use when perturbing properties for purposes of computing a finite difference approximation to the ODE system Jacobian.
* ``[odeAlgorithm]`` (default ``var_str('rungeKuttaCashKarp')``) — The algorithm to use in the ODE solver.
* ``[odeAlgorithmNonJacobian]`` (default ``var_str('rungeKuttaCashKarp')``) — The algorithm to use in the ODE solver.
* ``[odeLatentIntegratorType]`` (default ``var_str('trapezoidal')``) — The type of integrator to use for latent variables.
* ``[odeLatentIntegratorOrder]`` (default ``15``) — The order of the integrator for latent variables.
* ``[odeLatentIntegratorIntervalsMaximum]`` (default ``1000``) — The maximum number of intervals allowed in the integrator for latent variables.
* ``[profileOdeEvolver]`` (default ``.false.``) — Specifies whether or not to profile the ODE evolver.
* ``[reuseODEStepSize]`` (default ``.true.``) — If true, re-use the previous ODE step size when resuming the evolution of a node. Otherwise, the initial step size is not specified.
* ``[enforceNonNegativity]`` (default ``.false.``) — If true, properties that are marked as non-negative (e.g. masses) will be evolved in such a way as to enforce that non-negativity.
* ``[allTreesExistAtFinalTime]`` (default ``.true.``) — Specifies whether or not all merger trees are expected to exist at the final requested output time. If set to false, then trees which finish before a given output time will be ignored.
* ``[dumpTreeStructure]`` (default ``.false.``) — Specifies whether merger tree structure should be dumped to a `dot <http://www.graphviz.org/>`_ file.
* ``[timestepHostRelative]`` (default ``0.1d0``) — The maximum allowed relative timestep for node evolution relative to the time of the host halo.
* ``[timestepHostAbsolute]`` (default ``1.0d0``) — The maximum allowed absolute timestep (in Gyr) for node evolution relative to the time of the host halo.
* ``[fractionTimestepSatelliteMinimum]`` (default ``0.0d0``) — The minimum fraction of the timestep imposed by the "satellite in host" criterion to evolve over. If the timestep allowed is smaller than this fraction, the actual timestep will be reduced to zero. This avoids forcing satellites to take a large number of very small timesteps, and instead defers evolving a satellite until a large timestep can be taken.
* ``[backtrackToSatellites]`` (default ``.false.``) — If true, after successfully evolving a node with satellites, revisit the satellites and attempt to evolve them again.
* ``[profileSteps]`` (default ``.false.``) — Specifies whether or not to profile the ODE evolver.
* ``[outputsGroupName]`` (default ``var_str('Outputs')``) — The name of the HDF5 group to which outputs will be written.
* ``[outputReferences]`` (default ``.false.``) — Specifies whether or not references to individual merger tree datasets should be output.
* ``[xAxisLabel]`` (default ``var_str('x')``) — Axis label for the property (x-axis) of the output analysis.
* ``[yAxisLabel]`` (default ``var_str('y')``) — Axis label for the function value (y-axis) of the output analysis.
* ``[targetLabel]`` (default ``var_str('')``) — Label identifying the comparison/target dataset, if any.
* ``[xAxisIsLog]`` (default ``.false.``) — Whether the x-axis should be displayed on a logarithmic scale.
* ``[yAxisIsLog]`` (default ``.false.``) — Whether the y-axis should be displayed on a logarithmic scale.
* ``[valueTarget]`` — Target dataset values to compare against, one per bin of the output analysis.
* ``[covarianceTarget]`` — Target-dataset covariance matrix corresponding to the ``valueTarget`` array.
* ``[initialMassForSupernovaeTypeII]`` (default ``8.0d0``) — The minimum mass that a star must have in order that is result in a Type II supernova.
* ``[supernovaEnergy]`` (default ``1.0d51``) — The canonical energy released per supernova event (in ergs), used to compute the total mechanical energy input from the supernova population; the default value of :math:`10^{51}` erg corresponds to the standard core-collapse supernova energy.
* ``[efficiency]`` (default ``0.1d0``) — Specifies the efficiency with which outflowing gas is stripped from the hot halo, following the prescription of :cite:author:`font_colours_2008` (:cite:year:`font_colours_2008`; i.e. this is the parameter :math:`\epsilon_\mathrm{strip}` in their eqn. 6).