.. _physics-blackHoleBinarySeparationGrowthRate: Black Hole Binaries Separation Growth Rate ========================================== Class providing models of the rate of change of the binary separation (in Mpc Gyr\ :math:`^{-1}`) for a black hole binary during its inspiral toward coalescence. After the initial dynamical friction phase brings the two black holes close together, the hardening of the binary is driven by three-body stellar scattering, viscous gas torques, or gravitational wave emission depending on the separation. The separation growth rate (which is negative for inspiral) determines the merger timescale. **Default implementation:** ``blackHoleBinarySeparationGrowthRateZero`` Methods ------- ``growthRate`` → ``double precision`` Computes the rate of growth of the separation of the given black hole and its binary companion in units of Mpc/Gyr. * ``class(nodeComponentBlackHole), intent(inout) :: blackHole`` .. _physics-blackHoleBinarySeparationGrowthRateStandard: ``blackHoleBinarySeparationGrowthRateStandard`` ----------------------------------------------- A black hole binary separation growth class that computes the separation growth rate of the binaries following a modified version of :cite:t:`volonteri_assembly_2003` which include terms for dynamical friction, hardening due to scattering of stars and gravitational wave emission. .. math:: \dot{a} = \hbox{min} \left( - \frac{\mathrm{G}\rho _{*}a^2 H}{\sigma}, +\frac{2 \dot{v}_\mathrm{DF} a}{v_c} \right) - \frac{256 G^3 M_{\bullet, 1} M_{\bullet, 2} (M_{\bullet, 1} +M_{\bullet, 2})}{5 c^5 a^3} where :math:`a` is the black hole binary separation, :math:`H` is a dimensionless hardening parameter :math:`H\approx 15` in the limit of a very hard, equal mass binary, :math:`\rho _\star` is the density of stars, :math:`\dot{v}_\mathrm{DF}` is the acceleration (negative) due to dynamical friction, :math:`v_\mathrm{c}` is the circular velocity, :math:`\sigma` is the velocity dispersion of stars. Here the first factor represents hardening due to strong scattering of stars, the second results from dynamical friction with distant stars, gas and dark matter and the last results from the emission of gravitational waves :cite:t:`peters_gravitational_1964`. The acceleration due to dynamical friction is computed using Chandrasekhar's formula: .. math:: \dot{v}_\mathrm{DF}=- {2 \pi \mathrm{G}^2 M_\bullet \over V_\mathrm{C}^2} \sum_{i} \rho_i \log(1+\Lambda_i^2) \left[ \hbox{erf}(X_i)-\left\{ {2 X_i \over \sqrt{\pi}} \exp\left(-X_i^2\right) \right\} \right], where the sum is taken over the spheroid (gaseous plus stellar mass) and dark matter halo components\footnoteThe disk is ignored as the black hole is assumed to be orbiting in a circular orbit in the disk.. Here, .. math:: \Lambda_i = {a \sigma^2 \over \mathrm{G}(M_{\bullet, 1}+M_{\bullet, 2})}, is the Coulomb logarithm and .. math:: X_i = V_\mathrm{c} / \sqrt{2} \sigma. In all of the above equations, the velocity dispersion :math:`\sigma_i` is computed from the spherical Jeans equation assuming an isotropic velocity dispersion if ``[computeVelocityDispersion]``\ :math:`=`\ ``true``. Otherwise, :math:`\sigma_i` is set to the halo virial velocity for dark matter and to the spheroid characteristic velocity for the spheroid. In calculating the rate of hardening due to scattering of stars, the stellar density is reduced by a factor :cite:p:`volonteri_assembly_2003` .. math:: f_\rho = \hbox{min}\left\{ \left[ { 4 a \sigma_\mathrm{spheroid}^2 \over 3 \mathrm{G} (M_{\bullet, 1}+M_{\bullet, 2})} \log\left({\mathrm{G} M_{\bullet, 2} \over 4 \sigma_\mathrm{spheroid}^2 a }\right) \right]^2 , 1 \right\}, if ``[stellarDensityChangeBinaryMotion]``\ :math:`=`\ ``true`` to account for the ejection of stars from the loss cone. **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 `_ 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). .. _physics-blackHoleBinarySeparationGrowthRateZero: ``blackHoleBinarySeparationGrowthRateZero`` ------------------------------------------- A black hole binary separation growth class in which the separation does not grow. **(Default implementation)**