.. _physics-galacticDynamicsBarInstability: Bar instabilities in galactic disks =================================== Class providing models of bar instabilities in galactic disks---the timescale on which the stellar disk becomes bar-unstable and channels material into a central pseudo-bulge via the bar. When the disk mass is sufficiently large relative to the stabilizing dark matter halo, the disk is susceptible to the bar-mode instability :cite:p:`efstathiou_stability_1982`. The returned timescale, external torque, and angular momentum fractions govern the secular mass and angular momentum transfer from disk to bulge component. **Default implementation:** ``galacticDynamicsBarInstabilityEfstathiou1982`` Methods ------- ``timescale`` → ``void`` Returns a timescale on which the bar instability depletes material from a disk into a pseudo-bulge. A negative value indicates no instability. Also returns the net torque due to any external force causing this instability, and the fraction of the angular momentum of the material depleted into the pseudo-bulge which is retained by the disk and the spheroid. * ``type (treeNode), intent(inout) :: node`` * ``double precision , intent( out) :: timescale, externalDrivingSpecificTorque, fractionAngularMomentumRetainedDisk, fractionAngularMomentumRetainedSpheroid`` .. _physics-galacticDynamicsBarInstabilityEfstathiou1982: ``galacticDynamicsBarInstabilityEfstathiou1982`` ------------------------------------------------ A galactic dynamics bar instability class that uses the stability criterion of :cite:t:`efstathiou_stability_1982` to estimate when disks are unstable to bar formation: .. math:: \epsilon \left( \equiv {V_\mathrm{peak} \over \sqrt{\G M_\mathrm{disk}/r_\mathrm{disk}}} \right) < \epsilon_\mathrm{c}, for stability, where :math:`V_\mathrm{peak}` is the peak velocity in the rotation curve\footnoteIn practice, the velocity is evaluated at the disk scale radius and multiplied by the factor :math:`1.1800237580` which relates this velocity to the peak rotation velocity for an isolated, thin exponential disk., :math:`M_\mathrm{disk}` is the mass of the disk and :math:`r_\mathrm{disk}` is its scale length (assuming an exponential disk). The value of :math:`\epsilon_\mathrm{c}` is linearly interpolated in the disk gas fraction between values for purely gaseous and stellar disks as specified by ``[stabilityThresholdStellar]`` and ``[stabilityThresholdGaseous]`` respectively. For disks which are judged to be unstable, the timescale for bar formation is estimated to be .. math:: t_\mathrm{bar} = t_\mathrm{disk} \left( {\epsilon_\mathrm{c} - \epsilon_\mathrm{iso} \over \epsilon_\mathrm{c} - \epsilon} \right)^2, where :math:`\epsilon_\mathrm{iso}` is the value of :math:`\epsilon` for an isolated disk and :math:`t_\mathrm{disk}` is the disk dynamical time, defined as :math:`r/V`, at one scale length. This form gives an infinite timescale at the stability threshold, reducing to a dynamical time for highly unstable disks, while also ensuring that the slope of :math:`t_\mathrm{bar}` is continuous at the instability threshold. This method returns zero external driving torque. **(Default implementation)** **Methods** * ``estimator`` — Compute the stability estimator for the :cite:t:`efstathiou_stability_1982` model for galactic disk bar instability. **Parameters** * ``[stabilityThresholdStellar]`` (default ``1.1d0``) — The stability threshold in the :cite:t:`efstathiou_stability_1982` algorithm for purely stellar disks. * ``[stabilityThresholdGaseous]`` (default ``0.7d0``) — The stability threshold in the :cite:t:`efstathiou_stability_1982` algorithm for purely gaseous disks. * ``[timescaleMinimum]`` (default ``1.0d-9``) — The minimum absolute dynamical timescale (in Gyr) to use in the :cite:t:`efstathiou_stability_1982` algorithm. * ``[fractionAngularMomentumRetainedDisk]`` (default ``1.0d0``) — The fraction of angular momentum of material depleted from the disk by bar instability which is retained in the disk. * ``[fractionAngularMomentumRetainedSpheroid]`` (default ``1.0d0``) — The fraction of angular momentum of material depleted from the disk by bar instability which is retained in the spheroid. .. _physics-galacticDynamicsBarInstabilityEfstathiou1982Tidal: ``galacticDynamicsBarInstabilityEfstathiou1982Tidal`` ----------------------------------------------------- A galactic dynamics bar instability class that uses the stability criterion of :cite:t:`efstathiou_stability_1982` to estimate when disks are unstable to bar formation, but includes an additional term due to external tidal forces: .. math:: \epsilon \left( \equiv {V_\mathrm{peak} \over \sqrt{\G M_\mathrm{disk}/r_\mathrm{disk}} + \hbox{max}(\mathcal{T},0) } \right) < \epsilon_\mathrm{c}, for stability, where :math:`V_\mathrm{peak}` is the peak velocity in the rotation curve (computed here assuming an isolated exponential disk), :math:`M_\mathrm{disk}` is the mass of the disk, :math:`r_\mathrm{disk}` is its scale length (assuming an exponential disk), :math:`\mathcal{T} = \mathcal{F} r_\mathrm{disk}^2` is the external driving specific torque, and :math:`\mathcal{F}` is the external tidal field (evaluated using the selected method; see :galacticus-class:`satelliteTidalField`). The value of :math:`\epsilon_\mathrm{c}` is linearly interpolated in the disk gas fraction between values for purely gaseous and stellar disks as specified by ``stabilityThresholdStellar`` and ``stabilityThresholdGaseous`` respectively. For disks which are judged to be unstable, the timescale for bar formation is estimated to be .. math:: t_\mathrm{bar} = t_\mathrm{disk} {\epsilon_\mathrm{c} - \epsilon_\mathrm{iso} \over \epsilon_\mathrm{c} - \epsilon}, where :math:`\epsilon_\mathrm{iso}` is the value of :math:`\epsilon` for an isolated disk and :math:`t_\mathrm{disk}` is the disk dynamical time, defined as :math:`r/V`, at one scale length. This form gives an infinite timescale at the stability threshold, reducing to a dynamical time for highly unstable disks. **Methods** * ``tidalTensorRadial`` — Compute the radial term of the tidal tensor. **Parameters** * ``[massThresholdHarrassment]`` (default ``0.0d0``) — The host halo mass threshold for harassment to take effect. .. _physics-galacticDynamicsBarInstabilityFixedTimescale: ``galacticDynamicsBarInstabilityFixedTimescale`` ------------------------------------------------ A simple model for galactic disk bar instability in which the bar formation timescale is a fixed constant set by ``[timescale]``. Angular momentum redistributed during bar formation is partitioned between the disk and spheroid according to ``[fractionAngularMomentumRetainedDisk]`` and ``[fractionAngularMomentumRetainedSpheroid]``. **Parameters** * ``[timescale]`` (default ``1.0d0``) — The fixed timescale (in Gyr) for bar instability; the disk is depleted exponentially on this timescale, with the redistributed mass transferred to the spheroid. * ``[fractionAngularMomentumRetainedDisk]`` (default ``1.0d0``) — The fraction of angular momentum of material depleted from the disk by bar instability which is retained in the disk. * ``[fractionAngularMomentumRetainedSpheroid]`` (default ``1.0d0``) — The fraction of angular momentum of material depleted from the disk by bar instability which is retained in the spheroid. .. _physics-galacticDynamicsBarInstabilityStable: ``galacticDynamicsBarInstabilityStable`` ---------------------------------------- A galactic dynamics bar instability class which assumes perfect stability for galactic disks and so returns an infinite timescale, and no external driving torque.