.. _physics-mergerRemnantSize: Merger Remnant Sizes ==================== Class providing models of merger remnant sizes---the half-mass radius, circular velocity, and specific angular momentum of the spheroid formed when two galaxies merge. Energy and angular momentum conservation arguments relate the remnant size to the progenitor radii, masses, and orbital parameters. These quantities set the structural properties of merger-built bulges and determine the subsequent evolution of the stellar velocity dispersion and black hole mass in the remnant galaxy. **Default implementation:** ``mergerRemnantSizeCovington2008`` Methods ------- ``get`` → ``void`` Determine the half-mass radius, circular velocity, and specific angular momentum of the spheroidal remnant formed when two galaxies merge, using energy and angular momentum conservation arguments applied to the progenitor masses, radii, and orbital parameters. * ``type (treeNode), intent(inout) :: node`` * ``double precision , intent( out) :: radius, velocityCircular, angularMomentumSpecific`` .. _physics-mergerRemnantSizeCole2000: ``mergerRemnantSizeCole2000`` ----------------------------- A merger remnant size class which uses uses the algorithm of :cite:t:`cole_hierarchical_2000` to compute merger remnant spheroid sizes. Specifically .. math:: \frac{(M_1+M_2)^2}{ r_\mathrm{new}} = \frac{M_1^2}{r_1} + \frac{M_2^2}{r_2} + \frac{ f_\mathrm{orbit}}{c} \frac{M_1 M_2}{r_1+r_2}, where :math:`M_1` and :math:`M_2` are the baryonic masses of the components of the merging galaxies that will end up in the spheroid :term:`component` of the remnant\footnoteDepending on the merging rules (see :galacticus-class:`mergerMassMovements`) not all mass may be placed into the spheroid :term:`component` of the remnant. and :math:`r_1` and :math:`r_2` are the half mass radii of those same components of the merging galaxies\footnoteIn practice, Galacticus computes a weighted average of the disk and spheroid half-mass radii of each galaxy, with weights equal to the masses of each :term:`component` (disk and spheroid) which will become part of the spheroid :term:`component` of the remnant., :math:`r_\mathrm{new}` is the half mass radius of the spheroidal :term:`component` of the remnant galaxy and :math:`c` is a constant which depends on the distribution of the mass. For a Hernquist spheroid :math:`c=0.40` can be found by numerical integration while for a exponential disk :math:`c=0.49`. For simplicity a value of :math:`c=0.5` is adopted for all components. The parameter :math:`f_\mathrm{orbit}=`\ ``energyOrbital`` depends on the orbital parameters of the galaxy pair. For example, a value of :math:`f_\mathrm{orbit} = 1` corresponds to point mass galaxies in circular orbits about their center of mass. A subtlety arises because the above expression accounts for only the baryonic mass of material which becomes part of the spheroid :term:`component` of the remnant. In reality, there are additional terms in the energy equation due to the interaction of this material with any dark matter mass in each galaxy and any baryonic mass of each galaxy which does not become part of the spheroid :term:`component` of the remnant. To account for this additional matter, an effective boost factor, :math:`f_\mathrm{boost}`, to the specific angular momentum of each :term:`component` of each merging galaxy is computed: .. math:: f_\mathrm{boost} = {j \over \sqrt{\mathrm{G} M r_{1/2}}}, where :math:`j` is the specific angular momentum of the component, :math:`M` is its total baryonic mass and :math:`r_\mathrm{1/2}` is its half-mass radius. The mass-weighted mean boost factor is found by combining those of all components which will form part of the spheroid of the remnant. The final specific angular momentum of the remnant spheroid is then given by: .. math:: j_\mathrm{new} = \langle f_\mathrm{boost} \rangle r_\mathrm{new} V_\mathrm{new}, where .. math:: V_\mathrm{new}^2 = {\mathrm{G} (M_1+M_2)\over r_\mathrm{new}}. **Methods** * ``reform`` — Implements a halo reformation event. **Parameters** * ``[energyOrbital]`` (default ``1.0d0``) — The orbital energy used in the "cole2000" merger remnant sizes calculation in units of the characteristic orbital energy. * ``[ignoreUnphysicalConditions]`` (default ``.false.``) — If true, ignore unphysical conditions (e.g. negative masses) and leave the size unchanged. * ``[massFactorReformation]`` (default ``2.0d0``) — The factor by which halo mass must have increased to trigger a new formation event. * ``[reformationOnPromotionOnly]`` (default ``.false.``) — Specifies whether halo reformation should occur only at node promotion events, or at the precise time that the halo mass has increased sufficiently in mass. .. _physics-mergerRemnantSizeCovington2008: ``mergerRemnantSizeCovington2008`` ---------------------------------- A merger remnant size class which uses the algorithm of :cite:t:`covington_predicting_2008` to compute merger remnant spheroid sizes. Specifically .. math:: :label: eq-Covington2008Radius \frac{(M_1+M_2)^2}{ r_\mathrm{new}} = \left[ \frac{M_1^2}{r_1} + \frac{M_2^2}{r_2} + \frac{ f_\mathrm{orbit}}{c} \frac{M_1 M_2}{r_1+r_2}\right] \left( 1 + f_\mathrm{gas} C_\mathrm{rad} \right), where :math:`M_1` and :math:`M_2` are the baryonic masses of the merging galaxies and :math:`r_1` and :math:`r_2` are their half mass radii, :math:`r_\mathrm{new}` is the half mass radius of the spheroidal :term:`component` of the remnant galaxy and :math:`c` is a constant which depends on the distribution of the mass. For a Hernquist spheroid :math:`c=0.40` can be found by numerical integration while for a exponential disk :math:`c=0.49`. For simplicity a value of :math:`c=0.5` is adopted for all components. The parameter :math:`f_\mathrm{orbit}=`\ ``mergerRemnantSizeOrbitalEnergy`` depends on the orbital parameters of the galaxy pair. For example, a value of :math:`f_\mathrm{orbit} = 1` corresponds to point mass galaxies in circular orbits about their center of mass. The final term on the right hand side of eqn. (:eq:`eq-Covington2008Radius`) gives a correction to the final energy of the remnant due to dissipational losses based on the results of :cite:t:`covington_effects_2011`, with .. math:: f_\mathrm{gas} = {M_\mathrm{1,gas}+M_\mathrm{2,gas} \over M_1+M_2} begin the gas fraction of the progenitor galaxies. By default, :math:`C_\mathrm{rad}=2.75` :cite:p:`covington_effects_2011`. To account for the effects of dark matter and non-spheroid baryonic matter the same approach is used as in the :cite:t:`cole_hierarchical_2000` algorithm (see :galacticus-class:`mergerRemnantSizeCole2000`). **(Default implementation)** **Parameters** * ``[energyOrbital]`` (default ``1.0d0``) — The orbital energy in units of the characteristic orbital energy. * ``[efficiencyRadiative]`` (default ``2.75d0``) — The coefficient, :math:`C_\mathrm{rad}` energy used in the :cite:t:`covington_predicting_2008` merger remnant size algorithm. .. _physics-mergerRemnantSizeNull: ``mergerRemnantSizeNull`` ------------------------- A merger remnant size class which does nothing at all. It is useful, for example, when running Galacticus to study dark matter only (i.e. when no galaxy properties are computed). **Parameters** * ``[dimensionless]`` (default ``.true.``) — If true the null profile is considered to be dimensionless.