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

mergerRemnantSizeCole2000

A merger remnant size class which uses uses the algorithm of Cole et al. (2000) to compute merger remnant spheroid sizes. Specifically

\[\frac{(M_1+M_2)^2}{ r_\mathrm{new}} = \frac{M_1^2}{r_1} + \frac{M_2^2}{r_2} + \frac{ f_\mathrm{orbit}}{c} \frac{M_1 M_2}{r_1+r_2},\]

where \(M_1\) and \(M_2\) are the baryonic masses of the components of the merging galaxies that will end up in the spheroid component of the remnantfootnoteDepending on the merging rules (see mergerMassMovements) not all mass may be placed into the spheroid component of the remnant. and \(r_1\) and \(r_2\) are the half mass radii of those same components of the merging galaxiesfootnoteIn 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 component (disk and spheroid) which will become part of the spheroid component of the remnant., \(r_\mathrm{new}\) is the half mass radius of the spheroidal component of the remnant galaxy and \(c\) is a constant which depends on the distribution of the mass. For a Hernquist spheroid \(c=0.40\) can be found by numerical integration while for a exponential disk \(c=0.49\). For simplicity a value of \(c=0.5\) is adopted for all components. The parameter \(f_\mathrm{orbit}=\)energyOrbital depends on the orbital parameters of the galaxy pair. For example, a value of \(f_\mathrm{orbit} = 1\) 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 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 component of the remnant. To account for this additional matter, an effective boost factor, \(f_\mathrm{boost}\), to the specific angular momentum of each component of each merging galaxy is computed:

\[f_\mathrm{boost} = {j \over \sqrt{\mathrm{G} M r_{1/2}}},\]

where \(j\) is the specific angular momentum of the component, \(M\) is its total baryonic mass and \(r_\mathrm{1/2}\) 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:

\[j_\mathrm{new} = \langle f_\mathrm{boost} \rangle r_\mathrm{new} V_\mathrm{new},\]

where

\[V_\mathrm{new}^2 = {\mathrm{G} (M_1+M_2)\over r_\mathrm{new}}.\]

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.

mergerRemnantSizeCovington2008

A merger remnant size class which uses the algorithm of Covington et al. (2008) to compute merger remnant spheroid sizes. Specifically

(16)\[\frac{(M_1+M_2)^2}{ r_\mathrm{new}} = \left[ \frac{M_1^2}{r_1} + \frac{M_2^2}{r_2} + \frac{ f_\mathrm{orbit}}{c} \frac{M_1 M_2}{r_1+r_2}\right] \left( 1 + f_\mathrm{gas} C_\mathrm{rad} \right),\]

where \(M_1\) and \(M_2\) are the baryonic masses of the merging galaxies and \(r_1\) and \(r_2\) are their half mass radii, \(r_\mathrm{new}\) is the half mass radius of the spheroidal component of the remnant galaxy and \(c\) is a constant which depends on the distribution of the mass. For a Hernquist spheroid \(c=0.40\) can be found by numerical integration while for a exponential disk \(c=0.49\). For simplicity a value of \(c=0.5\) is adopted for all components. The parameter \(f_\mathrm{orbit}=\)mergerRemnantSizeOrbitalEnergy depends on the orbital parameters of the galaxy pair. For example, a value of \(f_\mathrm{orbit} = 1\) corresponds to point mass galaxies in circular orbits about their center of mass. The final term on the right hand side of eqn. ((16)) gives a correction to the final energy of the remnant due to dissipational losses based on the results of Covington et al. (2011), with

\[f_\mathrm{gas} = {M_\mathrm{1,gas}+M_\mathrm{2,gas} \over M_1+M_2}\]

begin the gas fraction of the progenitor galaxies. By default, \(C_\mathrm{rad}=2.75\) (Covington et al., 2011). To account for the effects of dark matter and non-spheroid baryonic matter the same approach is used as in the Cole et al. (2000) algorithm (see mergerRemnantSizeCole2000).

(Default implementation)

Parameters

  • [energyOrbital] (default 1.0d0) — The orbital energy in units of the characteristic orbital energy.

  • [efficiencyRadiative] (default 2.75d0) — The coefficient, \(C_\mathrm{rad}\) energy used in the Covington et al. (2008) merger remnant size algorithm.

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.