Black Hole Binaries Initial Separation

Class providing models of the initial physical separation (in Mpc) between two black holes immediately after the galaxies hosting them merge. When the two host galaxies coalesce the black holes begin to sink toward the merger remnant center by dynamical friction. The initial separation sets the starting point for the subsequent binary evolution and eventually determines the rate of energy emission by gravitational waves and the time until coalescence.

Default implementation: blackHoleBinaryInitialSeparationSpheroidRadiusFraction

Methods

separationInitial → double precision

Computes the initial separation of a newly formed black hole binary black holes.

• type(treeNode), intent(inout), target :: node, nodeHost

blackHoleBinaryInitialSeparationSpheroidRadiusFraction

A black hole binary initial separation class that assumes that the initial separation of the binary is equal to a fixed fraction [spheroidRadiusFraction] of the larger of the spheroid scale radii of the two merging galaxies.

(Default implementation)

Parameters

• [spheroidRadiusFraction] (default 0.0d0) — The fraction of the spheroid radius at which merging black holes will be initially placed.

blackHoleBinaryInitialSeparationTidalRadius

A black hole binary initial separation class that assumes an initial separation that corresponds to the distance at which the satellite galaxy is tidally stripped to its half-mass radius, thus only leaving the central massive black hole. Specifically, the initial radius is given by:

\[{M_\mathrm{sat} \over 2 r_\mathrm{sat,1/2}^3 } = - {\mathrm{d} \over \mathrm{d} r} {M_\mathrm{host}(r_\mathrm{initial}) \over r_\mathrm{initial}^2},\]

where \(M_\mathrm{sat}\) is the mass of the satellite galaxy, \(r_\mathrm{sat,1/2}\) is its half mass radius, \(M_\mathrm{host}(r)\) is the mass of the host galaxy within radius \(r\) and \(r_\mathrm{initial}\) is the initial radius.

blackHoleBinaryInitialSeparationVolonteri2003

A black hole binary initial separation class that assumes that the initial separation follows the relationship described in Volonteri et al. (2003)

\[ r_\mathrm{initial} = { \mathrm{G} (M_{\bullet,1} + M_{\bullet, 2}) \over 2 \sigma_\mathrm{DM}^2 }\]

where \(M_{\bullet, 1}\) and \(M_{\bullet, 2}\) are the masses of the black holes and \(\sigma_\mathrm{DM}\) is the velocity dispersion of the dark matter, which we assume to equal the virial velocity of the dark matter halo.