8.2 Interaction with cold gas

The specific angular momentum of a cold flow might easily exceed that of the binary. The gas then tends to settle into rotationally supported, geometrically thin rings and disks (recall that “cold” gas is colder than the virial temperature but can be hot enough to be ionized).

Observations offer abundant evidence for the presence of dense gas in galactic nuclei. Thin, Keplerian molecular disks on scales $0.1- 0.5pc$ have been seen in the water maser emission in the nuclei of Seyfert galaxies [154 , 59 , 81 ]. The Galactic nucleus contains a $6 4× 10 Mo .$ black hole surrounded by a $4 5 ~ (10 - 10 )Mo .$ molecular gas torus at distances $> 1 pc$ from the SBH [94 ]. Compact stellar disks on scales $> 20 pc$ , which are fossil evidence of past gas circularization, are evident in the nuclei of many galaxies [167 ]. Massive accretion disks must be present in quasars and the Narrow-Line Seyfert I nuclei to account for what appears to be rapid accretion onto the central SBHs in these systems. However, the structure of these disks at radii comparable to the size of a hard SBH binary is unknown. The principal challenges to constructing extended disk models are the instabilities related to incomplete ionization and the susceptibility to gravitational fragmentation [103 , 198 , 149 , 74 ].

If a disk surrounding a binary SBH is initially inclined with respect to the binary’s orbital plane, the quadrupole component of the binary’s gravitational potential causes differential precession in the disk at the rate [111 ]

which results in a warping of the disk. As in the Bardeen-Petterson mechanism [15 , 173 , 193 ], the warp either dissipates, or smears around the binary, resulting ultimately in a nearly axisymmetric disk in the binary’s orbital plane.

Interest in co-planar, circumbinary disks stems from their ability to extract a binary’s angular momentum via a form of tidal coupling. Two interrelated questions might be posed:

What is the response of a circumbinary disk to the binary’s tidal forcing?

and:

How does such a disk affect the evolution of the binary’s orbit?

Existing attempts to answer these questions have employed ad hoc models for the form of the binary-disk torque coupling [172 , 93 ], or have been restricted to binaries with components of very unequal mass [4 ], where an array of neighboring Lindblad resonances facilitates binary-disk coupling [71 ], much like the coupling between a massive planet and its natal gas disk [72 ]. Early numerical simulations of circumbinary disks with nearly equal masses [5 ], however, suggested that the disks are truncated exterior to the resonances, which was interpreted as a consequence of a collisionless nonlinear parametric instability [189 , 39 ]. Fluid dynamical theory of circumbinary disk truncation is still lacking.

In a circular binary the outer Lindblad resonances (OLR) are located at radii $r = (1 + 1/m)2/3 m$ , where $m = 1,2,...$ is the order in the decomposition of the binary’s gravitational potential into multipoles:

The outermost OLR is located at $r ~~ 1.6a$ . The resonances are radii in the disk where the natural, epicyclic frequency of radial oscillations in the disk is an integer multiple of the rate at which a packet of disk gas receives tidal “kicks” by the binary. The forcing near a resonance, as well as at a radius where surface density in the disk exhibits a large gradient, excites nonaxisymmetric propagating disturbances, or “density waves”, in the disk.

The gravitational potential of eccentric binaries contains low-frequency components that are absent in circular binaries. These low-frequency components activate resonances located at larger radii than in the circular case, and might lead to mutual excitation and reinforcement of the binary and the disk eccentricities [162 , 70 ]. Many extrasolar planets, which are thought to form in circumstellar disks, are notably eccentric² , suggesting that dynamical coupling between a binary point mass (a star and a planet, or a pair of black holes) and a gas disk is conducive to eccentricity growth. The observed circumbinary disks in young stellar binaries such as GG Tau, which are typically eccentric, are truncated at radii a few times the semimajor axis [130 ], which lends support to this hypothesis. Eccentricity in SBH binaries accelerates coalescence due to gravitational wave emission (Equation 7 ) and might be detectable in gravitational wave trains. Density waves transport angular momentum outward through the circumbinary disk. Angular momentum flux carried by the waves is extracted from the binary’s angular momentum. The binary experiences a negative torque equal and opposite to the total angular momentum flux transferred to the disk. The location of the inner edge of the disk reflects a balance between the angular momentum flux deposited into the disk, and the angular momentum flux transported through the disk by another, possibly viscous mechanism. Wave momentum is deposited into the disk material via a form of dissipative damping. The location in the disk where the waves are damped can be separated by many wavelengths from the location where they are excited. The damping could take place in the nonlinear steepening and the breaking of wave crests [192 , 179 ]. In marginally optically thick disks, radiation damping might also play a role [24 ]. Yet another form of damping could be due to the dissipation of wave shear if the disk is strongly viscous [207 ]. The amplitude of the density waves is a steeply decreasing function of the radius of excitation. The amplitude is diminished if the waves are nonlinear at excitation and damp in situ, but then one expects the inner edge to recede where in situ damping shuts off.

The intricate and insufficiently understood nature of binary-disk interactions calls for grid-based hydrodynamical simulations with a shock-capturing capability. The necessity that the radial wavelength, which is smaller than the vertical scale height of the disk, be resolved by multiple cells, places severe demands on the computational resources, especially if a three dimensional representation of the disk is required. It should also be noted that the radiative and thermal structure of accretion disks around single SBHs are not adequately understood on any radial scale.

As a binary’s semimajor axis decreases due to stellar, gas dynamical, or gravitational radiation processes, a circumbinary disk’s inner edge spreads inward viscously while maintaining constant edge-to-semimajor axis ratio, e.g. $redge/a ~ 2$ . In the final stages of the gravitational radiation-driven inspiral, however, the time scale on which the semimajor axis decays becomes shorter than the viscous time scale, and the disk can no longer keep up with the binary, resulting in binary-disk detachment. On the relevant length scales the disk might be dominated by radiation pressure and the electron scattering opacity; the structure and the stability of such disks is an active research area [210 ].