Evolution of binary black holes in self gravitating discs

Abstract

Context. Massive black hole binaries, formed in galaxy mergers, are expected to evolve in dense circumbinary discs. Understanding of the disc-binary coupled dynamics is vital to assess both the final fate of the system and its potentially observable features. Aims. Aimed at understanding the physical roots of the secular evolution of the binary, we study the interplay between gas accretion and gravity torques in changing the binary elements (semi-major axis and eccentricity) and its total angular momentum budget. We pay special attention to the gravity torques, by analysing their physical origin and location within the disc. Methods. We analysed three-dimensional smoothed particle hydrodynamics simulations of the evolution of initially quasi-circular massive black hole binaries (BHBs) residing in the central hollow (cavity) of massive self-gravitating circumbinary discs. We performed a set of simulations adopting different thermodynamics for the gas within the cavity and for the "numerical size" of the black holes. Results. We show that (i) the BHB eccentricity growth found in our previous work is a general result, independent of the accretion and the adopted thermodynamics; (ii) the semi-major axis decay depends not only on the gravity torques but also on their subtle interplay with the disc-binary angular momentum transfer due to accretion; (iii) the spectral structure of the gravity torques is predominately caused by disc edge overdensities and spiral arms developing in the body of the disc and, in general, does not reflect directly the period of the binary; (iv) the net gravity torque changes sign across the BHB corotation radius (positive inside vs negative outside) We quantify the relative importance of the two, which appear to depend on the thermodynamical properties of the instreaming gas, and which is crucial in assessing the disc-binary angular momentum transfer; (v) the net torque manifests as a purely kinematic (nonresonant) effect as it stems from the low density cavity, where the material flows in and out in highly eccentric orbits. Conclusions. Both accretion onto the black holes and the interaction with gas streams inside the cavity must be taken into account to assess the fate of the binary. Moreover, the total torque exerted by the disc affects the binary angular momentum by changing all the elements (mass, mass ratio, eccentricity, semimajor axis) of the black hole pair. Commonly used prescriptions equating tidal torque to semi-major axis shrinking might therefore be poor approximations for real astrophysical systems.

A reduced orbital period for the supermassive black hole binary candidate in the quasar PG 1302-102?

“…The two runs discussed below differ only in their BH mass ratio (q = 0.1 and q = 0.5). A wider range of simulations is needed in the future, to address possibilities such as eccentric (Roedig et al 2012), tilted (Hayasaki et al 2015), or retrograde (Nixon et al 2011) binary orbits.…”

“…Binaries with 0.3 ∼ < q ∼ < 0.8 clear a lopsided central cavity in the disc, causing variability on three time-scales. The dominant period, (3 − 8)t bin is that of an over dense lump, orbiting at the ridge of the cavity, with additional periodicities at t bin and ≈ 0.5t bin (MacFadyen & Milosavljević 2008;Shi et al 2012;Noble et al 2012;Roedig et al 2012;D'Orazio et al 2013;Farris et al 2014). The dominant period depends on the size of the cavity, and thus on disc parameters, such as temperature and viscosity.…”

Multiple periods in the variability of the supermassive black hole binary candidate quasar PG1302-102?

“…More specifically, if the binary is embedded in a thin disk, the gas will be expelled from the central region due to torques exerted by the binary, creating a cavity (Artymowicz & Lubow 1994). Several hydrodynamical simulations (Hayasaki, Mineshige & Sudou 2007;MacFadyen & Milosavljević 2008;Noble et al 2012;Shi et al 2012;Roedig et al 2012;D'Orazio, Haiman & MacFadyen 2013;Farris et al 2014) indicate that the interaction of the individual BHs with the inner edge of the accretion disk can pull gaseous streams into the cavity, resulting in periodic modulation of the accretion rate at timescales corresponding to ≈1/2 and 1 times the binary's orbital period. For high BH mass ratios (q ≡ M1/M2 ∼ > 0.3), the cavity is lopsided, leading to the formation of a hotspot in the accretion disk.…”

Massive Binary Black Holes in Galactic Nuclei and Their Path to Coalescence

“…(MacFadyen and Milosavljević 2008;Roedig et al 2012;Shi et al 2012). The above expression for the torque relates the rate of binary orbital decay to the local disc mass M edge d…”