Resonances in retrograde circumbinary discs

Abstract

We analyse the interaction of an eccentric binary with a circular coplanar circumbinary disc that rotates in a retrograde sense with respect to the binary. In the circular binary case, no Lindblad resonances lie within the disc and no Lindblad resonant torques are produced, as was previously known. By analytic means, we show that when the binary orbit is eccentric, there exist components of the gravitational potential of the binary which rotate in a retrograde sense to the binary orbit and so rotate progradely with respect to this disc, allowing a resonant interaction to occur between the binary and the disc. The resulting resonant torques distinctly alter the disc response from the circular binary case. We describe results of three-dimensional hydrodynamic simulations to explore this effect and categorise the response of the disc in terms of modes whose strengths vary as a function of binary mass ratio and eccentricity. These mode strengths are weak compared to the largest mode strengths expected in the prograde case where the binary and disc rotate in the same sense. However, for sufficiently high binary eccentricity, resonant torques open a gap in a retrograde circumbinary disc, while permitting gas inflow on to the binary via gas streams. The inflow results in a time varying accretion rate on to the binary that is modulated over the binary orbital period, as was previously found to occur in the prograde case.

Modelling circumbinary protoplanetary disks

“…Nixon & Lubow (2015) find that eccentric binaries produce modes with l m. In particular, in their retrograde circumbinary disk simulations, highly eccentric binaries (e b ≥ 0.6) produce powerful l = −1, m = 2 modes. We remove the time dependence of the disk disturbances by since our analysis is concerned with the eccentric Kepler-16 system (e b = 0.16) and because we focus only on a comparative study of the azimuthal mode strengths between simulations.…”

Planet formation and stability in polar circumbinary discs

“…Remarkably, r2 and r4 are in phase opposition and the oscillations are quickly damped over time (compared to r1 and r6). Also, for low inclinations (r5 and r6) the disc becomes coplanar more quickly in the retrograde configuration (r5) compared to the prograde (r6) because the inner cavity, opened by resonant torques, is smaller for retrograde configurations (Miranda & Lai 2015;Nixon & Lubow 2015). Therefore, the disc responds more quickly to the binary torques.…”

Linear analysis of the evolution of nearly polar low-mass circumbinary discs

“…AL94 determined circumbinary disc inner radii by this procedure for discs that are coplanar and rotate in the same sense as the central binary. For tilted circumbinary discs with respect to the orbital plane of the binary, the Lindblad resonance torques are weaker than the coplanar case, resulting in a decreasing central hole size with tilt (Nixon & Lubow 2015;Miranda & Lai 2015). The reasons for the decrease are that the disc can lie farther away from the binary in the noncoplanar case and also because the relative speeds of the disc and binary increases with tilt.…”

“…We determine the resonant torque exerted on a polar circumbinary disc due to an eccentric binary. We closely follow the approach of Nixon & Lubow (2015) that was applied to counter rotating discs. This approach has advantages over previous methods (e.g., Goldreich & Tremaine 1980;Artymowicz & Lubow 1994;Miranda & Lai 2015) that perform expansions in the binary eccentricity that is not generally small for binaries.…”