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.