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Circumbinary disk evolution in the presence of an outer companion star

We consider a hierarchical triple system consisting of an inner eccentric binary with an outer companion. A highly misaligned circumbinary disk around the inner binary is subject to two competing effects: (i) nodal precession about the inner binary eccentricity vector that leads to an increase in misalignment (polar alignment) and (ii) Kozai-Lidov (KL) oscillations of eccentricity and inclination driven by the outer companion that leads to a reduction in the misalignment. The outcome depends upon the ratio of the timescales of these effects. If the inner binary torque dominates, then the disk aligns to a polar orientation. If the outer companion torque dominates, then the disk undergoes KL oscillations. In that case, the highly eccentric and misaligned disk is disrupted and accreted by the inner binary, while some mass is transferred to the outer companion. However, when the torques are similar, the outer parts of the circumbinary disk can undergo large eccentricity oscillations while the inclination remains close to the polar orientation. The range of initial disk inclinations that evolve to a polar orientation is smaller in the presence of the outer companion. Disk breaking is also more likely, at least temporarily, during the polar alignment process. The stellar orbits in HD 98800 have parameters such that polar alignment of the circumbinary disk is expected. In the absence of the gas, solid particles are unstable at much smaller radii than the gas disk inner tidal truncation radius because KL driven eccentricity leads to close encounters with the binary.