Abstract
Dynamical studies suggest that most of the circumbinary discs (CBDs) should be coplanar. However, under certain initial conditions, the CBD can evolve toward polar orientation. Here we extend the parametric study of polar configurations around detached close-in binaries through N-body simulations. For polar configurations around binaries with mass ratios q below 0.7, the nominal location of the mean motion resonance (MMR) 1 : 4 predicts the limit of stability for eB > 0.1. Alternatively, for eB < 0.1 or q ∼ 1, the nominal location of the MMR 1 : 3 is the closest stable region. The presence of a giant planet increases the region of forbidden polar configurations around low mass ratio binaries with eccentricities eB∼ 0.4 with respect to rocky earth-like planets. For equal mass stars, the eccentricity excitation Δβ of polar orbits smoothly increases with decreasing distance to the binary. For q < 1, Δβ can reach values as high as 0.4. Finally, we studied polar configurations around HD 98800BaBb and show that the region of stability is strongly affected by the relative positions of the nodes. The most stable configurations in the system correspond to polar particles, which are not expected to survive on longer time-scales due to the presence of the external perturber HD 98800AaAb.
Highlights
Against all odds, the number of circumbinary planets is slowly increasing
Previous works based on Smoothed Particle Hydrodynamics (SPH) simulations studied specific conditions for polar alignment of the disc around binaries [21, 22]
The stability of single polar planets around binaries is weakly dependent on the planetary mass
Summary
The number of circumbinary planets is slowly increasing. To date, 22 circumbinary (P-type) planetary systems have been catalogued, with 11 transiting circumbinary planets detected by Kepler around nine binary star systems [1]. Stellar-tidal evolution models of short-period binaries show that the binary orbital period increases with time [11, 12] This translates into a larger region of dynamical instability around the binary, which could explain the lower frequency of P-type planets compared to S-type planets. Previous works based on Smoothed Particle Hydrodynamics (SPH) simulations studied specific conditions for polar alignment of the disc around binaries [21, 22]. This mechanism has been further investigated providing an analytical framework to describe the polar alignment of CBDs [23, 24]. We extend these results for a wider variety of configurations and analyse the case of HD 98800
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