Polar Alignment of a Protoplanetary Disc around an Eccentric Binary - II. Effect of Binary and Disc Parameters

In a recent paper Martin & Lubow showed that a circumbinary disc around an eccentric binary can undergo damped nodal oscillations that lead to the polar (perpendicular) alignment of the disc relative to the binary orbit. The disc angular momentum vector aligns to the eccentricity vector of the binary. We explore the robustness of this mechanism for a low-mass disc (0.001 of the binary mass) and its dependence on system parameters by means of hydrodynamic disc simulations. We describe how the evolution depends upon the disc viscosity, temperature, size, binary mass ratio, orbital eccentricity, and inclination. We compare results with predictions of linear theory. We show that polar alignment of a low-mass disc may occur over a wide range of binary-disc parameters. We discuss the application of our results to the formation of planetary systems around eccentric binary stars

Misaligned Accretion Disc Formation via Kozai-Lidov Oscillations

We investigate the formation and evolution of misaligned accretion discs around the secondary component of a binary through mass transfer driven by Kozai–Lidov (KL) oscillations of the circumprimary disc’s eccentricity and inclination. We perform smoothed particle hydrodynamics simulations to study the amount of mass transferred to the secondary star as a function of both the disc and binary parameters. For the range of parameters we explore, we find that increasing the disc aspect ratio, viscosity parameter, and initial inclination as well as decreasing the binary mass ratio leads to larger amount of mass transfer, up to a maximum of about 10 % of the initial mass of the primary disc. The circumsecondary disc forms with a high eccentricity and a high inclination and is also able to undergo KL oscillations. The circumsecondary disc oscillations have a shorter period than those in the disc around the primary. We find that some of the material that escapes the Roche lobe of the two components forms a misaligned circumbinary accretion disc. This study has implications for disc evolution in young binary star systems

Circumbinary Disk Inner Radius as a Diagnostic for Disk–Binary Misalignment

We investigate the misalignment of the circumbinary disk around the binary HD 98800 BaBb with eccentricity e sime 0.8. Kennedy et al. observed the disk to be either at an inclination of 48° or polar aligned to the binary orbital plane. Their simulations showed that alignment from 48° to a polar configuration can take place on a shorter timescale than the age of this system. We perform hydrodynamical numerical simulations in order to estimate the cavity size carved by the eccentric binary for different disk inclinations as an independent check of polar alignment. Resonance theory suggests that torques on the inner parts of a polar disk around such a highly eccentric binary are much weaker than in the coplanar case, indicating a significantly smaller central cavity than in the coplanar case. We show that the inferred inner radius (from carbon monoxide measurements) of the accretion disk around BaBb can exclude the possibility of it being mildly inclined with respect to the binary orbital plane and therefore confirm the polar configuration. This study constitutes an important diagnostic for misaligned circumbinary disks, since it potentially allows us to infer the disk inclination from observed gas disk inner radii

Alignment of a circumbinary disc around an eccentric binary with application to KH 15D

We analyse the evolution of a mildly inclined circumbinary disc that orbits an eccentric orbit binary by means of smoother particle hydrodynamic (SPH) simulations and linear theory. We show that the alignment process of an initially misaligned circumbinary disc around an eccentric orbit binary is significantly different than around a circular orbit binary and involves tilt oscillations. The more eccentric the binary, the larger the tilt oscillations and the longer it takes to damp these oscillations. A circumbinary disc that is only mildly inclined may increase its inclination by a factor of a few before it moves towards alignment. The results of the SPH simulations agree well with those of linear theory. We investigate the properties of the circumbinary disc/ring around KH 15D. We determine disc properties based on the observational constraints imposed by the changing binary brightness. We find that the inclination is currently at a local minimum and will increase substantially before setting to coplanarity. In addition, the nodal precession is currently near its most rapid rate. The recent observations that show a reappearance of Star B impose constraints on the thickness of the layer of obscuring material. Our results suggest that disc solids have undergone substantial inward drift and settling towards to disc midplane. For disc masses $\sim 0.001 M_\odot$, our model indicates that the level of disc turbulence is low $\alpha \ll 0.001$. Another possibility is that the disc/ring contains little gas.Comment: 16 pages, 16 figures; accepted for publication in MNRA

White Dwarf Pollution by Asteroids from Secular Resonances

In the past few decades, observations have revealed signatures of metals polluting the atmospheres of white dwarfs. The diffusion time-scale for metals to sink from the atmosphere of a white dwarf is of the order of days for a hydrogen-dominated atmosphere. Thus, there must be a continuous supply of metal-rich material accreting onto these white dwarfs. We investigate the role of secular resonances that excite the eccentricity of asteroids allowing them to reach star-grazing orbits leading them to tidal disruption and the formation of a debris disc. Changes in the planetary system during the evolution of the star lead to a change in the location of secular resonances. In our Solar system, the engulfment of the Earth will cause the ν6 resonance to shift outwards which will force previously stable asteroids to undergo secular resonant perturbations. With analytic models and N-body simulations we show that secular resonances driven by two outer companions can provide a source of continuous pollution. Secular resonances are a viable mechanism for the pollution of white dwarfs in a variety of exoplanetary system architectures

Polar Alignment of a Protoplanetary Disc Around an Eccentric Binary – III. Effect of Disc Mass

An initially sufficiently misaligned low-mass protoplanetary disc around an eccentric binary undergoes damped nodal oscillations of tilt angle and longitude of ascending node. Dissipation causes evolution towards a stationary state of polar alignment in which the disc lies perpendicular to the binary orbital plane with angular momentum aligned to the eccentricity vector of the binary. We use hydrodynamic simulations and analytical methods to investigate how the mass of the disc affects this process. The simulations suggest that a disc with non-zero mass settles into a stationary state in the frame of the binary, the generalized polar state, at somewhat lower levels of misalignment with respect to the binary orbital plane, in agreement with the analytical model. Provided that discs settle into this generalized polar state, the observational determination of the misalignment angle and binary properties can be used to determine the mass of a circumbinary disc. We apply this constraint to the circumbinary disc in HD 98800. We obtain analytical criteria for polar alignment of a circumbinary ring with mass that approximately agree with the simulation results. Very broad misaligned discs undergo breaking, but the inner regions at least may still evolve to a polar state. The long-term evolution of the disc depends on the evolution of the binary eccentricity that we find tends to decrease. Although the range of parameters required for polar alignment decreases somewhat with increasing disc mass, such alignment appears possible for a broad set of initial conditions expected in protostellar circumbinary discs