Eccentricity and Spin-Orbit Misalignment in Short-Period Stellar Binaries as a Signpost of Hidden Tertiary Companions

Abstract

Eclipsing binaries are observed to have a range of eccentricities and spin-orbit misalignments (stellar obliquities). Whether such properties are primordial, or arise from post-formation dynamical interactions remains uncertain. This paper considers the scenario in which the binary is the inner component of a hierarchical triple stellar system, and derives the requirements that the tertiary companion must satisfy in order to raise the eccentricity and obliquity of the inner binary. Through numerical integrations of the secular octupole-order equations of motion of stellar triples, coupled with the spin precession of the oblate primary star due to the torque from the secondary, we obtain a simple, robust condition for producing spin-orbit misalignment in the inner binary: In order to excite appreciable obliquity, the precession rate of the stellar spin axis must be smaller than the orbital precession rate due to the tertiary companion. This yields quantitative requirements on the mass and orbit of the tertiary. We also present new analytic expressions for the maximum eccentricity and range of inclinations allowing eccentricity excitation (Lidov-Kozai window), for stellar triples with arbitrary masses and including the non-Keplerian potentials introduced by general relativity, stellar tides and rotational bulges. The results of this paper can be used to place constraints on unobserved tertiary companions in binaries that exhibit high eccentricity and/or spin-orbit misalignment, and will be helpful in guiding efforts to detect external companions around stellar binaries. As an application, we consider the eclipsing binary DI Herculis, and identify the requirements that a tertiary companion must satisfy to produce the observed spin-orbit misalignment.

19 pages, 15 figures, accepted for publication in MNRAS

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• Inclination Evolution of Protoplanetary Disks Around Eccentric Binaries
• Spin-Orbit Misalignment of Merging Black-Hole Binaries with Tertiary Companions
• Rotation Periods, Inclinations, and Obliquities of Cool Stars Hosting Directly Imaged Substellar Companions: Spin-Orbit Misalignments are Common
• Moderately Eccentric Warm Jupiters from Secular Interactions with Exterior Companions
• Chaotic quadruple secular evolution and the production of misaligned exomoons and Warm Jupiters in stellar multiples
• Flipping spins in mass transferring binaries and origin of spin-orbit misalignment in binary black holes
• Properties of von Zeipel-Lidov-Kozai oscillations in triple systems at the quadrupole order: relaxing the test particle approximation
• Demographics of triple systems in dense star clusters
• Empirical Stability Boundary for Hierarchical Triples
• DI Herculis Revisited: Starspots, Gravity Darkening, and 3-D Obliquities
• Cumulative Shift of Periastron Time of Binary Pulsar with Kozai-Lidov Oscillation
• Excitation of Spin-Orbit Misalignments in Stellar Binaries with Circumbinary Disks: Application to DI Herculis
• Fundamental properties of the pre-main sequence eclipsing stars of MML 53 and the mass of the tertiary
• Were the Obliquities in DI Herculis Excited by an Unseen Tertiary Companion?