Physics of Eclipsing Binaries. III. Spin-Orbit Misalignment

TL;DR

This paper develops a comprehensive mathematical framework for modeling spin-orbit misalignment in binary systems, extending the PHOEBE code to accurately simulate and analyze such systems, including stellar shapes and equilibrium points.

Contribution

It introduces a rigorous framework for misalignment in binary systems and implements it in the PHOEBE code, enabling detailed analysis of tilted stellar and planetary systems.

Findings

Framework successfully models misaligned binaries and planets.

Implementation in PHOEBE allows for practical analysis and comparison.

Validated with known systems DI Her and Kepler-13.

Abstract

Binary systems where the axis of rotation (spin) of one or both components is tilted w.r.t. the axis of revolution are called misaligned binary systems. The angle of misalignment, obliquity, has been measured for a handful of stars and extrasolar planets to date. Here we present a mathematical framework for a complete and rigorous treatment of misalignment and introduce an extension to the public PHOEBE code that implements this framework. We discuss misalignment for the Roche geometry and introduce methods for computing stellar shapes, equilibrium (generalized Lagrange) points of the potential and minimal requirements for lobe existence. Efficient parametrization of misalignment is proposed in the plane-of-sky coordinates and implementation details in PHOEBE are given alongside the proof-of-concept toy model, comparison with a known misaligned binary DI Her, and comparison with a misaligned planetary system Kepler-13. We provide important mathematical details of the model in the Appendix. This paper accompanies the release of PHOEBE 2.1, which will be available soon from its website http://phoebe-project.org.