Breaking the Mass Inclination Degeneracy of Radial Velocity Measurements via Monitoring von Zeipel-Lidov-Kozai Cycles: Implications in the HD 41004 System

2025/07/14 by Qin, Zhizhen, Liu, Shang-Fei, Ma, Bo +1
#Earth and Planetary Astrophysics (astro-ph.EP) #FOS: Physical sciences #Instrumentation and Methods for Astrophysics (astro-ph.IM) #Solar and Stellar Astrophysics (astro-ph.SR)

paper · doi:10.48550/arxiv.2507.10653

Abstract

We investigate the dynamical stability of the S-type planet in the compact binary HD 41004. Using N-body simulations, we find that the planet could be dynamically stable at a mutual angle inclination up to ∼75^∘. The von Zeipel-Lidov-Kozai (vZLK) mechanism becomes active when the mutual inclination is greater than 39.2^∘. High-inclination orbits exhibit coupled oscillations in eccentricity and inclination, along with apsidal precession. Synthetic radial velocity (RV) modeling shows that these secular variations produce measurable signatures across a broad range of timescales, from full vZLK cycles to observationally accessible decades. For instance, a high mutual inclination at 75^∘ can induce RV drifts exceeding 5 m s^-1 per planetary orbit (∼ 1.9 m s^-1 yr^-1) in circular binary configurations. The presence of eccentric vZLK further accelerates these drifts, enhancing the detectability. Long-term RV observations of this system offer a unique pathway to dynamically constrain the orbital inclination, and thus determine the true mass of HD 41004 Ab. The degeneracy of mass-inclination is well known when using RV measurements alone. Our results highlight that HD 41004Ab and potentially other S-type planets in compact binaries are promising targets for breaking such a degeneracy by studying the dynamics induced by the vZLK mechanism through long-term high-precision RV monitoring.

Citations

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