# Nearly Polar orbit of the sub-Neptune HD3167 c: Constraints on a multi-planet system dynamical history

## TL;DR

This study measures the nearly polar orbit of the sub-Neptune HD3167 c, revealing a significant orbital misalignment with the star's spin axis, and explores the system's dynamical history and potential unseen companions.

## Contribution

First to measure the obliquity of HD3167 c using multiple methods, and to analyze the system's dynamics suggesting an outer companion influences the orbit.

## Key findings

- HD3167 c has a nearly polar orbit with λ = -97° ± 23°
- The system's planets are coplanar, but high obliquity likely caused by an outer companion
- Current data cannot fully explain the high obliquity without additional bodies

## Abstract

We present the obliquity measurement, that is, the angle between the normal angle of the orbital plane and the stellar spin axis, of the sub-Neptune planet HD3167 c, which transits a bright nearby K0 star. We study the orbital architecture of this multi-planet system to understand its dynamical history. We also place constraints on the obliquity of planet d based on the geometry of the planetary system and the dynamical study of the system. New observations obtained with HARPS-N at the Telescopio Nazionale Galileo (TNG) were employed for our analysis. The sky-projected obliquity was measured using three different methods: the Rossiter-McLaughlin anomaly, Doppler tomography, and reloaded Rossiter-McLaughlin techniques. We performed the stability analysis of the system and investigated the dynamical interactions between the planets and the star. HD3167 c is found to be nearly polar with sky-projected obliquity, $\lambda$ = -97$^{\circ} \pm$ 23$^{\circ}$. This misalignment of the orbit of planet c with the spin axis of the host star is detected with 97\% confidence. The analysis of the dynamics of this system yields coplanar orbits of planets c and d. It also shows that it is unlikely that the currently observed system can generate this high obliquity for planets c and d by itself. However, the polar orbits of planets c and d could be explained by the presence of an outer companion in the system. Follow-up observations of the system are required to confirm such a long-period companion.