Robustly determine the orbital geometry of the HD 3167 system

Determine the orbital geometry and mutual inclination of the HD 3167 planetary system robustly from additional or improved observations, resolving whether its planets follow nearly perpendicular, coplanar, or another configuration of orbits.

Background

HD 3167 contains two transiting planets whose previously reported Rossiter–McLaughlin measurements suggested nearly perpendicular orbits: planet b was reported to have a nearly equatorial orbit, whereas planet c was reported to have a nearly polar orbit. The paper reanalyzes the inner planet using three new Keck Planet Finder transit observations together with two archival ESPRESSO datasets and does not confirm the previously reported low obliquity.

The expanded dataset favors a projected obliquity for planet b of approximately $-66^{\circ}$, which is compatible with coplanar orbits, but the inferred projected stellar rotation velocity is higher than expected from independent line-width and rotation-period constraints. In addition, omitting the most discrepant transit dataset substantially broadens the obliquity uncertainty. Consequently, the available observations do not provide a robust determination of the system's three-dimensional orbital architecture or mutual inclination.