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Rotation Periods, Inclinations, and Obliquities of Cool Stars Hosting Directly Imaged Substellar Companions: Spin–Orbit Misalignments Are Common

• Authors: Brendan P. Bowler, Quang H. Tran, Zhoujian Zhang, Marvin Morgan, Katelyn B. Ashok, Sarah Blunt, Marta L. Bryan, Analis E. Evans, Kyle Franson, Daniel Huber, Vighnesh Nagpal, Ya-Lin Wu, Yifan Zhou

Brendan P. Bowler et al 2023 The Astronomical Journal 165 .

• Provider: AAS Journals

Caption: Figure 1.

Orbital and rotational geometry relevant for obliquity constraints of stars hosting imaged companions. The observer is looking down from the z-axis. The xy plane is the plane of the sky, and the star is centered on the origin. The x-axis points north and the y-axis points east. Left: the inclination of the companion’s orbital plane, i o , intersects the sky along the line of nodes, which is oriented by Ω o from true north to the ascending node. In this configuration the orbital angular momentum vector ﹩\overrightarrow{{L}_{o}}﹩ points in the hemisphere facing the observer, with ﹩\overrightarrow{{L}_{o}}﹩ pointing toward the observer along the z-axis when i o = 0°. Middle: the star’s orientation in space determines the inclination of its equatorial plane, i *, and the position angle of its line of nodes. The sense of the stellar spin sets its rotational angular momentum vector ﹩\overrightarrow{{L}_{* }}﹩ and the longitude of ascending node Ω*. Right: if only the inclinations i o and i * are measured, but not their true (or relative) orientations in the plane of the sky (Ω o and Ω*), then each angular momentum vector can fall anywhere along nested cones opening toward or away from the observer. If Ω o is known (point A 1 , for example), but not Ω*, then the obliquity can be as small as ∣i o i *∣ (at B 1 ), can reach i o + i * for prograde orbits (B 2 ), or can be as large as π − ∣i o i *∣ (B 3 ) for retrograde orbits.