TL;DR

We combine Gaia DR2 and Hipparcos astrometry to constrain the 3-D orbit of $\pi$ Men b ($P\approx2100$ d, $m \sin{I}\approx10.0 M_{\rm{Jup}}$), and find its orbit is highly misaligned with that of the inner transiting planet, $\pi$ Men c ($P\approx6.3$ d, $m\approx4.8 M_{\oplus}$), with $49^\circ < \Delta I < 131^\circ$ at $1\sigma$.

The $\pi$ Men system

Parameters from Huang+2018

Planet	$a$	$m \sin{I} \textrm{(b)}\ / m \textrm{(c)}$	$e$
$\pi$ Men b	$3.31$ au	$10.02$ $M_{\rm{Jup}}$	$0.637$
$\pi$ Men c	$0.068$ au	$4.8$ $M_{\oplus}$	$<0.3$

Gaia-Hipparcos Astrometry

Fig 1. Illustration of the astrometric method, image from Kervella+2019.

3-D Orbit of $\pi$ Men b

Fig 2. $I, \Omega, m$ for $\pi$ Men b

Mutual inclination $\Delta I$ between $\pi$ Men b and c:

• $49^\circ < \Delta I < 131^\circ$ at $1\sigma$,
• $28^\circ < \Delta I < 152^\circ$ at $2\sigma$,
• $9^\circ < \Delta I < 171^\circ$ at $3\sigma$,

Nodal Precession and Consequences

Video 1. Nodal precession of the inner orbit around the outer orbit.

Two major consequences:

• $\pi$ Men c only transits 10-20% of the time from our N-body simulations.
• $\pi$ Men c is likely misaligned with the stellar spin axis. This was confirmed by Kunovac Hodžic+2020.