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.