## Evidence for a high mutual inclination between the cold Jupiter and transiting super Earth in $$\pi$$ Men

Jerry Xuan (Cambridge, now at Caltech), Mark Wyatt (Cambridge)

Link to $$\pi$$ Men paper

2nd paper on planet-disk mutual inclinations

### 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.