A potential exomoon from the predicted planet obliquity of $\beta$ Pictoris b

Planet obliquity is the alignment or misalignment of a planet spin axis relative to its orbit normal. In a multiplanet system, this obliquity is a valuable signature of planet formation and evolutionary history. The young $\beta$ Pictoris system hosts two coplanar super-Jupiters and upcoming JWST observations of this system will constrain the obliquity of the outer planet, $\beta$ Pictoris b. This will be the first planet obliquity measurement in an extrasolar, multiplanet system. First, we show that this new planet obliquity is likely misaligned by using a wide range of simulated observations in combination with published measurements of the system. Motivated by current explanations for the tilted planet obliquities in the Solar System, we consider collisions and secular spin-orbit resonances. While collisions are unlikely to occur, secular spin-orbit resonance modified by the presence of an exomoon around the outer planet can excite a large obliquity. The largest induced obliquities ($\sim 60^\circ$) occur for moons with at least a Neptune-mass and a semimajor axis of $0.03-0.05 \mathrm{~au}$ ($40-70$ planet radii). For certain orbital alignments, such a moon may observably transit the planet (transit depth of $3-7\%$, orbital period of $3-7$ weeks). Thus, a nonzero obliquity detection of $\beta$ Pictoris b implies that it may host a large exomoon. Although we focus on the $\beta$ Pictoris system, the idea that the presence of exomoons can excite high obliquities is very general and applicable to other exoplanetary systems.