Significant Mutual Inclinations Between the Stellar Spin and the Orbits of Both Planets in the HAT-P-11 System

Planet–star obliquity and planet–planet mutual inclination encode a planetary system’s dynamical history, but both of their values are hard to measure for misaligned systems with close-in companions. HAT-P-11 is a K4 star with two known planets: a close-in, misaligned super-Neptune with a ≈5 day orbit, and an outer super-Jupiter with a ≈10 yr orbit. In this work we present a joint orbit fit of the HAT-P-11 system with astrometry and S -index corrected radial velocity data. By combining our results with previous constraints on the orientation of the star and the inner planet, we find that all three angular momenta—those of the star, planet b, and planet c—are significantly misaligned. We confirm the status of planet c as a super-Jupiter, with 2.68 ± 0.41 M Jup at a semimajor axis of 4.10 ± 0.06 au, and planet b’s mass of M b sini b = 0.074 ± 0.004 M Jup . We present the posterior probability distribution of obliquity between star A and planet c, and mutual inclination between planet b and planet c.