Long Period Jovian Tilts the Orbits of Two sub-Neptunes Relative to Stellar Spin Axis in Kepler-129

We present the discovery of Kepler-129 d ($P_d=7.2_{-0.3}^{+0.4}$ yr, $m\sin i_d=8.3_{-0.7}^{+1.1}{\mathrm{M}}_{\mathrm{J}\mathrm{u}\mathrm{p}}$, $e_d=0.15_{-0.05}^{+0.07}$) based on six years of radial velocity (RV) observations from Keck/HIRES. Kepler-129 also hosts two transiting sub-Neptunes: Kepler-129 b ($P_b=15.79$ days, $r_b=2.40\pm 0.04{\mathrm{R}}_{\oplus }$) and Kepler-129 c ($P_c=82.20$ days, $r_c=2.52\pm 0.07{\mathrm{R}}_{\oplus }$) for which we measure masses of $m_b<20{\mathrm{M}}_{\oplus }$ and $m_c=43_{-12}^{+13}{\mathrm{M}}_{\oplus }$. Kepler-129 is an hierarchical system consisting of two tightly-packed inner planets and an external companion whose mass is close to the deuterium burning limit. In such a system, two inner planets precess around the orbital normal of the outer companion, causing their inclinations to oscillate with time. Based on an asteroseismic analysis of Kepler data, we find tentative evidence that Kepler-129 b and c are misaligned with stellar spin axis by $\gtrsim 38$ deg, which could be torqued by Kepler-129 d if it is inclined by $\gtrsim 19$ deg relative to inner planets. Using N-body simulations, we provide additional constraints on the mutual inclination between Kepler-129 d and inner planets by estimating the fraction of time during which two inner planets both transit. The probability that two planets both transit decreases as their misalignment with Kepler-129 d increases. We also find a more massive Kepler-129 c enables the two inner planets to become strongly coupled and more resistant to perturbations from Kepler-129 d. The unusually high mass of Kepler-129 c provides a valuable benchmark for both planetary dynamics and interior structure, since the best-fit mass is consistent with this $\rm{2.5
R_{\oplus}}$ planet having a rocky surface.