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We present the discovery of Kepler-88 d ($P_d = 1403\pm14$ days,$M\mathrm{sin}i_d = 965\pm44\,M_\oplus = 3.04\pm0.14\,M_J$, $e_d =0.41\pm0.03$) based on six years of radial velocity (RV) follow-up from the W.M. Keck Observatory HIRES spectrograph. Kepler-88 has two previously identifiedplanets. Kepler-88 b (KOI-142.01) transits in the NASA \Kepler\ photometry andhas very large transit timing variations. \citet{Nesvorny2013} perfomed adynamical analysis of the TTVs to uniquely identify the orbital period and massof the perturbing planet (Kepler-88 c), which was later was confirmed with RVsfrom the Observatoire de Haute-Provence (OHP, Barros et al. 2014). To fullyexplore the architecture of this system, we performed photodynamical modelingon the \Kepler\ photometry combined with the RVs from Keck and OHP and stellarparameters from spectroscopy and Gaia. Planet d is not detectable in thephotometry, and long-baseline RVs are needed to ascertain its presence. Aphotodynamical model simultaneously optimized to fit the RVs and \Kepler\photometry yields the most precise planet masses and orbital properties yet forb and c: $P_b = 10.91647\pm0.00014\,\mathrm{days}$, $M_b=9.5\pm1.2\,M_\oplus$,$P_c=22.2649\pm0.0007\,\mathrm{days}$, and $M_c=214.1\pm5.3\,M_\oplus$. Thephotodynamical solution also finds that planets b and c have low eccentricitesand low mutual inclination, are apsidally anti-aligned, and have conjunctionson the same hemisphere of the star. Continued RV follow-up of systems withsmall planets will improve our understanding of the link between innerplanetary system architectures and giant planets.

The Discovery of the Long-Period, Eccentric Planet Kepler-88 d and System Characterization with Radial Velocities and Photodynamical Analysis