Planet Hunters TESS I: TOI 813, a subgiant hosting a transiting Saturn-sized planet on an 84-day orbit

We report on the discovery and validation of TOI 813 b (TIC 55525572 b), a transiting exoplanet identified by citizen scientists in data from NASA's Transiting Exoplanet Survey Satellite (TESS) and the first planet discovered by the Planet Hunters TESS project. The host star is a bright (V = 10.3 mag) subgiant (R_\star - 1.94 R_⊙, M_\star = 1.32 M_⊙). It was observed almost continuously by TESS during its first year of operations, during which time four individual transit events were detected. The candidate passed all the standard light curve-based vetting checks, and ground-based follow-up spectroscopy and speckle imaging enabled us to place an upper limit of 2 M_Jup (99 per cent confidence) on the mass of the companion, and to statistically validate its planetary nature. Detailed modelling of the transits yields a period of 83.8911_-0.0031^+0.0027 d, a planet radius of 6.71 ± 0.38 R_⊕ and a semimajor axis of 0.423_-0.037^+0.031 AU. The planet's orbital period combined with the evolved nature of the host star places this object in a relatively underexplored region of parameter space. We estimate that TOI 813 b induces a reflex motion in its host star with a semi-amplitude of ∼6 m s^-1, making this a promising system to measure the mass of a relatively long-period transiting planet.