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 813b (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 ($R_\star=1.94\,R_\odot$, $M_\star=1.32\,M_\odot$). 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 % confidence) on the mass of the companion, and to statistically validate its planetary nature. Detailed modelling of the transits yields a period of $83.8911_{ - 0.0031 } ^ { + 0.0027 }$ days, a planet radius of $6.71 \pm 0.38$ $R_{\oplus}$, and a semi major 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 under-explored region of parameter space. We estimate that TOI-813b induces a reflex motion in its host star with a semi-amplitude of $\sim6$ ms$^{-1}$, making this system a promising target to measure the mass of a relatively long-period transiting planet.