We report the discovery of Kepler-77b (alias KOI-127.01), a Saturn-mass transiting planet in a 3.6-day orbit around a metal-rich solar-like star. We combined the publicly available Kepler photometry (quarters 1-13) with high-resolution spectroscopy from the Sandiford@McDonald and FIES@NOT spectrographs. We derived the system parameters via a simultaneous joint fit to the photometric and radial velocity measurements. Our analysis is based on the Bayesian approach and is carried out by sampling the parameter posterior distributions using a Markov chain Monte Carlo simulation. Kepler-77b is a moderately inflated planet with a mass of Mp=0.430+/-0.032 Mjup, a radius of Rp=0.960+/-0.016 Rjup, and a bulk density of 0.603+/-0.055 g/cm^3. It orbits a slowly rotating (P=36+/-6 days) G5V star with M*=0.95+/-0.04 Msun, R*=0.99+/-0.02 Rsun, Teff=5520+/-60 K, [M/H]=0.20+/-0.05, that has an age of 7.5+/-2.0 Gyr. The lack of detectable planetary occultation with a depth higher than about 10 ppm implies a planet geometric and Bond albedo of Ag<0.087+/-0.008 and Ab<0.058+/-0.006, respectively, placing Kepler-77b among the gas-giant planets with the lowest albedo known so far. We found neither additional planetary transit signals nor transit-timing variations at a level of about 0.5 minutes, in accordance with the trend that close-in gas giant planets seem to belong to single-planet systems. The 106 transits observed in short-cadence mode by Kepler for nearly 1.2 years show no detectable signatures of the planets passage in front of starspots. We explored the implications of the absence of detectable spot-crossing events for the inclination of the stellar spin-axis, the sky-projected spin-orbit obliquity, and the latitude of magnetically active regions.
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