Three Super-Earths Orbiting HD 7924

We report the discovery of two super-Earth mass planets orbiting the nearby K0.5 dwarf HD 7924 which was previously known to host one small planet. The new companions have masses of 7.9 and 6.4 M$_\oplus$, and orbital periods of 15.3 and 24.5 days. We perform a joint analysis of high-precision radial velocity data from Keck/HIRES and the new Automated Planet Finder Telescope (APF) to robustly detect three total planets in the system. We refine the ephemeris of the previously known planet using five years of new Keck data and high-cadence observations over the last 1.3 years with the APF. With this new ephemeris, we show that a previous transit search for the inner-most planet would have covered 70% of the predicted ingress or egress times. Photometric data collected over the last eight years using the Automated Photometric Telescope shows no evidence for transits of any of the planets, which would be detectable if the planets transit and their compositions are hydrogen-dominated. We detect a long-period signal that we interpret as the stellar magnetic activity cycle since it is strongly correlated with the Ca II H and K activity index. We also detect two additional short-period signals that we attribute to rotationally-modulated starspots and a one month alias. The high-cadence APF data help to distinguish between the true orbital periods and aliases caused by the window function of the Keck data. The planets orbiting HD 7924 are a local example of the compact, multi-planet systems that the Kepler Mission found in great abundance.