Color Difference Makes a Difference: Four Planet Candidates around τ Ceti

The removal of noise typically correlated in time and wavelength is one of the main challenges for using the radial-velocity (RV) method to detect Earth analogues. We analyze τ Ceti RV data and find robust evidence for wavelength-dependent noise. We find that this noise can be modeled by a combination of moving average models and the so-called "differential radial velocities." We apply this noise model to various RV data sets for τ Ceti, and find four periodic signals at 20.0, 49.3, 160, and 642 days, which we interpret as planets. We identify two new signals with orbital periods of 20.0 and 49.3 days while the other two previously suspected signals around 160 and 600 days are quantified to a higher precision. The 20.0 days candidate is independently detected in Keck data. All planets detected in this work have minimum masses less than 4M_⊕ with the two long-period ones located around the inner and outer edges of the habitable zone, respectively. We find that the instrumental noise gives rise to a precision limit of the High Accuracy Radial Velocity Planet Searcher (HARPS) around 0.2 m s^-1. We also find correlation between the HARPS data and the central moments of the spectral line profile at around 0.5 m s^-1 level, although these central moments may contain both noise and signals. The signals detected in this work have semi-amplitudes as low as 0.3 m s^-1, demonstrating the ability of the RV technique to detect relatively weak signals.