The impact of red noise in radial velocity planet searches: only three planets orbiting GJ 581?

We perform a detailed analysis of the latest HARPS and Keck radial velocity data for the planet-hosting red dwarf GJ581, which attracted a lot of attention in recent time. We show that these data contain important correlated noise component ("red noise") with the correlation timescale of the order of 10 days. This red noise imposes a lot of misleading effects while we work in the traditional white-noise model. To eliminate these misleading effects, we propose a maximum-likelihood algorithm equipped by an extended model of the noise structure. We treat the red noise as a Gaussian random process with exponentially decaying correlation function. Using this method we prove that: (i) planets b and c do exist in this system, since they can be independently detected in the HARPS and Keck data, and regardless of the assumed noise models; (ii) planet e can also be confirmed independently by the both datasets, although to reveal it in the Keck data it is mandatory to take the red noise into account; (iii) the recently announced putative planets f and g are likely just illusions of the red noise; (iv) the reality of the planet candidate GJ581 d is questionable, because it cannot be detected from the Keck data, and its statistical significance in the HARPS data (as well as in the combined dataset) drops to a marginal level of $\sim 2\sigma$, when the red noise is taken into account. Therefore, the current data for GJ581 really support existence of no more than four (or maybe even only three) orbiting exoplanets. The planet candidate GJ581 d requests serious observational verification.