Hints of the fourth planet around upsilon Andromedae
We analyse the array of 288 recently published new and revised Lick observatory radial velocity (RV) measurements of $\upsilon$ And. The periodogram analysis reveals three RV periodicities of relatively small semi-amplitudes (about 10 m/s), in addition to the variations due to three known Jovian planets. These new periods are about 12 years, 180 and 360 days. The two latter variations cannot be interpreted as planetary signatures because of the dynamical stability argument. These annual variations have to be interpreted as errors in the RV data, which may have instrumental or data reduction nature.
The long-period RV variation may allow stable orbital configurations and is consistent with the fourth distant planetary companion. Its orbital period is unconstrained from the upper side (longer periods require higher eccentricities, up to a parabolic orbit), but its minimum mass $m\sin i$ is likely between 0.5 and 3.0 times Jupiter mass. The condition of the dynamical stability limits the set of possible orbits of the fourth planet to the 3/1, 4/1, 5/1, 6/1 mean-motion resonances with planet d or to longer-period elongated orbits with pericenter distance of 5-6 AU (with semi-major axis larger than ~10 AU).
We also discuss non-planetary interpretations for the long-term RV variation, which are currently difficult to rule out. Efficient confirmation and verification of this planet candidate can be done by means of, e.g., long-term astrometry and star magnetic activity monitoring.