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We report the discovery of a new planetary system around the K giant $\eta$Cet (HIP 5364, HD 6805) based on 118 high-precision optical radial velocitiestaken at Lick Observatory since July 2000. Since October 2011 an additionalnine near-infrared Doppler measurements have been taken using the ESO CRIRESspectrograph (VLT, UT1). The visible data set shows two clear periodicities.Although we cannot completely rule out that the shorter period is due torotational modulation of stellar features, the infrared data show the samevariations as in the optical, which strongly supports that the variations arecaused by two planets. Assuming the mass of $\eta$ Cet to be 1.7 $M_\odot$, thebest edge-on coplanar dynamical fit to the data is consistent with two massiveplanets ($m_b\sin i$ = 2.6 $\pm$ 0.2 $M_{\mathrm{Jup}}$, $m_c\sin i$ = 3.3$\pm$ 0.2 $M_{\mathrm{Jup}}$), with periods of $P_b$ = 407 $\pm$ 3 days and$P_c$ = 740 $\pm$ 5 days and eccentricities of $e_b$ = 0.12 $\pm$ 0.05 and$e_c$ = 0.08 $\pm$ 0.03. We tested a wide variety of edge-on coplanar andinclined planetary configurations for stability, which agree with the derivedradial velocities. We find that in certain coplanar orbital configurations withmoderate $e_b$ eccentricity, the planets can be effectively trapped in ananti-aligned 2:1 mean motion resonance. A much larger non-resonant stableregion exists in low-eccentricity parameter space, although it appears to bemuch farther from the best fit than the 2:1 resonant region. In all othercases, the system is categorized as unstable or chaotic. Another conclusionfrom the coplanar inclined dynamical test is that the planets can be at most afactor of $\sim$ 1.4 more massive than their suggested minimum masses. Thisstability constraint on the inclination excludes the possibility of two browndwarfs, and strongly favors a planetary system.

Precise radial velocities of giant stars VI. A possible 2:1 resonant planet pair around the K giant star $\eta$ Cet