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

Trifon Trifonov, S. Reffert+3 more|arXiv (Cornell University)|Jul 2, 2014

Stellar, planetary, and galactic studies69 references25 citations

TL;DR

This study presents evidence for a stable, 2:1 mean motion resonance planetary system around the K giant star η Cet, based on 118 optical and 9 near-infrared radial velocity measurements. The dynamical stability analysis confirms two massive planets (mb sin i = 2.6 ± 0.2 MJup, mc sin i = 3.3 ± 0.2 MJup) in a 2:1 resonance with moderate eccentricities, and rules out brown dwarf companions via stability constraints, strongly favoring a planetary system configuration.

ABSTRACT

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 velocities taken at Lick Observatory since July 2000. Since October 2011 an additional nine near-infrared Doppler measurements have been taken using the ESO CRIRES spectrograph (VLT, UT1). The visible data set shows two clear periodicities. Although we cannot completely rule out that the shorter period is due to rotational modulation of stellar features, the infrared data show the same variations as in the optical, which strongly supports that the variations are caused by two planets. Assuming the mass of $\eta$ Cet to be 1.7 $M_\odot$, the best edge-on coplanar dynamical fit to the data is consistent with two massive planets ($m_b\sin i$ = 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 and inclined planetary configurations for stability, which agree with the derived radial velocities. We find that in certain coplanar orbital configurations with moderate $e_b$ eccentricity, the planets can be effectively trapped in an anti-aligned 2:1 mean motion resonance. A much larger non-resonant stable region exists in low-eccentricity parameter space, although it appears to be much farther from the best fit than the 2:1 resonant region. In all other cases, the system is categorized as unstable or chaotic. Another conclusion from the coplanar inclined dynamical test is that the planets can be at most a factor of $\sim$ 1.4 more massive than their suggested minimum masses. This stability constraint on the inclination excludes the possibility of two brown dwarfs, and strongly favors a planetary system.

Motivation & Objective

• To detect and characterize multiple planetary companions around evolved giant stars, a class with sparse multiple planet detections.
• To determine whether the observed radial velocity variations in η Cet are due to planetary companions or stellar activity.
• To assess the dynamical stability of the proposed planetary system and constrain orbital parameters, inclinations, and masses.
• To test whether the system is in a 2:1 mean motion resonance and evaluate its long-term stability.
• To exclude the possibility of brown dwarf companions based on dynamical stability constraints.

Proposed method

• High-precision radial velocity measurements were obtained using the Hamilton spectrograph at Lick Observatory (118 optical observations) and the CRIRES spectrograph at the VLT (9 near-infrared observations) over 14 years.
• A double-Keplerian model was fitted to the radial velocity data, followed by a full dynamical model that accounts for gravitational interactions between the planets.
• Extensive N-body dynamical integrations were performed over 10^5 to 10^8 years to assess system stability across various orbital configurations.
• Stability maps were generated in the (eb, ec) plane for coplanar and inclined configurations, with inclination constrained via stability criteria.
• The analysis included coplanar edge-on, inclined, and mutually inclined orbital configurations, with stability evaluated via long-term integration and resonance angle behavior.
• The minimum masses were constrained by testing increasing inclinations; stability failure at higher inclinations ruled out more massive companions.

Experimental results

Research questions

• RQ1 Are the observed radial velocity variations in η Cet caused by planetary companions or stellar activity?
• RQ2 Can the system be dynamically stable over long timescales, and what orbital configurations support this?
• RQ3 Is the system in a 2:1 mean motion resonance, and what evidence supports this?
• RQ4 What are the upper limits on planetary masses based on dynamical stability, and can brown dwarfs be ruled out?
• RQ5 How do inclination and mutual inclination affect the stability and viability of the system?

Key findings

• The radial velocity data reveal two clear periodic signals with periods of 407 ± 3 days and 740 ± 5 days, consistent with two massive planets.
• The dynamical model provides a significantly better fit (reduced χ² improvement) than a double-Keplerian model, confirming gravitational interaction between the planets.
• The system is most likely in a 2:1 mean motion resonance with planets in an anti-aligned configuration, where resonant angles θb and θc librate with large amplitudes near ±180°.
• A stable 2:1 resonant island exists in the (eb, ec) plane at moderate eccentricities, approximately 1σ away from the best-fit orbital solution.
• A larger non-resonant stable region exists for nearly circular orbits, but it lies more than 3σ from the best fit and is therefore less likely.
• Stability constraints limit the planetary masses to no more than 1.4 times their minimum masses (mb sin i, mc sin i), ruling out brown dwarf companions and strongly favoring a planetary system.