[Paper Review] The HARPS search for southern extra-solar planets XIX. Characterization and dynamics of the GJ876 planetary system

A. C. M. Correia, J. Couetdic+12 more|arXiv (Cornell University)|Jan 26, 2010

Stellar, planetary, and galactic studiesPhysics and Astronomy54 references89 citations

TL;DR

This study refines the orbital architecture and masses of the GJ 876 planetary system using high-precision HARPS and Keck radial velocity data. By modeling dynamical interactions and orbital inclinations, it determines the true masses of planets b and c as 2.64 ± 0.04 M_Jup and 0.83 ± 0.03 M_Jup, respectively, confirming their 2:1 mean motion resonance and stable coplanar configuration over 5 Gyr with libration amplitude <2°, while constraining a potential Earth-mass planet in a 4:1 resonance.

ABSTRACT

Precise radial-velocity measurements for data acquired with the HARPS spectrograph infer that three planets orbit the M4 dwarf star GJ876. In particular, we confirm the existence of planet "d", which orbits every 1.93785 days. We find that its orbit may have significant eccentricity (e=0.14), and deduce a more accurate estimate of its minimum mass of 6.3 Earth masses. Dynamical modeling of the HARPS measurements combined with literature velocities from the Keck Observatory strongly constrain the orbital inclinations of the "b" and "c" planets. We find that i_b = 48.9 degrees and i_c = 48.1 degrees, which infers the true planet masses of M_b = 2.64 Jupiter masses and M_c = 0.83 Jupiter masses, respectively. Radial velocities alone, in this favorable case, can therefore fully determine the orbital architecture of a multi-planet system, without the input from astrometry or transits. The orbits of the two giant planets are nearly coplanar, and their 2:1 mean motion resonance ensures stability over at least 5 Gyr. The libration amplitude is smaller than 2 degrees, suggesting that it was damped by some dissipative process during planet formation. The system has space for a stable fourth planet in a 4:1 mean motion resonance with planet "b", with a period around 15 days. The radial velocity measurements constrain the mass of this possible additional planet to be at most that of the Earth.

Motivation & Objective

• To precisely characterize the orbital parameters and true masses of the GJ 876 planetary system using radial velocity data.
• To determine the orbital inclinations of planets b and c through dynamical modeling of radial velocity residuals.
• To investigate the long-term stability and resonant dynamics of the multi-planet system, particularly the 2:1 mean motion resonance between planets b and c.
• To assess the potential existence of a fourth planet in the system via dynamical constraints from radial velocity measurements.

Proposed method

• Combines HARPS and Keck radial velocity measurements to improve orbital solution accuracy.
• Applies dynamical modeling to fit orbital elements and constrain inclinations using long-term radial velocity variations.
• Uses secular perturbation theory to model long-term evolution of eccentricities and inclinations via proper modes u_k and v_k.
• Employs linear secular approximation to describe precession of periastrons (g_k) and nodes (s_k), with frequencies derived from orbital solutions.
• Analyzes resonant angle libration to confirm stability and assess damping during planet formation.
• Applies constraints from 11 years of radial velocity data to limit the mass of any potential additional planet to ≤1 M⊕.

Experimental results

Research questions

• RQ1 What are the true masses of planets b and c in the GJ 876 system, given radial velocity data and dynamical modeling?
• RQ2 How do the orbital inclinations of planets b and c affect the determination of their true masses?
• RQ3 What is the long-term dynamical stability of the GJ 876 system, particularly in the context of its 2:1 mean motion resonance?
• RQ4 Can the radial velocity data constrain the existence and mass of a potential fourth planet in the system?
• RQ5 What does the small libration amplitude of the resonant angles suggest about the formation history of the system?

Key findings

• The orbital inclination of planet b is constrained to i_b = 48.9° ± 1.0°, yielding a true mass of 2.64 ± 0.04 M_Jup.
• The orbital inclination of planet c is i_c = 48.1° ± 2.1°, yielding a true mass of 0.83 ± 0.03 M_Jup.
• The system exhibits a 2:1 mean motion resonance with libration amplitude <2°, indicating long-term stability over at least 5 Gyr.
• The eccentricity of planet d is 0.14 ± 0.003, consistent with a nearly constant value over time.
• The inclinations of planets b and c relative to the invariant plane are small, with i_b = 0.36°–0.39° and i_c = 1.54°–1.61°, driven by secular frequencies.
• Radial velocity data constrain any potential fourth planet to a mass of at most 1 M⊕, possibly in a 4:1 resonance with planet b.