[Paper Review] Orbital Motion of HR 8799 b,c, d using Hubble Space Telescope data from 1998: Constraints on Inclination, Eccentricity and Stability

Rémi Soummer, J. Hagan+4 more|arXiv (Cornell University)|Oct 6, 2011

Stellar, planetary, and galactic studies8 citations

TL;DR

This study uses Hubble Space Telescope archival data from 1998 to measure the orbital motion of HR 8799 b, c, and d, providing a ten-year baseline with 2008 discovery images. It confirms previous astrometry for planet b and presents new astrometry for c and d, favoring a stable 1d:2c:4b mean motion resonance with low eccentricity (e_d = 0.10) and inclination near 28.0°, constraining the system's orbital architecture and supporting dynamical stability.

ABSTRACT

HR 8799 is currently the only multiple-planet system that has been detected with direct imaging, with four giant planets orbiting at large separations from this young late A star. Orbital motion provides insight into the stability, and possible formation mechanisms of this planetary system. Dynamical studies can also provide constraints on the planets' masses, which help calibrate evolutionary models. Yet, measuring the orbital motion is a very difficult task because the long-period orbits (50-500 yr) require long time baselines and high-precision astrometry. This paper studies the three planets HR 8799b, c and d in the archival data set of HR 8799 obtained with the HST NICMOS coronagraph in 1998. The detection of all three planets is made possible by a careful optimization of the LOCI algorithm. This work confirms previous astrometry for planet b, and presents new detections and astrometry for c and d. These HST images provide a ten-year baseline with the discovery images from 2008, and therefore offer a unique opportunity to constrain their orbital motion now. Recent dynamical studies of this system show the existence of a few possible stable solutions involving mean motion resonances, where the interaction between c and d plays a major role. We study the compatibility of a few of these stable scenarios (1d:1c, 1d:2c, or 1d:2c:4d) with the new astrometric data from HST. In the hypothesis of a 1d:2c:4b mean motion resonance our best orbit fit is close to the stable solution previously identified for a three-planet system, and involves low eccentricity for planet d (ed = 0.10) and moderate inclination of the system (i = 28.0 deg), assuming a coplanar system, circular orbits for b and c, and exact resonance with integer period ratios. Under these assumptions, we can place strong constraints on the inclination of the system (27.3 - 31.4 deg) and on the eccentricity for d ed < 0.46.

Motivation & Objective

• To measure the orbital motion of HR 8799 b, c, and d using Hubble Space Telescope archival data from 1998, providing a ten-year baseline with 2008 discovery images.
• To test the compatibility of observed astrometry with proposed stable dynamical configurations, particularly mean motion resonances involving planets c and d.
• To constrain the system's inclination, eccentricity, and orbital architecture under the assumption of coplanar, circular orbits for b and c and exact integer period ratios.
• To assess the robustness of these constraints to small departures from exact resonance and to identify viable orbital solutions consistent with the data.
• To demonstrate the value of archival HST data and PSF libraries for future exoplanet studies, including James Webb Space Telescope missions.

Proposed method

• Applied the LOCI algorithm with careful optimization to detect and extract astrometric positions of planets b, c, and d in HST NICMOS coronagraphic images from 1998.
• Performed statistical analysis on a large number of reduced images to improve signal-to-noise and derive reliable astrometric measurements.
• Evaluated compatibility of observed astrometry with stable dynamical solutions, including 1d:1c, 1d:2c, and 1d:2c:4b mean motion resonances.
• Fitted orbital parameters under the assumption of circular orbits for planets b and c, coplanar system, and exact integer period ratios, using the star’s mass and one planet’s period to constrain the others.
• Assessed sensitivity of results to deviations from exact resonance and evaluated potential astrometric biases between datasets from different telescopes.
• Used photometric measurements in the F160W filter to supplement astrometric data for planets c and d.

Experimental results

Research questions

• RQ1 What are the orbital parameters (inclination, eccentricity, period) of HR 8799 b, c, and d based on a ten-year baseline from HST archival data?
• RQ2 Which stable dynamical configurations—particularly mean motion resonances—are compatible with the new astrometric measurements?
• RQ3 Can the system’s inclination and eccentricity be constrained under the assumption of coplanar, circular orbits for b and c?
• RQ4 How robust are the best-fit orbital solutions to small departures from exact integer period ratios?
• RQ5 Does the inclusion of HST data from 1998 rule out previously proposed stable configurations such as the 1d:1c resonance?

Key findings

• The best-fit orbital solution for the 1d:2c:4b mean motion resonance is very close to a previously identified stable three-planet solution, with low eccentricity for planet d (e_d = 0.10).
• The system’s inclination is constrained to 27.3–31.4 degrees under the 1d:2c:4b resonance hypothesis, with the best-fit at 28.0 degrees.
• Eccentricity for planet d is constrained to e_d < 0.46, with the best-fit value of 0.10, indicating moderate but not high eccentricity.
• The completely circular, face-on system hypothesis is rejected under the 1d:2c:4b resonance assumption, and possible inclinations are confined to a narrow range around 28.0 degrees.
• The 1d:1c resonance solution is unlikely given the HST data, and the 1d:2c resonance is ruled out for high-inclination or circular coplanar face-on configurations.
• The results are robust to small deviations from exact integer period ratios and are consistent with prior dynamical studies, supporting further investigation of the 1d:2c:4b resonance with full data sets.