The determination of planetary structure in tidally relaxed inclined systems
arXiv:1001.4079 · doi:10.1111/j.1365-2966.2010.16814.x
Abstract
[Abridged] The recent discovery of a transiting planet on a non-circular orbit with a massive highly eccentric companion orbiting HAT-P-13 offers the possibility of probing the structure of the short-period planet. The ability to do this relies on the system being in a quasi-equilibrium state in the sense that the eccentricities are constant on the usual secular timescale, and decay on a timescale which is much longer than the age of the system. Since the equilibrium eccentricity is effectively a function only of observable system parameters and the unknown Love number of the short-period planet, the latter can be determined with accurate measurements of the planet's eccentricity and radius. However, this analysis relies on the unlikely assumption that the system is coplanar. Here we generalize our recent analysis of this fixed-point phenomenon to mutually inclined systems and show that the fixed point of coplanar systems is replaced by a limit cycle, with the average value of the eccentricity decreasing and its amplitude of variation increasing with increasing mutual inclination. This behaviour significantly reduces the ability to unambiguously determine the Love number of the short-period planet if the mutual inclination is higher than around 10^o. We show that for Q-values less than 10^6, the HAT-P-13 system cannot have a mutual inclination between 54 and 126^o because Kozai oscillations coupled with tidal dissipation would act to quickly move the inclination outside this range, and that the behaviour of retrograde systems is the mirror image of that for prograde systems. We derive a relationship between the equilibrium radius of the short-period planet, its Q-value and its core mass, and show that given current estimates of e_b and the planet radius, the HAT-P-13 system is likely to be close to coplanar [...]
24 pages, 14 figures, Accepted for publication in MNRAS. **NOTE REFINED PREDICTION FOR MUTUAL INCLINATION
References in corpus (3)
Cited by in corpus (53)
- The PLATO 2.0 Mission
- Evidence for a Distant Giant Planet in the Solar System
- Secular Dynamics in Hierarchical Three-Body Systems
- Stellar Spin-Orbit Misalignment in a Multiplanet System
- In Situ Formation and Dynamical Evolution of Hot Jupiter Systems
- Exoplanet Biosignatures: A Framework for Their Assessment
- Thermal evolution and structure models of the transiting super-Earth GJ 1214b
- The Planet Nine Hypothesis
- On the Orbit of Exoplanet WASP-12b
- The Kepler-19 System: A Transiting 2.2 R_Earth Planet and a Second Planet Detected via Transit Timing Variations
- The HAT-P-13 Exoplanetary System: Evidence for Spin-Orbit Alignment and a Third Companion
- Retired A Stars and Their Companions VI. A Pair of Interacting Exoplanet Pairs Around the Subgiants 24 Sextanis and HD200964
- Long-Term Transit Timing Monitoring and Refined Light Curve Parameters of HAT-P-13b
- HAT-P-11: Discovery of a Second Planet and a Clue to Understanding Exoplanet Obliquities
- Mercury-T: A new code to study tidally evolving multi-planet systems. Applications to Kepler-62
- Low-Eccentricity Migration of Ultra-Short Period Planets in Multi-Planet Systems
- Giant Planets
- New developments for modern celestial mechanics. I. General coplanar three-body systems. Application to exoplanets
- Tidal dissipation in multi-planet systems and constraints to orbit-fitting
- HAT-P-44b, HAT-P-45b, and HAT-P-46b: Three Transiting Hot Jupiters in Possible Multi-Planet Systems
- BD+48 740 - Li overabundant giant star with a planet. A case of recent engulfment?
- Solar Obliquity Induced by Planet Nine
- The Time Dependence of hot Jupiters' Orbital Inclinations
- Transit light curve and inner structure of close-in planets
- The TESS-Keck Survey IV: A Retrograde, Polar Orbit for the Ultra-Low-Density, Hot Super-Neptune WASP-107b
- Dynamical Constraints on the Core Mass of Hot Jupiter HAT-P-13b
- Dynamical Evolution Induced by Planet Nine
- Compact planetary systems perturbed by an inclined companion: I. Vectorial representation of the secular model
- The Dynamics of the Multi-planet System Orbiting Kepler-56
- On planetary mass determination in the case of super-Earths orbiting active stars. The case of the CoRoT-7 system
- HAT-P-13: a multi-site campaign to detect the transit of the second planet in the system
- Constraining the interior of extrasolar giant planets with the tidal Love number k_2 using the example of HAT-P-13b
- Outer-planet scattering can gently tilt an inner planetary system
- Toward the Detection of Exoplanet Transits with Polarimetry
- Tidal decay and orbital circularization in close-in two-planet systems
- Self-Consistent Spin, Tidal and Dynamical Equations of Motion in the REBOUNDx Framework
- Analytical Model of Tidal Distortion and Dissipation for a Giant Planet with a Viscoelastic Core
- The Stellar Obliquity and the Long-period planet in the HAT-P-17 Exoplanetary System
- Dynamical Measurements of the Interior Structure of Exoplanets
- Teetering Stars: Resonant Excitation of Stellar Obliquities by Hot and Warm Jupiters with External Companions
- SOPHIE velocimetry of Kepler transit candidates XVIII. Radial velocity confirmation, absolute masses and radii, and origin of the Kepler-419 multiplanetary system
- The non-resonant, relativistic dynamics of circumbinary planets
- The Atmosphere and Interior Structure of HAT-P-13b from Spitzer Secondary Eclipses
- Schrödinger Evolution of Self-Gravitating Disks
- Characterizing Multi-planet Systems with Classical Secular Theory
- Transits of Inclined Exomoons - Hide and Seek and an Application to Kepler-1625
- Transit probability of precessing circumstellar planets in binaries and exomoons
- Resolving the Sin(I) degeneracy in Low-Mass Multi-Planet Systems
- A close outer companion to the ultra-hot Jupiter TOI-2109 b?
- Two neighbours of the ultra-short-period Earth-sized planet K2-157 b in the warm Neptunian savanna
- Explicit relations and criteria for eclipses, transits and occultations
- Secular dynamics of the triple system harbouring PSR J0337+1715 and implications for the origin of its orbital configuration
- Generating Stellar Obliquity in Systems with Broken Protoplanetary Disks