Tidal Evolution of a Secularly Interacting Planetary System

In a multi-planet system, a gradual change in one planet's semi-major axis will affect the eccentricities of all the planets, as angular momentum is distributed via secular interactions. If tidal dissipation in the planet is the cause of the change in semi-major axis, it also damps that planet's eccentricity, which in turn also contributes to the evolution of all the eccentricities. Formulae quantifying the combined effects on the whole system due to semi-major axis changes, as well as eccentricity damping, are derived here for a two-planet system. The CoRoT 7 system is considered as an example.Comment: Accepted for publication in the Astrophysical Journal, 17 pages, including 1 figur

Origin of the Structure of the Kuiper Belt during a Dynamical Instability in the Orbits of Uranus and Neptune

We explore the origin and orbital evolution of the Kuiper belt in the framework of a recent model of the dynamical evolution of the giant planets, sometimes known as the Nice model. This model is characterized by a short, but violent, instability phase, during which the planets were on large eccentricity orbits. One characteristic of this model is that the proto-planetary disk must have been truncated at roughly 30 to 35 AU so that Neptune would stop migrating at its currently observed location. As a result, the Kuiper belt would have initially been empty. In this paper we present a new dynamical mechanism which can deliver objects from the region interior to ~35 AU to the Kuiper belt without excessive inclination excitation. Assuming that the last encounter with Uranus delivered Neptune onto a low-inclination orbit with a semi-major axis of ~27 AU and an eccentricity of ~0.3, and that subsequently Neptune's eccentricity damped in ~1 My, our simulations reproduce the main observed properties of the Kuiper belt at an unprecedented level

Secure mass measurements from transit timing: 10 Kepler exoplanets between 3 and 8 M_⊕ with diverse densities and incident fluxes

We infer dynamical masses in eight multiplanet systems using transit times measured from Kepler's complete data set, including short-cadence data where available. Of the 18 dynamical masses that we infer, 10 pass multiple tests for robustness. These are in systems Kepler-26 (KOI-250), Kepler-29 (KOI-738), Kepler-60 (KOI-2086), Kepler-105 (KOI-115), and Kepler-307 (KOI-1576). Kepler-105 c has a radius of 1.3 R_⊕ and a density consistent with an Earth-like composition. Strong transit timing variation (TTV) signals were detected from additional planets, but their inferred masses were sensitive to outliers or consistent solutions could not be found with independently measured transit times, including planets orbiting Kepler-49 (KOI-248), Kepler-57 (KOI-1270), Kepler-105 (KOI-115), and Kepler-177 (KOI-523). Nonetheless, strong upper limits on the mass of Kepler-177 c imply an extremely low density of ~0.1 g cm^(−3). In most cases, individual orbital eccentricities were poorly constrained owing to degeneracies in TTV inversion. For five planet pairs in our sample, strong secular interactions imply a moderate to high likelihood of apsidal alignment over a wide range of possible eccentricities. We also find solutions for the three planets known to orbit Kepler-60 in a Laplace-like resonance chain. However, nonlibrating solutions also match the transit timing data. For six systems, we calculate more precise stellar parameters than previously known, enabling useful constraints on planetary densities where we have secure mass measurements. Placing these exoplanets on the mass–radius diagram, we find that a wide range of densities is observed among sub-Neptune-mass planets and that the range in observed densities is anticorrelated with incident flux

Characterizing Multi-planet Systems with Classical Secular Theory

Classical secular theory can be a powerful tool to describe the qualitative character of multi-planet systems and offer insight into their histories. The eigenmodes of the secular behavior, rather than current orbital elements, can help identify tidal effects, early planet-planet scattering, and dynamical coupling among the planets, for systems in which mean-motion resonances do not play a role. Although tidal damping can result in aligned major axes after all but one eigenmode have damped away, such alignment may simply be fortuitous. An example of this is 55 Cancri (orbital solution of Fischer et al., 2008) where multiple eigenmodes remain undamped. Various solutions for 55 Cancri are compared, showing differing dynamical groupings, with implications for the coupling of eccentricities and for the partitioning of damping among the planets. Solutions for orbits that include expectations of past tidal evolution with observational data, must take into account which eigenmodes should be damped, rather than expecting particular eccentricities to be near zero. Classical secular theory is only accurate for low eccentricity values, but comparison with other results suggests that it can yield useful qualitative descriptions of behavior even for moderately large eccentricity values, and may have advantages for revealing underlying physical processes and, as large numbers of new systems are discovered, for triage to identify where more comprehensive dynamical studies should have priority.Comment: Published in Celestial Mechanics and Dynamical Astronomy, 25 pages, 10 figure

A Machine Learns to Predict the Stability of Tightly Packed Planetary Systems

The requirement that planetary systems be dynamically stable is often used to vet new discoveries or set limits on unconstrained masses or orbital elements. This is typically carried out via computationally expensive N-body simulations. We show that characterizing the complicated and multi-dimensional stability boundary of tightly packed systems is amenable to machine-learning methods. We find that training an XGBoost machine-learning algorithm on physically motivated features yields an accurate classifier of stability in packed systems. On the stability timescale investigated (107 orbits), it is three orders of magnitude faster than direct N-body simulations. Optimized machine-learning classifiers for dynamical stability may thus prove useful across the discipline, e.g., to characterize the exoplanet sample discovered by the upcoming Transiting Exoplanet Survey Satellite. This proof of concept motivates investing computational resources to train algorithms capable of predicting stability over longer timescales and over broader regions of phase space

Planetary Candidates Observed by Kepler V: Planet Sample from Q1-Q12 (36 Months)

The Kepler mission discovered 2842 exoplanet candidates with 2 years of data. We provide updates to the Kepler planet candidate sample based upon 3 years (Q1-Q12) of data. Through a series of tests to exclude false-positives, primarily caused by eclipsing binary stars and instrumental systematics, 855 additional planetary candidates have been discovered, bringing the total number known to 3697. We provide revised transit parameters and accompanying posterior distributions based on a Markov Chain Monte Carlo algorithm for the cumulative catalogue of Kepler Objects of Interest. There are now 130 candidates in the cumulative catalogue that receive less than twice the flux the Earth receives and more than 1100 have a radius less than 1.5 Rearth. There are now a dozen candidates meeting both criteria, roughly doubling the number of candidate Earth analogs. A majority of planetary candidates have a high probability of being bonafide planets, however, there are populations of likely false-positives. We discuss and suggest additional cuts that can be easily applied to the catalogue to produce a set of planetary candidates with good fidelity. The full catalogue is publicly available at the NASA Exoplanet Archive.Comment: Accepted for publication, ApJ