Instabilities in Multi-Planet Circumbinary Systems

The majority of the discovered transiting circumbinary planets are located very near the innermost stable orbits permitted, raising questions about the origins of planets in such perturbed environments. Most favored formation scenarios invoke formation at larger distances and subsequent migration to their current locations. Disk-driven planet migration in multi-planet systems is likely to trap planets in mean motion resonances and drive planets inward into regions of larger dynamical perturbations from the binary. We demonstrate how planet-planet resonances can interact with the binary through secular forcing and mean-motion resonances, driving chaos in the system. We show how this chaos will shape the architecture of circumbinary systems, with specific applications to Kepler 47 and the Pluto-Charon system, limiting maximum possible stable eccentricities and indicating what resonances are likely to exist. We are also able to constrain the minimum migration rates of resonant circumbinary planets.Comment: Accepted for publication in MNRA

Dynamical Formation of Close Binaries During the Pre-main-sequence Phase

Solar-type binaries with short orbital periods ($P_{\rm close}$ $\equiv$ 1 - 10 days; $a$ $\lesssim$ 0.1 AU) cannot form directly via fragmentation of molecular clouds or protostellar disks, yet their component masses are highly correlated, suggesting interaction during the pre-main-sequence (pre-MS) phase. Moreover, the close binary fraction of pre-MS stars is consistent with that of their MS counterparts in the field ($F_{\rm close}$ = 2.1%). Thus we can infer that some migration mechanism operates during the early pre-MS phase ($\tau$ $\lesssim$ 5 Myr) that reshapes the primordial separation distribution. We test the feasibility of this hypothesis by carrying out a population synthesis calculation which accounts for two formation channels: Kozai-Lidov (KL) oscillations and dynamical instability in triple systems. Our models incorporate (1) more realistic initial conditions compared to previous studies, (2) octupole-level effects in the secular evolution, (3) tidal energy dissipation via weak-friction equilibrium tides at small eccentricities and via non-radial dynamical oscillations at large eccentricities, and (4) the larger tidal radius of a pre-MS primary. Given a 15% triple star fraction, we simulate a close binary fraction from KL oscillations alone of $F_{\rm close}$ $\approx$ 0.4% after $\tau$ = 5 Myr, which increases to $F_{\rm close}$ $\approx$ 0.8% by $\tau$ = 5 Gyr. Dynamical ejections and disruptions of unstable coplanar triples in the disk produce solitary binaries with slightly longer periods $P$ $\approx$ 10 - 100 days. The remaining $\approx$60% of close binaries with outer tertiaries, particularly those in compact coplanar configurations with log $P_{\rm out}$ (days) $\approx$ 2 - 5 ($a_{\rm out}$ $<$ 50 AU), can be explained only with substantial extra energy dissipation due to interactions with primordial gas.Comment: Accepted by ApJ; 23 pages; 8 figures; this version incorporates changes made to address comments by refere

Orbital Stability of Multi-Planet Systems: Behavior at High Masses

In the coming years, high contrast imaging surveys are expected to reveal the characteristics of the population of wide-orbit, massive, exoplanets. To date, a handful of wide planetary mass companions are known, but only one such multi-planet system has been discovered: HR8799. For low mass planetary systems, multi-planet interactions play an important role in setting system architecture. In this paper, we explore the stability of these high mass, multi-planet systems. While empirical relationships exist that predict how system stability scales with planet spacing at low masses, we show that extrapolating to super-Jupiter masses can lead to up to an order of magnitude overestimate of stability for massive, tightly packed systems. We show that at both low and high planet masses, overlapping mean motion resonances trigger chaotic orbital evolution, which leads to system instability. We attribute some of the difference in behavior as a function of mass to the increasing importance of second order resonances at high planet-star mass ratios. We use our tailored high mass planet results to estimate the maximum number of planets that might reside in double component debris disk systems, whose gaps may indicate the presence of massive bodies.Comment: Accepted to Ap

Star Hoppers: Planet Instability and Capture in Evolving Binary Systems

Many planets are observed in stellar binary systems, and their frequency may be comparable to that of planetary systems around single stars. Binary stellar evolution in such systems influences the dynamical evolution of the resident planets. Here we study the evolution of a single planet orbiting one star in an evolving binary system. We find that stellar evolution can trigger dynamical instabilities that drive planets into chaotic orbits. This instability leads to planet-star collisions, exchange of the planet between the binary stars ("star-hoppers"), and ejection of the planet from the system. The means by which planets can be recaptured is similar to the pull-down capture mechanism for irregular solar system satellites. Because planets often suffer close encounters with the primary on the asymptotic giant branch, captures during a collision with the stellar envelope are also possible. Such capture could populate the habitable zone around white dwarfs.Comment: acceptance pending minor revisions to ApJ, comments welcome, two movies available at http://www.cfa.harvard.edu/~kkratter/BinaryPlanet

On the Mass Function, Multiplicity, and Origins of Wide-Orbit Giant Planets

A major outstanding question regarding the formation of planetary systems is whether wide-orbit giant planets form differently than close-in giant planets. We aim to establish constraints on two key parameters that are relevant for understanding the formation of wide-orbit planets: 1) the relative mass function and 2) the fraction of systems hosting multiple companions. In this study, we focus on systems with directly imaged substellar companions, and the detection limits on lower-mass bodies within these systems. First, we uniformly derive the mass probability distributions of known companions. We then combine the information contained within the detections and detection limits into a survival analysis statistical framework to estimate the underlying mass function of the parent distribution. Finally, we calculate the probability that each system may host multiple substellar companions. We find that 1) the companion mass distribution is rising steeply toward smaller masses, with a functional form of $N\propto M^{-1.3\pm0.3}$, and consequently, 2) many of these systems likely host additional undetected sub-stellar companions. Combined, these results strongly support the notion that wide-orbit giant planets are formed predominantly via core accretion, similar to the better studied close-in giant planets. Finally, given the steep rise in the relative mass function with decreasing mass, these results suggest that future deep observations should unveil a greater number of directly imaged planets.Comment: 19 pages, 10 figures, accepted to Ap

The fragmentation criteria in local vertically stratified self-gravitating disk simulations

Massive circumstellar disks are prone to gravitational instabilities, which trigger the formation of spiral arms that can fragment into bound clumps under the right conditions. Two dimensional simulations of self-gravitating disks are useful starting points for studying fragmentation, allowing for high-resolution simulations of thin disks. However, convergence issues can arise in 2D from various sources. One of these sources is the 2D approximation of self-gravity, which exaggerates the effect of self-gravity on small scales when the potential is not smoothed to account for the assumed vertical extent of the disk. This effect is enhanced by increased resolution, resulting in fragmentation at longer cooling timescales $\beta$. If true, it suggests that the 3D simulations of disk fragmentation may not have the same convergence problem and could be used to examine the nature of fragmentation without smoothing self-gravity on scales similar to the disk scale height. To that end, we have carried out local 3D self-gravitating disk simulations with simple $\beta$ cooling with fixed background irradiation to determine if 3D is necessary to properly describe disk fragmentation. Above a resolution of $\sim 40$ grid cells per scale height, we find that our simulations converge with respect to the cooling timescale. This result converges in agreement with analytic expectations which place a fragmentation boundary at $\beta_\mathrm{crit} = 3$.Comment: 11 pages, 9 figures. Accepted for publication in Ap