[en] Both ground- and space-based transit observatories are poised to significantly increase the number of known transiting planets and the number of precisely measured transit times. The variation in a planet's transit times may be used to infer the presence of additional planets. Deducing the masses and orbital parameters of such planets from transit time variations (TTVs) alone is a rich and increasingly relevant dynamical problem. In this work, we evaluate the extent of the degeneracies in this process, systematically explore the dependence of TTV signals on several parameters, and provide phase space plots that could aid observers in planning future observations. Our explorations are focused on a likely-to-be prevalent situation: a known transiting short-period Neptune- or Jupiter-sized planet and a suspected external low-mass perturber on a nearly coplanar orbit. Through ∼10⁷ N-body simulations, we demonstrate how TTV signal amplitudes may vary by orders of magnitude due to slight variations in any one orbital parameter (10^-3 AU in a semimajor axis, 0.005 in eccentricity, or a few degrees in orbital angles), and quantify the number of consecutive transit observations necessary in order to obtain a reasonable opportunity of characterizing the unseen planet (∼>50 observations). Planets in or near period commensurabilities of the form p:q, where p ≤ 20 and q ≤ 3, produce distinct TTV signatures, regardless of whether the planets are actually locked in a mean motion resonance. We distinguish these systems from the secular systems in our explorations. Additionally, we find that computing the autocorrelation function of a TTV signal can provide a useful diagnostic for identifying possible orbits for additional planets and suggest that this method could aid integration of TTV signals in future studies of particular exosystems.

[en] In the 20+ years of Doppler observations of stars, scientists have uncovered a diverse population of extrasolar multi-planet systems. A common technique for characterizing the orbital elements of these planets is the Markov Chain Monte Carlo (MCMC), using a Keplerian model with random walk proposals and paired with the Metropolis-Hastings algorithm. For approximately a couple of dozen planetary systems with Doppler observations, there are strong planet-planet interactions due to the system being in or near a mean-motion resonance (MMR). An N-body model is often required to accurately describe these systems. Further computational difficulties arise from exploring a high-dimensional parameter space (∼7 × number of planets) that can have complex parameter correlations, particularly for systems near a MMR. To surmount these challenges, we introduce a differential evolution MCMC (DEMCMC) algorithm applied to radial velocity data while incorporating self-consistent N-body integrations. Our Radial velocity Using N-body DEMCMC (RUN DMC) algorithm improves upon the random walk proposal distribution of the traditional MCMC by using an ensemble of Markov chains to adaptively improve the proposal distribution. RUN DMC can sample more efficiently from high-dimensional parameter spaces that have strong correlations between model parameters. We describe the methodology behind the algorithm, along with results of tests for accuracy and performance. We find that most algorithm parameters have a modest effect on the rate of convergence. However, the size of the ensemble can have a strong effect on performance. We show that the optimal choice depends on the number of planets in a system, as well as the computer architecture used and the resulting extent of parallelization. While the exact choices of optimal algorithm parameters will inevitably vary due to the details of individual planetary systems (e.g., number of planets, number of observations, orbital periods, and signal-to-noise of each planet), we offer recommendations for choosing the DEMCMC algorithm's algorithmic parameters that result in excellent performance for a wide variety of planetary systems

[en] The chance that a planetary system will interact with another member of its host star's nascent cluster would be greatly increased if gas giant planets form in situ on wide orbits. In this paper, we explore the outcomes of planet-planet scattering for a distribution of multi-planet systems that all have one of the planets on an initial orbit of 100 AU. The scattering experiments are run with and without stellar flybys. We convolve the outcomes with distributions for protoplanetary disk and stellar cluster sizes to generalize the results where possible. We find that the frequencies of large mutual inclinations and high eccentricities are sensitive to the number of planets in a system, but not strongly to stellar flybys. However, flybys do play a role in changing the low and moderate portions of the mutual inclination distributions, and erase dynamically cold initial conditions on average. Wide-orbit planets can be mixed throughout the planetary system, and in some cases, can potentially become hot Jupiters, which we demonstrate using scattering experiments that include a tidal damping model. If planets form in situ on wide orbits, then there will be discernible differences in the proper-motion distributions of a sample of wide-orbit planets compared with a pure scattering formation mechanism. Stellar flybys can enhance the frequency of ejections in planetary systems, but autoionization is likely to remain the dominant source of free-floating planets.

[en] If the two planets in the HAT-P-13 system are coplanar, the orbital states provide a probe of the internal planetary structure. Previous analyses of radial velocity and transit timing data for the system suggested that the observational constraints on the orbital states were rather small. We reanalyze the available data, treating the jitter as an unknown MCMC parameter, and find that a wide range of jitter values are plausible, hence the system parameters are less well constrained than previously suggested. For slightly increased levels of jitter (∼4.5 m s^-1), the eccentricity of the inner planet can be in the range 0 < e_inner < 0.07, the period and eccentricity of the outer planet can be 440 days < P_outer < 470 days and 0.55 < e_outer < 0.85, respectively, while the relative pericenter alignment, η, of the planets can take essentially any value -180 deg. < η < +180 deg. It is therefore difficult to determine whether e_inner and η have evolved to a fixed-point state or a limit cycle or to use e_inner to probe the internal planetary structure. We perform various transit timing variation (TTV) analyses, demonstrating that current constraints merely restrict e_outer < 0.85, and rule out relative planetary inclinations within ∼2 deg. of i_rel = 90 deg., but that future observations could significantly tighten the restriction on both these parameters. We demonstrate that TTV profiles can readily distinguish the theoretically favored inclinations of i_rel = 0 deg. and 45 deg., provided that sufficiently precise and frequent transit timing observations of HAT-P-13b can be made close to the pericenter passage of HAT-P-13c. We note the relatively high probability that HAT-P-13c transits and suggest observational dates and strategies.

[en] Observations of clustering among the orbits of the most distant trans-Neptunian objects (TNOs) has inspired interest in the possibility of an undiscovered ninth planet lurking in the outskirts of the solar system. Numerical simulations by a number of authors have demonstrated that, with appropriate choices of planet mass and orbit, such a planet can maintain clustering in the orbital elements of the population of distant TNOs, similar to the observed sample. However, many aspects of the rich underlying dynamical processes induced by such a distant eccentric perturber have not been fully explored. We report the results of our investigation of the dynamics of coplanar test-particles that interact with a massive body on an circular orbit (Neptune) and a massive body on a more distant, highly eccentric orbit (the putative Planet Nine). We find that a detailed examination of our idealized simulations affords tremendous insight into the rich test-particle dynamics that are possible. In particular, we find that chaos and resonance overlap plays an important role in particles’ dynamical evolution. We develop a simple mapping model that allows us to understand, in detail, the web of overlapped mean-motion resonances explored by chaotically evolving particles. We also demonstrate that gravitational interactions with Neptune can have profound effects on the orbital evolution of particles. Our results serve as a starting point for a better understanding of the dynamical behavior observed in more complicated simulations that can be used to constrain the mass and orbit of Planet Nine.

[en] We perform numerical calculations of the expected transit timing variations (TTVs) induced on a hot-Jupiter by an Earth-mass perturber. Motivated by the recent discoveries of retrograde transiting planets, we concentrate on an investigation of the effect of varying relative planetary inclinations, up to and including completely retrograde systems. We find that planets in low-order (e.g., 2:1) mean-motion resonances (MMRs) retain approximately constant TTV amplitudes for 0 deg. < i < 170 deg., only reducing in amplitude for i>170 deg. Systems in higher order MMRs (e.g., 5:1) increase in TTV amplitude as inclinations increase toward 45 deg., becoming approximately constant for 45 deg. < i < 135 deg., and then declining for i>135 deg. Planets away from resonance slowly decrease in TTV amplitude as inclinations increase from 0 deg. to 180 deg., whereas planets adjacent to resonances can exhibit a huge range of variability in TTV amplitude as a function of both eccentricity and inclination. For highly retrograde systems (135 deg. < i ≤ 180 deg.), TTV signals will be undetectable across almost the entirety of parameter space, with the exceptions occurring when the perturber has high eccentricity or is very close to an MMR. This high inclination decrease in TTV amplitude (on and away from resonance) is important for the analysis of the known retrograde and multi-planet transiting systems, as inclination effects need to be considered if TTVs are to be used to exclude the presence of any putative planetary companions: absence of evidence is not evidence of absence.

[en] Transit surveys combined with Doppler data have revealed a class of gas giant planets that are massive and highly enriched in heavy-elements (e.g., HD 149026b, GJ436b, and HAT-P-20b). It is tempting to consider these planets as validation of core accretion plus gas capture because it is often assumed that disk instability planets should be of nebular composition. We show in this paper, to the contrary, that gas giants that form by disk instability can have a variety of heavy-element compositions, ranging from sub- to super-nebular values. High levels of enrichment can be achieved through one or multiple mechanisms, including enrichment at birth, planetesimal capture, and differentiation plus tidal stripping. As a result, the metallicity of an individual gas giant cannot be used to discriminate between gas giant formation modes.

[en] Three-body interactions are ubiquitous in astrophysics. For instance, Kozai–Lidov oscillations in hierarchical triple systems have been studied extensively and applied to a wide range of astrophysical systems. However, mildly hierarchical triples also play an important role, but they are less explored. In this work, we consider the secular dynamics of a test particle in a mildly hierarchical configuration. We find the limit within which the secular approximation is reliable when the outer perturber is in a circular orbit. In addition, we present resonances and chaotic regions using surface-of-section plots, and characterize regions of phase space that allow large eccentricity and inclination variations. Finally, we apply the secular results to the outer Solar System. We focus on the distribution of extreme trans-Neptunian objects (eTNOs) under the perturbation of a possible outer planet (Planet 9), and find that in addition to a low-inclination Planet 9, a polar or a counter-orbiting one could also produce pericenter clustering of eTNOs, while the polar one leads to a wider spread of eTNO inclinations.

[en] The standard model of planet formation considers an initial phase in which planetesimals form from a dust disk, followed by a phase of mutual planetesimal-planetesimal collisions, leading eventually to the formation of planetary embryos. However, there is a potential transition phase (which we call the 'snowball phase'), between the formation of the first planetesimals and the onset of mutual collisions amongst them, which has often been either ignored or underestimated in previous studies. In this snowball phase, isolated planetesimals move in Keplerian orbits and grow solely via the direct accretion of subcentimeter-sized dust entrained with the gas in the protoplanetary disk. Using a simplified model in which planetesimals are progressively produced from the dust, we consider the expected sizes to which the planetesimals can grow before mutual collisions commence and derive the dependence of this size on a number of critical parameters, including the degree of disk turbulence, the planetesimal size at birth, and the rate of planetesimal creation. For systems in which turbulence is weak and the planetesimals are created at a low rate and with relatively small birth size, we show that the snowball growth phase can be very important, allowing planetesimals to grow by a factor of 10⁶ in mass before mutual collisions take over. In such cases, the snowball growth phase can be the dominant mode to transfer mass from the dust to planetesimals. Moreover, such growth can take place within the typical lifetime of a protoplanetary gas disk. A noteworthy result is that, for a wide range of physically reasonable parameters, mutual collisions between planetesimals become significant when they reach sizes ∼100 km, irrespective of their birth size. This could provide an alternative explanation for the turnover point in the size distribution of the present-day asteroid belt. For the specific case of close binaries such as α Centauri, the role of snowball growth could be even more important. Indeed, it provides a safe way for bodies to grow through the problematic ∼1-50 km size range for which the perturbed environment of the binary can prevent mutual accretion of planetesimals. From a more general perspective, these preliminary results suggest that an efficient snowball growth phase provides a large amount of 'room at the bottom' for theories of planet formation.

[en] Most detected planet-bearing binaries are in wide orbits, for which a high inclination, i_B , between the binary orbital plane and the plane of the planetary disk around the primary is likely to be common. In this paper, we investigate the intermediate stages-from planetesimals to planetary embryos/cores-of planet formation in such highly inclined cases. Our focus is on the effects of gas drag on the planetesimals' orbital evolution, in particular on the evolution of the planetesimals' semimajor axis distribution and their mutual relative velocities. We first demonstrate that a non-evolving axisymmetric disk model is a good approximation for studying the effects of gas drag on a planetesimal in the highly inclined case (30 deg. < i_B < 150 deg.). We then find that gas drag plays a crucial role, and the results can be generally divided into two categories, i.e., the Kozai-on regime and the Kozai-off regime, depending on the specific value of i_B . For both regimes, a robust outcome over a wide range of parameters is that planetesimals migrate/jump inward and pile up, leading to a severely truncated and dense planetesimal disk around the primary. In this compact and dense disk, collision rates are high but relative velocities are low, providing conditions that are favorable for planetesimal growth and potentially allow for the subsequent formation of planets.