arXiv subjects

Eric B. Ford

Publications and source records attributed to Eric B. Ford.

At least 199 records · Page 11Linked to original sources

arXiv2010

Transit Timing Variations for Inclined and Retrograde Exoplanetary Systems

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 $0<\,^{\circ}i<170\,^{\circ}$, only reducing in amplitude for $i > 170\,^{\circ}$. Systems in higher order MMRs (E.g. 5:1) increase in TTV amplitude as inclinations increase towards $45\,^{\circ}$, becoming approximately constant for $45 < i < 135$, and then declining for $i > 135\,^{\circ}$. Planets away from resonance slowly decrease in TTV amplitude as inclinations increase from 0 to 180, where-as 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 ($135\,^{\circ} < i \leq 180\,^{\circ}$), 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 a 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.

astro-ph.EP↗

arXiv2009

The Formation Mechanism of Gas Giants on Wide Orbits

The recent discoveries of massive planets on ultra-wide orbits of HR 8799 (Marois et al. 2008) and Fomalhaut (Kalas et al. 2008) present a new challenge for planet formation theorists. Our goal is to figure out which of three giant planet formation mechanisms--core accretion (with or without migration), scattering from the inner disk, or gravitational instability--could be responsible for Fomalhaut b, HR 8799 b, c and d, and similar planets discovered in the future. This paper presents the results of numerical experiments comparing the long-period planet formation efficiency of each possible mechanism in model A star, G star and M star disks. First, a simple core accretion simulation shows that planet cores forming beyond 35 AU cannot reach critical mass, even under the most favorable conditions one can construct. Second, a set of N-body simulations demonstrates that planet-planet scattering does not create stable, wide-orbit systems such as HR 8799. Finally, a linear stability analysis verifies previous work showing that global spiral instabilities naturally arise in high-mass disks. We conclude that massive gas giants on stable orbits with semimajor axes greater than 35 AU form by gravitational instability in the disk. We recommend that observers examine the planet detection rate as a function of stellar age, controlling for planet dimming with time. If planet detection rate is found to be independent of stellar age, it would confirm our prediction that gravitational instability is the dominant mode of producing detectable planets on wide orbits. We also predict that the occurrence ratio of long-period to short-period gas giants should be highest for M dwarfs due to the inefficiency of core accretion and the expected small fragment mass in their disks.

astro-ph.EP↗

arXiv2009

The Transit Ingress and the Tilted Orbit of the Extraordinarily Eccentric Exoplanet HD 80606b

We present the results of a transcontinental campaign to observe the 2009 June 5 transit of the exoplanet HD 80606b. We report the first detection of the transit ingress, revealing the transit duration to be 11.64 +/- 0.25 hr and allowing more robust determinations of the system parameters. Keck spectra obtained at midtransit exhibit an anomalous blueshift, giving definitive evidence that the stellar spin axis and planetary orbital axis are misaligned. The Keck data show that the projected spin-orbit angle is between 32-87 deg with 68.3% confidence and between 14-142 deg with 99.73% confidence. Thus the orbit of this planet is not only highly eccentric (e=0.93), but is also tilted away from the equatorial plane of its parent star. A large tilt had been predicted, based on the idea that the planet's eccentric orbit was caused by the Kozai mechanism. Independently of the theory, it is noteworthy that all 3 exoplanetary systems with known spin-orbit misalignments have massive planets on eccentric orbits, suggesting that those systems migrate differently than lower-mass planets on circular orbits.

astro-ph.EP↗

arXiv2009

Benefits of Ground-Based Photometric Follow-Up for Transiting Extrasolar Planets Discovered with Kepler and CoRoT

Currently, over forty transiting planets have been discovered by ground-based photometric surveys, and space-based missions like Kepler and CoRoT are expected to detect hundreds more. Follow-up photometric observations from the ground will play an important role in constraining both orbital and physical parameters for newly discovered planets, especially those with small radii (R_p less than approximately 4 Earth radii) and/or intermediate to long orbital periods (P greater than approximately 30 days). Here, we simulate transit light curves from Kepler-like photometry and ground-based observations in the near-infrared (NIR) to determine how jointly modeling space-based and ground-based light curves can improve measurements of the transit duration and planet-star radius ratio. We find that adding observations of at least one ground-based transit to space-based observations can significantly improve the accuracy for measuring the transit duration and planet-star radius ratio of small planets (R_p less than approximately 4 Earth radii) in long-period (~1 year) orbits, largely thanks to the reduced effect of limb darkening in the NIR. We also demonstrate that multiple ground-based observations are needed to gain a substantial improvement in the measurement accuracy for small planets with short orbital periods (~3 days). Finally, we consider the role that higher ground-based precisions will play in constraining parameter measurements for typical Kepler targets. Our results can help inform the priorities of transit follow-up programs (including both primary and secondary transit of planets discovered with Kepler and CoRoT), leading to improved constraints for transit durations, planet sizes, and orbital eccentricities.

astro-ph.EP↗

arXiv2009

A Third Planet Orbiting HIP 14810

We present new precision radial velocities and a three-planet Keplerian orbit fit for the V = 8.5, G5 V star HIP 14810. We began observing this star at Keck Observatory as part of the N2K Planet Search Project. Wright et al. (2007) announced the inner two planets to this system, and subsequent observations have revealed the outer planet planet and the proper orbital solution for the middle planet. The planets have minimum masses of 3.9, 1.3, and 0.6 M_Jup and orbital periods of 6.67, 147.7, and 952 d, respectively. We have numerically integrated the family of orbital solutions consistent with the data and find that they are stable for at least 10^6 yr. Our photometric search shows that the inner planet does not transit.

astro-ph.SR↗

arXiv2009

Type II migration of planets on eccentric orbits

The observed extrasolar planets possess both large masses (with a median M sin i of 1.65 MJ) and a wide range in orbital eccentricity (0 < e < 0.94). As planets are thought to form in circumstellar disks, one important question in planet formation is determining whether, and to what degree, a gaseous disk affects an eccentric planet's orbit. Recent studies have probed the interaction between a disk and a terrestrial planet on an eccentric orbit, and the interaction between a disk and a gas giant on a nearly circular orbit, but little is known about the interaction between a disk and an eccentric gas giant. Such a scenario could arise due to scattering while the disk is still present, or perhaps through planet formation via gravitational instability. We fill this gap with simulations of eccentric, massive (gap-forming) planets in disks using the hydrodynamical code FARGO. Although the long-term orbital evolution of the planet depends on disk properties, including the boundary conditions used, the disk always acts to damp eccentricity when the planet is released into the disk. This eccentricity damping takes place on a timescale of 40 years, 15 times faster than the migration timescale.

astro-ph.EP↗

arXiv2009

Ten New and Updated Multi-planet Systems, and a Survey of Exoplanetary Systems

We present the latest velocities for 10 multi-planet systems, including a re-analysis of archival Keck and Lick data, resulting in improved velocities that supersede our previously published measurements. We derive updated orbital fits for ten Lick and Keck systems, including two systems (HD 11964, HD 183263) for which we provide confirmation of second planets only tentatively identified elsewhere, and two others (HD 187123, and HD 217107) for which we provide a major revision of the outer planet's orbit. We compile orbital elements from the literature to generate a catalog of the 28 published multiple-planet systems around stars within 200 pc. From this catalog we find several intriguing patterns emerging: - Including those systems with long-term radial velocity trends, at least 28% of known planetary systems appear to contain multiple planets. - Planets in multiple-planet systems have somewhat smaller eccentricities than single planets. - The distribution of orbital distances of planets in multi-planet systems and single planets are inconsistent: single-planet systems show a pile-up at P ~ 3 days and a jump near 1 AU, while multi-planet systems show a more uniform distribution in log-period. In addition, among all planetary systems we find: - There may be an emerging, positive correlation between stellar mass and giant-planet semi-major axis. - Exoplanets more massive than Jupiter have eccentricities broadly distributed across 0 < e < 0.5, while lower-mass exoplanets exhibit a distribution peaked near e = 0.

astro-ph↗

arXiv2009

Formation, Survival, and Detectability of Planets Beyond 100 AU

Direct imaging searches have begun to detect planetary and brown dwarf companions and to place constraints on the presence of giant planets at large separations from their host star. This work helps to motivate such planet searches by predicting a population of young giant planets that could be detectable by direct imaging campaigns. Both the classical core accretion and the gravitational instability model for planet formation are hard-pressed to form long-period planets in situ. Here, we show that dynamical instabilities among planetary systems that originally formed multiple giant planets much closer to the host star could produce a population of giant planets at large (~100 AU - 100000 AU) separations. We estimate the limits within which these planets may survive, quantify the efficiency of gravitational scattering into both stable and unstable wide orbits, and demonstrate that population analyses must take into account the age of the system. We predict that planet scattering creates a population of detectable giant planets on wide orbits that decreases in number on timescales of ~10 Myr. We demonstrate that several members of such populations should be detectable with current technology, quantify the prospects for future instruments, and suggest how they could place interesting constraints on planet formation models.

astro-ph.EP↗

arXiv2008

Parallel Algorithm for Solving Kepler's Equation on Graphics Processing Units: Application to Analysis of Doppler Exoplanet Searches

[Abridged] We present the results of a highly parallel Kepler equation solver using the Graphics Processing Unit (GPU) on a commercial nVidia GeForce 280GTX and the "Compute Unified Device Architecture" programming environment. We apply this to evaluate a goodness-of-fit statistic (e.g., chi^2) for Doppler observations of stars potentially harboring multiple planetary companions (assuming negligible planet-planet interactions). We tested multiple implementations using single precision, double precision, pairs of single precision, and mixed precision arithmetic. We find that the vast majority of computations can be performed using single precision arithmetic, with selective use of compensated summation for increased precision. However, standard single precision is not adequate for calculating the mean anomaly from the time of observation and orbital period when evaluating the goodness-of-fit for real planetary systems and observational data sets. Using all double precision, our GPU code outperforms a similar code using a modern CPU by a factor of over 60. Using mixed-precision, our GPU code provides a speed-up factor of over 600, when evaluating N_sys > 1024 models planetary systems each containing N_pl = 4 planets and assuming N_obs = 256 observations of each system. We conclude that modern GPUs also offer a powerful tool for repeatedly evaluating Kepler's equation and a goodness-of-fit statistic for orbital models when presented with a large parameter space.

astro-ph↗

arXiv2008

Dynamical Simulations of the Planetary System HD69830

HD 69830 exhibits radial velocity variations attributed to three planets as well as infrared emission attributed to a warm debris disk. Previous studies have developed models for the planet migration and mass growth (Alibert et al. 2006) and the replenishment of warm grains (Wyatt et al. 2007). We perform n-body integrations in order to explore the implications of these models for: 1) the excitation of planetary eccentricity, 2) the accretion and clearing of a putative planetesimal disk, 3) the distribution of planetesimal orbits following migration, and 4) the implications for the origin of the IR emission. We find that: i) It is not possible to explain the observed planetary eccentricities (e~0.1) purely as the result of planetary perturbations during migration unless the planetary system is nearly face-on. ii) The rate of accretion of planetesimals onto planets in our n-body simulations is significantly different to that assumed in the semi-analytic models, suggesting that one cannot successfully treat planetesimal accretion in the simplified manner of Alibert et al. (2006). iii) Eccentricity damping of planetesimals does not act as an insurmountable obstacle to the existence of an excited eccentric disk: All simulations result in at least 25 Earth-masses of material remaining bound in the region ~1-9 AU, even after all three planets have migrated through the region. iv) Gas drag works to size-sort the planetesimals, with the largest bodies preferentially occupying the highest eccentricity and longest-lived orbits. Further work will be required to understand whether these eccentricity distributions are high enough to explain the level of dust emission observed despite mass loss via steady state collisional evolution. [abridged]

astro-ph↗

arXiv2008

Secular Evolution of HD 12661: A System Caught at an Unlikely Time

The eccentricity evolution of multiple planet systems can provide valuable constraints on planet formation models. Unfortunately, the inevitable uncertainties in the current orbital elements can lead to significant ambiguities in the nature of the secular evolution. Integrating any single set of orbital elements inadequately describes the full range of secular evolutions consistent with current observations. Thus, we combine radial velocity observations of HD 12661 with Markov Chain Monte Carlo sampling to generate ensembles of initial conditions for direct n-body integrations. We find that any mean motion resonances are quite weak and do not significantly impact the secular evolution, and that current observations indicate circulation or large amplitude libration of the periapses. The eccentricity of the outer planet undergoes large oscillations for nearly all of the allowed two-planet orbital solutions. This type of secular evolution would arise if planet c had been impulsively perturbed, perhaps due to strong scattering of an additional planet that was subsequently accreted onto the star. Finally, we note that the secular evolution implied by the current orbital configuration implies that planet c spends ~96% of the time following an orbit more eccentric than that presently observed. Either this system is being observed during a relatively rare state, or additional planets are affecting the observed radial velocities and/or the system's secular eccentricity evolution.

astro-ph↗

arXiv2008

Origins of Eccentric Extrasolar Planets: Testing the Planet-Planet Scattering Model

(Abridged) In planetary systems with two or more giant planets, dynamical instabilities can lead to collisions or ejections through strong planet--planet scattering. Previous studies for simple initial configurations with two equal-mass planets revealed some discrepancies between the results of numerical simulations and the observed orbital elements of extrasolar planets. Here, we show that simulations with two unequal mass planets starting on nearly circular orbits predict a reduced frequency of collisions and a broader range of final eccentricities. The two-planet scattering model can easily reproduce the observed eccentricities with a plausible distribution of planet mass ratios. Further, the two-planet scattering model predicts a maximum eccentricity of about 0.8, independent of the distribution of planet mass ratios, provided that both planets are initially place on nearly circular orbits. This compares favorably with current observations and will be tested by future planet discoveries. The combination of planet--planet scattering and tidal circularization may be able to explain the existence of some giant planets with very short period orbits. Orbital migration due to planet scattering could play an important role in explaining the increased rate of giant planets with very short period orbits. We also re-examine and discuss various possible correlations between eccentricities and other properties of observed extrasolar planets. We demonstrate that the observed distribution of planet masses, orbital periods, and eccentricities can provide constraints for models of planet formation and evolution.

astro-ph↗

arXiv2008

Dynamical Outcomes of Planet-Planet Scattering

Observations in the past decade have revealed extrasolar planets with a wide range of orbital semimajor axes and eccentricities. Based on the present understanding of planet formation via core accretion and oligarchic growth, we expect that giant planets often form in closely packed configurations. While the protoplanets are embedded in a protoplanetary gas disk, dissipation can prevent eccentricity growth and suppress instabilities from becoming manifest. However, once the disk dissipates, eccentricities can grow rapidly, leading to close encounters between planets. Strong planet--planet gravitational scattering could produce both high eccentricities and, after tidal circularization, very short-period planets, as observed in the exoplanet population. We present new results for this scenario based on extensive dynamical integrations of systems containing three giant planets, both with and without residual gas disks. We assign the initial planetary masses and orbits in a realistic manner following the core accretion model of planet formation. We show that, with realistic initial conditions, planet--planet scattering can reproduce quite well the observed eccentricity distribution. Our results also make testable predictions for the orbital inclinations of short-period giant planets formed via strong planet scattering followed by tidal circularization.

astro-ph↗

arXiv2008

Identifying the rotation rate and the presence of dynamic weather on extrasolar Earth-like planets from photometric observations

With the recent discoveries of hundreds of extrasolar planets, the search for planets like Earth and life in the universe, is quickly gaining momentum. In the future, large space observatories could directly detect the light scattered from rocky planets, but they would not be able to spatially resolve a planet's surface. Using reflectance models and real cloud data from satellite observations, here we show that, despite Earth's dynamic weather patterns, the light scattered by the Earth to a hypothetical distant observer as a function of time contains sufficient information to accurately measure Earth's rotation period. This is because ocean currents and continents result in relatively stable averaged global cloud patterns. The accuracy of these measurements will vary with the viewing geometry and other observational constraints. If the rotation period can be measured with accuracy, data spanning several months could be coherently combined to obtain spectroscopic information about individual regions of the planetary surface. Moreover, deviations from a periodic signal can be used to infer the presence of relatively short-live structures in its atmosphere (i.e., clouds). This could provide a useful technique for recognizing exoplanets that have active weather systems, changing on a timescale comparable to their rotation. Such variability is likely to be related to the atmospheric temperature and pressure being near a phase transition and could support the possibility of liquid water on the planet's surface.

astro-ph↗

arXiv2008

Characterizing the Orbital Eccentricities of Transiting Extrasolar Planets with Photometric Observations

The discovery of over 200 extrasolar planets with the radial velocity (RV) technique has revealed that many giant planets have large eccentricities, in striking contrast with most of the planets in the solar system and prior theories of planet formation. The realization that many giant planets have large eccentricities raises a fundamental question: ``Do terrestrial-size planets of other stars typically have significantly eccentric orbits or nearly circular orbits like the Earth?'' Here, we demonstrate that photometric observations of transiting planets could be used to characterize the orbital eccentricities for individual transiting planets, as well the eccentricity distribution for various populations of transiting planets (e.g., those with a certain range of orbital periods or physical sizes). Such characterizations can provide valuable constraints on theories for the excitation of eccentricities and tidal dissipation. We outline the future prospects of the technique given the exciting prospects for future transit searches, such as those to be carried out by the CoRoT and Kepler missions.

astro-ph↗

arXiv2008

Cadence Optimisation and Exoplanetary Parameter Sensitivity

To achieve maximum planet yield for a given radial velocity survey, the observing strategy must be carefully considered. In particular, the adopted cadence can greatly affect the sensitivity to exoplanetary parameters such as period and eccentricity. Here we describe simulations which aim to maximise detections based upon the target parameter space of the survey.

astro-ph↗

arXiv2007

Adaptive Scheduling Algorithms for Planet Searches

High-precision radial velocity planet searches have surveyed over ~2000 nearby stars and detected over ~200 planets. While these same stars likely harbor many additional planets, they will become increasingly challenging to detect, as they tend to have relatively small masses and/or relatively long orbital periods. Therefore, observers are increasing the precision of their observations, continuing to monitor stars over decade timescales, and also preparing to survey thousands more stars. Given the considerable amounts of telescope time required for such observing programs, it is important use the available resources as efficiently as possible. Previous studies have found that a wide range of predetermined scheduling algorithms result in planet searches with similar sensitivities. We have developed adaptive scheduling algorithms which have a solid basis in Bayesian inference and information theory and also are computationally feasible for modern planet searches. We have performed Monte Carlo simulations of plausible planet searches to test the power of adaptive scheduling algorithms. Our simulations demonstrate that planet searches performed with adaptive scheduling algorithms can simultaneously detect more planets, detect less massive planets, and measure orbital parameters more accurately than comparable surveys using a non-adaptive scheduling algorithm. We expect that these techniques will be particularly valuable for the N2K radial velocity planet search for short-period planets as well as future astrometric planet searches with the Space Interferometry Mission which aim to detect terrestrial mass planets.

astro-ph↗

arXiv2007

Role of Dynamical Research in the Detection and Characterization of Exoplanets

(Abridged) The discovery of extrasolar planetary systems revealed an unexpected diversity of planetary systems that has revolutionized planet formation theory. A strong program of theoretical research is essential to maximize both the discovery potential and the scientific returns of future observational programs, so as to achieve a deeper understanding of the formation and evolution of planetary systems. We outline three broad categories of theoretical research: detailed studies of specific planetary systems, testing planet formation models by comparing their predictions to the observed exoplanet population, and detailed modeling of specific physical processes. We describe how such theoretical research plays an important role in analyzing observations for a wide range detection methods and contributes to understanding the Earth's place in the universe and the potential for Earth-like life beyond our solar system. In this white paper, we suggest how to maximize the scientific return of future exoplanet observations. Our recommendations include a strong theory program, support for multiple observational programs that will study a diverse set of planets and stars, significant observing time devoted to follow-up observations, and healthy collaboration between observers and theorists.

astro-ph↗