arXiv subjects

Eric B. Ford

Publications and source records attributed to Eric B. Ford.

At least 127 records · Page 7Linked to original sources

arXiv2013

RUN DMC: An efficient, parallel code for analyzing Radial Velocity Observations using N-body Integrations and Differential Evolution Markov chain Monte Carlo

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 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 ($\sim$7 x number of planets) that can have complex parameter correlations. To surmount these challenges, we introduce a differential evolution MCMC (DEMCMC) 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. 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, we offer recommendations for choosing the DEMCMC algorithm's algorithmic parameters that result in excellent performance for a wide variety of planetary systems.

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arXiv2013

MARVELS-1: A face-on double-lined binary star masquerading as a resonant planetary system; and consideration of rare false positives in radial velocity planet searches

We have analyzed new and previously published radial velocity observations of MARVELS-1, known to have an ostensibly substellar companion in a ~6- day orbit. We find significant (~100 m/s) residuals to the best-fit model for the companion, and these residuals are naively consistent with an interior giant planet with a P = 1.965d in a nearly perfect 3:1 period commensuribility (|Pb/Pc - 3| < 10^{-4}). We have performed several tests for the reality of such a companion, including a dynamical analysis, a search for photometric variability, and a hunt for contaminating stellar spectra. We find many reasons to be critical of a planetary interpretation, including the fact that most of the three-body dynamical solutions are unstable. We find no evidence for transits, and no evidence of stellar photometric variability. We have discovered two apparent companions to MARVELS-1 with adaptive optics imaging at Keck; both are M dwarfs, one is likely bound, and the other is likely a foreground object. We explore false-alarm scenarios inspired by various curiosities in the data. Ultimately, a line profile and bisector analysis lead us to conclude that the ~100 m/s residuals are an artifact of spectral contamination from a stellar companion contributing ~15-30% of the optical light in the system. We conclude that origin of this contamination is the previously detected radial velocity companion to MARVELS-1, which is not, as previously reported, a brown dwarf, but in fact a G dwarf in a face-on orbit.

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arXiv2013

Stellar Spin-Orbit Misalignment in a Multiplanet System

Stars hosting hot Jupiters are often observed to have high obliquities, whereas stars with multiple co-planar planets have been seen to have low obliquities. This has been interpreted as evidence that hot-Jupiter formation is linked to dynamical disruption, as opposed to planet migration through a protoplanetary disk. We used asteroseismology to measure a large obliquity for Kepler-56, a red giant star hosting two transiting co-planar planets. These observations show that spin-orbit misalignments are not confined to hot-Jupiter systems. Misalignments in a broader class of systems had been predicted as a consequence of torques from wide-orbiting companions, and indeed radial-velocity measurements revealed a third companion in a wide orbit in the Kepler-56 system.

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arXiv2013

Characterizing the Orbital and Dynamical State of the HD 82943 Planetary System With Keck Radial Velocity Data

We present an updated analysis of radial velocity data of the HD 82943 planetary system based on 10 years of measurements obtained with the Keck telescope. Previous studies have shown that the HD 82943 system has two planets that are likely in 2:1 mean-motion resonance (MMR), with the orbital periods about 220 and 440 days (Lee et al. 2006). However, alternative fits that are qualitatively different have also been suggested, with two planets in a 1:1 resonance (Gozdziewski & Konacki 2006) or three planets in a Laplace 4:2:1 resonance (Beauge et al. 2008). Here we use \c{hi}2 minimization combined with parameter grid search to investigate the orbital parameters and dynamical states of the qualitatively different types of fits, and we compare the results to those obtained with the differential evolution Markov chain Monte Carlo method. Our results support the coplanar 2:1 MMR configuration for the HD 82943 system, and show no evidence for either the 1:1 or 3-planet Laplace resonance fits. The inclination of the system with respect to the sky plane is well constrained at about 20(+4.9 -5.5) degree, and the system contains two planets with masses of about 4.78 MJ and 4.80 MJ (where MJ is the mass of Jupiter) and orbital periods of about 219 and 442 days for the inner and outer planet, respectively. The best fit is dynamically stable with both eccentricity-type resonant angles θ1 and θ2 librating around 0 degree.

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arXiv2013

Kepler's Unparalleled Exploration of the Time Dimension

We show that the Kepler spacecraft in two-reaction wheel mode of operation is very well suited for the study of eclipsing binary star systems. Continued observations of the Kepler field will provide the most enduring and long-term valuable science. It will enable the discovery and characterization of eclipsing binaries with periods greater than 1 year - these are the most important, yet least understood binaries for habitable-zone planet background considerations. The continued mission will also enable the investigation of hierarchical multiple systems (discovered through eclipse timing variations), and provide drastically improved orbital parameters for circumbinary planetary systems.

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arXiv2013

A Habitable Zone Census via Transit Timing and the Imperative for Continuing to Observe the Kepler Field

We propose a scientific program to complete a census of planets, characterizing their masses, orbital properties, and dynamical histories using continued observations of the Kepler field of view with the Kepler spacecraft in a two reaction wheel mission. Even with a significantly reduced photometric precision, extending time-domain observations of this field is uniquely capable of pursuing several critical science goals: 1) measuring the architectures of planetary systems by identifying non-transiting planets interleaved among known transiting planets, 2) establishing the mass-radius relationship for planets in the important transition region between small, gas-rich sub-Neptune planets and large, rocky super-Earths, and 3) uncovering dynamical evidence of the formation and evolution of the inner regions of planetary systems. To meet these objectives, the unique multi-object observing capabilities of Kepler will be used in a set of concurrent campaigns with specific motivations. These campaigns focus largely on the ability to interpret Transit Timing Variations (TTVs) that result from dynamical interactions among planets in a system and include: 1) observations of systems that exhibit large TTVs and are particularly rich in dynamical information, 2) observations of systems where additional transit times will yield mass measurements of the constituent planets, 3) observations of systems where the TTV signal evolves over very long timescales, and 4) observations of systems with long-period planet candidates where additional transits will remove orbital period ambiguities caused by gaps in the original Kepler data.

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arXiv2013

Transit Timing Observations from Kepler. VIII Catalog of Transit Timing Measurements of the First Twelve Quarters

Following Ford et al. (2011, 2012) and Steffen et al. (2012) we derived the transit timing of 1960 Kepler KOIs using the pre-search data conditioning (PDC) light curves of the first twelve quarters of the Kepler data. For 721 KOIs with large enough SNRs, we obtained also the duration and depth of each transit. The results are presented as a catalog for the community to use. We derived a few statistics of our results that could be used to indicate significant variations. Including systems found by previous works, we have found 130 KOIs that showed highly significant TTVs, and 13 that had short-period TTV modulations with small amplitudes. We consider two effects that could cause apparent periodic TTV - the finite sampling of the observations and the interference with the stellar activity, stellar spots in particular. We briefly discuss some statistical aspects of our detected TTVs. We show that the TTV period is correlated with the orbital period of the planet and with the TTV amplitude.

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arXiv2013

The Formation of Systems with Tightly-packed Inner Planets (STIPs) via Aerodynamic Drift

The NASA Kepler mission has revealed an abundant class of Systems with Tightly-packed Inner Planets (STIPs). The current paradigm for planet formation suggests that small planetesimals will quickly spiral into the host star due to aerodynamic drag, preventing rocky planet formation. In contrast, we find that aerodynamic drift, when acting on an ensemble of solids, can concentrate mass at short orbital periods in gaseous disks. Sublimation fronts may further aid this process. Kepler data suggest that the innermost known planets are found near the silicate sublimation zone. STIP planets should have a wide range of volatile fractions due to aerodynamic drift and H2 dissociation-driven gas accretion. We further propose that the low mass of Mars is evidence that the Solar System was once a proto-STIP.

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arXiv2013

A sub-Mercury-sized exoplanet

Since the discovery of the first exoplanet we have known that other planetary systems can look quite unlike our own. However, until recently we have only been able to probe the upper range of the planet size distribution. The high precision of the Kepler space telescope has allowed us to detect planets that are the size of Earth and somewhat smaller, but no previous planets have been found that are smaller than those we see in our own Solar System. Here we report the discovery of a planet significantly smaller than Mercury. This tiny planet is the innermost of three planets that orbit the Sun-like host star, which we have designated Kepler-37. Owing to its extremely small size, similar to that of Earth's Moon, and highly irradiated surface, Kepler-37b is probably a rocky planet with no atmosphere or water, similar to Mercury.

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arXiv2013

Measuring Transit Signal Recovery in the Kepler Pipeline I: Individual Events

The Kepler Mission was designed to measure the frequency of Earth-size planets in the habitable zone of Sun-like stars. A crucial component for recovering the underlying planet population from a sample of detected planets is understanding the completeness of that sample - what fraction of the planets that could have been discovered in a given data set were actually detected. Here we outline the information required to determine the sample completeness, and describe an experiment to address a specific aspect of that question, which is the issue of transit signal recovery. We investigate the extent to which the Kepler pipeline preserves individual transit signals by injecting simulated transits into the pixel-level data, processing the modified pixels through the pipeline, and comparing the measured transit signal-to-noise ratio (SNR) to that expected without perturbation by the pipeline. We inject simulated transit signals across the full focal plane for a set of observations of length 89 days. On average, we find that the SNR of the injected signal is recovered at MS = 0.9973(+/-0.0012)xBS-0.0151(+/-0.0049), where MS is the measured SNR and BS is the baseline, or expected, SNR. The 1σ width of the distribution around this correlation is +/-2.64%. We discuss the pipeline processes that cause the measured SNR to deviate significantly from the baseline SNR; these are primarily the handling of data adjacent to spacecraft re-pointings and the removal of harmonics prior to the measurement of the SNR. Finally we outline the further work required to characterise the completeness of the Kepler pipeline.

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arXiv2013

Kepler-68: Three Planets, One With a Density Between That of Earth and Ice Giants

NASA's Kepler Mission has revealed two transiting planets orbiting Kepler-68. Follow-up Doppler measurements have established the mass of the innermost planet and revealed a third jovian-mass planet orbiting beyond the two transiting planets. Kepler-68b, in a 5.4 day orbit has mass 8.3 +/- 2.3 Earth, radius 2.31 +/- 0.07 Earth radii, and a density of 3.32 +/- 0.92 (cgs), giving Kepler-68b a density intermediate between that of the ice giants and Earth. Kepler-68c is Earth-sized with a radius of 0.953 Earth and transits on a 9.6 day orbit; validation of Kepler-68c posed unique challenges. Kepler-68d has an orbital period of 580 +/- 15 days and minimum mass of Msin(i) = 0.947 Jupiter. Power spectra of the Kepler photometry at 1-minute cadence exhibit a rich and strong set of asteroseismic pulsation modes enabling detailed analysis of the stellar interior. Spectroscopy of the star coupled with asteroseismic modeling of the multiple pulsation modes yield precise measurements of stellar properties, notably Teff = 5793 +/- 74 K, M = 1.079 +/- 0.051 Msun, R = 1.243 +/- 0.019 Rsun, and density 0.7903 +/- 0.0054 (cgs), all measured with fractional uncertainties of only a few percent. Models of Kepler-68b suggest it is likely composed of rock and water, or has a H and He envelope to yield its density of about 3 (cgs).

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arXiv2013

A Search for Exozodiacal Clouds with Kepler

Planets embedded within dust disks may drive the formation of large scale clumpy dust structures by trapping dust into resonant orbits. Detection and subsequent modeling of the dust structures would help constrain the mass and orbit of the planet and the disk architecture, give clues to the history of the planetary system, and provide a statistical estimate of disk asymmetry for future exoEarth-imaging missions. Here we present the first search for these resonant structures in the inner regions of planetary systems by analyzing the light curves of hot Jupiter planetary candidates identified by the Kepler mission. We detect only one candidate disk structure associated with KOI 838.01 at the 3-sigma confidence level, but subsequent radial velocity measurements reveal that KOI 838.01 is a grazing eclipsing binary and the candidate disk structure is a false positive. Using our null result, we place an upper limit on the frequency of dense exozodi structures created by hot Jupiters. We find that at the 90% confidence level, less than 21% of Kepler hot Jupiters create resonant dust clumps that lead and trail the planet by ~90 degrees with optical depths >~5*10^-6, which corresponds to the resonant structure expected for a lone hot Jupiter perturbing a dynamically cold dust disk 50 times as dense as the zodiacal cloud.

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arXiv2012

On The Relative Sizes of Planets Within Kepler Multiple Candidate Systems

We present a study of the relative sizes of planets within the multiple candidate systems discovered with the $Kepler$ mission. We have compared the size of each planet to the size of every other planet within a given planetary system after correcting the sample for detection and geometric biases. We find that for planet-pairs for which one or both objects is approximately Neptune-sized or larger, the larger planet is most often the planet with the longer period. No such size--location correlation is seen for pairs of planets when both planets are smaller than Neptune. Specifically, if at least one planet in a planet-pair has a radius of $\gtrsim 3R_\oplus$, $68\pm 6%$ of the planet pairs have the inner planet smaller than the outer planet, while no preferred sequential ordering of the planets is observed if both planets in a pair are smaller than $\lesssim3 R_\oplus$.

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arXiv2012

The Discovery of HD 37605c and a Dispositive Null Detection of Transits of HD 37605b

We report the radial-velocity discovery of a second planetary mass companion to the K0 V star HD 37605, which was already known to host an eccentric, P~55 days Jovian planet, HD 37605b. This second planet, HD 37605c, has a period of ~7.5 years with a low eccentricity and an Msini of ~3.4 MJup. Our discovery was made with the nearly 8 years of radial velocity follow-up at the Hobby-Eberly Telescope and Keck Observatory, including observations made as part of the Transit Ephemeris Refinement and Monitoring Survey (TERMS) effort to provide precise ephemerides to long-period planets for transit follow-up. With a total of 137 radial velocity observations covering almost eight years, we provide a good orbital solution of the HD 37605 system, and a precise transit ephemeris for HD 37605b. Our dynamic analysis reveals very minimal planet-planet interaction and an insignificant transit time variation. Using the predicted ephemeris, we performed a transit search for HD 37605b with the photometric data taken by the T12 0.8-m Automatic Photoelectric Telescope (APT) and the Microvariability and Oscillations of Stars (MOST) satellite. Though the APT photometry did not capture the transit window, it characterized the stellar activity of HD 37605, which is consistent of it being an old, inactive star, with a tentative rotation period of 57.67 days. The MOST photometry enabled us to report a dispositive null detection of a non-grazing transit for this planet. Within the predicted transit window, we exclude an edge-on predicted depth of 1.9% at >>10sigma, and exclude any transit with an impact parameter b>0.951 at greater than 5sigma. We present the BOOTTRAN package for calculating Keplerian orbital parameter uncertainties via bootstrapping. We found consistency between our orbital parameters calculated by the RVLIN package and error bars by BOOTTRAN with those produced by a Bayesian analysis using MCMC.

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arXiv2012

Swarm-NG: a CUDA Library for Parallel n-body Integrations with focus on Simulations of Planetary Systems

We present Swarm-NG, a C++ library for the efficient direct integration of many n-body systems using highly-parallel Graphics Processing Unit (GPU), such as NVIDIA's Tesla T10 and M2070 GPUs. While previous studies have demonstrated the benefit of GPUs for n-body simulations with thousands to millions of bodies, Swarm-NG focuses on many few-body systems, e.g., thousands of systems with 3...15 bodies each, as is typical for the study of planetary systems. Swarm-NG parallelizes the simulation, including both the numerical integration of the equations of motion and the evaluation of forces using NVIDIA's "Compute Unified Device Architecture" (CUDA) on the GPU. Swarm-NG includes optimized implementations of 4th order time-symmetrized Hermite integration and mixed variable symplectic integration, as well as several sample codes for other algorithms to illustrate how non-CUDA-savvy users may themselves introduce customized integrators into the Swarm-NG framework. To optimize performance, we analyze the effect of GPU-specific parameters on performance under double precision. Applications of Swarm-NG include studying the late stages of planet formation, testing the stability of planetary systems and evaluating the goodness-of-fit between many planetary system models and observations of extrasolar planet host stars (e.g., radial velocity, astrometry, transit timing). While Swarm-NG focuses on the parallel integration of many planetary systems,the underlying integrators could be applied to a wide variety of problems that require repeatedly integrating a set of ordinary differential equations many times using different initial conditions and/or parameter values.

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arXiv2012

Planets in Open Clusters Detectable by Kepler

While hundreds of planets have been discovered around field stars, only a few are known in star clusters. To explain the lack of short-period giant planets in globular clusters (GC), such as 47 Tucane and ω Centauri, it has been suggested that their low metallicities may have prevented planet formation. Alternatively, the high rates of close stellar encounters in these clusters may have influenced the formation and subsequent evolution of planetary systems. How common are planets in clusters around normal main-sequence stars? Here we consider whether this question can be addressed using data from the Kepler mission. The Kepler field of view contains 4 low-density (relative to GCs) open clusters where the metallicities are about solar (or even higher) and stellar encounters are much less frequent than in typical GCs. We provide detailed $N$-body models and show that most planets in Kepler-detectable orbits are not significantly perturbed by stellar encounters in these open clusters. We focus on the most massive cluster, NGC 6791, which has super-solar metallicity, and find that if planets formed in this cluster at the same frequency as observed in the field, Kepler could detect 1 -- 20 transiting planets depending on the planet-size distribution and the duration of data collection. Due to the large distance to NGC 6791 Kepler will have to search relatively faint ($K_p<20$) stars for the full extended mission to achieve such a yield.

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arXiv2012

Kepler-47: A Transiting Circumbinary Multi-Planet System

We report the detection of Kepler-47, a system consisting of two planets orbiting around an eclipsing pair of stars. The inner and outer planets have radii 3.0 and 4.6 times that of the Earth, respectively. The binary star consists of a Sun-like star and a companion roughly one-third its size, orbiting each other every 7.45 days. With an orbital period of 49.5 days, eighteen transits of the inner planet have been observed, allowing a detailed characterization of its orbit and those of the stars. The outer planet's orbital period is 303.2 days, and although the planet is not Earth-like, it resides within the classical "habitable zone", where liquid water could exist on an Earth-like planet. With its two known planets, Kepler-47 establishes that close binary stars can host complete planetary systems.

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arXiv2012

The Neptune-Sized Circumbinary Planet Kepler-38b

We discuss the discovery and characterization of the circumbinary planet Kepler-38b. The stellar binary is single-lined, with a period of 18.8 days, and consists of a moderately evolved main-sequence star (M_A = 0.949 +/- 0.059 solar masses and R_A = 1.757 +/- 0.034 solar radii) paired with a low-mass star (M_B = 0.249 +/- 0.010 solar masses and R_B = 0.2724 +/- 0.0053 solar radii) in a mildly eccentric (e=0.103) orbit. A total of eight transits due to a circumbinary planet crossing the primary star were identified in the Kepler light curve (using Kepler Quarters 1 through 11), from which a planetary period of 105.595 +/- 0.053 days can be established. A photometric dynamical model fit to the radial velocity curve and Kepler light curve yields a planetary radius of 4.35 +/- 0.11 Earth radii, or 1.12 +/- 0.03 Neptune radii. Since the planet is not sufficiently massive to observably alter the orbit of the binary from Keplerian motion, we can only place an upper limit on the mass of the planet of 122 Earth masses (7.11 Neptune masses or 0.384 Jupiter masses) at 95% confidence. This upper limit should decrease as more Kepler data become available.

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