arXiv subjects

Eric B. Ford

Publications and source records attributed to Eric B. Ford.

At least 91 records · Page 5Linked to original sources

arXiv2019

The Efficiency of Geometric Samplers for Exoplanet Transit Timing Variation Models

Transit timing variations (TTVs) are a valuable tool to determine the masses and orbits of transiting planets in multi-planet systems. TTVs can be readily modeled given knowledge of the interacting planets' orbital configurations and planet-star mass ratios, but such models are highly nonlinear and difficult to invert. Markov chain Monte Carlo (MCMC) methods are often used to explore the posterior distribution for model parameters, but, due to the high correlations between parameters, nonlinearity, and potential multi-modality in the posterior, many samplers perform very inefficiently. Therefore, we assess the performance of several MCMC samplers that use varying degrees of geometric information about the target distribution. We generate synthetic datasets from multiple models, including the TTVFaster model and a simple sinusoidal model, and test the efficiencies of various MCMC samplers. We find that sampling efficiency can be greatly improved for all models by sampling from a parameter space transformed using an estimate of the covariance and means of the target distribution. No one sampler performs the best for all datasets, but several samplers, such as Differential Evolution Monte Carlo and Geometric adaptive Monte Carlo, have consistently efficient performance. For datasets with near Gaussian posteriors, Hamiltonian Monte Carlo samplers with 2 or 3 leapfrog steps obtained the highest efficiencies. Based on differences in effective sample sizes per time, we show that the right choice of sampler can improve sampling efficiencies by several orders of magnitude.

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arXiv2018

Identifying inflated super-Earths and photo-evaporated cores

We present empirical evidence, supported by a planet formation model, to show that the curve $R/R_\oplus = 1.05\,(F/F_\oplus)^{0.11}$ approximates the location of the so-called photo-evaporation valley. Planets below that curve are likely to have experienced complete photo-evaporation, and planets just above it appear to have inflated radii; thus we identify a new population of inflated super-Earths and mini-Neptunes. Our N-body simulations are set within an evolving protoplanetary disk and include prescriptions for orbital migration, gas accretion, and atmospheric loss due to giant impacts. Our simulated systems broadly match the sizes and periods of super-Earths in the Kepler catalog. They also reproduce the relative sizes of adjacent planets in the same system, with the exception of planet pairs that straddle the photo-evaporation valley. This latter group is populated by planet pairs with either very large or very small size ratios ($R_{\rm out} / R_{\rm in} \gg 1$ or $R_{\rm out} / R_{\rm in} \ll 1$) and a dearth of size ratios near unity. It appears that this feature could be reproduced if the planet outside the photo-evaporation valley (typically the outer planet, but some times not) has its atmosphere significantly expanded by stellar irradiation. This new population of planets may be ideal targets for future transit spectroscopy observations with the upcoming James Webb Space Telescope.

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arXiv2018

Habitability of Exoplanet Waterworlds

Many habitable zone exoplanets are expected to form with water mass fractions higher than that of the Earth. For rocky exoplanets with 10-1000x Earth's H2O but without H2, we model the multi-Gyr evolution of ocean temperature and chemistry, taking into account C partitioning, high-pressure ice phases, and atmosphere-lithosphere exchange. Within our model, for Sun-like stars, we find that: (1)~the duration of habitable surface water is strongly affected by ocean chemistry; (2)~possible ocean pH spans a wide range; (3)~surprisingly, many waterworlds retain habitable surface water for >1 Gyr, and (contrary to previous claims) this longevity does not necessarily involve geochemical cycling. The key to this cycle-independent planetary habitability is that C exchange between the convecting mantle and the water ocean is curtailed by seafloor pressure on waterworlds, so the planet is stuck with the ocean mass and ocean cations that it acquires during the first 1% of its history. In our model, the sum of positive charges leached from the planetary crust by early water-rock interactions is - coincidentally - often within an order of magnitude of the early-acquired atmosphere+ocean inorganic C inventory overlaps. As a result, pCO2 is frequently in the "sweet spot" (0.2-20 bar) for which the range of semimajor axis that permits surface liquid water is about as wide as it can be. Because the width of the HZ in semimajor axis defines (for Sun-like stars) the maximum possible time span of surface habitability, this effect allows for Gyr of habitability as the star brightens. We illustrate our findings by using the output of an ensemble of N-body simulations as input to our waterworld evolution code. Thus (for the first time in an end-to-end calculation) we show that chance variation of initial conditions, with no need for geochemical cycling, can yield multi-Gyr surface habitability on waterworlds.

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arXiv2018

Improving the Accuracy of Planet Occurrence Rates from Kepler using Approximate Bayesian Computation

We present a new framework to characterize the occurrence rates of planet candidates identified by Kepler based on hierarchical Bayesian modeling, Approximate Bayesian Computing (ABC), and sequential importance sampling. For this study we adopt a simple 2-D grid in planet radius and orbital period as our model and apply our algorithm to estimate occurrence rates for Q1-Q16 planet candidates orbiting around solar-type stars. We arrive at significantly increased planet occurrence rates for small planet candidates ($R_p<1.25 R_{\oplus}$) at larger orbital periods ($P>80$d) compared to the rates estimated by the more common inverse detection efficiency method. Our improved methodology estimates that the occurrence rate density of small planet candidates in the habitable zone of solar-type stars is $1.6^{+1.2}_{-0.5}$ per factor of 2 in planet radius and orbital period. Additionally, we observe a local minimum in the occurrence rate for strong planet candidates marginalized over orbital period between 1.5 and 2$R_{\oplus}$ that is consistent with previous studies. For future improvements, the forward modeling approach of ABC is ideally suited to incorporating multiple populations, such as planets, astrophysical false positives and pipeline false alarms, to provide accurate planet occurrence rates and uncertainties. Furthermore, ABC provides a practical statistical framework for answering complex questions (e.g., frequency of different planetary architectures) and providing sound uncertainties, even in the face of complex selection effects, observational biases, and follow-up strategies. In summary, ABC offers a powerful tool for accurately characterizing a wide variety of astrophysical populations.

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arXiv2018

The crucial role of ground-based, Doppler measurements for the future of exoplanet science

We outline the important role that ground-based, Doppler monitoring of exoplanetary systems will play in advancing our theories of planet formation and dynamical evolution. A census of planetary systems requires a well designed survey to be executed over the course of a decade or longer. A coordinated survey to monitor several thousand targets each at ~1000 epochs (~3-5 million new observations) will require roughly 40 dedicated spectrographs. We advocate for improvements in data management, data sharing, analysis techniques, and software testing, as well as possible changes to the funding structures for exoplanet science.

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arXiv2018

Exoplanet Diversity in the Era of Space-based Direct Imaging Missions

This whitepaper discusses the diversity of exoplanets that could be detected by future observations, so that comparative exoplanetology can be performed in the upcoming era of large space-based flagship missions. The primary focus will be on characterizing Earth-like worlds around Sun-like stars. However, we will also be able to characterize companion planets in the system simultaneously. This will not only provide a contextual picture with regards to our Solar system, but also presents a unique opportunity to observe size dependent planetary atmospheres at different orbital distances. We propose a preliminary scheme based on chemical behavior of gases and condensates in a planet's atmosphere that classifies them with respect to planetary radius and incident stellar flux.

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arXiv2018

Planetary Candidates Observed by Kepler. VIII. A Fully Automated Catalog With Measured Completeness and Reliability Based on Data Release 25

We present the Kepler Object of Interest (KOI) catalog of transiting exoplanets based on searching four years of Kepler time series photometry (Data Release 25, Q1-Q17). The catalog contains 8054 KOIs of which 4034 are planet candidates with periods between 0.25 and 632 days. Of these candidates, 219 are new and include two in multi-planet systems (KOI-82.06 and KOI-2926.05), and ten high-reliability, terrestrial-size, habitable zone candidates. This catalog was created using a tool called the Robovetter which automatically vets the DR25 Threshold Crossing Events (TCEs, Twicken et al. 2016). The Robovetter also vetted simulated data sets and measured how well it was able to separate TCEs caused by noise from those caused by low signal-to-noise transits. We discusses the Robovetter and the metrics it uses to sort TCEs. For orbital periods less than 100 days the Robovetter completeness (the fraction of simulated transits that are determined to be planet candidates) across all observed stars is greater than 85%. For the same period range, the catalog reliability (the fraction of candidates that are not due to instrumental or stellar noise) is greater than 98%. However, for low signal-to-noise candidates between 200 and 500 days around FGK dwarf stars, the Robovetter is 76.7% complete and the catalog is 50.5% reliable. The KOI catalog, the transit fits and all of the simulated data used to characterize this catalog are available at the NASA Exoplanet Archive.

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arXiv2017

Insights on the Spectral Signatures of Stellar Activity and Planets from PCA

Photospheric velocities and stellar activity features such as spots and faculae produce measurable radial velocity signals that currently obscure the detection of sub-meter-per-second planetary signals. However, photospheric velocities are imprinted differently in a high-resolution spectrum than Keplerian Doppler shifts. Photospheric activity produces subtle differences in the shapes of absorption lines due to differences in how temperature or pressure affects the atomic transitions. In contrast, Keplerian Doppler shifts affect every spectral line in the same way. With high enough S/N and high enough resolution, statistical techniques can exploit differences in spectra to disentangle the photospheric velocities and detect lower-amplitude exoplanet signals. We use simulated disk-integrated time-series spectra and principal component analysis (PCA) to show that photospheric signals introduce spectral line variability that is distinct from Doppler shifts. We quantify the impact of instrumental resolution and S/N for this work.

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arXiv2017

Evidence for Two Hot Jupiter Formation Paths

Disk migration and high-eccentricity migration are two well-studied theories to explain the formation of hot Jupiters. The former predicts that these planets can migrate up until the planet-star Roche separation ($a_{Roche}$) and the latter predicts they will tidally circularize at a minimum distance of 2$a_{Roche}$. Considering long-running radial velocity and transit surveys have identified a couple hundred hot Jupiters to date, we can revisit the classic question of hot Jupiter formation in a data-driven manner. We approach this problem using data from several exoplanet surveys (radial velocity, Kepler, HAT, and WASP) allowing for either a single population or a mixture of populations associated with these formation channels, and applying a hierarchical Bayesian mixture model of truncated power laws of the form $x^{γ-1}$ to constrain the population-level parameters of interest (e.g., location of inner edges, $γ$, mixture fractions). Within the limitations of our chosen models, we find the current radial velocity and Kepler sample of hot Jupiters can be well explained with a single truncated power law distribution with a lower cutoff near 2$a_{Roche}$, a result that still holds after a decade, and $γ=-0.51\pm^{0.19}_{0.20}$. However, the HAT and WASP data show evidence for multiple populations (Bayes factor $\approx 10^{21}$). We find that $15\pm^{9}_{6}\%$ reside in a component consistent with disk migration ($γ=-0.04\pm^{0.53}_{1.27}$) and $85\pm^{6}_{9}\%$ in one consistent with high-eccentricity migration ($γ=-1.38\pm^{0.32}_{0.47}$). We find no immediately strong connections with some observed host star properties and speculate on how future exoplanet surveys could improve upon hot Jupiter population inference.

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arXiv2017

Outer Architecture of Kepler-11: Constraints from Coplanarity

The outer architectures of Kepler's compact systems of multiple transiting planets remain poorly constrained and few of these systems have lower bounds on the orbital distance of any massive outer planets. We infer a minimum orbital distance and upper limits on the inclination of a hypothetical Jovian-mass planet orbiting exterior to the six transiting planets at Kepler-11. Our constraints are derived from dynamical models together with observations provided by the Kepler mission. Firstly, the lack of transit timing variations (TTV) in the outermost transiting planet Kepler-11 g imply that the system does not contain a Jovian mass perturber within 2 AU from the star. Secondly, we test under what initial conditions a Jovian-mass planet moderately inclined from the transiting planets would make their co-transiting configuration unlikely. The transiting planets are secularly coupled and exhibit small mutual inclinations over long time-scales, although the outermost transiting planet, Kepler-11 g is weakly coupled to the inner five. We rule out a Jovian-mass planet on a 3 degree inclination within 3.0 AU, and higher inclinations out to further orbital distances, unless an undetected planet exists orbiting in the dynamical gap between Kepler-11 f and Kepler-11 g. Our constraints depend little on whether we assume the six transiting planets of Kepler-11 were initially perfectly co-planar or whether a minimum initial mutual inclination between the transiting planets is adopted based on the measured impact parameters of the transiting planets.

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arXiv2016

A resonant chain of four transiting, sub-Neptune planets

Surveys have revealed many multi-planet systems containing super-Earths and Neptunes in orbits of a few days to a few months. There is debate whether in situ assembly or inward migration is the dominant mechanism of the formation of such planetary systems. Simulations suggest that migration creates tightly packed systems with planets whose orbital periods may be expressed as ratios of small integers (resonances), often in a many-planet series (chain). In the hundreds of multi-planet systems of sub-Neptunes, more planet pairs are observed near resonances than would generally be expected, but no individual system has hitherto been identified that must have been formed by migration. Proximity to resonance enables the detection of planets perturbing each other. Here we report transit timing variations of the four planets in the Kepler-223 system, model these variations as resonant-angle librations, and compute the long-term stability of the resonant chain. The architecture of Kepler-223 is too finely tuned to have been formed by scattering, and our numerical simulations demonstrate that its properties are natural outcomes of the migration hypothesis. Similar systems could be destabilized by any of several mechanisms, contributing to the observed orbital-period distribution, where many planets are not in resonances. Planetesimal interactions in particular are thought to be responsible for establishing the current orbits of the four giant planets in the Solar System by disrupting a theoretical initial resonant chain similar to that observed in Kepler-223.

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arXiv2016

A Dynamical Analysis of the Kepler-80 System of Five Transiting Planets

Kepler has discovered hundreds of systems with multiple transiting exoplanets which hold tremendous potential both individually and collectively for understanding the formation and evolution of planetary systems. Many of these systems consist of multiple small planets with periods less than ~50 days known as Systems with Tightly-spaced Inner Planets, or STIPs. One especially intriguing STIP, Kepler-80 (KOI-500), contains five transiting planets: f, d, e, b, and c with periods of 1.0, 3.1, 4.6, 7.1, 9.5 days, respectively. We provide measurements of transit times and a transit timing variation (TTV) dynamical analysis. We find that TTVs cannot reliably detect eccentricities for this system, though mass estimates are not affected. Restricting the eccentricity to a reasonable range, we infer masses for the outer four planets (d, e, b, and c) to be $6.75^{+0.69}_{-0.51}$, $4.13^{+0.81}_{-0.95}$, $6.93^{+1.05}_{-0.70}$, and $6.74^{+1.23}_{-0.86}$ Earth masses, respectively. The similar masses but different radii are consistent with terrestrial compositions for d and e and $\sim$2% H/He envelopes for b and c. We confirm that the outer four planets are in a rare dynamical configuration with four interconnected three-body resonances that are librating with few degree amplitudes. We present a formation model that can reproduce the observed configuration by starting with a multi-resonant chain and introducing dissipation. Overall, the information-rich Kepler-80 planets provide an important perspective into exoplanetary systems.

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arXiv2016

Three Temperate Neptunes Orbiting Nearby Stars

We present the discovery of three modestly-irradiated, roughly Neptune-mass planets orbiting three nearby Solar-type stars. HD 42618 b has a minimum mass of $15.4 \pm 2.4$ M$_{\oplus}$, a semi-major axis of 0.55 AU, an equilibrium temperature of 337 K, and is the first planet discovered to orbit the solar analogue host star, HD 42618. We also discover new planets orbiting the known exoplanet host stars HD 164922 and HD 143761 ($ρ$ CrB). The new planet orbiting HD 164922 has a minimum mass of $12.9 \pm 1.6$ M$_{\oplus}$ and orbits interior to the previously known Jovian mass planet orbiting at 2.1 AU. HD 164922 c has a semi-major axis of 0.34 AU and an equilibrium temperature of 418 K. HD 143761 c orbits with a semi-major axis of 0.44 AU, has a minimum mass of $25 \pm 2$ M$_{\oplus}$, and is the warmest of the three new planets with an equilibrium temperature of 445 K. It orbits exterior to the previously known warm Jupiter in the system. A transit search using space-based CoRoT data and ground-based photometry from the Automated Photometric Telescopes (APTs) at Fairborn Observatory failed to detect any transits, but the precise, high-cadence APT photometry helped to disentangle planetary-reflex motion from stellar activity. These planets were discovered as part of an ongoing radial velocity survey of bright, nearby, chromospherically-inactive stars using the Automated Planet Finder (APF) telescope at Lick Observatory. The high-cadence APF data combined with nearly two decades of radial velocity data from Keck Observatory and gives unprecedented sensitivity to both short-period low-mass, and long-period intermediate-mass planets.

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arXiv2016

Transit Timing Observations from Kepler. IX. Catalog of the Full Long-Cadence Data Set

We present a new transit timing catalog of 2599 Kepler Objects of Interest (=KOIs), using the PDC-MAP long-cadence light curves that include the full seventeen quarters of the mission (ftp://wise- ftp.tau.ac.il/pub/tauttv/TTV/ver_112). The goal is to produce an easy-to-use catalog that can stimulate further analyses of interesting systems. For 779 KOIs with high enough SNRs, we derived the timing, duration and depth of 69,914 transits. For 1820 KOIs with lower SNR, we derived only the timing of 225,273 transits. After removal of outlier timings, we derived various statistics for each KOI that were used to indicate significant variations. Including systems found by previous works, we have detected 260 KOIs which showed significant TTVs with long-term variations (>100 day), and another fourteen KOIs with periodic modulations shorter than 100 day and small amplitudes. For five of those, the periodicity is probably due to the crossing of rotating stellar spots by the transiting planets.

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arXiv2016

Kepler-1647b: the largest and longest-period Kepler transiting circumbinary planet

We report the discovery of a new Kepler transiting circumbinary planet (CBP). This latest addition to the still-small family of CBPs defies the current trend of known short-period planets orbiting near the stability limit of binary stars. Unlike the previous discoveries, the planet revolving around the eclipsing binary system Kepler-1647 has a very long orbital period (~1100 days) and was at conjunction only twice during the Kepler mission lifetime. Due to the singular configuration of the system, Kepler-1647b is not only the longest-period transiting CBP at the time of writing, but also one of the longest-period transiting planets. With a radius of 1.06+/-0.01 RJup it is also the largest CBP to date. The planet produced three transits in the light-curve of Kepler-1647 (one of them during an eclipse, creating a syzygy) and measurably perturbed the times of the stellar eclipses, allowing us to measure its mass to be 1.52+/-0.65 MJup. The planet revolves around an 11-day period eclipsing binary consisting of two Solar-mass stars on a slightly inclined, mildly eccentric (e_bin = 0.16), spin-synchronized orbit. Despite having an orbital period three times longer than Earth's, Kepler-1647b is in the conservative habitable zone of the binary star throughout its orbit.

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arXiv2016

Probabilistic Mass-Radius Relationship for Sub-Neptune-Sized Planets

The Kepler Mission has discovered thousands of planets with radii $<4\ R_\oplus$, paving the way for the first statistical studies of the dynamics, formation, and evolution of these sub-Neptunes and super-Earths. Planetary masses are an important physical property for these studies, and yet the vast majority of Kepler planet candidates do not have theirs measured. A key concern is therefore how to map the measured radii to mass estimates in this Earth-to-Neptune size range where there are no Solar System analogs. Previous works have derived deterministic, one-to-one relationships between radius and mass. However, if these planets span a range of compositions as expected, then an intrinsic scatter about this relationship must exist in the population. Here we present the first probabilistic mass-radius relationship (M-R relation) evaluated within a Bayesian framework, which both quantifies this intrinsic dispersion and the uncertainties on the M-R relation parameters. We analyze how the results depend on the radius range of the sample, and on how the masses were measured. Assuming that the M-R relation can be described as a power law with a dispersion that is constant and normally distributed, we find that $M/M_\oplus=2.7(R/R_\oplus)^{1.3}$, a scatter in mass of $1.9\ M_\oplus$, and a mass constraint to physically plausible densities, is the "best-fit" probabilistic M-R relation for the sample of RV-measured transiting sub-Neptunes ($R_{pl}<4\ R_\oplus$). More broadly, this work provides a framework for further analyses of the M-R relation and its probable dependencies on period and stellar properties.

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arXiv2016

Secure TTV Mass Measurements: Ten Kepler Exoplanets between 3 and 8 Earth Masses with Diverse Densities and Incident Fluxes

We infer dynamical masses in eight multi-planet systems using transit times measured from Kepler's complete dataset, including short-cadence data where available. Of the eighteen dynamical masses that we infer, ten 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 density consistent with an Earth-like composition. Strong 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 at; Kepler-49 (KOI-248), Kepler-57 (KOI-1270), Kepler-105 (KOI-115) and Kepler-177 (KOI-523). Strong upper limits on the mass of Kepler-177 c imply an extremely low density ~0.1 g cm$^{-3}$. In most cases, individual orbital eccentricities were poorly constrained due 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, non-librating 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 robust mass measurements. Placing these exoplanets on the mass-radius diagram, we find a wide range of densities is observed among sub-Neptune mass planets and that the range in observed densities is anti-correlated with incident flux.

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arXiv2016

State of the Field: Extreme Precision Radial Velocities

The Second Workshop on Extreme Precision Radial Velocities defined circa 2015 the state of the art Doppler precision and identified the critical path challenges for reaching 10 cm/s measurement precision. The presentations and discussion of key issues for instrumentation and data analysis and the workshop recommendations for achieving this precision are summarized here. Beginning with the HARPS spectrograph, technological advances for precision radial velocity measurements have focused on building extremely stable instruments. To reach still higher precision, future spectrometers will need to produce even higher fidelity spectra. This should be possible with improved environmental control, greater stability in the illumination of the spectrometer optics, better detectors, more precise wavelength calibration, and broader bandwidth spectra. Key data analysis challenges for the precision radial velocity community include distinguishing center of mass Keplerian motion from photospheric velocities, and the proper treatment of telluric contamination. Success here is coupled to the instrument design, but also requires the implementation of robust statistical and modeling techniques. Center of mass velocities produce Doppler shifts that affect every line identically, while photospheric velocities produce line profile asymmetries with wavelength and temporal dependencies that are different from Keplerian signals. Exoplanets are an important subfield of astronomy and there has been an impressive rate of discovery over the past two decades. Higher precision radial velocity measurements are required to serve as a discovery technique for potentially habitable worlds and to characterize detections from transit missions. The future of exoplanet science has very different trajectories depending on the precision that can ultimately be achieved with Doppler measurements.

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