arXiv subjects

Eric B. Ford

Publications and source records attributed to Eric B. Ford.

At least 217 records · Page 12Linked to original sources

arXiv2007

Using Transit Timing Observations to Search for Trojans of Transiting Extrasolar Planets

Theoretical studies predict that Trojans are likely a frequent byproduct of planet formation and evolution. We examine the sensitivity of transit timing observations for detecting Trojan companions to transiting extrasolar planets. We demonstrate that this method offers the potential to detect terrestrial-mass Trojans using existing ground-based observatories. We compare the transit timing variation (TTV) method with other techniques for detecting extrasolar Trojans and outline the future prospects for this method.

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arXiv2007

Detecting and Characterizing Planetary Systems with Transit Timing

In the coming decades, research in extrasolar planets aims to advance two goals: 1) detecting and characterizing low-mass planets increasingly similar to the Earth, and 2) improving our understanding of planet formation. We present a new planet detection method that is capable of making large advances towards both of these objectives and describe a modest network of telescopes that is able to make the requisite observations. In a system where a known planet transits its host star, a second planet in that system will cause the time between transits to vary. These transit timing variations can be used to infer the orbital elements and mass of the perturbing planet even if it has a mass that is smaller than the mass of the Earth. This detection technique complements other techniques because it is most sensitive in mean-motion resonances where, due to degeneracies, other techniques have reduced sensitivity. Small ground-based observatories have already exceeded the photometric precision necessary to detect sub-Earth mass planets. However, TTV planet searches are currently limited by the relatively small number of high-precision transit data and insufficient observing time on existing telescopes. These issues will be compounded as the number of known transiting planets suitable for TTV study will increase substantially in the near future. A relatively modest investment in a ground-based network of small ($\sim 0.5 {\rm m}$ telescopes could provide the needed coverage and so dramatically increase the effectiveness of transit timing observations.

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arXiv2007

The Formation of Ice Giants in a Packed Oligarchy: Instability and Aftermath

As many as 5 ice giants--Neptune-mass planets composed of 90% ice and rock and 10% hydrogen--are thought to form at heliocentric distances of 10-25 AU on closely packed orbits spaced ~5 Hill radii apart. Such oligarchies are ultimately unstable. Once the parent disk of planetesimals is sufficiently depleted, oligarchs perturb one another onto crossing orbits. We explore both the onset and the outcome of the instability through numerical integrations, including dynamical friction cooling of planets by a planetesimal disk whose properties are held fixed. To trigger instability and the ejection of the first ice giant in systems having an original surface density in oligarchs of Sigma ~ 1 g/cm^2, the disk surface density s must fall below 0.1 g/cm^2. Ejections are predominantly by Jupiter and occur within 10 Myr. To eject more than 1 oligarch requires s < 0.03 g/cm^2. Systems starting with up to 4 oligarchs in addition to Jupiter and Saturn can readily yield solar-system-like outcomes in which 2 surviving ice giants lie inside 30 AU and have their orbits circularized by dynamical friction. Our numerical simulations support the idea that planetary systems begin in more crowded and compact configurations, like those of shear-dominated oligarchies. In contrast to previous studies, we identify s < 0.1 Sigma as the regime relevant for understanding the evolution of the outer solar system, and we encourage future studies to concentrate on this regime while relaxing our assumption of a fixed planetesimal disk.

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arXiv2006

Observational Constraints on Trojans of Transiting Extrasolar Planets

Theoretical studies predict that Trojans are likely a frequent byproduct of planet formation and evolution. We present a novel method of detecting Trojan companions to transiting extrasolar planets which involves comparing the time of central eclipse with the time of the stellar reflex velocity null. We demonstrate that this method offers the potential to detect terrestrial-mass Trojans using existing ground-based observatories. This method rules out Trojan companions to HD 209458b and HD 149026b more massive than ~13 Earth masses and \~25 Earth masses at a 99.9% confidence level. Such a Trojan would be dynamically stable, would not yet have been detected by photometric or spectroscopic monitoring, and would be unrecognizable from radial velocity observations alone. We outline the future prospects for this method, and show that the detection of a "Hot Trojan" of any mass would place a significant constraint on theories of orbital migration.

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arXiv2006

Structure and Evolution of Nearby Stars with Planets II. Physical Properties of ~1000 Cool Stars from the SPOCS Catalog

We derive detailed theoretical models for 1074 nearby stars from the SPOCS (Spectroscopic Properties of Cool Stars) Catalog. The California and Carnegie Planet Search has obtained high-quality echelle spectra of over 1000 nearby stars taken with the Hamilton spectrograph at Lick Observatory, the HIRES spectrograph at Keck, and UCLES at the Anglo Australian Observatory. A uniform analysis of the high-resolution spectra has yielded precise stellar parameters, enabling systematic error analyses and accurate theoretical stellar modeling. We have created a large database of theoretical stellar evolution tracks using the Yale Stellar Evolution Code (YREC) to match the observed parameters of the SPOCS stars. Our very dense grids of evolutionary tracks eliminate the need for interpolation between stellar evolutionary tracks and allow precise determinations of physical stellar parameters (mass, age, radius, size and mass of the convective zone, etc.). Combining our stellar models with the observed stellar atmospheric parameters and uncertainties, we compute the likelihood for each set of stellar model parameters separated by uniform time steps along the stellar evolutionary tracks. The computed likelihoods are used for a Bayesian analysis to derive posterior probability distribution functions for the physical stellar parameters of interest. We provide a catalog of physical parameters for 1074 stars that are based on a uniform set of high quality spectral observations, a uniform spectral reduction procedure, and a uniform set of stellar evolutionary models. We explore this catalog for various possible correlations between stellar and planetary properties, which may help constrain the formation and dynamical histories of other planetary systems.

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arXiv2006

Bayesian Model Selection and Extrasolar Planet Detection

Radial velocity (RV) planet searches are increasingly finding planets with small velocity amplitudes, with long orbital periods, or in multiple planet systems. Bayesian inference has the potential to improve the interpretation of existing observations, the planning of future observations and ultimately inferences concerning the overall population of planets. In recent years, the refinement of Markov chain Monte Carlo (MCMC) algorithms has made it practical to accurately characterize orbital parameters and their uncertainties from RV observations of single-planet and weakly interacting multiple-planet systems. Unfortunately, MCMC is not sufficient for Bayesian model selection, i.e., comparing the marginal posterior probability of models, as is necessary to determine how strongly the observational data favor a model with n+1 planets over a model with just n planets. Many of the obvious estimators for the marginal posterior probability suffer from poor convergence properties. We compare several estimators of the marginal likelihood and feature those that display desirable convergence properties based on the analysis of a sample data set for HD 88133b. We find that methods based on importance sampling are most efficient, provided that a good analytic approximation of the posterior probability distribution is available. We present a simple algorithm for using a sample from the posterior to construct a mixture distribution that approximates the posterior and can be used for importance sampling and Bayesian model selection. We conclude with some suggestions for the development and refinement of computationally efficient and robust estimators of marginal posterior probabilities.

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arXiv2006

The N2K Consortium VI: Doppler Shifts Without Templates and Three New Short-Period Planets

We present a modification to the iodine cell Doppler technique that eliminates the need for an observed stellar template spectrum. For a given target star, we iterate toward a synthetic template spectrum beginning with an existing spectrum of a similar star. We then perturb the shape of this first-guess template to match the program observation of the target star taken through an iodine cell. The elimination of a separate template observation saves valuable telescope time, a feature that is ideally suited for the quick-look strategy employed by the ``Next 2000 Stars'' (N2K) planet search program. Tests using Keck/HIRES spectra indicate that synthetic templates yield a short-term precision of 3 m/s and a long-term, run-to-run precision of 5 m/s. We used this new Doppler technique to discover three new planets: a 1.5 Mjup planet in a 2.1375 d orbit around HD 86081; a 0.71 Mjup planet in circular, 26.73 d orbit around HD 224693; and a Saturn-mass planet in an 18.179 d orbit around HD 33283. The remarkably short period of HD 86081b bridges the gap between the extremely short-period planets detected in the OGLE survey and the 16 Doppler-detected hot jupiters (P < 15 d), which have an orbital period distribution that piles up at about three days. We have acquired photometric observations of two of the planetary host stars with the automated photometric telescopes at Fairborn Observatory. HD 86081 and HD 224693 both lack detectable brightness variability on their radial velocity periods, supporting planetary-reflex motion as the cause of the radial velocity variability. HD 86081 shows no evidence of planetary transits in spite of a 17.6% transit probability.

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arXiv2006

The First Extrasolar Planet Discovered with a New Generation High Throughput Doppler Instrument

We report the detection of the first extrasolar planet, ET-1 (HD 102195b), using the Exoplanet Tracker (ET), a new generation Doppler instrument. The planet orbits HD 102195, a young star with solar metallicity that may be part of the local association. The planet imparts radial velocity variability to the star with a semiamplitude of $63.4\pm2.0$ m s$^{-1}$ and a period of 4.11 days. The planetary minimum mass ($m \sin i$) is $0.488\pm0.015$ $M_J$.

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arXiv2005

What do Multiple Planet Systems Teach us about Planet Formation?

For centuries, our knowledge of planetary systems and ideas about planet formation were based on a single example, our solar system. During the last thirteen years, the discovery of ~170 planetary systems has ushered in a new era for astronomy. I review the surprising properties of extrasolar planetary systems and discuss how they are reshaping theories of planet formation. I focus on how multiple planet systems constrain the mechanisms proposed to explain the large eccentricities typical of extrasolar planets. I suggest that strong planet-planet scattering is common and most planetary systems underwent a phase of large eccentricities. I propose that a planetary system's final eccentricities may be strongly influenced by how much mass remains in a planetesimal disk after the last strong planet-planet scattering event.

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arXiv2005

On the Relation Between Hot Jupiters & the Roche Limit

Many of the known extrasolar planets are ``hot Jupiters,'' giant planets with orbital periods of just a few days. We use the observed distribution of hot Jupiters to constrain the location of its inner edge in the mass--period diagram. If we assume a slope corresponding to the classical Roche limit, then we find that the edge corresponds to a separation close to_twice_ the Roche limit, as expected if the planets started on highly eccentric orbits that were later circularized. In contrast, any migration scenario would predict an inner edge right at the Roche limit, which applies to planets approaching on nearly circular orbits. However, the current sample of hot Jupiters is not sufficient to provide a precise constraint simultaneously on both the location and slope of the inner edge.

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arXiv2005

Improving the Efficiency of Markov Chain Monte Carlo for Analyzing the Orbits of Extrasolar Planets

Precise radial velocity measurements have led to the discovery of ~170 extrasolar planetary systems. Understanding the uncertainties in the orbital solutions will become increasingly important as the discovery space for extrasolar planets shifts to planets with smaller masses and longer orbital periods. The method of Markov chain Monte Carlo (MCMC) provides a rigorous method for quantifying the uncertainties in orbital parameters in a Bayesian framework (Ford 2005a). The main practical challenge for the general application of MCMC is the need to construct Markov chains which quickly converge. The rate of convergence is very sensitive to the choice of the candidate transition probability distribution function (CTPDF). Here we explain one simple method for generating alternative CTPDFs which can significantly speed convergence by one to three orders of magnitude. We have numerically tested dozens of CTPDFs with simulated radial velocity data sets to identify those which perform well for different types of orbits and suggest a set of CTPDFs for general application. Additionally, we introduce other refinements to the MCMC algorithm for radial velocity planets, including an improved treatment of the uncertainties in the radial velocity observations, an algorithm for automatically choosing step sizes, an algorithm for automatically determining reasonable stopping times, and the use of importance sampling for including the dynamical evolution of multiple planet systems. Together, these improvements make it practical to apply MCMC to multiple planet systems. We demonstrate the improvements in efficiency by analyzing a variety of extrasolar planetary systems.

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arXiv2005

The Effects of Multiple Companions on the Efficiency of the SIM Planet Searches

The Space Interferometry Mission (SIM) is expected to make precise astrometric measurements that can be used to detect low mass planets around nearby stars. Since most nearby stars are members of multiple star systems, many stars will have a measurable acceleration due to their companion, which must be included when solving for astrometric parameters and searching for planetary perturbations. Additionally, many of the stars with one radial velocity planet show indications of additional planets. Therefore, astrometric surveys like SIM must be capable of detecting planets and measuring orbital parameters in systems with multiple stellar and/or planetary companions. We have conducted Monte Carlo simulations to investigate how the presence of multiple companions affects the sensitivity of an astrometric survey such as SIM. We find that the detection efficiency for planets in wide binary systems is relatively unaffected by the presence of a binary companion, if the planetary orbital period is less than half the duration of the astrometric survey. For longer orbital periods, there are significant reductions in the sensitivity of an astrometric survey. Additionally, we find that the signal required to detect a planet can be increased significantly due to the presence of an additional planet orbiting the same star. Fortunately, adding a modest number of precision radial velocity observations significantly improves the sensitivity for many multiple planet systems. Thus, the combination of radial velocity observations and astrometric observations by SIM will be a particularly valuable for studying multiple planet systems.

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arXiv2005

On the relation between Hot-Jupiters and the Roche Limit

Many of the known extrasolar planets are ``hot Jupiters,'' giant planets with orbital periods of just a few days. We use the observed distribution of hot Jupiters to constrain the location of the ``inner edge'' and planet migration theory. If we assume the location of the inner edge is proportional to the Roche limit, then we find that this edge is located near twice the Roche limit, as expected if the planets were circularized from a highly eccentric orbit. If confirmed, this result would place significant limits on migration via slow inspiral. However, if we relax our assumption for the slope of the inner edge, then the current sample of hot Jupiters is not sufficient to provide a precise constraint on both the location and power law index of the inner edge.

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arXiv2005

Vegetation's Red Edge: A Possible Spectroscopic Biosignature of Extraterrestrial Plants

Earth's deciduous plants have a sharp order-of-magnitude increase in leaf reflectance between approximately 700 and 750 nm wavelength. This strong reflectance of Earth's vegetation suggests that surface biosignatures with sharp spectral features might be detectable in the spectrum of scattered light from a spatially unresolved extrasolar terrestrial planet. We assess the potential of Earth's step-function-like spectroscopic feature, referred to as the "red edge", as a tool for astrobiology. We review the basic characteristics and physical origin of the red edge and summarize its use in astronomy: early spectroscopic efforts to search for vegetation on Mars and recent reports of detection of the red edge in the spectrum of Earthshine (i.e., the spatially integrated scattered light spectrum of Earth). We present Earthshine observations from Apache Point Observatory to emphasize that time variability is key to detecting weak surface biosignatures such as the vegetation red edge. We briefly discuss the evolutionary advantages of vegetation's red edge reflectance, and speculate that while extraterrestrial "light harvesting organisms" have no compelling reason to display the exact same red edge feature as terrestrial vegetation, they might have similar spectroscopic features at different wavelengths than terrestrial vegetation. This implies that future terrestrial-planet-characterizing space missions should obtain data that allow time-varying, sharp spectral features at unknown wavelengths to be identified. We caution that some mineral reflectance edges are similar in slope and strength to vegetation's red edge (albeit at different wavelengths); if an extrasolar planet reflectance edge is detected care must be taken with its interpretation.

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arXiv2005

Evidence for Planet-Planet Scattering in Upsilon Andromedae

Doppler spectroscopy has detected 136 planets around nearby stars. A major puzzle is why their orbits are highly eccentric, while all planets in our Solar System are on nearly circular orbits, as expected if they formed by accretion processes in a protostellar disk. Several mechanisms have been proposed to generate large eccentricities after planet formation, but so far there has been little observational evidence to support any particular one. Here we report that the current orbital configuration of the three giant planets around Upsilon Andromedae (ups And) provides evidence for a close dynamical interaction with another planet, now lost from the system. The planets started on nearly circular orbits, but chaotic evolution caused the outer planet (ups And d) to be perturbed suddenly into a higher-eccentricity orbit. The coupled evolution of the system then causes slow periodic variations in the eccentricity of the middle planet (ups And c). Indeed, we show that ups And c periodically returns to a very nearly circular state every 9000 years. Our analysis shows that strong planet-planet scattering, one of several mechanisms previously discussed for increasing orbital eccentricities, must have operated in this system.

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arXiv2004

Choice of Observing Schedules for Astrometric Planet Searches

The Space Interferometry Mission (SIM) will make precise astrometric measurements that can be used to detect planets around nearby stars. Since observational time will be extremely valuable, it is important to consider how the choice of the observing schedule influences the efficiency of SIM planet searches. We have conducted Monte Carlo simulations of astrometric observations to understand the effects of different scheduling algorithms. We find that the efficiency of planet searches is relatively insensitive to the observing schedule for most reasonable observing schedules.

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arXiv2004

Quantifying the Uncertainty in the Orbits of Extrasolar Planets

Precise radial velocity measurements have led to the discovery of ~100 extrasolar planetary systems. We investigate the uncertainty in the orbital solutions that have been fit to these observations. Understanding these uncertainties will become more and more important as the discovery space for extrasolar planets shifts to longer and longer periods. While detections of short period planets can be rapidly refined, planets with long orbital periods will require observations spanning decades to constrain the orbital parameters precisely. Already in some cases, multiple distinct orbital solutions provide similarly good fits, particularly in multiple planet systems. We present a method for quantifying the uncertainties in orbital fits and addressing specific questions directly from the observational data rather than relying on best fit orbital solutions. This Markov chain Monte Carlo (MCMC) technique has the advantage that it is well suited for the high dimensional parameter spaces necessary for the multiple planet systems. We apply the MCMC technique to several extrasolar planetary systems, assessing the uncertainties in orbital elements for several systems. Our MCMC simulations demonstrate that for some systems there are strong correlations between orbital parameters and/or significant non-Gaussianities in parameter distributions, even though the measurement errors are nearly Gaussian. Once these effects are considered the actual uncertainties in orbital elements can be significantly larger or smaller than the published uncertainties. We also present simple applications of our methods such as predicting the times of possible transits for GJ 876.

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arXiv2003

Planet finding prospects for the Space Interferometry Mission

The Space Interferometry Mission (SIM) will make precise astrometric measurements that can be used to detect planets around nearby stars. We have simulated SIM observations and estimated the ability of SIM to detect planets with given masses and orbital periods and measure their orbital elements. We combine these findings with an estimate of the mass and period distribution of planets determined from radial velocity surveys to predict the number and characteristics of planets SIM would likely find. Our predictions are based on extrapolating the mass distribution of known extrasolar planets by up to a factor of 100. This extrapolation provides the best prediction we can make of the actual number of planets that SIM will detect and characterize, but may substantially over- or underestimate the frequency of Earth-mass planets, especially if these form by a different mechanism than giant planets. We find that SIM is likely to detect 1-5 planets with masses less than 3 M_Earth (depending on mission parameters). SIM would measure masses and orbits with 30% accuracy for 0-2 of these planets, but is unlikely to measure orbits with 10% accuracy for more than one of them. SIM is likely to detect 5-25 planets with mass less than 20 M_Earth, measure masses and orbits with 30% accuracy for 2-12 of these, and measure masses and orbits with 10% accuracy for 2-8 such planets. SIM is likely to find 25-160 planets of all masses, depending on the observing strategy and mission lifetime.

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