Eric B. Ford - Research Interests

Extrasolar Planetary Systems - Planetary Dynamics - Planet Formation - Exoplanet Searches - Modeling Stars & Planets - Astrobiology - Astrostatistics - High Performance Computing

Research Interests

For centuries, theories of planet formation had been designed to explain our own Solar System. Over the past decade, the discovery of ~200 extrasolar planets orbiting solar-type stars has reinvigorated the study of planet formation. Several striking differences between extrasolar planetary systems and our Solar System have led to the realization that planet formation theory must be generalized in order to accommodate these new observations. For example, traditional theories predict that giant planetslike Jupiter & Saturn would form beyond a few AUone "AU" is the average distance between the Earth and the Sun. At those distances temperatures are cold enough for ices to initiate the growth of grains that could then accumulate into planetesimalssmall rocky bodies that form the building blocks for planets. However, we now know of many giant planets that are very close to their parent stars. Similarly, it had long been assumed that planets formed in circular orbits as a result of strong dissipative forces in the protoplanetary diskthe disk of gas & small grains that orbit the star during the early stages of planet formation. However, over half of the known extrasolar planets beyond 0.1AU have significantly elliptical orbits. These discoveries provide many exciting new puzzles for theorists to unravel in the coming years.

Planet Search Collaborations

While primarily a theorist, I collaborate with several observational teams in an effort to acheive the maximum scientific return by working at the interface of theory and observations. Click for list of projects

Planet Formation Theory

Theorists have offered numerous possible mechanisms to explain the existance of extrasolar planets with short-period planets and highly ellipitcal orbits. For example, my own research has investigated the roles of close encounters with other planets, tidal dissipationwhen stars and planets raise tides on each other, friction causes energy to be transformed into heat, and long-term gravitational perturbations from nearby stars. In addition to developing theoretical models, I also test planet formation models by performing large numerical simulations to quantify the predictions of these models and make detailed comparisons with the properties of the currently known extrasolar planets. Click for publications

Origins of Eccentric Extrasolar Planets: Testing the Planet-Planet Scattering Model
Ford, E.B. & Rasio, F.A.
(Abridged) Any planetary system with two or more giant planets may become dynamically unstable, leading to collisions or ejections through strong planet--planet scattering. Following an ejection, the other planet is left in a highly eccentric orbit. 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 for two planets with_unequal masses_ predict a reduced frequency of collisions and a broader range of final eccentricities (compared to simulations of two equal mass planets). We show that 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 This compares favorably with current observations and will be tested by future planet discoveries. Moreover, we show that 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. However, the presence of giant planets in circular orbits at slightly larger orbital periods (small enough to require significant migration, but large enough that tidal circularization is ineffective) is more difficult to explain. As part of this work, 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.

Dynamical Outcomes of Planet-Planet Scattering
Chatterjee, S., Ford, E.B., Rasio, F.A.
Observations in the past decade have revealed extrasolar planets with a wide range of semi-major 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 nebula, dissipation prevents eccentricity growth and can suppress instabilities from becoming manifest. However, once the disk dissipates, eccentricities can grow rapidly, leading to close encounters between the planets. In this study we explore strong gravitational scattering in a gas-free multi-planet system as a mechanism to explain the orbital properties of exoplanets. We numerically investigate the long-term stability of representative multi-planet systems containing three giant planets in orbit around a solar-like central star. We assign the planet masses in a realistic manner following the core accretion scenario of planet formation. In contrast to the case of two planets, there is no sharp stability boundary for 3-planet systems, so numerical integrations of 3-planet systems can approach instability naturally, even without including dissipation, mass growth, or migration. We characterize the timescale to reach instability as a function of the initial planet--planet separation. We discuss strong gravitational scattering as a possible mechanism to create high eccentricities as well as the close-in planetary orbits in the observed exoplanet population. We find that this mechanism can reasonably reproduce the observed eccentricity distribution. Our results also make testable predictions for the inclinations of short-period giant planets that are formed via strong planet scattering followed by tidal circularization.

The Formation of Ice Giants in a Packed Oligarchy: Instability and Aftermath"
Ford, E.B. & Chiang, E.I. 2007 ApJ, 661, 602.
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 Σ~1 g/cm², the disk surface density σ must fall below ~0.1g/cm². Ejections are predominantly by Jupiter and occur within ~10 Myr. To eject more than 1 oligarch requires σ< 0.03 g/cm². For certain choices of σ and initial semi-major axes of planets, 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 findings support the idea that planetary systems may begin in more crowded and compact configurations, like those of shear-dominated oligarchies. In contrast to previous studies, we identify σ < 0.1 Σ 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. Whether evidence of the instability can be found in Kuiper belt objects (KBOs) is unclear, since in none of our simulations do marauding oligarchs excite as large a population of KBOs having inclinations >20^o as is observed.

"On the Relation between Hot Jupiters and the Roche Limit"
Ford, E.B. & Rasio, F.A. 2006 ApJ, 638, L45.
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 the slope of the inner edge.

"What do Multiple Planet Systems Teach us about Planet Formation?"
Ford, E.B. 2005, in Frank N. Bash Symposium 2005: New Horizons in Astronomy (arXiv:astro-ph/0512635)
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.

"Planet-planet scattering in the upsilon Andromedae system"
Ford, E.B., Lystad, V., Rasio, F.A. 2005, Nature, 434, 873.
Doppler spectroscopy has detected 152 planets around nearby stars. A major puzzle is why many of their orbits are highly eccentric; all planets in our Solar System are on nearly circular orbits, as is 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 model. Here we report that the current orbital configuration of the three giant planets around upsilon Andromedae (Ups And) probably results from 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 6,700 years.

"Dynamical Instabilities in Extrasolar Planetary Systems"
Ford, E.B., Rasio, F.A., Yu, K. 2003, in Scientific Frontiers in Research on Extrasolar Planets, ASP Conf. Series, Vol. 294, eds. Drake Deming & Sara Seager, pp 181-188.
Instabilities and strong dynamical interactions between multiple giant planets have been proposed as a possible explanation for the surprising orbital properties of extrasolar planetary systems. In particular, dynamical instabilities seem to provide a natural mechanism for producing the highly eccentric orbits seen in many systems. Previously, we performed numerical integrations for the dynamical evolution of planetary systems containing two giant planets of equal masses initially in nearly circular orbits very close to the dynamical stability limit. We found the ratio of collisions to ejections in these simulations was greater than the ratio of circular orbits to eccentric orbits among the known extrasolar planets. Further, the mean eccentricity of the planets remaining after an ejection was larger than the mean eccentricity of the known extrasolar planets. Recently, we have performed additional integrations, generalizing to consider two planets of unequal masses. Our new simulations reveal that the two-planet scattering model can produce a distribution of eccentricities consistent with the observed eccentricity distribution for plausible mass distributions. Additionally, this model predicts a maximum eccentricity of about 0.8, in agreement with observations. Early results from simulations of three equal-mass planets also reveal a reduced frequency of collisions and a broad range of final eccentricities for the retained inner planet.

"Dynamical Instabilities in Extrasolar Planetary Systems Containing Two Giant Planets"
Ford, E.B., Havlickova, M., Rasio, F.A. 2001, Icarus 150,303.
Instabilities and strong dynamical interactions between several giant planets have been proposed as a possible explanation for the surprising orbital properties of extrasolar planetary systems. In particular, dynamical instabilities seem to provide a natural mechanism for producing the highly eccentric orbits seen in many systems. Here we present results from a new set of numerical integrations for the dynamical evolution of planetary systems containing two identical giant planets in nearly circular orbits very close to the dynamical stability limit. We determine the statistical properties of the three main types of systems resulting from the development of an instability: systems containing one planet, following either a collision between the two initial planets, or the ejection of one of them to infinity, and systems containing two planets in a new, quasi-stable configuration. We discuss the implications of our results for the formation and evolution of observed extrasolar planetary systems. We conclude that the distributions of eccentricities and semimajor axes for observed systems cannot be explained easily by invoking dynamical interactions between two planets initially on circular orbits. While highly eccentric orbits can be produced naturally by these interactions, collisions between the two planets, which occur frequently in the range of observed semimajor axes, would result in many more nearly circular orbits than in the observed sample.

"Secular Evolution of Hierarchical Triple Star Systems"
Ford, E.B., Kozinsky, B., Rasio, F.A. 2000, ApJ 535, 385.
We derive octupole-level secular perturbation equations for hierarchical triple systems, using classical Hamiltonian perturbation techniques. Our equations describe the secular evolution of the orbital eccentricities and inclinations over timescales that are long compared to the orbital periods. By extending previous work done to leading (quadrupole) order to octupole level (i.e., including terms of order ~3, where alpha=a1/a2<1 is the ratio of semimajor axes), we obtain expressions that are applicable to a much wider range of parameters. In particular, our results can be applied to high-inclination as well as coplanar systems, and our expressions are valid for almost all mass ratios for which the system is in a stable hierarchical configuration. In contrast, the standard quadrupole-level theory of Kozai gives a vanishing result in the limit of zero relative inclination. The classical planetary perturbation theory, while valid to all orders in alpha, applies only to orbits of low-mass objects orbiting a common central mass, with low eccentricities and low relative inclinations. For triple systems containing a close inner binary, we also discuss the possible interaction between the classical Newtonian perturbations and the general relativistic precession of the inner orbit. In some cases we show that this interaction can lead to resonances and a significant increase in the maximum amplitude of eccentricity perturbations. We establish the validity of our analytic expressions by providing detailed comparisons with the results of direct numerical integrations of the three-body problem obtained for a large number of representative cases. In addition, we show that our expressions reduce correctly to previously published analytic results obtained in various limiting regimes. We also discuss applications of the theory in the context of several observed triple systems of current interest, including the millisecond pulsar PSR B1620-26 in M4, the giant planet in 16 Cygni, and the protostellar binary TMR-1.

"Theoretical Implications of the PSR B1620-26 Triple System and Its Planet"
Ford, E.B., Joshi, K.J., Rasio, F.A., Zbarsky, B. 2000, ApJ 528, 335
We present a new theoretical analysis of the PSR B1620-26 triple system in the globular cluster M4, based on the latest radio pulsar timing data, which now include measurements of five time derivatives of the pulse frequency. These data allow us to determine the mass and orbital parameters of the second companion completely (up to the usual unknown orbital inclination angle i2). The current best-fit parameters correspond to a second companion of planetary mass, m2sini2~=7x10-3 Msolar , in an orbit of eccentricity e2~=0.45 and semimajor axis a2~=60 AU. Using numerical scattering experiments, we study a possible formation scenario for the triple system, which involves a dynamical exchange interaction between the binary pulsar and a primordial star-planet system. The current orbital parameters of the triple are consistent with such a dynamical origin and suggest that the separation of the parent star-planet system was very large, ~>50 AU. We also examine the possible origin of the anomalously high eccentricity of the inner binary pulsar. While this eccentricity could have been induced during the same dynamical interaction that created the triple, we find that it could equally well arise from long-term secular perturbation effects in the triple, combining the general relativistic precession of the inner orbit with the Newtonian gravitational perturbation of the planet. The detection of a planet in this system may be taken as evidence that large numbers of extrasolar planetary systems, not unlike those discovered recently in the solar neighborhood, also exist in old star clusters.

"Dynamical instabilities and the formation of extrasolar planetary systems"
Rasio, F.A. & Ford, E.B. 1996, Science 274, 954.
The existence of a dominant massive planet, Jupiter, in our solar system, although perhaps essential for long-term dynamical stability and the development of life, may not be typical of planetary systems that form around other stars. In a system containing two Jupiter-like planets, the possibility exists that a dynamical instability will develop. Computer simulations suggest that in many cases this instability leads to the ejection of one planet while the other is left in a smaller, eccentric orbit. In extreme cases, the eccentric orbit has a small enough periastrom distance that it may circularize at an orbital period as short as a few days through tidal dissipation. This may explain the recently detected Jupiter-mass planets in very tight circular orbits and wider eccentric orbits around nearby stars.

Interpretation of Extrasolar Planet Observations

The first extrasolar planets discovered around solar-type stars caused large velocity variations (~100m/s) and were in short period orbits (~3 days-1 year), so it was practical to observe them for multiple orbital periods and determine accurate orbits. Now, these surveys are discovering planets with smaller masses (~10 Earth masses) and/or longer orbital periods (~10 years), making it much more difficult to measure the orbits accurately. These challenges are even more severe for multiple planet systems due to the large number of model parameters. I develop efficient computational algorithms to perform Bayesian analyses of extrasolar planetary systems and apply these tools to obtain accurate and precise constraints for dynamical studies. Click for publications

"Bayesian Model Selection and Extrasolar Planet Detection"
Ford, E.B. & Gregory, P. 2007 in Statistical Challenges in Modern Astronomy IV, ed.s G.J. Babu & E.D. Feigelson, San Francisco: Astron. Soc. Pacific
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.

"Improving the Efficiency of Markov Chain Monte Carlo for Analyzing the Orbits of Extrasolar Planets"
Ford, E.B. 2006, ApJ 642, 505
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 (Paper I). The main practical challenge for the general application of MCMC is the need to construct Markov chains that 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 that can significantly speed convergence by 1-3 orders of magnitude. We have numerically tested dozens of CTPDFs with simulated radial velocity data sets to identify those that perform well for different types of orbits and suggest a set of CTPDFs for general application. In addition, 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.

"Quantifying the Uncertainty in the Orbits of Extrasolar Planets"
Ford, E.B. 2005, AJ 129, 1706
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 fitted 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 to 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.

Design of Exoplanet Searches & Follow-up Observations

Modern planet searches require substantial investments of limited observing facilities, research funds, and human time. Therefore, I perform large simulations of proposed planet searches to optimize their design and estimate the expected scientific yield. Based on my expertise in the design of planet searches and the analysis of extrasolar planet observations, I collaborate with observers on several current and proposed radial velocity and astrometric planet searches and follow-up programs. Click for publications

Using Transit Timing Observations to Search for Trojans of Transiting Extrasolar Planets
Ford, E.B. & Holman, M.J. 2007, submitted to ApJL.
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.

"Observational Constraints on Trojans of Transiting Extrasolar Planets"
Ford, E.B. & Gaudi, S.B. 2006 ApJL 652, L137.
Theoretical studies predict that Trojans are likely a frequent by-product of planet formation and evolution. We present a novel method of detecting Trojan companions to transiting extrasolar planets that involves comparing the midtime of 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 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.

"The M Dwarf GJ 436 and its Neptune-Mass Planet"
Maness, H. L., Marcy, G. W., Ford, E. B., Hauschildt, P. H., Shreve, A. T., Basri, G. B., Butler, R. P., Vogt, S. S., 2007, PASP 851, 90.
We determine stellar parameters for the M dwarf GJ 436 that hosts a Neptune-mass planet. We employ primarily spectral modeling at low and high resolution, examining the agreement between model and observed optical spectra of five comparison stars of type, M0-M3. Modeling high resolution optical spectra suffers from uncertainties in TiO transitions, affecting the predicted strengths of both atomic and molecular lines in M dwarfs. The determination of Teff, gravity, and metallicity from optical spectra remains at ~10%. As molecules provide opacity both in lines and as an effective continuum, determing molecular transition parameters remains a challenge facing models such as the PHOENIX series, best verified with high resolution and photometric spectra. Our analysis of GJ 436 yields an effective temperature of Teff = 3350 +/- 300 K and a mass of 0.44 Msun. New Doppler measurements for GJ 436 with a precision of 3 m/s taken during 6 years improve the Keplerian model of the planet, giving a minimum mass, M sin i = 0.0713 Mjup = 22.7 Mearth, period, P = 2.6439 d, and e = 0.16 +/- 0.02. The noncircular orbit contrasts with the tidally circularized orbits of all close-in exoplanets, implying either ongoing pumping of eccentricity by a more distant companion, or a higher Q value for this low-mass planet. The velocities indeed reveal a long term trend, indicating a possible distant companion.

"The First Extrasolar Planet Discovered with a New-Generation High-Throughput Doppler Instrument"
Ge, J. et al. 2006, ApJ, 648, 683.
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+/-2.0 m s-1 and a period of 4.11 days. The planetary minimum mass (msini) is 0.488MJ+/-0.015MJ. The planet was initially detected in the spring of 2005 with the Kitt Peak National Observatory (KPNO) 0.9 m coude feed telescope. The detection was confirmed by radial velocity observations with the ET at the KPNO 2.1 m telescope and also at the 9 m Hobby-Eberly Telescope (HET) with its High Resolution Spectrograph. This planetary discovery with a 0.9 m telescope around a V=8.05 magnitude star was made possible by the high throughput of the instrument: 49% measured from the fiber output to the detector. The ET's interferometer-based approach is an effective method for planet detection. In addition, the ET concept is adaptable to multiple-object Doppler observations or very high precision observations with a cross-dispersed echelle spectrograph to separate stellar fringes over a broad wavelength band. In addition to spectroscopic observations of HD 102195, we obtained brightness measurements with one of the automated photometric telescopes at Fairborn Observatory. Those observations reveal that HD 102195 is a spotted variable star with an amplitude of ~0.015 mag and a 12.3+/-0.3 day period. This is consistent with spectroscopically observed Ca II H and K emission levels and line-broadening measurements but inconsistent with rotational modulation of surface activity as the cause of the radial velocity variability. Our photometric observations rule out transits of the planetary companion.

"The N2K Consortium. VI. Doppler Shifts without Templates and Three New Short-Period Planets"
Johnson, J.A. 2006, ApJ 647, 600.
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 template 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 (High Resolution Echelle Spectrometer) spectra indicate that synthetic templates yield a short-term precision of 3 m s-1 and a long-term, run-to-run precision of 5 m s-1. We used this new Doppler technique to discover three new planets: a 1.50MJ planet in a 2.1375 day orbit around HD 86081; a 0.71MJ planet in circular, 26.73 day orbit around HD 224693; and a Saturn-mass planet in an 18.179 day orbit around HD 33283. The remarkably short period of HD 86081b bridges the gap between the extremely short period planets detected in the Optical Gravitational Lensing Experiment (OGLE) survey and the 16 Doppler-detected hot Jupiters (P < 15 days), which have an orbital period distribution that piles up at about 3 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. We have too few photometric observations to detect or rule out transits for HD 224693.

"The Effects of Multiple Companions on the Efficiency of Space Interferometry Mission Planet Searches"
Ford, E.B. 2006, PASP, 118, 364.
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 of them will have a measurable acceleration due to their companion, which must be included when solving for astrometric parameters and searching for planetary perturbations. In addition, many of the stars with one radial velocity planet show indications of additional planets. Therefore, astrometric surveys such as 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. In addition, 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 particularly valuable for studying multiple-planet systems.

"Exoplanets and the Space Interferometry Mission"
Marcy, G. W., Fischer, D. A., McCarthy, C., Ford, E. B. 2005, Astrometry in the Age of the Next Generation of Large Telescopes, ASP Conf. Series, Vol. 338, eds. P. Kenneth Seidelmann & Alice K. B. Monet. San Francisco: Astronomical Society of the Pacific, p. 191.
The Doppler technique has revealed exoplanets with masses as low as 15 MEarth orbiting between 0.03 and 5.5 AU. The distribution of planet masses rises toward the lowest detectable masses and an increasing number of planets reside in larger orbits. The majority of planets reside in non-circular orbits and multiple planet systems are common, often trapped in resonances. The Space Interferometry Mission (SIM) will detect planets with masses less than 10 MEarth orbiting within 2 AU of nearby stars. It will measure the masses and orbits of rocky planets, testing theories of their formation and dynamical evolution in protoplanetary disks. For the closest stars, planets with masses as low as 3 MEarth within 1 AU are detectable at a secure level, and marginal detections of planets of 1 MEarth can be made. SIM will be the first mission to find rocky planets near the habitable zone of nearby stars, allowing follow-up by later imaging and spectroscopic missions, such as the "Terrestrial Planet Finder" and Darwin. Thus, SIM will provide TPF and Darwin a set of target stars enriched in rocky planets, increasing the efficiency of those missions by factors of at least ~3. Indeed, SIM can dictate the timing of imaging observations by selecting orbital phases when the planet resides outside the diffraction blind spot.

"Vegetation's Red Edge: A Possible Spectroscopic Biosignature of Extraterrestrial Plants"
Seager, S., Turner, E.L., Schafer, J., Ford, E.B. 2005, Astrobiology 5, 372.
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 (New Mexico) 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-planetcharacterizing 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.

"Choice of Observing Schedules for Astrometric Planet Searches"
Ford, E.B. 2004, PASP 116, 1083.
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.

"Adaptive Scheduling Algorithms for Planet Searches"
Ford, E.B. 2004, arXiv:astro-ph/0412703.
High-precision radial velocity planet searches have surveyed ~2000 nearby stars and detected ~130 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.

"Planet-Finding Prospects for the Space Interferometry Mission"
Ford, E.B. & Tremaine, S. 2003, PASP 115, 1171.
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 measured 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 a SIM key project is likely to detect around one to five planets with masses <=3 M_Earth (depending on mission parameters). SIM would measure masses and orbits with 30% accuracy for around zero to two of these planets, but is unlikely to measure orbits with 10% accuracy for more than one of them. SIM is likely to detect around five to 25 planets with mass less than 20 M_Earth, measure masses and orbits with 30% accuracy for around two to 12 of these, and measure masses and orbits with 10% accuracy for around two to eight such planets. SIM is likely to find ~25-160 planets of all masses, depending on the observing strategy and mission lifetime. Roughly 25%-65% of the planets detected by SIM have sufficiently large masses and short orbital periods that they can also be detected by radial velocity surveys. Radial velocity surveys could measure orbital parameters (not including inclination) for 30%-70% of the planets whose orbital parameters will be determined to within 30% by SIM.

"Early-Type Stars: Most Favorable Targets for Astrometrically Detectable Planets in the Habitable Zone"
Gould, A., Ford, E.B., Fischer, D.A. 2003, ApJL 591, L155.
Early-type stars appear to be a difficult place to look for planets astrometrically. First, they are relatively heavy, and for fixed planetary mass the astrometric signal falls inversely as the stellar mass. Second, they are relatively rare (and so tend to be more distant), and for fixed orbital separation the astrometric signal falls inversely as the distance. Nevertheless, because early-type stars are relatively more luminous, their habitable zones are at larger semimajor axis. Since astrometric signal scales directly as orbital size, this gives early-type stars a strong advantage, which more than compensates for the other two factors. Using the Hipparcos Catalog, we show that F and A stars constitute the majority of viable targets for astrometric searches for planets with semimajor axes currently in the habitable zone. Thus, astrometric surveys are complementary to transit searches, which are primarily sensitive to habitable planets around late-type stars.

"The 4-m space telescope for investigating extrasolar Earth-like planets in starlight: TPF is HST2"
Brown, R.A. et al. 2003, Future EUV/UV and Visible Space Astrophysics Missions and Instrumentation. eds. J. Chris Blades & Oswald H. W. Siegmund. Proc. SPIE, Vol. 4854, pp. 95-107.
Recent advances in deformable mirror technology for correcting wavefront errors and in pupil shapes and masks for coronagraphic suppression of diffracted starlight enable a powerful approach to detecting extrasolar planets in reflected (scattered) starlight at visible wavelengths. We discuss the planet-finding performance of Hubble-like telescopes using these technical advances. A telescope of aperture of at least 4 meters could accomplish the goals of the Terrestrial Planet Finder (TPF) mission. The '4mTPF' detects an Earth around a Sun at five parsecs in about one hour of integration time. It finds molecular oxygen, ozone, water vapor, the 'red edge' of chlorophyll-containing land-plant leaves, and the total atmospheric column density -- all in forty hours or less. The 4mTPF has a strong science program of discovery and characterization of extrasolar planets and planetary systems, including other worlds like Earth. With other astronomical instruments sharing the focal plane, the 4mTPF could also continue and expand the general program of astronomical research of the Hubble Space Telescope.

"Characterization of extrasolar terrestrial planets from diurnal photometric variability"
Ford, E.B., Seager, S., Turner, E.L. 2001, Nature, 412, 885
The detection of massive planets orbiting nearby stars has become almost routine, but current techniques are as yet unable to detect terrestrial planets with masses comparable to the Earth's. Future space-based observatories to detect Earth-like planets are being planned. Terrestrial planets orbiting in the habitable zones of stars-where planetary surface conditions are compatible with the presence of liquid water-are of enormous interest because they might have global environments similar to Earth's and even harbour life. The light scattered by such a planet will vary in intensity and colour as the planet rotates; the resulting light curve will contain information about the planet's surface and atmospheric properties. Here we report a model that predicts features that should be discernible in the light curve obtained by low-precision photometry. For extrasolar planets similar to Earth, we expect daily flux variations of up to hundreds of per cent, depending sensitively on ice and cloud cover as well as seasonal variations. This suggests that the meteorological variability, composition of the surface (for example, ocean versus land fraction) and rotation period of an Earth-like planet could be derived from photometric observations. Even signatures of Earth-like plant life could be constrained or possibly, with further study, even uniquely determined.

Physical Models of Stars & Planets

I construct stellar interior models to determine the physical properties of stars that host extrasolar planets (e.g., the stellar age, mass, radius, and size of their convective zones). This has helped constrain theories of tidal dissipation and accretion of planets onto stars. I also construct physical models of extrasolar planets to investigate novel techniques for characterizing the properties of extrasolar planets with ambitious space missions, such as NASA's coronagraphic Terrestrial Planet Finder (TPF-C). Click for publications

"Structure and Evolution of Nearby Stars with Planets II. Physical Properties of ~1000 Cool Stars from the SPOCS Catalog"
Takeda, G., Ford, E.B., Sills, A., Rasio, F.A., Fischer, D.A., Valenti, J.A. 2006, submitted to ApJS, 168, 297.
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.

"Vegetation's Red Edge: A Possible Spectroscopic Biosignature of Extraterrestrial Plants"
Seager, S., Turner, E.L., Schafer, J., Ford, E.B. 2005, Astrobiology 5, 372.
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 (New Mexico) 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-planetcharacterizing 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.

"Characterization of extrasolar terrestrial planets from diurnal photometric variability"
Ford, E.B., Seager, S., Turner, E.L. 2001, Nature, 412, 885
The detection of massive planets orbiting nearby stars has become almost routine, but current techniques are as yet unable to detect terrestrial planets with masses comparable to the Earth's. Future space-based observatories to detect Earth-like planets are being planned. Terrestrial planets orbiting in the habitable zones of stars-where planetary surface conditions are compatible with the presence of liquid water-are of enormous interest because they might have global environments similar to Earth's and even harbour life. The light scattered by such a planet will vary in intensity and colour as the planet rotates; the resulting light curve will contain information about the planet's surface and atmospheric properties. Here we report a model that predicts features that should be discernible in the light curve obtained by low-precision photometry. For extrasolar planets similar to Earth, we expect daily flux variations of up to hundreds of per cent, depending sensitively on ice and cloud cover as well as seasonal variations. This suggests that the meteorological variability, composition of the surface (for example, ocean versus land fraction) and rotation period of an Earth-like planet could be derived from photometric observations. Even signatures of Earth-like plant life could be constrained or possibly, with further study, even uniquely determined.

"Structure and Evolution of Nearby Stars with Planets. I. Short-Period Systems"
Ford, E.B., Rasio, F.A., Sills, A. 1999, ApJ 514, 411.
Using the Yale stellar evolution code, we have calculated theoretical models for nearby stars with planetary-mass companions in short-period nearly circular orbits: 51 Pegasi, tau Bootis, upsilon Andromedae, rho^1 Cancri, and rho Coronae Borealis. We present tables listing key stellar parameters such as mass, radius, age, and size of the convective envelope as a function of the observable parameters (luminosity, effective temperature, and metallicity), as well as the unknown helium fraction. For each star we construct best models based on recently published spectroscopic data and the present understanding of galactic chemical evolution. We discuss our results in the context of planet formation theory and, in particular, tidal dissipation effects and stellar metallicity enhancements.

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Last updated: January 7, 2008
Created: December 9, 2005