Showing papers by "Eric B. Ford published in 2010"

Kepler Planet-Detection Mission: Introduction and First Results

Abstract: The Kepler mission was designed to determine the frequency of Earth-sized planets in and near the habitable zone of Sun-like stars. The habitable zone is the region where planetary temperatures are suitable for water to exist on a planet’s surface. During the first 6 weeks of observations, Kepler monitored 156,000 stars, and five new exoplanets with sizes between 0.37 and 1.6 Jupiter radii and orbital periods from 3.2 to 4.9 days were discovered. The density of the Neptune-sized Kepler-4b is similar to that of Neptune and GJ 436b, even though the irradiation level is 800,000 times higher. Kepler-7b is one of the lowest-density planets (~0.17 gram per cubic centimeter) yet detected. Kepler-5b, -6b, and -8b confirm the existence of planets with densities lower than those predicted for gas giant planets.

Kepler-9: a system of multiple planets transiting a Sun-like star, confirmed by timing variations.

Abstract: The Kepler spacecraft is monitoring more than 150,000 stars for evidence of planets transiting those stars. We report the detection of two Saturn-size planets that transit the same Sun-like star, based on 7 months of Kepler observations. Their 19.2- and 38.9-day periods are presently increasing and decreasing at respective average rates of 4 and 39 minutes per orbit; in addition, the transit times of the inner body display an alternating variation of smaller amplitude. These signatures are characteristic of gravitational interaction of two planets near a 2:1 orbital resonance. Six radial-velocity observations show that these two planets are the most massive objects orbiting close to the star and substantially improve the estimates of their masses. After removing the signal of the two confirmed giant planets, we identified an additional transiting super-Earth–size planet candidate with a period of 1.6 days.

Modeling Kepler transit light curves as false positives: Rejection of blend scenarios for Kepler-9, and validation of Kepler-9d, a super-Earth-size planet in a multiple system

Abstract: Light curves from the Kepler Mission contain valuable information on the nature of the phenomena producing the transit-like signals. To assist in exploring the possibility that they are due to an astrophysical false positive, we describe a procedure (BLENDER) to model the photometry in terms of a "blend" rather than a planet orbiting a star. A blend may consist of a background or foreground eclipsing binary (or star-planet pair) whose eclipses are attenuated by the light of the candidate and possibly other stars within the photometric aperture. We apply BLENDER to the case of Kepler-9, a target harboring two previously confirmed Saturn-size planets (Kepler-9b and Kepler-9c) showing transit timing variations, and an additional shallower signal with a 1.59-day period suggesting the presence of a super-Earth-size planet. Using BLENDER together with constraints from other follow-up observations we are able to rule out all blends for the two deeper signals, and provide independent validation of their planetary nature. For the shallower signal we rule out a large fraction of the false positives that might mimic the transits. The false alarm rate for remaining blends depends in part (and inversely) on the unknown frequency of small-size planets. Based on several realistic estimates of this frequency we conclude with very high confidence that this small signal is due to a super-Earth-size planet (Kepler-9d) in a multiple system, rather than a false positive. The radius is determined to be 1.64 (+0.19/-0.14) R(Earth), and current spectroscopic observations are as yet insufficient to establish its mass.

Five Kepler target stars that show multiple transiting exoplanet candidates

Abstract: We present and discuss five candidate exoplanetary systems identified with the Kepler spacecraft. These five systems show transits from multiple exoplanet candidates. Should these objects prove to be planetary in nature, then these five systems open new opportunities for the field of exoplanets and provide new insights into the formation and dynamical evolution of planetary systems. We discuss the methods used to identify multiple transiting objects from the Kepler photometry as well as the false-positive rejection methods that have been applied to these data. One system shows transits from three distinct objects while the remaining four systems show transits from two objects. Three systems have planet candidates that are near mean motion commensurabilities—two near 2:1 and one just outside 5:2. We discuss the implications that multi-transiting systems have on the distribution of orbital inclinations in planetary systems, and hence their dynamical histories, as well as their likely masses and chemical compositions. A Monte Carlo study indicates that, with additional data, most of these systems should exhibit detectable transit timing variations (TTVs) due to gravitational interactions, though none are apparent in these data. We also discuss new challenges that arise in TTV analyses due to the presence of more than two planets in a system.

Observational biases in determining extrasolar planet eccentricities in single‐planet systems

Abstract: We investigate potential biases in the measurements of exoplanet orbital parameters obtained from radial velocity observations for single-planet systems. We create a mock catalogue of radial velocity data, choosing input planet masses, periods and observing patterns from actual radial velocity surveys and varying input eccentricities. We apply Markov chain Monte Carlo simulations and compare the resulting orbital parameters to the input values. We find that a combination of the effective signal-to-noise ratio of the data, the maximal gap in phase coverage, and the total number of periods covered by observations is a good predictor of the quality of derived orbit parameters. As eccentricity is positive definite, we find that eccentricities of planets on nearly circular orbits are preferentially overestimated, with typical bias of one to two times the median eccentricity uncertainty in a survey (e.g. 0.04 in the Butler et al. catalogue). When performing population analysis, we recommend using the mode of the marginalized posterior eccentricity distribution to minimize potential biases. While the Butler et al. catalogue reports eccentricities below 0.05 for just 17 per cent of single-planet systems, we estimate that the true fraction of e ≤ 0.05 orbits is about f 0.05 = 38 ± 9 per cent. For planets with P > 10d, we find f 0.05 = 28 ± 8 per cent versus 10 per cent from Butler et al. These planets either never acquired a large eccentricity or were circularized following any significant eccentricity excitation.

Retired A Stars and Their Companions VI. A Pair of Interacting Exoplanet Pairs Around the Subgiants 24 Sextanis and HD200964

Abstract: We report radial velocity measurements of the G-type subgiants 24 Sextanis (=HD90043) and HD200964. Both are massive, evolved stars that exhibit periodic variations due to the presence of a pair of Jovian planets. Photometric monitoring with the T12 0.80m APT at Fairborn Observatory demonstrates both stars to be constant in brightness to <= 0.002 mag, thus strengthening the planetary interpretation of the radial velocity variations. 24 Sex b,c have orbital periods of 453.8 days and 883~days, corresponding to semimajor axes 1.333 AU and 2.08 AU, and minimum masses (Msini) 1.99 Mjup and 0.86 Mjup, assuming a stellar mass 1.54 Msun. HD200964 b,c have orbital periods of 613.8 days and 825 days, corresponding to semimajor axes 1.601 AU and 1.95 AU, and minimum masses 1.85 Mjup and 0.90 Mjup, assuming M* = 1.44 Msun. We also carry out dynamical simulations to properly account for gravitational interactions between the planets. Most, if not all, of the dynamically stable solutions include crossing orbits, suggesting that each system is locked in a mean motion resonance that prevents close encounters and provides long-term stability. The planets in the 24 Sex system likely have a period ratio near 2:1, while the HD200964 system is even more tightly packed with a period ratio close to 4:3. However, we caution that further radial velocity observations and more detailed dynamical modelling will be required to provide definitive and unique orbital solutions for both cases, and to determine whether the two systems are truly resonant.

Secular orbital dynamics of hierarchical two-planet systems

Abstract: The discovery of multi-planet extrasolar systems has kindled interest in using their orbital evolution as a probe of planet formation. Accurate descriptions of planetary orbits identify systems that could hide additional planets or be in a special dynamical state, and inform targeted follow-up observations. We combine published radial velocity data with Markov Chain Monte Carlo analyses in order to obtain an ensemble of masses, semimajor axes, eccentricities, and orbital angles for each of the five dynamically active multi-planet systems: HD 11964, HD 38529, HD 108874, HD 168443, and HD 190360. We dynamically evolve these systems using 52,000 long-term N-body integrations that sample the full range of possible line-of-sight and relative inclinations, and we report on the system stability, secular evolution, and the extent of the resonant interactions. We find that planetary orbits in hierarchical systems exhibit complex dynamics and can become highly eccentric and maybe significantly inclined. Additionally, we incorporate the effects of general relativity in the long-term simulations and demonstrate that it can qualitatively affect the dynamics of some systems with high relative inclinations. The simulations quantify the likelihood of different dynamical regimes for each system and highlight the dangers of restricting simulation phase space to a single set of initial conditions or coplanar orbits.

Characterizing transiting extrasolar planets with narrow-band photometry and GTC/OSIRIS

Abstract: We report the first extrasolar planet observations from the 10.4-m Gran Telescopio Canarias (GTC), currently the world's largest, fully steerable, single-aperture optical telescope. We used the Optical System for Imaging and low Resolution Integrated Spectroscopy (OSIRIS) tunable filter imager on the GTC to acquire high-precision, narrow-band photometry of the transits of the giant exoplanets, TrES-2b and TrES-3b. We obtained near-simultaneous observations in two near-infrared wavebands (790.2 and 794.4 ± 2.0 nm) specifically chosen to avoid water vapour absorption and skyglow so as to minimize the atmospheric effects that often limit the precision of ground-based photometry. Our results demonstrate a very-high photometric precision with minimal atmospheric contamination despite relatively poor atmospheric conditions and some technical problems with the telescope. We find the photometric precision for the TrES-2 observations to be 0.343 and 0.412 mmag for the 790.2- and 794.4-nm light curves, and the precision of the TrES-3 observations was found to be 0.470 and 0.424 mmag for the 790.2- and 794.4-nm light curves, respectively. We also discuss how future follow-up observations of transiting planets with this novel technique can contribute to the characterization of Neptune- and super-Earth-size planets to be discovered by space-based missions like CoRoT and Kepler, as well as measure atmospheric properties of giant planets, such as the strength of atmospheric absorption features.

Transit timing variations for inclined and retrograde exoplanetary systems

Abstract: We perform numerical calculations of the expected transit timing variations (TTVs) induced on a hot-Jupiter by an Earth-mass perturber. Motivated by the recent discoveries of retrograde transiting planets, we concentrate on an investigation of the effect of varying relative planetary inclinations, up to and including completely retrograde systems. We find that planets in low-order (e.g., 2:1) mean-motion resonances (MMRs) retain approximately constant TTV amplitudes for 0° 170°. Systems in higher order MMRs (e.g., 5:1) increase in TTV amplitude as inclinations increase toward 45°, becoming approximately constant for 45° 135°. Planets away from resonance slowly decrease in TTV amplitude as inclinations increase from 0° to 180°, whereas planets adjacent to resonances can exhibit a huge range of variability in TTV amplitude as a function of both eccentricity and inclination. For highly retrograde systems (135° < i ≤ 180°), TTV signals will be undetectable across almost the entirety of parameter space, with the exceptions occurring when the perturber has high eccentricity or is very close to an MMR. This high inclination decrease in TTV amplitude (on and away from resonance) is important for the analysis of the known retrograde and multi-planet transiting systems, as inclination effects need to be considered if TTVs are to be used to exclude the presence of any putative planetary companions: absence of evidence is not evidence of absence.

Secular Orbital Dynamics of Hierarchical Two Planet Systems

Abstract: The discovery of multi-planet extrasolar systems has kindled interest in using their orbital evolution as a probe of planet formation. Accurate descriptions of planetary orbits identify systems which could hide additional planets or be in a special dynamical state, and inform targeted follow-up observations. We combine published radial velocity data with Markov Chain Monte Carlo analyses in order to obtain an ensemble of masses, semimajor axes, eccentricities and orbital angles for each of 5 dynamically active multi-planet systems: HD 11964, HD 38529, HD 108874, HD 168443, and HD 190360. We dynamically evolve these systems using 52,000 long-term N-body integrations that sample the full range of possible line-of-sight and relative inclinations, and we report on the system stability, secular evolution and the extent of the resonant interactions. We find that planetary orbits in hierarchical systems exhibit complex dynamics and can become highly eccentric and maybe significantly inclined. Additionally we incorporate the effects of general relativity in the long-term simulations and demonstrate that can qualitatively affect the dynamics of some systems with high relative inclinations. The simulations quantify the likelihood of different dynamical regimes for each system and highlight the dangers of restricting simulation phase space to a single set of initial conditions or coplanar orbits.

MARVELS-1b: A Short-Period, Brown Dwarf Desert Candidate from the SDSS-III MARVELS Planet Search

Abstract: We present a new short-period brown dwarf candidate around the star TYC 1240-00945-1. This candidate was discovered in the first year of the Multi-object APO Radial Velocity Exoplanets Large-area Survey (MARVELS), which is part of the third phase of the Sloan Digital Sky Survey (SDSS-III), and we designate the brown dwarf as MARVELS-1b. MARVELS uses the technique of dispersed fixed-delay interferometery to simultaneously obtain radial velocity measurements for 60 objects per field using a single, custom-built instrument that is fiber fed from the SDSS 2.5-m telescope. From our 20 radial velocity measurements spread over a ~370 d time baseline, we derive a Keplerian orbital fit with semi-amplitude K=2.533+/-0.025 km/s, period P=5.8953+/-0.0004 d, and eccentricity consistent with circular. Independent follow-up radial velocity data confirm the orbit. Adopting a mass of 1.37+/-0.11 M_Sun for the slightly evolved F9 host star, we infer that the companion has a minimum mass of 28.0+/-1.5 M_Jup, a semimajor axis 0.071+/-0.002 AU assuming an edge-on orbit, and is probably tidally synchronized. We find no evidence for coherent instrinsic variability of the host star at the period of the companion at levels greater than a few millimagnitudes. The companion has an a priori transit probability of ~14%. Although we find no evidence for transits, we cannot definitively rule them out for companion radii ~<1 R_Jup.

Detectability of Earth-like Planets in Multi-Planet Systems: Preliminary Report

Abstract: We ask if Earth-like planets (terrestrial mass and habitable-zone orbit) can be detected in multi-planet systems, using astrometric and radial velocity observations. We report here the preliminary results of double-blind calculations designed to answer this question.

Ground-Based Multisite Observations of Two Transits of HD 80606b

Abstract: We present ground-based optical observations of the 2009 September and 2010 January transits of HD 80606b. Based on three partial light curves of the 2009 September event, we derive a midtransit time of T_c [HJD] = 2455099.196 ± 0.026, which is about 1σ away from the previously predicted time. We observed the 2010 January event from nine different locations, with most phases of the transit being observed by at least three different teams. We determine a midtransit time of Tc [HJD] = 2455210.6502 ± 0.0064, which is within 1.3σ of the time derived from a Spitzer observation of the same event.

Ground-based multisite observations of two transits of HD 80606b

Abstract: We present ground-based optical observations of the September 2009 and January 2010 transits of HD 80606b. Based on 3 partial light curves of the September 2009 event, we derive a midtransit time of T_c [HJD] = 2455099.196 +- 0.026, which is about 1 sigma away from the previously predicted time. We observed the January 2010 event from 9 different locations, with most phases of the transit being observed by at least 3 different teams. We determine a midtransit time of T_c [HJD] = 2455210.6502 +- 0.0064, which is within 1.3 sigma of the time derived from a Spitzer observation of the same event.

Five Kepler target stars that show multiple transiting exoplanet candidates

Abstract: We present and discuss five candidate exoplanetary systems identified with the Kepler spacecraft. These five systems show transits from multiple exoplanet candidates. Should these objects prove to be planetary in nature, then these five systems open new opportunities for the field of exoplanets and provide new insights into the formation and dynamical evolution of planetary systems. We discuss the methods used to identify multiple transiting objects from the Kepler photometry as well as the false-positive rejection methods that have been applied to these data. One system shows transits from three distinct objects while the remaining four systems show transits from two objects. Three systems have planet candidates that are near mean motion commensurabilities---two near 2:1 and one just outside 5:2. We discuss the implications that multitransiting systems have on the distribution of orbital inclinations in planetary systems, and hence their dynamical histories; as well as their likely masses and chemical compositions. A Monte Carlo study indicates that, with additional data, most of these systems should exhibit detectable transit timing variations (TTV) due to gravitational interactions---though none are apparent in these data. We also discuss new challenges that arise in TTV analyses due to the presence of more than two planets in a system.

Quantifying the challenges of detecting unseen planetary companions with transit timing variations

Abstract: Both ground and space-based transit observatories are poised to significantly increase the number of known transiting planets and the number of precisely measured transit times. The variation in a planet's transit times may be used to infer the presence of additional planets. Deducing the masses and orbital parameters of such planets from transit time variations (TTVs) alone is a rich and increasingly relevant dynamical problem. In this work, we evaluate the extent of the degeneracies in this process, systematically explore the dependence of TTV signals on several parameters and provide phase space plots that could aid observers in planning future observations. Our explorations are focused on a likely-to-be prevalent situation: a known transiting short-period Neptune or Jupiter-sized planet and a suspected external low-mass perturber on a nearly-coplanar orbit. Through approximately 10^7 N-body simulations, we demonstrate how TTV signal amplitudes may vary by orders of magnitude due to slight variations in any one orbital parameter (0.001 AU in semimajor axis, 0.005 in eccentricity, or a few degrees in orbital angles), and quantify the number of consecutive transit observations necessary in order to obtain a reasonable opportunity to characterize the unseen planet (approximately greater or equal to 50 observations). Planets in or near period commensurabilities of the form p:q, where p < 21 and q < 4, produce distinct TTV signatures, regardless of whether the planets are actually locked in a mean motion resonance. We distinguish these systems from the secular systems in our explorations. Additionally, we find that computing the autocorrelation function of a TTV signal can provide a useful diagnostic for identifying possible orbits for additional planets and suggest that this method could aid integration of TTV signals in future studies of particular exosystems.

Probing potassium in the atmosphere of HD 80606b with tunable filter transit spectrophotometry from the Gran Telescopio Canarias

Abstract: We report observations of HD 80606 using the 10.4-m Gran Telescopio Canarias (GTC) and the OSIRIS tunable filter imager. We acquired very-high-precision, narrow-band photometry in four bandpasses around the K I absorption feature during the January 2010 transit of HD 80606b and during out-of-transit observations conducted in January and April of 2010. We obtained differential photometric precisions of \sim 2.08e-4 for the in-transit flux ratio measured at 769.91-nm, which probes the K I line core. We find no significant difference in the in-transit flux ratio between observations at 768.76 and 769.91 nm. Yet, we find a difference of \sim 8.09 \pm 2.88e-4 between these observations and observations at a longer wavelength that probes the K I wing (777.36 nm). While the presence of red noise in the transit data has a non-negligible effect on the uncertainties in the flux ratio, the 777.36-769.91 nm colour during transit shows no effects from red noise and also indicates a significant colour change, with a mean value of \sim 8.99\pm0.62e-4. This large change in the colour is equivalent to a \sim 4.2% change in the apparent planetary radius with wavelength, which is much larger than the atmospheric scale height. This implies the observations probed the atmosphere at very low pressures as well as a dramatic change in the pressure at which the slant optical depth reaches unity between \sim770 and 777 nm. We hypothesize that the excess absorption may be due to K I in a high-speed wind being driven from the exoplanet's exosphere. We discuss the viability of this and alternative interpretations, including stellar limb darkening, starspots, and effects from Earth's atmosphere. We strongly encourage follow-up observations of HD 80606b to confirm the signal measured here. Finally, we discuss the future prospects for exoplanet characterization using tunable filter spectrophotometry.

Characterizing Transiting Extrasolar Planets with Narrow-Band Photometry and GTC/OSIRIS

Abstract: We report the first extrasolar planet observations from the 10.4-m Gran Telescopio Canarias (GTC), currently the world's largest, fully steerable, single-aperture optical telescope. We used the OSIRIS tunable filter imager on the GTC to acquire high-precision, narrow-band photometry of the transits of the giant exoplanets, TrES-2b and TrES-3b. We obtained near-simultaneous observations in two near-infrared (NIR) wavebands (790.2 and 794.4 +/- 2.0 nm) specifically chosen to avoid water vapor absorption and skyglow so as to minimize the atmospheric effects that often limit the precision of ground-based photometry. Our results demonstrate a very-high photometric precision with minimal atmospheric contamination despite relatively poor atmospheric conditions and some technical problems with the telescope. We find the photometric precision for the TrES-2 observations to be 0.343 and 0.412 mmag for the 790.2 and 794.4 nm light curves, and the precision of the TrES-3 observations was found to be 0.470 and 0.424 mmag for the 790.2 and 794.4 nm light curves. We also discuss how future follow-up observations of transiting planets with this novel technique can contribute to the characterization of Neptune- and super-Earth-size planets to be discovered by space-based missions like CoRoT and Kepler, as well as measure atmospheric properties of giant planets, such as the strength of atmospheric absorption features.

Observational biases in determining extrasolar planet eccentricities in single-planet systems

Abstract: We investigate potential biases in the measurements of exoplanet orbital parameters obtained from radial velocity observations for single-planet systems. We create a mock catalog of radial velocity data, choosing input planet masses, periods, and observing patterns from actual radial velocity surveys and varying input eccentricities. We apply Markov Chain Monte Carlo (MCMC) simulations and compare the resulting orbital parameters to the input values. We find that a combination of the effective signal-to-noise ratio of the data, the maximal gap in phase coverage, and the total number of periods covered by observations is a good predictor of the quality of derived orbit parameters. As eccentricity is positive definite, we find that eccentricities of planets on nearly circular orbits are preferentially overestimated, with typical bias of 1-2 times the median eccentricity uncertainty in a survey (e.g., 0.04 in the Butler et al. 2006 catalog). When performing population analysis, we recommend using the mode of the marginalized posterior eccentricity distribution to minimize potential biases. While the Butler et al. (2006) catalog reports eccentricities below 0.05 for just 17% of single-planet systems, we estimate that the true fraction of e 10 days, we find f(0.05)=28\pm 8% versus 10% from Butler et al. (2006). These planets either never acquired a large eccentricity or were circularized following any significant eccentricity excitation.

Survival and Detectability of Long Period Planets Beyond 100 AU

Abstract: Direct imaging searches have begun to detect planetary and brown dwarf companions and to place constraints on the presence of giant planets at large separations from their host star. This work helps to motivate such planet searches by predicting a population of young giant planets that could be detectable by direct imaging campaigns. Both the classical core accretion and the gravitational instability model for planet formation are hard-pressed to form such planets in situ . Therefore, direct imaging searches have traditionally appealed to the possibility of in situ planet formation via a large scale gravitational instability. Here, we show that dynamical instabilities among planetary systems that originally formed multiple giant planets much closer to the host star could produce a population of giant planets at large separations. The number and distribution of such planets is a strong function of time, complicating the statistical analysis of direct imaging surveys. The number and radial distribution of such planets is related to the number of giant planets formed per host star and the timescale for the disk evolution. Thus, direct imaging programs with sufficient sensitivity and survey size could place interesting constraints on planet formation models.

Probing potassium in the atmosphere of HD 80606b with tunable filter transit spectrophotometry from the Gran

Abstract: We report observations of HD 80606 using the 10.4-m Gran Telescopio Canarias (GTC) and the OSIRIS tunable filter imager. We acquired very-high-precision, narrow-band photometry in four bandpasses around the K i absorption feature during the January 2010 transit of HD 80606b and during out-of-transit observations conducted in April 2010. We obtained differential photometric precisions as small as � 2:9 × 10 5 . We find no significant difference between observations at 768.76 and 769.91 nm, which probe the K i line core. Yet, we observe significant differences (3:08 ± 0:53 × 10 4 and 7:00 ± 0:40 × 10 4 ) between these observations and observations at two longer wavelengths that probe the K i wing (773.66 and 777.36 nm). The large change in the apparent planetary radius with wavelength (� 3:6%) is much larger than the atmospheric scale height. This implies the observations probed the atmosphere at low pressures as well as a dramatic change in the pressure at which the slant optical depth reaches unity between �770 and 777 nm. We hypothesize that the excess absorption may be due to K i in a high-speed wind being driven from the exoplanet’s exosphere. We discuss the viability of this and alternative interpretations. Finally, we discuss the future prospects for exoplanet characterization using tunable filter spectrophotometry.

Transit Timing Variations for Inclined and Retrograde Exoplanetary Systems

Abstract: We perform numerical calculations of the expected transit timing variations (TTVs) induced on a Hot-Jupiter by an Earth-mass perturber. Motivated by the recent discoveries of retrograde transiting planets, we concentrate on an investigation of the effect of varying relative planetary inclinations, up to and including completely retrograde systems. We find that planets in low order (E.g. 2:1) mean-motion resonances (MMRs) retain approximately constant TTV amplitudes for $0 170\,^{\circ}$. Systems in higher order MMRs (E.g. 5:1) increase in TTV amplitude as inclinations increase towards $45\,^{\circ}$, becoming approximately constant for $45 135\,^{\circ}$. Planets away from resonance slowly decrease in TTV amplitude as inclinations increase from 0 to 180, where-as planets adjacent to resonances can exhibit a huge range of variability in TTV amplitude as a function of both eccentricity and inclination. For highly retrograde systems ($135\,^{\circ} < i \leq 180\,^{\circ}$), TTV signals will be undetectable across almost the entirety of parameter space, with the exceptions occurring when the perturber has high eccentricity or is very close to a MMR. This high inclination decrease in TTV amplitude (on and away from resonance) is important for the analysis of the known retrograde and multi-planet transiting systems, as inclination effects need to be considered if TTVs are to be used to exclude the presence of any putative planetary companions: absence of evidence is not evidence of absence.

Observational biases in determining extrasolar planet eccentricities

Abstract: We investigate biases in the measurement of exoplanet orbital parameters – especially eccentricity – from radial velocity (RV) observations. In this contribution we consider single-planet systems. We create a mock catalog of RV data, choosing planet masses and orbital periods, and observing patterns to mimic those of actual RV surveys. Using Markov chain Monte Carlo (MCMC) simulations, we generate a posterior sample for each mock data set, calculate best-fit orbital parameters for each data set, and compare these to the true values. We find that the precision of our derived eccentricities is most closely related to the effective signal-to-noise ratio, K √ N / σ , where K is the velocity amplitude, σ is the effective single-measurement precision, and N is the number of observations. We also find that eccentricities of planets on nearly circular ( e ) orbits are preferentially overestimated. While the Butler et al. (2006) catalog reports e for just 20% of its planets, we estimate that the true fraction of e orbits is about 50%. We investigate the accuracy, precision, and bias of alternative sets of summary statistics and find that the median values of h = e sin ω and k = e cos ω (where ω is the longitude of periapse) of the posterior sample typically provide more accurate, more precise, and less biased estimates of eccentricity than traditional measures.

Dynamical Simulations of the Planetary System HD 69830

Abstract: The planetary system of HD 69830 is uniquely constrained by observations of (i) an infrared excess indicative of a debris disk with warm dust and (ii) radial velocity variations indicative of three planets. This presents a valuable opportunity to test planet formation models by integrating dynamical models of planetary formation and migration with those for the sculpting of a dust-producing planetesimal disk. We perform n -body simulations and investigate the excitation of both planet and planetesimal eccentricities, the accretion of planetesimals onto the planets, and the clearing of a planetesimal disk by the planets as they grow in mass and migrate through the disk. In simulations tuned to closely follow previous semi-analytic models for the growth and migration of the planets, we find that the inner planet accretes significantly more planetesimals than previously estimated. We find that eccentricity excitation due to mutual planetary perturbations during and after the migration do not naturally produce the observed eccentricities. Our simulations suggest that this discrepancy may be reduced or possibly reconciled if the planets are significantly more massive than expected (possible if the planetary system's angular momentum were nearly parallel to our line of sight). Even if the planets are significantly more massive than previously assumed, we find that the migrating planets are inefficient at clearing the outer planetesimal disk and that a significant fraction of the planetesimal population beyond 1 AU remains bound on moderately eccentric and inclined orbits. While much of the remaining planetesimal belt would have eroded via a collisional cascade and radiation pressure, we explore whether some of the highly excited planetesimals may be able to persist over the age of the central star, producing the dust observed in the HD 69830 system.

Modeling Kepler transit light curves as false positives: Rejection of blend scenarios for KOI-377, and strong evidence for a super-Earth-size planet in a multiple system

Abstract: Light curves from the Kepler Mission contain valuable information on the nature of the phenomena producing the transit-like signals To assist in exploring the possibility that they are due to an astrophysical false positive, we describe a procedure (BLENDER) to model the photometry in terms of a "blend" rather than a planet orbiting a star A blend may consist of a background or foreground eclipsing binary (or star-planet pair) whose eclipses are attenuated by the light of the candidate and possibly other stars within the photometric aperture We apply BLENDER to the case of Kepler-9, a target harboring two previously confirmed Saturn-size planets (Kepler-9b and Kepler-9c) showing transit timing variations, and an additional shallower signal with a 159-day period suggesting the presence of a super-Earth-size planet Using BLENDER together with constraints from other follow-up observations we are able to rule out all blends for the two deeper signals, and provide independent validation of their planetary nature For the shallower signal we rule out a large fraction of the false positives that might mimic the transits The false alarm rate for remaining blends depends in part (and inversely) on the unknown frequency of small-size planets Based on several realistic estimates of this frequency we conclude with very high confidence that this small signal is due to a super-Earth-size planet (Kepler-9d) in a multiple system, rather than a false positive The radius is determined to be 164 (+019/-014) R(Earth), and current spectroscopic observations are as yet insufficient to establish its mass

Conference Summary & Outlook

Abstract: This timely meeting (appropriately held in Torun, the “city of Copernicus”) provided an excellent venue for researchers to review the theoretical and observational progress in the intervening years, share recent results, and make preparations for progress in the quests to learn whether our Solar System is typical and to understand how our own Solar System relates to the rest of the Universe. It had been nearly six years since the last major scientific meeting focusing soley on multiple planet systems and planets in multiple star systems in Saas Fee, Switzerland during September of 2002 (Udry et al. 2006). Here I review some of the observational and theoretical progress in understanding multi-body systems reported in Torun.