W. Benz

Universität Bern, Berna, Bern, Switzerland

Are you W. Benz?

Claim your profile

Publications (346)1110.87 Total impact

  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We present the analysis of the entire HARPS observations of three stars that host planetary systems: HD1461, HD40307, and HD204313. The data set spans eight years and contains more than 200 nightly averaged velocity measurements for each star. This means that it is sensitive to both long-period and low-mass planets and also to the effects induced by stellar activity cycles. We modelled the data using Keplerian functions that correspond to planetary candidates and included the short- and long-term effects of magnetic activity. A Bayesian approach was taken both for the data modelling, which allowed us to include information from activity proxies such as $\log{(R'_{\rm HK})}$ in the velocity modelling, and for the model selection, which permitted determining the number of significant signals in the system. The Bayesian model comparison overcomes the limitations inherent to the traditional periodogram analysis. We report an additional super-Earth planet in the HD1461 system. Four out of the six planets previously reported for HD40307 are confirmed and characterised. We discuss the remaining two proposed signals. In particular, we show that when the systematic uncertainty associated with the techniques for estimating model probabilities are taken into account, the current data are not conclusive concerning the existence of the habitable-zone candidate HD40307 g. We also fully characterise the Neptune-mass planet that orbits HD204313 in 34.9 days.
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Many attempts have already been made for detecting exomoons around transiting exoplanets but the first confirmed discovery is still pending. The experience that have been gathered so far allow us to better optimize future space telescopes for this challenge, already during the development phase. In this paper we focus on the forthcoming CHaraterising ExOPlanet Satellite (CHEOPS),describing an optimized decision algorithm with step-by-step evaluation, and calculating the number of required transits for an exomoon detection for various planet-moon configurations that can be observable by CHEOPS. We explore the most efficient way for such an observation which minimizes the cost in observing time. Our study is based on PTV observations (photocentric transit timing variation, Szab\'o et al. 2006) in simulated CHEOPS data, but the recipe does not depend on the actual detection method, and it can be substituted with e.g. the photodynamical method for later applications. Using the current state-of-the-art level simulation of CHEOPS data we analyzed transit observation sets for different star-planet-moon configurations and performed a bootstrap analysis to determine their detection statistics. We have found that the detection limit is around an Earth-sized moon. In the case of favorable spatial configurations, systems with at least such a large moon and with at least Neptune-sized planet, 80\% detection chance requires at least 5-6 transit observations on average. There is also non-zero chance in the case of smaller moons, but the detection statistics deteriorates rapidly, while the necessary transit measurements increase fast. (abridged)
    Publications of the Astronomical Society of the Pacific 08/2015; 127(956). DOI:10.1086/683392 · 3.50 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We explore the possibility that the stellar relative abundances of different species can be used to constrain the bulk abundances of known transiting rocky planets. We use high resolution spectra to derive stellar parameters and chemical abundances for Fe, Si, Mg, O, and C in three stars hosting low mass, rocky planets: CoRoT-7, Kepler-10, and Kepler-93. These planets follow the same line along the mass-radius diagram, pointing toward a similar composition. The derived abundance ratios are compared with the solar values. With a simple stoichiometric model, we estimate the iron mass fraction in each planet, assuming stellar composition. We show that in all cases, the iron mass fraction inferred from the mass-radius relationship seems to be in good agreement with the iron abundance derived from the host star's photospheric composition. The results suggest that stellar abundances can be used to add constraints on the composition of orbiting rocky planets.
    Astronomy and Astrophysics 07/2015; 580. DOI:10.1051/0004-6361/201526850 · 4.38 Impact Factor
  • Source
    S. Pfyffer · Y. Alibert · W. Benz · D. Swoboda ·
    [Show abstract] [Hide abstract]
    ABSTRACT: We extend the results of planetary formation synthesis by computing the long-term evolution of synthetic systems from the clearing of the gas disk into the dynamical evolution phase. We use the symplectic integrator SyMBA to numerically integrate the orbits of planets for 100 Ma, using populations from previous studies as initial conditions.We show that within the populations studied, mass and semi-major axis distributions experience only minor changes from post-formation evolution. We also show that, depending upon their initial distribution, planetary eccentricities can statistically increase or decrease as a result of gravitational interactions. We find that planetary masses and orbital spacings provided by planet formation models do not result in eccentricity distributions comparable to observed exoplanet eccentricities, requiring other phenomena such as e.g. stellar fly-bys to account for observed eccentricities.
    Astronomy and Astrophysics 02/2015; 579. DOI:10.1051/0004-6361/201424295 · 4.38 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We present an inversion method based on Bayesian analysis to constrain the interior structure of terrestrial exoplanets, in the form of chemical composition of the mantle and core size. Specifically, we identify what parts of the interior structure of terrestrial exoplanets can be determined from observations of mass, radius, and stellar elemental abundances. We perform a full probabilistic inverse analysis to formally account for observational and model uncertainties and obtain confidence regions of interior structure models. This enables us to characterize how model variability depends on data and associated uncertainties. We test our method on terrestrial solar system planets and find that our model predictions are consistent with independent estimates. Furthermore, we apply our method to synthetic exoplanets up to 10 Earth masses and up to 1.7 Earth radii as well as to exoplanet Kepler-36b. Importantly, the inversion strategy proposed here provides a framework for understanding the level of precision required to characterize the interior of exoplanets. Our main conclusions are: (1) observations of mass and radius are sufficient to constrain core size; (2) stellar elemental abundances (Fe, Si, Mg) are key constraints to reduce degeneracy in interior structure models and to constrain mantle composition; (3) the inherent degeneracy in determining interior structure from mass and radius observations does not only depend on measurement accuracies but also on the actual size and density of the exoplanet. We argue that precise observations of stellar elemental abundances are central in order to place constraints on planetary bulk composition and to reduce model degeneracy. [...]
    Astronomy and Astrophysics 02/2015; 577. DOI:10.1051/0004-6361/201424915 · 4.38 Impact Factor
  • Source
    J. Venturini · Y. Alibert · W. Benz · M. Ikoma ·
    [Show abstract] [Hide abstract]
    ABSTRACT: Context. Within the core accretion scenario of planetary formation, most simulations performed so far always assume the accreting envelope to have a solar composition. From the study of meteorite showers on Earth and numerical simulations, we know that planetesimals must undergo thermal ablation and disruption when crossing a protoplanetary envelope. Once the protoplanet has acquired an atmosphere, the primordial envelope gets enriched in volatiles and silicates from the planetesimals. This change of envelope composition during the formation can have a significant effect in the final atmospheric composition and on the formation timescale of giant planets. Aims. To investigate the physical implications of considering the envelope enrichment of protoplanets due to the disruption of icy planetesimals during their way to the core. Particular focus is placed on the effect on the critical core mass for envelopes where condensation of water can occur. Methods. Internal structure models are numerically solved with the implementation of updated opacities for all ranges of metallicities and the software CEA to compute the equation of state. CEA computes the chemical equilibrium for an arbitrary mixture of gases and allows the condensation of some species, including water. This means that the latent heat of phase transitions is consistently incorporated in the total energy budget. Results. The critical core mass is found to decrease significantly when an enriched envelope composition is considered in the internal structure equations. A particular strong reduction of the critical core mass is obtained for planets whose envelope metallicity is larger than Z=0.45 when the outer boundary conditions are suitable for condensation of water to occur in the top layers of the atmosphere. We show that this effect is qualitatively preserved when the atmosphere is out of chemical equilibrium.
    Astronomy and Astrophysics 02/2015; 576. DOI:10.1051/0004-6361/201424008 · 4.38 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We describe radial-velocity time series obtained by HARPS on the 3.60 m telescope in La Silla (ESO, Chile) over ten years and report the discovery of five new giant exoplanets in distant orbits; these new planets orbit the stars HD 564, HD 30669, HD 108341, and BD-114672. Their periods range from 492 to 1684 days, semi-major axes range from 1.2 to 2.69 AU, and eccentricities range from 0 to 0.85. Their minimum mass ranges from 0.33 to 3.5 Mjup. We also refine the parameters of two planets announced previously around HD 113538, based on a longer series of measurements. The planets have a period of 663+-8 and 1818+-25 days, orbital eccentricities of 0.14+-0.08 and 0.20+-0.04, and minimum masses of 0.36+-0.04 and 0.93+-0.06 Mjup. Finally, we report the discovery of a new hot-Jupiter planet around an active star, HD 103720; the planet has a period of 4.5557+-0.0001 days and a minimum mass of 0.62+-0.025 Mjup. We discuss the fundamental parameters of these systems and limitations due to stellar activity in quiet stars with typical 2m/s radial velocity precision.
    Astronomy and Astrophysics 12/2014; 576. DOI:10.1051/0004-6361/201424965 · 4.38 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: PLATO 2.0 is a mission candidate for ESA's M3 launch opportunity (2022/24). It addresses fundamental questions such as: How do planetary systems form and evolve? Are there other systems with planets like ours, able to develop life? The PLATO 2.0 instrument consists of 34 small aperture telescopes providing a wide field-of-view and a large photometric magnitude range. It targets bright stars in wide fields to detect and characterize planets down to Earth-size by photometric transits, whose masses can then be determined by ground-based radial-velocity follow-up measurements. Asteroseismology will be performed for stars <=11mag to obtain highly accurate stellar parameters, including masses and ages. The combination of bright targets and asteroseismology results in high accuracy for the bulk planet parameters: 2%, 4-10% and 10% for planet radii, masses and ages, respectively. The foreseen baseline observing strategy includes two long pointings (2-3 years) to detect and bulk characterize planets reaching into the habitable zone (HZ) of solar-like stars and an additional step-and-stare phase to cover in total about 50% of the sky. PLATO 2.0 will observe up to 1,000,000 stars and detect and characterize hundreds of small planets, and thousands of planets in the Neptune to gas giant regime out to the HZ. It will therefore provide the first large-scale catalogue of bulk characterized planets with accurate radii, masses, mean densities and ages. This catalogue will include Earth-like planets at intermediate orbital distances, where surface temperatures are moderate. Coverage of this parameter range with statistical numbers of bulk characterized planets is unique to PLATO 2.0. ...
    Experimental Astronomy 10/2014; 38:249. DOI:10.1007/s10686-014-9383-4 · 1.99 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: The CHaracterizing ExOPlanet Satellite (CHEOPS) is an ESA Small Mission whose launch is planned for the end of 2017. It is a Ritchey-Chretien telescope with a 320 mm aperture providing a FoV of 0.32 degrees, which will target nearby bright stars already known to host planets, and measure, through ultrahigh precision photometry, the radius of exo-planets, allowing to determine their composition. This paper will present the details of the AIV plan for a demonstration model of the CHEOPS Telescope with equivalent structure but different CTEs. Alignment procedures, needed GSEs and devised verification tests will be described and a path for the AIV of the flight model, which will take place at industries premises, will be sketched.
    SPIE Astronomical Telescopes + Instrumentation; 08/2014
  • Thibault Kuntzer · Andrea Fortier · Willy Benz ·
    [Show abstract] [Hide abstract]
    ABSTRACT: Stray light contamination reduces considerably the precision of photometric of faint stars for low altitude spaceborne observatories. When measuring faint objects, the necessity of coping with stray light contamination arises in order to avoid systematic impacts on low signal-to-noise images. Stray light contamination can be represented by a flat offset in CCD data. Mitigation techniques begin by a comprehensive study during the design phase, followed by the use of target pointing optimisation and post-processing methods. We present a code that aims at simulating the stray-light contamination in low-Earth orbit coming from reflexion of solar light by the Earth. StrAy Light SimulAtor (SALSA) is a tool intended to be used at an early stage as a tool to evaluate the effective visible region in the sky and, therefore to optimise the observation sequence. SALSA can compute Earth stray light contamination for significant periods of time allowing missionwide parameters to be optimised (e.g. impose constraints on the point source transmission function (PST) and/or on the altitude of the satellite). It can also be used to study the behaviour of the stray light at different seasons or latitudes. Given the position of the satellite with respect to the Earth and the Sun, SALSA computes the stray light at the entrance of the telescope following a geometrical technique. After characterising the illuminated region of the Earth, the portion of illuminated Earth that affects the satellite is calculated. Then, the flux of reflected solar photons is evaluated at the entrance of the telescope. Using the PST of the instrument, the final stray light contamination at the detector is calculated. The analysis tools include time series analysis of the contamination, evaluation of the sky coverage and an objects visibility predictor. Effects of the South Atlantic Anomaly and of any shutdown periods of the instrument can be added. Several designs or mission concepts can be easily tested and compared. The code is not thought as a stand-alone mission designer. Its mandatory inputs are a time series describing the trajectory of the satellite and the characteristics of the instrument. This software suite has been applied to the design and analysis of CHEOPS (CHaracterizing ExOPlanet Satellite). This mission requires very high precision photometry to detect very shallow transits of exoplanets. Different altitudes and characteristics of the detector have been studied in order to find the best parameters, that reduce the effect of contamination.
    SPIE Astronomical Telescopes + Instrumentation; 08/2014
  • [Show abstract] [Hide abstract]
    ABSTRACT: The CHaracterising ExOPlanet Satellite (CHEOPS) is a joint ESA-Switzerland space mission (expected to launch in 2017) dedicated to search for exoplanet transits by means of ultra-high precision photometry. CHEOPS will provide accurate radii for planets down to Earth size. Targets will mainly come from radial velocity surveys. The CHEOPS instrument is an optical space telescope of 30 cm clear aperture with a single focal plane CCD detector. The tube assembly is passively cooled and thermally controlled to support high precision, low noise photometry. The telescope feeds a re-imaging optic, which supports the straylight suppression concept to achieve the required Signal to Noise.
    SPIE Astronomical Telescopes + Instrumentation; 08/2014
  • [Show abstract] [Hide abstract]
    ABSTRACT: Spreading the PSF over a quite large amount of pixels is an increasingly used observing technique in order to reach extremely precise photometry, such as in the case of exoplanets searching and characterization via transits observations. A PSF top-hat profile helps to minimize the errors contribution due to the uncertainty on the knowledge of the detector flat field. This work has been carried out during the recent design study in the framework of the ESA small mission CHEOPS. Because of lack of perfect flat-fielding information, in the CHEOPS optics it is required to spread the light of a source into a well defined angular area, in a manner as uniform as possible. Furthermore this should be accomplished still retaining the features of a true focal plane onto the detector. In this way, for instance, the angular displacement on the focal plane is fully retained and in case of several stars in a field these look as separated as their distance is larger than the spreading size. An obvious way is to apply a defocus, while the presence of an intermediate pupil plane in the Back End Optics makes attractive to introduce here an optical device that is able to spread the light in a well defined manner, still retaining the direction of the chief ray hitting it. This can be accomplished through an holographic diffuser or through a lenslet array. Both techniques implement the concept of segmenting the pupil into several sub-zones where light is spread to a well defined angle. We present experimental results on how to deliver such PSF profile by mean of holographic diffuser and lenslet array. Both the devices are located in an intermediate pupil plane of a properly scaled laboratory setup mimicking the CHEOPS optical design configuration.
    SPIE Astronomical Telescopes + Instrumentation; 08/2014
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Solar and extrasolar planets are the subject of numerous studies aiming to determine their chemical composition and internal structure. In the case of extrasolar planets, the composition is important as it partly governs their potential habitability. Moreover, observational determination of chemical composition of planetary atmospheres are becoming available, especially for transiting planets. The present works aims at determining the chemical composition of planets formed in stellar systems of solar chemical composition. The main objective of this work is to provide valuable theoretical data for models of planet formation and evolution, and future interpretation of chemical composition of solar and extrasolar planets. We have developed a model that computes the composition of ices in planets in different stellar systems with the use of models of ice and planetary formation. We provide the chemical composition, ice/rock mass ratio and C:O molar ratio for planets in stellar systems of solar chemical composition. From an initial homogeneous composition of the nebula, we produce a wide variety of planetary chemical compositions as a function of the mass of the disk and distance to the star. The volatile species incorporated in planets are mainly composed of H2O, CO, CO2, CH3OH, and NH3. Icy or ocean planets have systematically higher values of molecular abundances compared to giant and rocky planets. Gas giant planets are depleted in highly volatile molecules such as CH4, CO, and N2 compared to icy or ocean planets. The ice/rock mass ratio in icy or ocean and gas giant planets is, respectively, equal at maximum to 1.01+-0.33 and 0.8+-0.5, and is different from the usual assumptions made in planet formation models, which suggested this ratio to be 2-3. The C:O molar ratio in the atmosphere of gas giant planets is depleted by at least 30% compared to solar value.
    Astronomy and Astrophysics 07/2014; 570. DOI:10.1051/0004-6361/201423431 · 4.38 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Solar and extrasolar comets and extrasolar planets are the subject of numerous studies in order to determine their chemical composition and internal structure. In the case of planetesimals, their compositions are important as they govern in part the composition of future planets. The present works aims at determining the chemical composition of icy planetesimals, believed to be similar to present day comets, formed in stellar systems of solar chemical composition. The main objective of this work is to provide valuable theoretical data on chemical composition for models of planetesimals and comets, and models of planet formation and evolution. We have developed a model that calculates the composition of ices formed during the cooling of the stellar nebula. Coupled with a model of refractory element formation, it allows us to determine the chemical composition and mass ratio of ices to rocks in icy planetesimals throughout in the protoplanetary disc. We provide relationships for ice line positions (for different volatile species) in the disc, and chemical compositions and mass ratios of ice relative to rock for icy planetesimals in stellar systems of solar chemical composition. From an initial homogeneous composition of the nebula, a wide variety of chemical compositions of planetesimals were produced as a function of the mass of the disc and distance to the star. Ices incorporated in planetesimals are mainly composed of H2O, CO, CO2, CH3OH, and NH3. The ice/rock mass ratio is equal to 1+-0.5 in icy planetesimals following assumptions. This last value is in good agreement with observations of solar system comets, but remains lower than usual assumptions made in planet formation models, taking this ratio to be of 2-3.
    Astronomy and Astrophysics 07/2014; 570. DOI:10.1051/0004-6361/201322207 · 4.38 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: The asteroid 4 Vesta was recently found to have two large impact craters near its south pole, exposing subsurface material. Modelling suggested that surface material in the northern hemisphere of Vesta came from a depth of about 20 kilometres, whereas the exposed southern material comes from a depth of 60 to 100 kilometres. Large amounts of olivine from the mantle were not seen, suggesting that the outer 100 kilometres or so is mainly igneous crust. Here we analyse the data on Vesta and conclude that the crust–mantle boundary (or Moho) is deeper than 80 kilometres.
    Nature 07/2014; 511(7509):303. DOI:10.1038/nature13499 · 41.46 Impact Factor
  • Source
    W. Benz · S. Ida · Y. Alibert · D. N. C. Lin · C. Mordasini ·
    [Show abstract] [Hide abstract]
    ABSTRACT: With the increasing number of exoplanets discovered, statistical properties of the population as a whole become unique constraints on planet formation models provided a link between the description of the detailed processes playing a role in this formation and the observed population can be established. Planet population synthesis provides such a link. The approach allows to study how different physical models of individual processes (e.g., proto-planetary disc structure and evolution, planetesimal formation, gas accretion, migration, etc.) affect the overall properties of the population of emerging planets. By necessity, planet population synthesis relies on simplified descriptions of complex processes. These descriptions can be obtained from more detailed specialised simulations of these processes. The objective of this chapter is twofold: 1) provide an overview of the physics entering in the two main approaches to planet population synthesis and 2) present some of the results achieved as well as illustrate how it can be used to extract constraints on the models and to help interpret observations.
  • [Show abstract] [Hide abstract]
    ABSTRACT: Abstract A scientific forum on "The Future Science of Exoplanets and Their Systems," sponsored by Europlanet (*) and the International Space Science Institute (ISSI) (†) and co-organized by the Center for Space and Habitability (CSH) (‡) of the University of Bern, was held during December 5 and 6, 2012, in Bern, Switzerland. It gathered 24 well-known specialists in exoplanetary, Solar System, and stellar science to discuss the future of the fast-expanding field of exoplanetary research, which now has nearly 1000 objects to analyze and compare and will develop even more quickly over the coming years. The forum discussions included a review of current observational knowledge, efforts for exoplanetary atmosphere characterization and their formation, water formation, atmospheric evolution, habitability aspects, and our understanding of how exoplanets interact with their stellar and galactic environment throughout their history. Several important and timely research areas of focus for further research efforts in the field were identified by the forum participants. These scientific topics are related to the origin and formation of water and its delivery to planetary bodies and the role of the disk in relation to planet formation, including constraints from observations as well as star-planet interaction processes and their consequences for atmosphere-magnetosphere environments, evolution, and habitability. The relevance of these research areas is outlined in this report, and possible themes for future ISSI workshops are identified that may be proposed by the international research community over the coming 2-3 years. Key Words: Exoplanets-Disks-Planet formation-Stellar activity-Water origin-Water delivery-Habitability. Astrobiology 13, xxx-xxx.
    Astrobiology 09/2013; 13(9). DOI:10.1089/ast.2013.0997 · 2.59 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: We present 3-D simulations of impacts into asteroid 21 Lutetia, the subject of a fly-by by the European Space Agency's Rosetta mission to comet 67P/Churyumov-Gerasimenko. Using a 3-D shape model of the asteroid, impacts of sizes sufficient to reproduce the observed craters in Lutetia's North Polar Crater Cluster (NPCC) as observed by the OSIRIS experiment have been simulated using the smoothed particle hydrodynamics technique. The asteroid itself has been modelled both as a homogeneous body and as a body with an iron core.
    European Planetary Science Congress 2013, held 8-13 September in London, UK.; 09/2013
  • Source
    R Ziethe · O Nyffenegger · T Schröter · W Benz ·
    [Show abstract] [Hide abstract]
    ABSTRACT: The formation of a planetary core in terrestrial planets is still not well understood. It is commonly assumed that the separation of the iron and silicate phase happened rather rapidly. However, it is still unclear how and when this process took place. Recent re-search has lead to the conclusion that even relatively small bodies like asteroids can be differentiated. Merk et.al. (2002) showed that the interior is strongly heated due to the decay of 26 Al. Sometimes even the solidus temperature of silicate material is exceeded. Yoshino et. al. (2003) showed that heating within planetesimals by decay of short-lived radionuclides can increase the temperature sufficiently above the iron-sulphur melting point(≈ 1000 • C) and thus trigger the fast segregation of iron alloy. Therefore even small planetesimals (30km radius) are expected to be at least partially differentiated. Since these objects would have been most abundant in the terrestrial re-gion of the protoplanetary nebula (Kokubo, 2000), it is not unlikely that the Earth and other terrestial planets formed by accretion of previously differentiated planetesimals. From the above it is clear that planet formation and differentiation happened more or less simultaneously and therefore must also be considered simultaneously in a con-sistent theory. We propose a model in which the dynamics of planetary accretion and core accretion are made consistent. The timescale for differentiation of planetesimals by sinking of iron droplets is calculated for bodies of different sizes and compared to the typical collision timescale involving these planetesimals. We argue that by the time (or equivalently size of planetesimals) the two timescale become equal, planetary growth proceeds with differentiated bodies only.
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The formation of a planetary core in terrestrial planets is still not well understood. Since planet differentiation already sets in during planet formation both mechanisms should also be considered simultaneously in a consistent theory. We propose a model in which the dynamics of planetary accre-tion and core formation are made consistent. The timescale for iron silicate segregation is computed for bodies of dif-ferent sizes and compared to the typical collision timescale involving these planetesimals. We argue that by the time (or equivalently size of planetesimals) the two timescales be-come equal, planetary growth proceeds with differentiated bodies only.
    EPSC 2008; 08/2013

Publication Stats

9k Citations
1,110.87 Total Impact Points


  • 1998-2015
    • Universität Bern
      • • Physics Institute
      • • Space Research & Planetary Sciences Division
      Berna, Bern, Switzerland
    • University of California, Santa Cruz
      Santa Cruz, California, United States
  • 2010
    • University of Porto
      • Departamento de Física e Astronomia
      Oporto, Porto, Portugal
  • 2009
    • Pierre and Marie Curie University - Paris 6
      • Institut d'astrophysique de Paris
      Paris, Ile-de-France, France
  • 1988-2006
    • Harvard-Smithsonian Center for Astrophysics
      • Smithsonian Astrophysical Observatory
      Cambridge, Massachusetts, United States
  • 2005
    • Loyola University Maryland
      Baltimore, Maryland, United States
    • French National Centre for Scientific Research
      Lutetia Parisorum, Île-de-France, France
  • 2003
    • The University of Edinburgh
      • School of Mathematics
      Edinburgh, Scotland, United Kingdom
  • 2002
    • University of Maryland, College Park
      • Department of Astronomy
      CGS, Maryland, United States
  • 1999
    • Max Planck Institute for Astronomy
      Heidelburg, Baden-Württemberg, Germany
  • 1992-1998
    • The University of Arizona
      • Department of Planetary Sciences
      Tucson, Arizona, United States
  • 1993
    • United States Naval Observatory
      Washington, Maine, United States
  • 1986-1992
    • Los Alamos National Laboratory
      • • Theoretical Division
      • • Applied Theoretical Physics Division
      Лос-Аламос, California, United States