G. Fontaine

Université de Montréal, Montréal, Quebec, Canada

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Publications (475)

  • N. Giammichele · S. Charpinet · G. Fontaine · P. Brassard
    [Show abstract] [Hide abstract] ABSTRACT: We present a prescription for parametrizing the chemical profile in the core of white dwarfs in the light of the recent discovery that pulsation modes may sometimes be deeply confined in some cool pulsating white dwarfs. Such modes may be used as unique probes of the complicated chemical stratification that results from several processes that occurred in previous evolutionary phases of intermediate-mass stars. This effort is part of our ongoing quest for more credible and realistic seismic models of white dwarfs using static, parametrized equilibrium structures. Inspired from successful techniques developed in design optimization fields (such as aerodynamics), we exploit Akima splines for the tracing of the chemical profile of oxygen (carbon) in the core of a white dwarf model. A series of tests are then presented to better seize the precision and significance of the results that can be obtained in an asteroseismological context. We also show that the new parametrization passes an essential basic test, as it successfully reproduces the chemical stratification of a full evolutionary model.
    Article · Oct 2016
  • M. Latour · P. Chayer · E. M. Green · G. Fontaine
    [Show abstract] [Hide abstract] ABSTRACT: We present our current work on the spectral analysis of the hot sdO star Feige 34. We combine high S/N optical spectra and fully-blanketed non-LTE model atmospheres to derive its fundamental parameters (Teff, log g) and helium abundance. Our best fits indicate Teff =63 000 K, log g=6.0 and log N(He)/N(H)=-1.8. We also use available ultraviolet spectra (IUE and FUSE) to measure metal abundances. We find the star to be enriched in iron and nickel by a factor of ten with respect to the solar values, while lighter elements have subsolar abundances. The FUSE spectrum suggests that the spectral lines could be broadened by rotation.
    Article · Oct 2016
  • P. Dufour · S. Blouin · S. Coutu · [...] · G. Fontaine
    [Show abstract] [Hide abstract] ABSTRACT: We present the "Montreal White Dwarf Database" (MWDD), an accessible database with sortable/filterable table and interactive plots that will, when fully completed, allow the community to explore the physical properties of all white dwarfs ever analyzed by the Montreal group, as well as display data and analyses from the literature. We present its current capability and show how it will continuously be updated to instantly reflect improvements made on both the theoretical and observational fronts.
    Article · Oct 2016
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    A Gianninas · Brandon Curd · Gilles Fontaine · [...] · Mukremin Kilic
    [Show abstract] [Hide abstract] ABSTRACT: We report the discovery of pulsations in three mixed atmosphere, extremely low-mass white dwarf (ELM WD, M < 0.3M⊙) precursors. Following the recent discoveries of pulsations in both ELM and pre-ELM WDs, we targeted pre-ELM WDs with mixed H/He atmospheres with high-speed photometry. We find significant optical variability in all three observed targets with periods in the range 320–590 s, consistent in time-scale with theoretical predictions of p-mode pulsations in mixed-atmosphere ≈ 0.18 M⊙ He-core pre-ELM WDs. This represents the first empirical evidence that pulsations in pre-ELM WDs can only occur if a significant amount of He is present in the atmosphere. Future, more extensive, time-series photometry of the brightest of the three new pulsators offers an excellent opportunity to constrain the thickness of the surface H layer which regulates the cooling timescales for ELM WDs.
    Full-text available · Article · May 2016
  • N. Giammichele · G. Fontaine · P. Brassard · S. Charpinet
    [Show abstract] [Hide abstract] ABSTRACT: We present the second of a two-part seismic analysis of the bright, hot ZZ Ceti stars GD 165 and Ross 548. In this second part, we report the results of detailed searches in parameter space for identifying an optimal model for each star that can account well for the observed periods, while being consistent with the spectroscopic constraints derived in our first paper. We find optimal models for each target that reproduce the six observed periods well within ~0.3% on the average. We also find that there is a sensitivity on the core composition for Ross 548, while there is practically none for GD 165. Our optimal model of Ross 548, with its thin envelope, indeed shows weight functions for some confined modes that extend relatively deep into the interior, thus explaining the sensitivity of the period spectrum on the core composition in that star. In contrast, our optimal seismic model of its spectroscopic sibling, GD 165 with its thick envelope, does not trap/confine modes very efficiently, and we find weight functions for all six observed modes that do not extend into the deep core, hence accounting for the lack of sensitivity in that case. Furthermore, we exploit after the fact the observed multiplet structure that we ascribe to rotation. We are able to map the rotation profile in GD 165 (Ross 548) over the outermost ~20% (~5%) of its radius, and we find that the profile is consistent with solid-body rotation.
    Article · Mar 2016 · The Astrophysical Journal Supplement Series
  • S.K. Randall · A. Calamida · G. Fontaine · [...] · T.R. Marsh
    [Show abstract] [Hide abstract] ABSTRACT: We present an extensive survey for rapid pulsators among Extreme Horizontal Branch (EHB) stars in omega Cen. The observations performed consist of nearly 100 hours of time-series photometry, as well as low-resolution spectroscopy. We obtained photometry for some 300 EHB stars. Based on the spectroscopy, we derive reliable values of log g, Teff and log(N(He)/N(H)) for 38 targets, as well as estimates of the effective temperature for another nine targets. The survey uncovered a total of five rapid variables with multi-periodic oscillations between 85 and 125 s. Spectroscopically, they form a homogeneous group of hydrogen-rich subdwarf O stars clustered between 48,000 and 54,000 K. For each of the variables we are able to measure between two and three significant pulsations believed to constitute independent harmonic oscillations. In addition to the rapid variables, we found an EHB star with an apparently periodic luminosity variation of ~2700 s, which we tentatively suggest may be caused by ellipsoidal variations in a close binary. Using the overlapping photometry and spectroscopy sample we are able to map an empirical omega Cen instability strip. This can be directly compared to the pulsation driving predicted from the Montreal "second-generation" models. We find that the region where p-mode excitation occurs is bifurcated, and the well-known instability strip between 29,000-36,000 K where the rapid subdwarf B pulsators are found is complemented by a second one above 50,000 K. While significant challenges remain at the quantitative level, we believe that the same kappa-mechanism that drives the pulsations in hot B subdwarfs is also responsible for the excitation of the rapid oscillations observed in the omega Cen variables.
    Article · Feb 2016 · Astronomy and Astrophysics
  • N. Giammichele · G. Fontaine · P. Bergeron · [...] · G. Vauclair
    [Show abstract] [Hide abstract] ABSTRACT: We present the first of a two-part seismic analysis of the two bright hot ZZ Ceti stars GD 165 and Ross 548. In this first part, we report the results of frequency extraction exercises based on time-series data sets of exceptional quality. We uncovered up to 13 independent pulsation modes in GD 165, regrouped into six main frequency multiplets. These include 9 secure (signal-to-noise ratio, S/N > 4) detections and 4 possible ones (4 >= S/N >= 3). Likewise, we isolated 11 independent modes in Ross 548 (9 secure and 2 possible detections), also regrouped into 6 multiplets. The multiplet structure is likely caused by rotational splitting. We also provide updated estimates of the time-averaged atmospheric properties of these two pulsators in the light of recent developments on the front of atmospheric modeling for DA white dwarfs.
    Article · Dec 2015 · The Astrophysical Journal
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    P. -E. Tremblay · G. Fontaine · B. Freytag · [...] · P. Brassard
    [Show abstract] [Hide abstract] ABSTRACT: We present the first radiation magnetohydrodynamics simulations of the atmosphere of white dwarf stars. We demonstrate that convective energy transfer is seriously impeded by magnetic fields when the plasma-beta parameter, the thermal to magnetic pressure ratio, becomes smaller than unity. The critical field strength that inhibits convection in the photosphere of white dwarfs is in the range B = 1-50 kG, which is much smaller than the typical 1-1000 MG field strengths observed in magnetic white dwarfs, implying that these objects have radiative atmospheres. We have then employed evolutionary models to study the cooling process of high-field magnetic white dwarfs, where convection is entirely suppressed during the full evolution (B > 10 MG). We find that the inhibition of convection has no effect on cooling rates until the effective temperature (Teff) reaches a value of around 5500 K. In this regime, the standard convective sequences start to deviate from the ones without convection owing to the convective coupling between the outer layers and the degenerate reservoir of thermal energy. Since no magnetic white dwarfs are currently known at the low temperatures where this coupling significantly changes the evolution, effects of magnetism on cooling rates are not expected to be observed. This result contrasts with a recent suggestion that magnetic white dwarfs with Teff < 10,000 K cool significantly slower than non-magnetic degenerates.
    Full-text available · Article · Sep 2015 · The Astrophysical Journal
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    V. Van Grootel · G. Fontaine · P. Brassard · M.-A. Dupret
    [Show abstract] [Hide abstract] ABSTRACT: Aims. We aim to determine the theoretical instability strips of white dwarfs with diverse H and He content in their atmospheres, from a solar composition to a H-depleted atmosphere. Pulsators with mixed H-He atmospheres are indeed known to exist, and these are the white dwarfs in cataclysmic accreting systems of the GW Lib type. We thus also aim to determine the range of periods of excited pulsation modes, and to qualitatively compare these to the observed periods in GW Lib white dwarf pulsators. Methods. In the first full nonadiabatic stability analysis of pulsators of this kind, we applied a time-dependent convection treatment and an energy leakage argument to compute, for cooling models of white dwarfs with various masses and envelope compositions, the location of the blue and the red edges, as well as the properties of pulsation modes. Results. We find that our derived instability strips form a true continuum in the log g-Teff plane and that their individual location depends uniquely on the assumed atmospheric composition, from the solar composition models at low effective temperatures to the H-depleted models at much higher temperatures. Taking into account our previous results from the ZZ Ceti (pure H atmosphere) and V777 Her (pure He atmosphere) white dwarf pulsators, this implies that all of these instability domains are connected via the same fundamental driving mechanism. Applying our results to the case of white dwarf pulsators of the GW Lib type, we find that our theoretical instability strips can qualitatively account for all of the known cases. The computed range of periods of excited modes also compares qualitatively very well to the observed ones. Conclusions. The GW Lib pulsators are very similar in nature to ZZ Ceti and V777 Her white dwarfs. It is the diverse chemical compositions in their atmosphere and envelope that defines their specific pulsation properties. Beyond GW Lib pulsators, white dwarfs can sometimes exhibit mixed H-He atmospheres, such as in the recently found proto-He white dwarf pulsators. Our results open the way towards quantitative asteroseismology of these various kinds of white dwarfs.
    Full-text available · Article · Mar 2015 · Astronomy and Astrophysics
  • S. K. Randall · S. Bagnulo · E. Ziegerer · [...] · G. Fontaine
    [Show abstract] [Hide abstract] ABSTRACT: The intermediate Helium subdwarf B star LS IV$-$14$^\circ$116 is a unique object showing extremely peculiar atmospheric abundances as well as long-period pulsations that cannot be explained in terms of the usual opacity mechanism. One hypothesis invoked was that a strong magnetic field may be responsible. We discredit this possibility on the basis of FORS2 spectro-polarimetry, which allows us to rule out a mean longitudinal magnetic field down to 300 G. Using the same data, we derive the atmospheric parameters for LS IV$-$14$^\circ$116 to be $T_{\rm eff}$ = 31,150$\pm$111 K, $\log{g}$ = 5.88$\pm$0.02 and $\log{N(\rm He)/N(\rm H)}$ = $-$0.62$\pm$0.01. The high surface gravity in particular is at odds with the theory that LS IV$-$14$^\circ$116 has not yet settled onto the Helium Main Sequence, and that the pulsations are excited by an $\epsilon$ mechanism acting on the Helium-burning shells present after the main Helium flash. Archival UVES spectroscopy reveals LS IV$-$14$^\circ$116 to have a radial velocity of 149.1$\pm$2.1 km/s. Running a full kinematic analysis, we find that it is on a retrograde orbit around the Galactic centre, with a Galactic radial velocity component $U$=13.23$\pm$8.28 km/s and a Galactic rotational velocity component $V$=$-$55.56$\pm$22.13 km/s. This implies that LS IV$-$14$^\circ$116 belongs to the halo population, an intriguing discovery.
    Article · Feb 2015 · Astronomy and Astrophysics
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    [Show abstract] [Hide abstract] ABSTRACT: We present high-speed photometric observations of ZZ Ceti white dwarf candidates drawn from the spectroscopic survey of bright DA stars from the Villanova White Dwarf Catalog by Gianninas et al., and from the recent spectroscopic survey of white dwarfs within 40 parsecs of the Sun by Limoges et al. We report the discovery of six new ZZ Ceti pulsators from these surveys, and several photometrically constant DA white dwarfs, which we then use to refine the location of the ZZ Ceti instability strip.
    Full-text available · Article · Feb 2015
  • N. Giammichele · G. Fontaine · S. Charpinet · [...] · S. Greiss
    [Show abstract] [Hide abstract] ABSTRACT: We present the first self-consistent seismic analysis of a white dwarf star, GD 1212, in the Kepler2 field. We precisely establish the fundamental parameters of the star using the forward method based on physically sound models. We unravel the internal structure as well as the rotation profile of GD1212 deeper than in any other ZZCeti stars studied so far. This opens up interesting prospects for future analyses of the white dwarf pulsators monitored in the Kepler and Kepler2 fields.
    Article · Jan 2015 · The European Physical Journal Conferences
  • [Show abstract] [Hide abstract] ABSTRACT: A calibration of the mixing-length parameter in the local mixing-length theory (MLT) is presented for the lower part of the convection zone in pure-hydrogen atmosphere white dwarfs. The parameterization is performed from a comparison of 3D CO5BOLD simulations with a grid of 1D envelopes with a varying mixing-length parameter. In many instances, the 3D simulations are restricted to the upper part of the convection zone. The hydrodynamical calculations suggest, in those cases, that the entropy of the upflows does not change significantly from the bottom of the convection zone to regions immediately below the photosphere. We rely on this asymptotic entropy value, characteristic of the deep and adiabatically stratified layers, to calibrate 1D envelopes. The calibration encompasses the convective hydrogen-line (DA) white dwarfs in the effective temperature range 6000 < Teff (K) < 15,000 and the surface gravity range 7.0 < log g < 9.0. It is established that the local MLT is unable to reproduce simultaneously the thermodynamical, flux, and dynamical properties of the 3D simulations. We therefore propose three different parameterizations for these quantities. The resulting calibration can be applied to structure and envelope calculations, in particular for pulsation, chemical diffusion, and convective mixing studies. On the other hand, convection has no effect on the white dwarf cooling rates until there is a convective coupling with the degenerate core below Teff ~ 5000 K. In this regime, the 1D structures are insensitive to the MLT parameterization and converge to the mean 3D results, hence remain fully appropriate for age determinations.
    Article · Dec 2014 · The Astrophysical Journal
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    [Show abstract] [Hide abstract] ABSTRACT: HD76431 is a slow rotating post-HB star that shows an underabundance of helium by 0.5 dex relative to the solar value. These observational facts suggest that atomic diffusion could be active in its atmosphere. We have used the MMT and Bok spectra to estimate the atmospheric parameters of the target star using the model atmospheres and synthetic spectra calculated with TLUSTY and SYNSPEC. The derived values of the effective temperature, surface gravity, helium abundance are consistent with those obtained by Ramspeck et al. (2001b). It appears that NLTE effect are not important for HD76431. We have used Stokes I spectra from ESPaDOnS at CFHT to perform an abundance analysis and a search for observational evidence of vertical stratification of the abundance of certain elements. The results of our abundance analysis are in good agreement with previously published data with respect to average abundances. Our numerical simulations show that carbon and nitrogen reveal signatures of vertical abundance stratification in the atmosphere of HD76431. It appears that the carbon abundance increases toward the deeper atmospheric layers. Nitrogen also shows a similar behaviour, but in deeper atmospheric layers we obtain a significant dispersion for the estimates of its abundance. To our knowledge, this is the first demonstration of vertical abundance stratification of metals in a post-HB star and up to now it is the hottest star to show such stratification features. We also report the detection of two SiIII and one TiIII emission lines in the spectra of HD76431 that were not detected in previous studies.
    Full-text available · Article · Sep 2014 · Monthly Notices of the Royal Astronomical Society
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    [Show abstract] [Hide abstract] ABSTRACT: KIC10001893 is one out of 19 subdwarf-B (sdB) pulsators observed by the Kepler spacecraft in its primary mission. In addition to tens of pulsation frequencies in the g-mode domain, its Fourier spectrum shows three weak peaks at very low frequencies, which is too low to be explained in terms of g modes. The most convincing explanation is that we are seeing the orbital modulation of three Earth-size planets (or planetary remnants) in very tight orbits, which are illuminated by the strong stellar radiation. The orbital periods are P1=5.273, P2=7.807, and P3=19.48 hours, and the period ratios P2/P1=1.481 and P3/P2=2.495 are very close to the 3:2 and 5:2 resonances, respectively. One of the main pulsation modes of the star at 210.68 {\mu}Hz corresponds to the third harmonic of the orbital frequency of the inner planet, suggesting that we see, for the first time in an sdB star, g-mode pulsations tidally excited by a planetary companion. The extreme planetary system that emerges from the Kepler data is very similar to the recent discovery of two Earth-size planets orbiting the sdB pulsator KIC05807616 (Charpinet et al. 2011a).
    Full-text available · Article · Sep 2014 · Astronomy and Astrophysics
  • Marilyn Latour · Suzanna K. Randall · Gilles Fontaine · [...] · Pierre Brassard
    [Show abstract] [Hide abstract] ABSTRACT: Taking advantage of a recent FORS2/VLT spectroscopic sample of Extreme Horizontal Branch (EHB) stars in $\omega$ Cen, we isolate 38 spectra well suited for detailed atmospheric studies and determine their fundamental parameters ($T_{\rm eff}$, log $g$, and log $N$(He)/$N$(H)) using NLTE, metal line-blanketed models. We find that our targets can be divided into three groups: 6 stars are hot ($T_{\rm eff}$$\buildrel>\over\sim\ $ 45,000 K) H-rich subdwarf O stars, 7 stars are typical H-rich sdB stars ($T_{\rm eff}$$ \buildrel<\over\sim\ $35,000 K), and the remaining 25 targets at intermediate effective temperatures are He-rich (log $N$(He)/$N$(H)$ \buildrel>\over\sim\ $ $-$1.0) subdwarfs. Surprisingly and quite interestingly, these He-rich hot subdwarfs in $\omega$ Cen cluster in a narrow temperature range ($\sim$35,000 K to $\sim$40,000 K). We additionally measure the atmospheric carbon abundance and find a most interesting positive correlation between the carbon and helium atmospheric abundances. This correlation certainly bears the signature of diffusion processes - most likely gravitational settling impeded by stellar winds or internal turbulence - but also constrains possible formation scenarios proposed for EHB stars in $\omega$ Cen. For the He-rich objects in particular, the clear link between helium and carbon enhancement points towards a late hot flasher evolutionary history.
    Article · Sep 2014 · The Astrophysical Journal
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    M. Latour · G. Fontaine · E. M. Green · [...] · P. Chayer
    [Show abstract] [Hide abstract] ABSTRACT: As part of a multifaceted effort to better exploit the asteroseismological potential of the pulsating sdB star Feige 48, we present an improved spectroscopic analysis of that star based on new grids of NLTE, fully line-blanketed model atmospheres. To that end, we gathered four high signal-to-noise ratio time-averaged optical spectra of varying spectral resolutions from 1.0 Å to 8.7 Å, and we made use of the results of four independent studies to fix the abundances of the most important metals in the atmosphere of Feige 48. The mean atmospheric parameters we obtained from our four spectra of Feige 48 are: T eff = 29,850 ± 60 K, log g = 5.46 ± 0.01, and log N(He)/N(H) = –2.88 ± 0.02. We also modeled, for the first time, the He II line at 1640 Å from the STIS archive spectrum of the star, and with this line we found an effective temperature and a surface gravity that match well with the values obtained with the optical data. With some fine tuning of the abundances of the metals visible in the optical domain, we were able to achieve a very good agreement between our best available spectrum and our best-fitting synthetic one. Our derived atmospheric parameters for Feige 48 are in rather good agreement with previous estimates based on less sophisticated models. This underlines the relatively small effects of the NLTE approach combined with line blanketing in the atmosphere of this particular star, implying that the current estimates of the atmospheric parameters of Feige 48 are reliable and secure.
    Full-text available · Article · May 2014 · The Astrophysical Journal
  • E. Green · C. Johnson · S. Wallace · [...] · G. Fontaine
    [Show abstract] [Hide abstract] ABSTRACT: Compared to subdwarf B (sdB) stars, the evolutionary channels that produce subdwarf O (sdO) stars are not at all well understood. Various theories have been advanced to explain the existence of sdO stars and account for their observed properties. Masses of sdO stars are mostly unknown, because there seem to be very few sdO counterparts to the short-period binaries that are common among sdB stars and because none of the handful of known sdO pulsators are useful candidates for asteroseismic investigations. During a recent (negative) search for bright field counterparts of the rapid sdO pulsators in Omega Cen, we noticed that our precision light curves for many sdO stars sometimes exhibited very small, irregular variations on time scales of several minutes to several tens of minutes. Although the significance of the weakest variations is uncertain, repeated observations for two of these stars, one helium-rich sdO, PG 1427+196, and another helium-poor sdO, PG 1610+519, caught them unexpectedly dropping in luminosity by up to 0.05-0.10 mag for at least a couple of hours, during which their light flickered irregularly in a manner reminiscent of the light from accretion disks in cataclysmic variables. A similar luminosity decrease and flickering was observed in a helium-rich sdB binary, PG 1544+488. The light curves for these three stars suggest the presence of accretion disks analogous to those in in VY Scl stars. The small luminosity variations we observed in a number of other sdO stars indicate that they too could occasionally be capable of similar larger luminosity variations, and thus accretion disks might be associated with a significant number of sdO stars. However, the structure of such sdO systems is not at all clear.
    Article · Mar 2014
  • S. Charpinet · P. Brassard · V. Van Grootel · G. Fontaine
    [Show abstract] [Hide abstract] ABSTRACT: Long period B subdwarf (sdB) pulsators, when observed from space with the satellites CoRoT and Kepler, show particularly rich g-mode oscillation spectra with often hundreds of frequencies. In many of these pulsation spectra, regularities in the observed period distributions typical of high order g-modes in chemically homogeneous stars have been reported. This led to a claim that sdB stars could be much less chemically stratified than previously thought. In this paper, we show that such an interpretation is unfounded. We reinvestigate trapping effects on g-modes in sdB stars in view of current observations and show that "standard" stratified models can also produce nearly quasi-constant period spacings in the low frequency range which are comparable to those observed in the g-mode spectra of these stars.
    Article · Mar 2014
  • M. Latour · G. Fontaine · P. Chayer · [...] · E. Green
    [Show abstract] [Hide abstract] ABSTRACT: We present a detailed analysis of the UV spectrum of the calibration star BD+28°4211 using high-quality spectra obtained with the HST and FUSE satellites. To this aim, we compare quantitatively the observed data with model spectra obtained from state-of-the-art non-LTE metal line-blanketed model atmospheres and synthetic spectra calculated with TLUSTY and SYNSPEC. We thus determine in a self-consistent way the abundances of 11 elements with well-defined lines in the UV. The derived abundances range from about solar to 1/10 solar and the overall quality of the derived spectral fits is very satisfying. Our analysis can be used to constrain rather tightly the effective temperature of BD+28°4211 to a value of Teff = 82,000±5000 K. We also estimate conservatively that its surface gravity falls in the range log g = 6.2-0.1+0.3. Assuming that the Hipparcos measurement for BD+28°4211 is fully reliable and that our model atmospheres are reasonably realistic, we can reconcile our spectroscopic constraints with the available parallax measurement only if the mass of BD+28°4211 is significantly less than the canonical value of 0.5 M☉ for a representative post-EHB star.
    Article · Mar 2014

Publication Stats

9k Citations


  • 1970-2015
    • Université de Montréal
      • Department of Physics
      Montréal, Quebec, Canada
  • 2002-2013
    • Université du Québec à Montréal
      • Department of Music
      Montréal, Quebec, Canada
  • 2012
    • Fonds de la Recherche Scientifique (FNRS)
      Bruxelles, Brussels Capital Region, Belgium
  • 2010
    • University of Toulouse
      Tolosa de Llenguadoc, Midi-Pyrénées, France
  • 2009
    • The University of Arizona
      • Department of Astronomy
      Tucson, Arizona, United States
  • 2006
    • University of Victoria
      • Department of Physics and Astronomy
      Victoria, British Columbia, Canada
  • 2005
    • Friedrich-Alexander Universität Erlangen-Nürnberg
      Erlangen, Bavaria, Germany
  • 1998
    • Iowa State University
      • Department of Physics and Astronomy
      Ames, Iowa, United States
    • University of California, Berkeley
      Berkeley, California, United States
  • 1987
    • University of Rochester
      • Department of Physics and Astronomy
      Rochester, New York, United States
  • 1979-1982
    • The University of Western Ontario
      • Department of Physics and Astronomy
      London, Ontario, Canada