P. Mathias

Research Institute in Astrophysics and Planetology, Toulouse, Midi-Pyrenees, France

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Publications (77)74.12 Total impact

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    Dataset: aa5408-06
  • Article: Understanding the dynamical structure of pulsating stars: The Baade-Wesselink projection factor of the delta Scuti stars AI Vel and beta Cas
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    ABSTRACT: Aims. The Baade-Wesselink method of distance determination is based on the oscillations of pulsating stars. The key parameter of this method is the projection factor used to convert the radial velocity into the pulsation velocity. Our analysis was aimed at deriving for the first time the projection factor of delta Scuti stars, using high-resolution spectra of the high-amplitude pulsator AI Vel and of the fast rotator beta Cas. Methods. The geometric component of the projection factor (i.e. p0) was calculated using a limb-darkening model of the intensity distribution for AI Vel, and a fast-rotator model for beta Cas. Then, using SOPHIE/OHP data for beta Cas and HARPS/ESO data for AI Vel, we compared the radial velocity curves of several spectral lines forming at different levels in the atmosphere and derived the velocity gradient associated to the spectral-line-forming regions in the atmosphere of the star. This velocity gradient was used to derive a dynamical projection factor p. Results. We find a flat velocity gradient for both stars and finally p = p0 = 1.44 for AI Vel and p = p0 = 1.41 for beta Cas. By comparing Cepheids and delta Scuti stars, these results bring valuable insights into the dynamical structure of pulsating star atmospheres. They suggest that the period-projection factor relation derived for Cepheids is also applicable to delta Scuti stars pulsating in a dominant radial mode.
    01/2013;
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    Article: The CoRoT B-type binary HD50230: a prototypical hybrid pulsator with g-mode period and p-mode frequency spacings
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    ABSTRACT: B-type stars are promising targets for asteroseismic modelling, since their frequency spectrum is relatively simple. We deduce and summarise observational constraints for the hybrid pulsator, HD50230, earlier reported to have deviations from a uniform period spacing of its gravity modes. The combination of spectra and a high-quality light curve measured by the CoRoT satellite allow a combined approach to fix the position of HD50230 in the HR diagram. To describe the observed pulsations, classical Fourier analysis was combined with short-time Fourier transformations and frequency spacing analysis techniques. Visual spectra were used to constrain the projected rotation rate of the star and the fundamental parameters of the target. In a first approximation, the combined information was used to interpret multiplets and spacings to infer the true surface rotation rate and a rough estimate of the inclination angle. We identify HD50230 as a spectroscopic binary and characterise the two components. We detect the simultaneous presence of high-order g modes and low-order p and g-modes in the CoRoT light curve, but were unable to link them to line profile variations in the spectroscopic time series. We extract the relevant information from the frequency spectrum, which can be used for seismic modelling, and explore possible interpretations of the pressure mode spectrum.
    04/2012;
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    Article: Pulsation spectrum of Delta Sct stars: the binary HD 50870 as seen with CoRoT and HARPS
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    ABSTRACT: Aims. We present the results obtained with the CoRoT satellite for HD 50870, a δ Sct star which was observed for 114.4 d. The aim of these observations was to evaluate the results obtained for HD 50844, the first δ Sct star monitored with CoRoT, on a longer time baseline. Methods. The 307,570 CoRoT datapoints were analysed with different techniques. The photometric observations were complemented over 15 nights of high-resolution spectroscopy with HARPS on a baseline of 25 d. These spectra were analysed to study the line profile variations and to derive the stellar physical parameters. Some uvby photometric observations were also obtained to better characterize the pulsation modes. Results. HD 50870 proved to be a low-amplitude, long-period spectroscopic binary system seen almost pole-on (i ≃ 21 o). The brighter component, which also has the higher rotational velocity (v sin i = 37.5 km s −1), is a δ Sct-type variable with a full light amplitude variation of about 0.04 mag. There is a dominant axisymmetric mode (17.16 d −1). Moreover, there are two groups of frequencies (about 19) in the intervals 6-9 and 13-18 d −1 , with amplitudes ranging from a few mmag to 0.3 mmag. After the detection of about 250 terms (corresponding to an amplitude of about 0.045 mmag) a flat plateau appears in the power spectrum in the low-frequency region up to about 35 d −1 . We were able to detect this plateau only thanks to the short cadence sampling of the CoRoT measurements (32 s). The density distribution vs. frequency of the detected frequencies seems rule out the possibility that this plateau is the result of a process with a continuum power spectrum. The spacings of the strongest modes suggest a quasi-periodic pattern. We failed to find a satisfactory seismic model that simultaneously matches the frequency range, the position in the HR diagram, and the quasi-periodic pattern interpreted as a large separation. Nineteen modes were detected spectroscopically from the line profile variations and associated to the photometric ones. Tentative ℓ, m values have been attributed to the modes detected spectroscopically. Prograde as well as retrograde modes are present with ℓ values up to 9. There are no traces of variability induced by solar-like oscillations.
    04/2012;
  • Article: Strong interactions between g- and p-modes in the hybrid gamma Doradus-delta Scuti CoRoT star ID105733033
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    ABSTRACT: CoRoT ID 105733033 is an excellent example of hybrid pulsators as it shows g- and p-modes with almost similar amplitudes in two clearly distinct frequency domains. Classical Fourier analysis allows the dectection of frequencies with an amplitude as small as 0.1 mmag up to 50c/d. The frequency spectrum of CoRoT ID 105733033 clearly consists of two distinct ranges, which are typical of gamma Doradus and delta Scuti pulsation. Focus was placed on the identification of linear combinations and frequencies due to the coupling between gamma Doradus and delta Scuti modes. We detect 198 gamma Doradus type frequencies in the range [0.25;4]c/d, of which 180 are not combination frequencies, and 24 of them are separated by a constant period-interval Delta P=0.03074d. According to the asymptotic theory, these 24 frequencies correspond to a series of g-modes of the same ell-degree and different radial orders n. We also detect 246 delta Scuti type frequencies in the range [10.1;63.4]c/d. The dominant frequency F=12.6759c/d was identified as the fundamental radial mode. Our most noteworthy result is that all the main gamma Doradus frequencies f_i are also detected in the delta Scuti domain as F +- f_i with four times smaller amplitudes. Once these frequencies were removed, only 59 can be considered as individual delta Scuti frequencies. A coupling between g- and p-modes is proposed to be a tool for detecting g-modes in the Sun, but this coupling has never yet been observed. Our present study may be valuable input to theoretical studies, addressing the mutual influence of g- and p-mode cavities and the deviation from classical theory. Furthermore, we identify a sequence of g-modes belonging to the same ell but with consecutive orders n.
    03/2012;
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    Article: The variability of the CoRoT target HD171834: gamma Dor pulsations and/or activity?
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    ABSTRACT: We present the preliminary results of a frequency and line-profile analysis of the CoRoT gamma Dor candidate HD171834. The data consist of 149 days of CoRoT light curves and a ground-based dataset of more than 1400 high-resolution spectra, obtained with six different instruments. Low-amplitude frequencies between 0 and 5 c/d, dominated by a frequency near 0.96 c/d and several of its harmonics, are detected. These findings suggest that HD171834 is not a mere gamma Dor pulsator and that stellar activity plays an important role in its variable behaviour. Based on CoRoT space data and on ground-based observations with ESO Telescopes at the La Silla Observatory under the ESO Large Programmes ESO LP 178.D-0361 and ESO LP 182.D-0356 (FEROS/2.2m and HARPS/3.6m), and data collected with FOCES/2.2m at the Centro Astronomico Hispano Aleman at Calar Alto, SOPHIE/1.93m at Observatoire de Haute Provence, FIES/NOT at Observatorio del Roque de los Muchachos, and HERCULES/1.0m at Mount John University Observatory.
    11/2011;
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    Article: The Kepler characterization of the variability among A- and F-type stars. I. General overview
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    ABSTRACT: The Kepler spacecraft is providing time series of photometric data with micromagnitude precision for hundreds of A-F type stars. We present a first general characterization of the pulsational behaviour of A-F type stars as observed in the Kepler light curves of a sample of 750 candidate A-F type stars. We propose three main groups to describe the observed variety in pulsating A-F type stars: gamma Dor, delta Sct, and hybrid stars. We assign 63% of our sample to one of the three groups, and identify the remaining part as rotationally modulated/active stars, binaries, stars of different spectral type, or stars that show no clear periodic variability. 23% of the stars (171 stars) are hybrid stars, which is a much larger fraction than what has been observed before. We characterize for the first time a large number of A-F type stars (475 stars) in terms of number of detected frequencies, frequency range, and typical pulsation amplitudes. The majority of hybrid stars show frequencies with all kinds of periodicities within the gamma Dor and delta Sct range, also between 5 and 10 c/d, which is a challenge for the current models. We find indications for the existence of delta Sct and gamma Dor stars beyond the edges of the current observational instability strips. The hybrid stars occupy the entire region within the delta Sct and gamma Dor instability strips, and beyond. Non-variable stars seem to exist within the instability strips. The location of gamma Dor and delta Sct classes in the (Teff,logg)-diagram has been extended. We investigate two newly constructed variables 'efficiency' and 'energy' as a means to explore the relation between gamma Dor and delta Sct stars. Our results suggest a revision of the current observational instability strips, and imply an investigation of other pulsation mechanisms to supplement the kappa mechanism and convective blocking effect to drive hybrid pulsations.
    07/2011;
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    Article: Kepler observations: Light shed on the hybrid γ Doradus – δ Scuti pulsation phenomenon
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    ABSTRACT: Through the observational study of stellar pulsations, the internal structure of stars can be probed and theoretical models can be tested. The main sequence -γ Doradus (Dor) and δ Scuti (Sct) stars with masses 1.2–2.5 M⊙ are particularly interesting for asteroseismic study. The -γ Dor stars pulsate in high-order gravity (g) modes, with pulsational periods of order of one day. The δ Sct stars, on the other hand, show low-order g and pressure (p) modes with periods of order of 2 hours. Theory predicts the existence of ‘hybrid’ stars, i.e. stars pulsating in both types of modes, in an overlap region between the instability strips of -γ Dor and δ Sct stars in the Hertzsprung-Russell diagram. Hybrid stars are particularly interesting as the two types of modes probe different regions of the stellar interior and hence provide complementary model constraints. Before the advent of Kepler, only a few hybrid stars had been confirmed. The Kepler satellite is providing a true revolution in the study of and search for hybrid stars. Analysis of the first 50 days of Kepler data of hundreds of -γ Dor and δ Sct candidates reveals extremely rich frequency spectra, with most stars showing frequencies in both the δ Sct and -γ Dor frequency range. As these results show that there are practically no pure δ Sct or -γ Dor pulsators, a new observational classification scheme is proposed by Grigahcène et al. (2010). We present their results and characterize 234 stars in terms of δ Sct, -γ Dor, δ Sct/-γ Dor or -γ Dor/δ Sct hybrids (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Astronomische Nachrichten 11/2010; 331(9‐10):989 - 992. · 1.01 Impact Factor
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    Article: An investigation of the close environment of beta Cep with the VEGA/CHARA interferometer
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    ABSTRACT: High-precision interferometric measurements of pulsating stars help to characterize their close environment. In 1974, a close companion was discovered around the pulsating star beta Cep using the speckle interferometry technique and features at the limit of resolution (20 milli-arcsecond or mas) of the instrument were mentioned that may be due to circumstellar material. Beta Cep has a magnetic field that might be responsible for a spherical shell or ring-like structure around the star as described by the MHD models. Using the visible recombiner VEGA installed on the CHARA long-baseline interferometer at Mt. Wilson, we aim to determine the angular diameter of beta Cep and resolve its close environment with a spatial resolution up to 1 mas level. Medium spectral resolution (R=6000) observations of beta Cep were secured with the VEGA instrument over the years 2008 and 2009. These observations were performed with the S1S2 (30m) and W1W2 (100m) baselines of the array. We investigated several models to reproduce our observations. A large-scale structure of a few mas is clearly detected around the star with a typical flux relative contribution of 0.23 +- 0.02. Our best model is a co-rotational geometrical thin ring around the star as predicted by magnetically-confined wind shock models. The ring inner diameter is 8.2 +- 0.8 mas and the width is 0.6 +- 0.7 mas. The orientation of the rotation axis on the plane of the sky is PA = 60 +- 1 deg, while the best fit of the mean angular diameter of beta Cep gives UD[V] = 0.22 +- 0.05 mas. Our data are compatible with the predicted position of the close companion of beta Cep. These results bring additional constraints on the fundamental parameters and on the future MHD and asteroseismological models of the star. Comment: Paper accepted for publication in A&A (in press)
    10/2010;
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    Article: Gamma Dor and Gamma Dor - Delta Sct Hybrid Stars In The CoRoT LRa01
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    ABSTRACT: A systematic search for gamma Dor and gamma Dor - delta Scuti hybrid pulsators was conducted on the CoRoT LRa01 Exo-archive yielding a total of 418 gamma Dor and 274 hybrid candidates. After an automatic jump correction 194 and 167 respectively, show no more obvious jumps and were investigated in more detail. For about 25\% of these candidates classification spectra from the Anglo-Australian Observatory (AAO) are available. The detailed frequency analysis and a check for combination frequencies together with spectroscopic information allowed us to identify I) 34 gamma Dor stars which show very different pulsation spectra where mostly two modes dominate. Furthermore, a search for regularities in their oscillation spectra allowed to derive recurrent period spacings for 5 of these gamma Dor stars. II) 25 clear hybrid pulsators showing frequencies in the gamma Dor and delta Sct domain and are of A-F spectral type. Comment: Proceedings of the 4th HELAS International Conference held in Lanzarote, 2010
    07/2010;
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    Article: Ground-based observations of Kepler asteroseismic targets
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    ABSTRACT: We present the ground-based activities within the different working groups of the Kepler Asteroseismic Science Consortium (KASC). The activities aim at the systematic characterization of the 5000+ KASC targets, and at the collection of ground-based follow-up time-series data of selected promising Kepler pulsators. So far, 36 different instruments at 31 telescopes on 23 different observatories in 12 countries are in use, and a total of more than 530 observing nights has been awarded. (Based on observations made with the Isaac Newton Telescope, William Herschel Telescope, Nordic Optical Telescope, Telescopio Nazionale Galileo, Mercator Telescope (La Palma, Spain), and IAC-80 (Tenerife, Spain). Also based on observations taken at the observatories of Sierra Nevada, San Pedro Martir, Vienna, Xinglong, Apache Point, Lulin, Tautenburg, Loiano, Serra la Nave, Asiago, McDonald, Skinakas, Pic du Midi, Mauna Kea, Steward Observatory, Mt Wilson, Bialkow Observatory of the Wroclaw University, Piszkesteto Mountain Station, Observatoire de Haute Provence, and Centro Astronomico Hispano Aleman at Calar Alto. Based on data from the AAVSO International Database.) Comment: 4 pages, Astronomische Nachrichten, HELASIV Conference, Lanzarote, February 2010, submitted
    03/2010;
  • Article: Hybrid γ Doradus-δ Scuti Pulsators: New Insights into the Physics of the Oscillations from Kepler Observations
    [show abstract] [hide abstract]
    ABSTRACT: Observations of the pulsations of stars can be used to infer their interior structure and test theoretical models. The main-sequence γ Doradus (Dor) and δ Scuti (Sct) stars with masses 1.2-2.5 M ☉ are particularly useful for these studies. The γ Dor stars pulsate in high-order g-modes with periods of order 1 day, driven by convective blocking at the base of their envelope convection zone. The δ Sct stars pulsate in low-order g- and p-modes with periods of order 2 hr, driven by the κ mechanism operating in the He II ionization zone. Theory predicts an overlap region in the Hertzsprung-Russell diagram between instability regions, where "hybrid" stars pulsating in both types of modes should exist. The two types of modes with properties governed by different portions of the stellar interior provide complementary model constraints. Among the known γ Dor and δ Sct stars, only four have been confirmed as hybrids. Now, analysis of combined Quarter 0 and Quarter 1 Kepler data for hundreds of variable stars shows that the frequency spectra are so rich that there are practically no pure δ Sct or γ Dor pulsators, i.e., essentially all of the stars show frequencies in both the δ Sct and the γ Dor frequency range. A new observational classification scheme is proposed that takes into account the amplitude as well as the frequency and is applied to categorize 234 stars as δ Sct, γ Dor, δ Sct/γ Dor or γ Dor/δ Sct hybrids.
    The Astrophysical Journal Letters 03/2010; 713(2):L192. · 5.53 Impact Factor
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    Article: Hybrid gamma Doradus - delta Scuti pulsators: New insights into the physics of the oscillations from Kepler observations
    [show abstract] [hide abstract]
    ABSTRACT: Observations of the pulsations of stars can be used to infer their interior structure and test theoretical models. The main sequence $\gamma$ Doradus (Dor) and $\delta$ Scuti (Sct) stars with masses 1.2-2.5 $M_{\sun}$ are particularly useful for these studies. The $\gamma$ Dor stars pulsate in high-order $g$ modes with periods of order 1 day, driven by convective blocking at the base of their envelope convection zone. The $\delta$ Sct stars pulsate in low-order $g$ and $p$ modes with periods of order 2 hours, driven by the $\kappa$ mechanism operating in the Heii ionization zone. Theory predicts an overlap region in the Hertzsprung-Russell diagram between instability regions, where 'hybrid' stars pulsating in both types of modes should exist. The two types of modes with properties governed by different portions of the stellar interior provide complementary model constraints. Among the known $\gamma$ Dor and $\delta$ Sct stars, only four have been confirmed as hybrids. Now, analysis of combined Quarter 0 and Quarter 1 Kepler data for hundreds of variable stars shows that the frequency spectra are so rich that there are practically no pure $\delta$ Sct or $\gamma$ Dor pulsators, i.e. essentially all of the stars show frequencies in both the $\delta$ Sct and $\gamma$ Dor frequency range. A new observational classification scheme is proposed that takes into account the amplitude as well as the frequency, and is applied to categorize 234 stars as $\delta$ Sct, $\gamma$ Dor, $\delta$ Sct/$\gamma$ Dor or $\gamma$ Dor/$\delta$ Sct hybrids. Comment: 6 pages with 4 figures and 1 table - submitted to ApJL
    The Astrophysical Journal Letters 01/2010; 713:L197. · 5.53 Impact Factor
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    Article: CoRoT photometry and high‐resolution spectroscopy of the interacting eclipsing binary AU Monocerotis★
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    ABSTRACT: Analyses of very accurate CoRoT space photometry, past Johnson V photoelectric photometry and high-resolution echelle spectra led to the determination of improved and consistent fundamental stellar properties of both components of AU Monocerotis. We derived new, accurate ephemerides for both the orbital motion (with a period of ) and the long-term, overall brightness variation (with a period of ) of this strongly interacting Be + G semi-detached binary. It is shown that this long-term variation must be due to attenuation of the total light by some variable circumbinary material. We derived the binary mass ratio MG/MB= 0.17 ± 0.03 based on the assumption that the G-type secondary fills its Roche lobe and rotates synchronously. Using this value of the mass ratio as well as the radial velocities of the G-star, we obtained a consistent light curve model and improved estimates of the stellar masses, radii, luminosities and effective temperatures. We demonstrate that the observed lines of the B-type primary may not be of photospheric origin. We also discover rapid and periodic light changes visible in the high-quality residual CoRoT light curves. AU Mon is put into perspective by a comparison with known binaries exhibiting long-term cyclic light changes.
    Monthly Notices of the Royal Astronomical Society 12/2009; 401(1):418 - 432. · 4.90 Impact Factor
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    Article: The tip of the iceberg: the frequency content of the Delta Sct star HD 50844 from CoRoT space photometry
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    ABSTRACT: It has been suggested that the detection of a wealth of very low amplitude modes in Delta Sct stars was only a matter of signal--to--noise ratio. Access to this treasure, impossible from the ground, is one of the scientific aims of the space mission CoRoT, developed and operated by CNES. This work presents the results obtained on HD 50844: the 140,016 datapoints allowed us to reach the level of 10^{-5} mag in the amplitude spectra. The frequency analysis of the CoRoT timeseries revealed hundreds of terms in the frequency range 0--30 d^{-1}. The initial guess that Delta Sct stars have a very rich frequency content is confirmed. The spectroscopic mode identification gives theoretical support since very high--degree modes (up to ell=14) are identified. We also prove that cancellation effects are not sufficient in removing the flux variations associated to these modes at the noise level of the CoRoT measurements. The ground--based observations indicate that HD 50844 is an evolved star that is slightly underabundant in heavy elements, located on the Terminal Age Main Sequence. The predominant term (f_1=6.92 d^{-1}) has been identified as the fundamental radial mode combining ground-based photometric and spectroscopic data. This work is based on observations made with ESO telescopes under the Large Programme LP 178.D-0361. Comment: Proceedings of the International Conference "Stellar Pulsation: Challenges for Theory and Observation", AIP, Vol.1170, p. 435
    10/2009;
  • Article: From the Dynamics of Cepheids to the Milky Way Rotation, and the Distance Scale Calibration
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    ABSTRACT: High precision spectroscopic measurements of 10 southern Galactic Cepheids with HARPS allowed us to analyse in detail the dynamical structure of their atmosphere and close environment. Our results have consequences on the distance scale calibration, and show that the rotation of the milky way is probably simpler than previously thought. However, the full understanding of spectral line asymmetries still requires the development of dedicated models.
    AIP Conference Proceedings. 09/2009; 1170(1):13-17.
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    Article: gamma Doradus stars in the COROT exoplanets fields: first inspection
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    ABSTRACT: We present here preliminary results concerning 32 stars identified as main gamma Doradus candidates by the COROT Variable Classifier (CVC) among the 4 first fields of the exoplanet CCDs. Comment: To appear in "Stellar Pulsation: Challenges for Theory and Observation", AIP
    09/2009;
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    Article: The asteroseismic ground-based observational counterpart of CoRoT
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    ABSTRACT: We present different aspects of the ground-based observational counterpart of the CoRoT satellite mission. We give an overview of the selected asteroseismic targets, the numerous instruments and observatories involved, and the first scientific results. Comment: 3 pages, 2 tables, 1 figure, to be published in the conference proceedings 'Stellar Pulsation: Challenges for Theory and Observation' (31 May - 5 June, Santa Fe, New Mexico, US), publishers: American Institute of Physics
    07/2009;
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    Article: Ground-based observations of the beta Cephei CoRoT main target HD 180642
    Communications in Asteroseismology 06/2009; 158:292.
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    Article: HD 50844: the new look of Delta Sct stars from CoRoT space photometry
    [show abstract] [hide abstract]
    ABSTRACT: It has also been suggested that the detection of a wealth of very low amplitude modes in Delta Sct stars was only a matter of signal--to--noise ratio. Access to this treasure, impossible from the ground, is one of the scientific aims of the space mission CoRoT, a space mission developed and operated by CNES. This work presents the results obtained on HD 50844: the 140,016 datapoints were analysed using independent approaches and several checks performed. A level of 10^{-5} mag was reached in the amplitude spectra of the CoRoT timeseries. The frequency analysis of the CoRoT timeseries revealed hundreds of terms in the frequency range 0--30 d^{-1}. All the cross--checks confirmed this new result. The initial guess that Delta Sct stars have a very rich frequency content is confirmed. The spectroscopic mode identification gives theoretical support since very high--degree modes (up to ell=14) are identified. We also prove that cancellation effects are not sufficient in removing the flux variations associated to these modes at the noise level of the CoRoT measurements. The ground--based observations indicate that HD 50844 is an evolved star that is slightly underabundant in heavy elements, located on the Terminal Age Main Sequence. Probably due to this unfavourable evolutionary status, no clear regular distribution is observed in the frequency set. The predominant term (f_1=6.92 d^{-1}) has been identified as the fundamental radial mode combining ground-based photometric and spectroscopic data. This work is also based on observations made with ESO telescopes under the ESO Large Programme LP178.D-0361 and on data collected at the Observatorio de Sierra Nevada, at the Observatorio Astronomico Nacional San Pedro Martir, and at the Piszkesteto Mountain Station of Konkoly Observatory. Comment: 10 pages, 11 figures. Accepted for publication in Astronomy & Astrophysics
    06/2009;

Institutions

  • 2012
    • Research Institute in Astrophysics and Planetology
      Toulouse, Midi-Pyrenees, France
  • 2005–2012
    • Centre national de la recherche scientifique
      • • Institut d'astrophysique spatiale (IAS)
      • • Observatoire de la Côte d'Azur (OCA)
      Paris, Ile-de-France, France
  • 2009
    • Radboud Universiteit Nijmegen
      Nijmegen, Provincie Gelderland, Netherlands
  • 1997–2009
    • Observatoire de la Côte d'Azur
      Grasse, Provence-Alpes-Cote d'Azur, France
  • 2008
    • Université de Nice - Sophia Antipolis
      Valbonne, Provence-Alpes-Cote d'Azur, France
  • 2007
    • Collège de France
      Paris, Ile-de-France, France
  • 2000
    • KU Leuven
      • Institute of Astronomy
      Leuven, VLG, Belgium