References of "Van Grootel, Valérie"
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See detailKepler detection of a new extreme planetary system orbiting the subdwarf-B pulsator KIC 10001893
Silvotti, R.; Charpinet, S.; Green, E.M. et al

in Astronomy and Astrophysics (in press)

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See detailBasic Principles of White Dwarf Asteroseismology
Fontaine, Gilles; Brassard, Pierre; Charpinet, Stéphane et al

in Napiwotzki, R.; Burleigh, M. (Eds.) The White Dwarfs Stars (in press)

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See detailThe soundtrack of RR Lyrae in Omega Cen at high-frequency
Calamida, A.S.; Randall, S.K.; Monelli, M. et al

in Memorie della Società Astronomica Italiana : Journal of the Italian Astronomical Society (in press)

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See detailThe PLATO 2.0 Mission
Rauer, H.; Catala, C.; Aerts, C. et al

in Experimental Astronomy (2014)

PLATO 2.0 has recently been selected for ESA’s M3 launch opportunity (2022/24). Providing accurate key planet parameters (radius, mass, density and age) in statistical numbers, it addresses fundamental ... [more ▼]

PLATO 2.0 has recently been selected for ESA’s M3 launch opportunity (2022/24). Providing accurate key planet parameters (radius, mass, density and age) in statistical numbers, it addresses fundamental questions such as: How do planetary systems form and evolve? Are there other systems with planets like ours, including potentially habitable planets? The PLATO 2.0 instrument consists of 34 small aperture telescopes (32 with 25 s readout cadence and 2 with 2.5 s candence) providing a wide field-of-view (2232 deg 2) and a large photometric magnitude range (4–16 mag). It focusses on bright (4–11 mag) 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 these bright stars 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 planned 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 terrestrial 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. The PLATO 2.0 catalogue allows us to e.g.: - complete our knowledge of planet diversity for low-mass objects, - correlate the planet mean density-orbital distance distribution with predictions from planet formation theories,- constrain the influence of planet migration and scattering on the architecture of multiple systems, and - specify how planet and system parameters change with host star characteristics, such as type, metallicity and age. The catalogue will allow us to study planets and planetary systems at different evolutionary phases. It will further provide a census for small, low-mass planets. This will serve to identify objects which retained their primordial hydrogen atmosphere and in general the typical characteristics of planets in such low-mass, low-density range. Planets detected by PLATO 2.0 will orbit bright stars and many of them will be targets for future atmosphere spectroscopy exploring their atmosphere. Furthermore, the mission has the potential to detect exomoons, planetary rings, binary and Trojan planets. The planetary science possible with PLATO 2.0 is complemented by its impact on stellar and galactic science via asteroseismology as well as light curves of all kinds of variable stars, together with observations of stellar clusters of different ages. This will allow us to improve stellar models and study stellar activity. A large number of well-known ages from red giant stars will probe the structure and evolution of our Galaxy. Asteroseismic ages of bright stars for different phases of stellar evolution allow calibrating stellar age-rotation relationships. Together with the results of ESA’s Gaia mission, the results of PLATO 2.0 will provide a huge legacy to planetary, stellar and galactic science. [less ▲]

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See detailThe instability strip of ZZ Ceti white dwarfs
Van Grootel, Valérie ULg; Fontaine, G.; Brassard, P. et al

Conference (2014, August)

The determination of the location of the theoretical ZZ Ceti instability strip in the log g − Teff diagram has remained a challenge over the years, due to the lack of a suitable treatment for convection ... [more ▼]

The determination of the location of the theoretical ZZ Ceti instability strip in the log g − Teff diagram has remained a challenge over the years, due to the lack of a suitable treatment for convection in these stars. We report here a detailed stability survey over the whole ZZ Ceti regime, including the low and extremely low masses. We computed to this aim 29 evolutionary sequences of DA models with various masses, chemical layering, and core compositions. These models are characterized by the so- called ML2/α=1.0 convective efficiency and take into account the important feedback effect of convection on the atmospheric structure. We computed pulsation spectra for these models with the Liège nonadiabatic pulsation code MAD, which is the only one to conveniently incorporate a full time-dependent convection treatment and, thus, provides the best available description of the blue edge of the instability strip. On the other hand, given the failure of all nonadiabatic codes to account properly for the red edge of the strip, including MAD, we tested the idea that the red edge is due to energy leakage through the atmosphere. Using this approach, we found that our theoretical ZZ Ceti instability strip accounts remarkably well for the boundaries of the empirical strip. [less ▲]

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See detailA First Look at the Nonadiabatic Properties of Pulsating Accreting White Dwarfs of the GW Lib Type
Van Grootel, Valérie ULg; Fontaine, G.; Brassard, P. et al

Poster (2014, August)

We present results of a detailed stability survey of the pulsation properties of accreting white dwarfs of the GW Lib type. This is based on several state-of-the- art white dwarf evolutionary sequences ... [more ▼]

We present results of a detailed stability survey of the pulsation properties of accreting white dwarfs of the GW Lib type. This is based on several state-of-the- art white dwarf evolutionary sequences with varying envelope compositions, from pure hydrogen to pure helium. Using the same tools as in Van Grootel et al. (2013), where we have presented the first consistent view of the ZZ Ceti instability strip, we have mapped the GW Lib instability strip over the effective temperature-surface gravity plane, and as a function of envelope composition. We find that the location of the GW Lib instability domain is a strong and continuous function of the assumed envelope composition. We can accomodate all of the known GW Lib pulsators in various strips according to their atmospheric compositions. [less ▲]

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See detailWASP-117b: a 10-day-period Saturn in an eccentric and misaligned orbit
Lendl, Monika ULg; Triaud, A. H. M. J.; Anderson, D. R. et al

in Astronomy and Astrophysics (2014), 568

We report the discovery of WASP-117b, the first planet with a period beyond 10 days found by the WASP survey. The planet has a mass of M_p = 0.2755 (+/-0.0090) M_jup, a radius of R_p = 1.021 (-0.065 +0 ... [more ▼]

We report the discovery of WASP-117b, the first planet with a period beyond 10 days found by the WASP survey. The planet has a mass of M_p = 0.2755 (+/-0.0090) M_jup, a radius of R_p = 1.021 (-0.065 +0.076) R_jup and is in an eccentric (e = 0.302 +/-0.023), 10.02165 +/- 0.00055 d orbit around a main-sequence F9 star. The host star's brightness (V=10.15 mag) makes WASP-117 a good target for follow-up observations, and with a planetary equilibrium temperature of T_eq = 1024 (-26 +30) K and a low planetary density (rho_p = 0.259 (-0.048 +0.054) rho_jup) it is one of the best targets for transmission spectroscopy among planets with periods around 10 days. From a measurement of the Rossiter-McLaughlin effect, we infer a projected angle between the planetary orbit and stellar spin axes of beta = -44 (+/-11) deg, and we further derive an orbital obliquity of psi = 69.5 (+3.6 -3.1) deg. Owing to the large orbital separation, tidal forces causing orbital circularization and realignment of the planetary orbit with the stellar plane are weak, having had little impact on the planetary orbit over the system lifetime. WASP-117b joins a small sample of transiting giant planets with well characterized orbits at periods above ~8 days. [less ▲]

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See detailHD 97658 and its super-Earth. Spitzer & MOST transit analysis and modeling of the host star
Van Grootel, Valérie ULg; Gillon, Michaël ULg; Valencia, D. et al

Conference (2014, July)

Super-Earths transiting nearby bright stars are key objects that simultaneously allow for accurate measurements of both their mass and radius, providing essential constraints on their internal composition ... [more ▼]

Super-Earths transiting nearby bright stars are key objects that simultaneously allow for accurate measurements of both their mass and radius, providing essential constraints on their internal composition. We present here the confirmation, based on Spitzer transit observations, that the super-Earth HD 97658 b transits its host star. HD 97658 is a low-mass ($M_*=0.77\pm0.05\,M_{\odot}$) K1 dwarf, as determined from the Hipparcos parallax and stellar evolution modeling. To constrain the planet parameters, we carry out Bayesian global analyses of Keck-HIRES radial velocities, and MOST and Spitzer photometry. HD 97658 b is a massive ($M_P=7.55^{+0.83}_{-0.79} M_{\oplus}$) and large ($R_{P} = 2.247^{+0.098}_{-0.095} R_{\oplus}$ at 4.5 $\mu$m) super-Earth. We investigate the possible internal compositions for HD 97658 b. Our results indicate a large rocky component, by at least 60% by mass, and very little H-He components, at most 2% by mass. We also discuss how future asteroseismic observations can improve the knowledge of the HD 97658 system, in particular by constraining its age. Orbiting a bright host star, HD 97658 b will be a key target for coming space missions TESS, CHEOPS, PLATO, and also JWST, to characterize thoroughly its structure and atmosphere. [less ▲]

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See detailPrecision Asteroseismology of the Pulsating White Dwarf GD 1212 Using a Two-wheel-controlled Kepler Spacecraft
Hermes, J.J.; Charpinet, Stéphane; Barclay, Thomas et al

in Astrophysical Journal (2014), 789

We present a preliminary analysis of the cool pulsating white dwarf (WD) GD 1212, enabled by more than 11.5 days of space-based photometry obtained during an engineering test of the two-reaction-wheel ... [more ▼]

We present a preliminary analysis of the cool pulsating white dwarf (WD) GD 1212, enabled by more than 11.5 days of space-based photometry obtained during an engineering test of the two-reaction-wheel-controlled Kepler spacecraft. We detect at least 19 independent pulsation modes, ranging from 828.2-1220.8 s, and at least 17 nonlinear combination frequencies of those independent pulsations. Our longest uninterrupted light curve, 9.0 days in length, evidences coherent difference frequencies at periods inaccessible from the ground, up to 14.5 hr, the longest-period signals ever detected in a pulsating WD. These results mark some of the first science to come from a two-wheel-controlled Kepler spacecraft, proving the capability for unprecedented discoveries afforded by extending Kepler observations to the ecliptic. [less ▲]

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See detailTransit confirmation and improved stellar and planet parameters for the super-Earth HD 97658 b and its host star
Van Grootel, Valérie ULg; Gillon, Michaël ULg; Valencia, D. et al

in Astrophysical Journal (2014), 786

Super-Earths transiting nearby bright stars are key objects that simultaneously allow for accurate measurements of both their mass and radius, providing essential constraints on their internal composition ... [more ▼]

Super-Earths transiting nearby bright stars are key objects that simultaneously allow for accurate measurements of both their mass and radius, providing essential constraints on their internal composition. We present here the confirmation, based on Spitzer transit observations, that the super-Earth HD 97658 b transits its host star. HD 97658 is a low-mass ($M_*=0.77\pm0.05\,M_{\odot}$) K1 dwarf, as determined from the Hipparcos parallax and stellar evolution modeling. To constrain the planet parameters, we carry out Bayesian global analyses of Keck-HIRES radial velocities, and MOST and Spitzer photometry. HD 97658 b is a massive ($M_P=7.55^{+0.83}_{-0.79} M_{\oplus}$) and large ($R_{P} = 2.247^{+0.098}_{-0.095} R_{\oplus}$ at 4.5 $\mu$m) super-Earth. We investigate the possible internal compositions for HD 97658 b. Our results indicate a large rocky component, by at least 60% by mass, and very little H-He components, at most 2% by mass. We also discuss how future asteroseismic observations can improve the knowledge of the HD 97658 system, in particular by constraining its age. Orbiting a bright host star, HD 97658 b will be a key target for coming space missions TESS, CHEOPS, PLATO, and also JWST, to characterize thoroughly its structure and atmosphere. [less ▲]

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See detailTransiting planets from WASP-South, Euler and TRAPPIST: WASP-68 b, WASP-73 b and WASP-88 b, three hot Jupiters transiting evolved solar-type stars
Delrez, Laetitia ULg; Van Grootel, Valérie ULg; Anderson, D. R. et al

in Astronomy and Astrophysics (2014)

Using the WASP transit survey, we report the discovery of three new hot Jupiters, WASP-68 b, WASP-73 b and WASP-88 b. The planet WASP-68 bhas a mass of 0.95 ± 0.03 MJup, a radius of 1.24-0.06+0.10 RJup ... [more ▼]

Using the WASP transit survey, we report the discovery of three new hot Jupiters, WASP-68 b, WASP-73 b and WASP-88 b. The planet WASP-68 bhas a mass of 0.95 ± 0.03 MJup, a radius of 1.24-0.06+0.10 RJup, and orbits a V = 10.7 G0-type star (1.24 ± 0.03 M&sun; 1.69-0.06+0.11 R&sun;, Teff = 5911 ± 60 K) with a period of 5.084298 ± 0.000015 days. Its size is typical of hot Jupiters with similar masses. The planet WASP-73 bis significantly more massive (1.88-0.06+0.07 MJup) and slightly larger (1.16-0.08+0.12 RJup) than Jupiter. It orbits a V = 10.5 F9-type star (1.34-0.04+0.05 M&sun;, 2.07-0.08+0.19 R&sun;, Teff = 6036 ± 120 K) every 4.08722 ± 0.00022 days. Despite its high irradiation (~2.3 × 109 erg s-1 cm-2), WASP-73 b has a high mean density (1.20-0.30+0.26 rhoJup) that suggests an enrichment of the planet in heavy elements. The planet WASP-88 bis a 0.56 ± 0.08 MJuphot Jupiter orbiting a V = 11.4 F6-type star (1.45 ± 0.05 M&sun;, 2.08-0.06+0.12 R&sun;, Teff = 6431 ± 130 K) with a period of 4.954000 ± 0.000019 days. With a radius of 1.70-0.07+0.13 RJup, it joins the handful of planets with super-inflated radii. The ranges of ages we determine through stellar evolution modeling are 4.5-7.0 Gyr for WASP-68, 2.8-5.7 Gyr for WASP-73 and 1.8-4.3 Gyr for WASP-88. The star WASP-73 appears to be significantly evolved, close to or already in the subgiant phase. The stars WASP-68 and WASP-88 are less evolved, although in an advanced stage of core H-burning. [less ▲]

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See detailMode identification based on time-series spectrophotometry for the bright rapid sdB pulsator EC 01541-1409
Randall, Suzanna K; Fontaine, Gilles; Geier, Stephan et al

in Astronomy and Astrophysics (2014), 563

We present an analysis of time-resolved spectrophotometry gathered with FORS/VLT for the rapidly pulsating hot B subdwarf EC 01541-1409 with the aim of identifying the degree index ℓ of the larger ... [more ▼]

We present an analysis of time-resolved spectrophotometry gathered with FORS/VLT for the rapidly pulsating hot B subdwarf EC 01541-1409 with the aim of identifying the degree index ℓ of the larger amplitude modes. This mode identification can be extremely useful in detailed searches for viable asteroseismic models in parameter space, and can be crucial for testing the validity of a solution a posteriori. To achieve it, we exploit the ℓ-dependence of the monochromatic amplitude, phase, and velocity-to-amplitude ratio of a mode as a function of wavelength. We use the ℓ-sensitive phase lag between the flux perturbation and the radial velocity as an additional diagnostic tool. On this basis, we are able to unambiguously identify the dominant 140.5 s pulsation of our target as a radial mode, and the second-highest amplitude periodicity at 145.8 s as an ℓ = 2 mode. We further exploit the exceptionally high-sensitivity data that we gathered for the dominant mode to infer modal properties that are usually quite difficult to estimate in sdB pulsators, namely the physical values of the dimensionless radius, temperature, and surface gravity perturbations. [less ▲]

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See detailPulsations in white dwarf stars
Fontaine, Gilles; Bergeron, Pierre; Brassard, Pierre et al

in Proceedings of the International Astronomical Union (2014, February), 301

We first present a brief description of the six distinct families of pulsating white dwarfs that are now known. These are all opacity-driven pulsators showing low- to mid-order, low-degree gravity modes ... [more ▼]

We first present a brief description of the six distinct families of pulsating white dwarfs that are now known. These are all opacity-driven pulsators showing low- to mid-order, low-degree gravity modes. We then discuss some recent highlights that have come up in the field of white dwarf asteroseismology. [less ▲]

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See detailOrigin and Pulsation of Hot Subdwarfs
Randall, Suzanna K; Fontaine, Gilles; Charpinet, Stéphane et al

in Proceedings of the International Astronomical Union (2014, February), 301

We briefly introduce hot subdwarfs and their evolutionary status before discussing the different types of known pulsators in more detail. Currently, at least six apparently distinct types of variable are ... [more ▼]

We briefly introduce hot subdwarfs and their evolutionary status before discussing the different types of known pulsators in more detail. Currently, at least six apparently distinct types of variable are known among hot subdwarfs, encompassing p- as well as g-mode pulsators and objects in the Galactic field as well as in globular clusters. Most of the oscillations detected can be explained in terms of an iron opacity mechanism, and quantitative asteroseismology has been very successful for some of the pulsators. In addition to helping constrain possible evolutionary scenarios, studies focussing on stellar pulsations have also been used to infer planets and characterize the rotation of the host star. [less ▲]

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See detailG-mode trapping and period spacings in hot B subdwarf stars
Charpinet, Stéphane; Van Grootel, Valérie ULg; Brassard, Pierre et al

in Proceedings of the International Astronomical Union (2014, February), 301

Hot B subdwarfs (sdB) are hot and compact helium core burning stars of nearly half a solar mass that can develop pulsational instabilities driving acoustic and/or gravity modes. These evolved stars are ... [more ▼]

Hot B subdwarfs (sdB) are hot and compact helium core burning stars of nearly half a solar mass that can develop pulsational instabilities driving acoustic and/or gravity modes. These evolved stars are expected to be chemically stratified with an almost pure hydrogen envelope surrounding a helium mantle on top of a carbon/oxygen enriched core. However, the sdB stars pulsating in g-modes show regularities in their observed period distributions that, surprisingly (at first sight), are typical of the behavior of high order g-modes in chemically homogeneous (i.e., non-stratified) stars. This led to a claim that hot B subdwarfs could be much less chemically stratified than previously thought. Here, we reinvestigate trapping effects affecting g-modes in sdB stars. We show that standard stratified models of such stars can also produce nearly constant period spacings in the low frequency range similar to those found in g-mode spectra of sdB stars monitored with Kepler. [less ▲]

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See detailWASP-103b: a new planet at the edge of tidal disruption
Gillon, Michaël ULg; Anderson, D. R.; Collier-Cameron, A. et al

in Astronomy and Astrophysics (2014)

We report the discovery of WASP-103b, a new ultra-short-period planet (P=22.2 hr) transiting a 12.1 V-magnitude F8-type main-sequence star (1.22+-0.04 Msun, 1.44-0.03+0.05 Rsun, Teff = 6110+-160 K). WASP ... [more ▼]

We report the discovery of WASP-103b, a new ultra-short-period planet (P=22.2 hr) transiting a 12.1 V-magnitude F8-type main-sequence star (1.22+-0.04 Msun, 1.44-0.03+0.05 Rsun, Teff = 6110+-160 K). WASP-103b is significantly more massive (1.49+-0.09 Mjup) and larger (1.53-0.07+0.05 Rjup) than Jupiter. Its large size and extreme irradiation (around 9 10^9 erg/s/cm^2) make it an exquisite target for a thorough atmospheric characterization with existing facilities. Furthermore, its orbital distance is less than 20% larger than its Roche radius, meaning that it might be significantly distorted by tides and might experience mass loss through Roche-lobe overflow. It thus represents a new key object for understanding the last stage of the tidal evolution of hot Jupiters. [less ▲]

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See detailModeling the hot subdwarf PB 8783 by asteroseismology
Van Grootel, Valérie ULg; Charpinet, Stephane; Fontaine, Gilles et al

in Astronomical Society of the Pacific Conference Series (2014), 481

We present the preliminary seismic modeling of one of the hottest and most compact subdwarf pulsators, PB 8783 (EO Ceti). This is a well observed hot subdwarf star, including a 78 d campaign in white ... [more ▼]

We present the preliminary seismic modeling of one of the hottest and most compact subdwarf pulsators, PB 8783 (EO Ceti). This is a well observed hot subdwarf star, including a 78 d campaign in white light photometry that we carried out at Mount Bigelow, Arizona, during the fall 2007. PB 8783 has also been observed at length in spectroscopy, revealing a spectrum highly contaminated by a main sequence companion. It is extremely difficult to disentangle the contribution of the two components and, as a consequence of this, the exact nature of the hot subdwarf (sdB or sdO star) is undetermined. We propose here to test the two hypotheses by asteroseismology. Although the sdB possibility cannot be excluded, the pulsation modes observed in PB 8783 are much better accommodated in the case of an sdO star. [less ▲]

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See detailThe Mass Distribution of sdB Stars Derived by Asteroseismology and Other Means: Implications for Stellar Evolution Theory
Van Grootel, Valérie ULg; Charpinet, Stéphane; Fontaine, Gilles et al

in Astronomical Society of the Pacific Conference Series (2014), 481

Understanding the formation of sdB stars is one of the remaining challenges of stellar evolution theory. Competing scenarios have been proposed to account for the existence of such evolved objects. They ... [more ▼]

Understanding the formation of sdB stars is one of the remaining challenges of stellar evolution theory. Competing scenarios have been proposed to account for the existence of such evolved objects. They give quite different mass distributions for resulting sdB stars. Detailed asteroseismic analyses, including mass estimates, of 15 pulsating hot B subdwarfs have been published in the past decade. Masses have also been reliably determined by light curve modeling and spectroscopy for 7 sdB components of eclipsing or reflection binaries. We present here the empirical mass distribution of sdB stars on the basis of these samples. Implications are also briefly discussed. [less ▲]

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See detailMode Identification in Subdwarf B Stars from Multi-Wavelength Observations
Randall, Suzanna K; Fontaine, Gilles; Brassard, Pierre et al

in Astronomical Society of the Pacific Conference Series (2014), 481

We present several examples of partial mode identification for rapidly pulsating subdwarf B stars on the basis of multi-colour observations. Three targets (V391 Per, Balloon 090100001, and EC 11583−2708 ... [more ▼]

We present several examples of partial mode identification for rapidly pulsating subdwarf B stars on the basis of multi-colour observations. Three targets (V391 Per, Balloon 090100001, and EC 11583−2708) were analysed from multi-colour photometry, while studies were conducted from time-series spectrophotometry for two further stars (EC 20338−1925 and EC 01541−1409). In all cases, periodicities strongly dominating the frequency spectrum are associated with radial modes, indicating a clear hierarchy according to visibility when integrating over the visible disk of the star. [less ▲]

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See detailPrecision and Accuracy of Asteroseismology Applied to sdB stars Using the Forward Modeling Method
Charpinet, Stéphane; Van Grootel, Valérie ULg; Brassard, Pierre et al

in Astronomical Society of the Pacific Conference Series (2014), 481

Detailed seismic studies of hot B subdwarf (sdB) stars using the forward modeling approach provide measurements of their fundamental parameters at very interesting precisions. For instance, masses, radii ... [more ▼]

Detailed seismic studies of hot B subdwarf (sdB) stars using the forward modeling approach provide measurements of their fundamental parameters at very interesting precisions. For instance, masses, radii, and log g values derived this way are typically claimed at ∼ 1 − 2%, ∼ 0.5%, and ∼ 0.1 % precision, respectively. However, this method relies on still imperfect stellar models that contains various uncertainties associated with their inner structure and the underlying microphysics. A signature of these imperfections is the inability of current best-fit seismic models to reproduce all the observed oscillation frequencies at the precision of the observations. Therefore, the question of the accuracy (as opposed to the precision) of the derived parameters obtained from this approach is legitimate. Here, we revisit the question of precision and accuracy based on new, third generation, complete static models of sdB stars developed for asteroseismology and applied to the case of the eclipsing system PG 1336-018. This allows us to evaluate the reliability of the method and quantify the impact of various uncertainties in the stellar models on the derived stellar parameters. Finally, we discuss the intrinsic potential of asteroseismology for precise measurements of stellar parameters and show that we are far from having fully exploited this technique in terms of precision that can, in principle, be achieved. [less ▲]

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