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Journal Article•DOI•

Line-profile variations due to adiabatic non-radial pulsations in rotating stars. I. Observable characteristics of spheroidal modes

C Schrijvers1, J. H. Telting1, Conny Aerts2, E Ruymaekers, H.F. Henrichs1 •
University of Amsterdam1, Katholieke Universiteit Leuven2
01 Feb 1997-Astronomy & Astrophysics Supplement Series (EDP Sciences)-Vol. 121, Iss: 2, pp 343-368
TL;DR: In this paper, the surface-velocity field of a rotating, adiabatically pulsating star, which accounts for the effects of the Coriolis force, is considered.
Abstract: We present a useful formulation of the surface-velocity field of a rotating, adiabatically pulsating star, which accounts for the effects of the Coriolis force. We use this model to investigate the observable spectroscopic characteristics of non-radial pulsations. We calculate time series of absorption line profiles in a carefully chosen domain of parameter space. Only mono-periodic spheroidal modes are investigated; atmospheric changes due to the pulsation are neglected. The line-profile variations, as well as their behavior inferred from two well-defined diagnostics, are presented in two-dimensional parameter grids. We show that the intensity variations in time series of theoretical spectra, at each position in the line profile, cannot be described by a single sinusoid: at least one harmonic sinusoid needs to be included. Across the line profile the relative amplitudes and phases of these sinusoids vary independently. The blue-to-red phase difference found at the main pulsation frequency turns out to be an indicator of the degree , rather than the azimuthal order ; the phase difference of the variations with the first harmonic frequency is an indicator of . Hence, the evaluation of the variability at the harmonic frequency can improve the results derived from an analysis of observed line profiles. We find, that if line-profile variations at the line center dominate over the variations in the line wings, this does not give conclusive information on the ratio of the horizontal to the vertical pulsational surface motions. Tesseral modes, when observed at not too high inclinations, are as much capable of producing considerable line-profile variations as sectoral modes. We find that, within the limits of our model, the effects of rotation on the appearance of the line-profile variations are important for low-degree sectoral modes, and for the sub-class of the tesseral modes with an even number.

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Citations
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Journal Article•DOI•
A new method for the spectroscopic identification of stellar non-radial pulsation modes. I. The method and numerical tests

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W. Zima1•
Katholieke Universiteit Leuven1
21 Jun 2006-arXiv: Astrophysics
TL;DR: In this article, the Fourier parameter fit method was used to identify stellar radial and non-radial pulsation modes based on the high-resolution time-series spectroscopy of absorption-line profiles.
Abstract: We present the Fourier parameter fit method, a new method for spectroscopically identifying stellar radial and non-radial pulsation modes based on the high-resolution time-series spectroscopy of absorption-line profiles. In contrast to previous methods this one permits a quantification of the statistical significance of the computed solutions. The application of genetic algorithms in seeking solutions makes it possible to search through a large parameter space. The mode identification is carried out by minimizing chi-square, using the observed amplitude and phase across the line profile and their modeled counterparts. Computations of the theoretical line profiles are based on a stellar displacement field, which is described as superposition of spherical harmonics and that includes the first order effects of the Coriolis force. We made numerical tests of the method on a grid of different mono- and multi-mode models for 0 <= l <= 4 in order to explore its capabilities and limitations. Our results show that whereas the azimuthal order m can be unambiguously identified for low-order modes, the error of l is in the range of pm 1. The value of m can be determined with higher precision than with other spectroscopic mode identification methods. Improved values for the inclination can be obtained from the analysis of non-axisymmetric pulsation modes. The new method is ideally suited to intermediatley rotating Delta Scuti and Beta Cephei stars.

60 citations

Journal Article•DOI•
A high-resolution spectroscopy survey of β Cephei pulsations in bright stars

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J. H. Telting1, C. Schrijvers2, C. Schrijvers3, Ilya Ilyin, K. Uytterhoeven4, J. De Ridder4, Conny Aerts4, Conny Aerts5, H.F. Henrichs2 •
IAC1, University of Amsterdam2, Royal Netherlands Meteorological Institute3, Katholieke Universiteit Leuven4, Radboud University Nijmegen5
01 Jun 2006-Astronomy and Astrophysics
TL;DR: In this article, the authors present a study of absorption line-profile variations in early-B type near-main-sequence stars without emission lines, and they conclude that about half of the sample stars show evidence for line profile variations (LPV) and that it is likely that these LPV are of pulsational origin.
Abstract: We present a study of absorption line-profile variations in early-B type near-main-sequence stars without emission lines. We have surveyed a total of 171 bright stars using the Nordic Optical Telescope (NOTSA), William Herschel Telescope (ING) and Coude Auxiliary Telescope (ESO). Our sample contains 75% of all O9.5−B2.5 III-V non-emission-line stars brighter than 5.5 mag. We obtained high signal-to-noise, high-resolution spectra of the SiIII λ4560 triplet – for 125 stars of our sample we obtained more than one spectrum – and examined these for pulsational-like line-profile variations and/or structure. We conclude that about half of our sample stars show evidence for line-profile variations (LPV). We find evidence for LPV in about 65% of our sample stars brighter than V = 5.5. For stars with rotational broadening V sini ∼ 100 km s −1 , we find evidence for LPV in about 75% of the cases. We argue that it is likely that these LPV are of pulsational origin, and that hence more than half of the solar-neighbourhood O9.5-B2.5 III−V stars is pulsating in modes that can be detected with high-resolution spectroscopy. We detected LPV in 64 stars previously unknown to be pulsators, and label these stars as new β Cep candidates. We conclude that there is no obvious difference in incidence of (pulsational) LPV for early-B type near-main-sequence stars in binaries or in OB associations, with respect to single field stars.

55 citations

Additional excerpts

  • ...The surface temperature and surface velocity variations associated with non-radial pulsations will give rise to a pattern of moving bumps in the line profiles (Vogt & Penrod 1983; and e.g. Schrijvers et al. 1997)....

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Journal Article•DOI•
β Cep stars from a spectroscopic point of view

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Conny Aerts1, Peter De Cat1•
Katholieke Universiteit Leuven1
01 Jan 2003-Space Science Reviews
TL;DR: In this article, the authors present the current status of line profile-variation studies of β Cep stars and summarize the interpretations based on them in terms of the excited pulsation modes.
Abstract: In this review we present the current status of line-profile-variation studies of β Cep stars. Such studies have been performed for 26 bright members of this class of pulsating stars in the past 25 years. We describe all these currently available data and summarize the interpretations based on them in terms of the excited pulsation modes. We emphasize that line-profile variations offer a much more detailed picture of the pulsational behaviour of pulsating stars compared to ground-based photometric data. The latter, however, remain necessary to unravel the often complex frequency pattern and to achieve unambiguous mode identification for multiperiodic β Cep stars and also to derive the pulsational properties of the faint members of the class. We highlight the statistical properties of the sample of 26 stars for which accurate spectroscopic studies are available and point out some future prospects.

52 citations

Journal Article•DOI•
A new method for the spectroscopic identification of stellar non-radial pulsation modes - I. The method and numerical tests

[...]

W. Zima1•
Katholieke Universiteit Leuven1
01 Aug 2006-Astronomy and Astrophysics
TL;DR: In this article, the Fourier parameter fit method was used to identify stellar radial and non-radial pulsation modes based on the high-resolution time-series spectroscopy of absorption-line profiles.
Abstract: Aims. We present the Fourier parameter fit method, a new method for spectroscopically identifying stellar radial and non-radial pulsation modes based on the high-resolution time-series spectroscopy of absorption-line profiles. In contrast to previous methods this one permits a quantification of the statistical significance of the computed solutions. The application of genetic algorithms in seeking solutions makes it possible to search through a large parameter space. Methods. The mode identification is carried out by minimizing Χ 2 , using the observed amplitude and phase across the line profile and their modeled counterparts. Computations of the theoretical line profiles are based on a stellar displacement field, which is described as superposition of spherical harmonics and that includes the first order effects of the Coriolis force. Results. We made numerical tests of the method on a grid of different mono- and multi-mode models for 0 ≤ l ≤ 4 in order to explore its capabilities and limitations. Our results show that whereas the azimuthal order m can be unambiguously identified for low-order modes, the error of l is in the range of ±1. The value of m can be determined with higher precision than with other spectroscopic mode identification methods. Improved values for the inclination can be obtained from the analysis of non-axisymmetric pulsation modes. The new method is ideally suited to intermediatley rotating 6 Scuti andβ Cephei stars.

51 citations

Cites background or methods from "Line-profile variations due to adia..."

  • ...…a time t by ξ = √ 4π [ as, ⎛⎜⎜⎜⎜⎜⎝1, k ∂∂θ , k 1sin θ ∂∂φ ⎞⎟⎟⎟⎟⎟⎠ Ym (θ, φ) eiωt +at, +1 ⎛⎜⎜⎜⎜⎜⎝0, 1sin θ ∂∂φ,− ∂∂θ , ⎞⎟⎟⎟⎟⎟⎠ Ym +1(θ, φ) ei(ωt+ π2 ) +at, −1 ⎛⎜⎜⎜⎜⎜⎝0, 1sin θ ∂∂φ,− ∂∂θ , ⎞⎟⎟⎟⎟⎟⎠ Ym −1(θ, φ) ei(ωt− π2 ) ] (A.4) (Martens & Smeyers 1982; Aerts & Waelkens 1993; Schrijvers et al. 1997)....

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  • ...…amplitude, which allows the distinction between p- and g-modes, can be approximated in the limit of slow rotation by the following relation (Schrijvers et al. 1997) k ≡ ah as = k0 + 2m Ω ω [ 1 + k0 ( + 1) −C ,n ] (A.6) where ah and as are the horizontal and vertical amplitude and C ,n is…...

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  • ...Our description of the Lagrangian displacement field is valid in the limit of slow rotation taking the effects of the Coriolis force to the first order into account (Schrijvers et al. 1997)....

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  • ...These include the intensity-period search (IPS) method (Schrijvers et al. 1997), where and m are determined from the amplitude and phase distribution across the line profile by applying empirically derived relations, and the pixel-by-pixel method (PPM) described by Mantegazza (2000)....

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  • ...In a series of four papers, Schrijvers et al. (1997), Telting & Schrijvers (1997a,b), and Schrijvers & Telting (1999) have extensively tested the distribution of amplitude and phase across the line profile for different settings of mode input parameters....

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Journal Article•DOI•
An asteroseismic study of the β Cephei star β Canis Majoris

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Anwesh Mazumdar1, Maryline Briquet1, M. Desmet1, Conny Aerts1•
Katholieke Universiteit Leuven1
01 Nov 2006-Astronomy and Astrophysics
TL;DR: In this paper, a detailed analysis of ground-based, high-resolution high S/N spectroscopic measurements spread over 4.5 years for β Canis Majoris with the aim of determining the pulsational characteristics of this star was presented.
Abstract: Aims. We present the results of a detailed analysis of 452 ground-based, high-resolution high S/N spectroscopic measurements spread over 4.5 years for β Canis Majoris with the aim of determining the pulsational characteristics of this star, and then using them to derive seismic constraints on the stellar parameters. Methods. We determined pulsation frequencies in the Si III 4553 A line with Fourier methods. We identified the m-value of the modes by taking the photometric identifications of the degrees l into account. To this end we used the moment method together with the amplitude and phase variations across the line profile. The frequencies of the identified modes were used for a seismic interpretation of the structure of the star. Results. We confirm the presence of the three pulsation frequencies already detected in previous photometric datasets: f 1 = 3.9793 c d -1 (46.057 μHz), f 2 = 3.9995 cd -1 (46.291 μHz), and f 3 = 4.1832 cd -1 (48.417 μHz). For the two modes with the highest amplitudes, we unambiguously identify (l 1 , m 1 ) = (2,2) and (l 2 , m 2 ) = (0,0). We cannot conclude anything for the third mode identification, except that m 3 > 0. We also deduce an equatorial rotational velocity of 31 ± 5 km s -1 for the star. We show that the mode f 1 must be close to an avoided crossing. Constraints on the mass (13.5 ± 0.5 M ⊙ ), age (12.4 ± 0.7 Myr), and core overshoot (0.20 ± 0.05 Hp) of β CMa are obtained from seismic modelling using f 1 and f 2 .

45 citations

Cites background from "Line-profile variations due to adia..."

  • ...Telting & Schrijvers (1997) and Schrijvers et al. (1997) showed that, when there is a minimum (almost zero) in the amplitude and a corresponding phase shift of π near the center of the line profile, one can conclude to be dealing with a radial or a dipole mode....

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References
More filters
Book•
Hydrodynamic and magnetohydrodynamic problems in the sun and stars : proceedings of the Workshop in Honor of Professor Wasaburo Unno's 60th Birthday, 1986 February 26 - 28, Tokyo

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洋二 尾崎, 和三郎 海野
01 Jan 1986

15 citations

"Line-profile variations due to adia..." refers background in this paper

  • ...Many authors (e.g. Smith 1986; Gies & Kullavanijaya 1988; Kambe & Osaki 1988; Yang et al. 1988; Kambe et al. 1990) have used the number of visible bumps or, equivalently, the blue-to-red phase difference ∆Ψ0 to identify |m| according to ∆Ψ0 = |m|π....

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  • ...In his discussion of the so called k-problem, Smith (1986) mentioned that for high k(0)-values, the toroidal term(s) caused by rotation might be able to mimic the amplitude-distribution characteristics of a low-k(0) mode....

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  • ...The difficulty to derive k-values from amplitude diagrams The determination of the k-value from observed lineprofiles has been discussed by several authors (e.g. Smith 1986; Kambe et al. 1990; Lee & Saio 1990)....

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