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Journal ArticleDOI

Spectroscopic modelling of non-radial pulsation in rotating early-type stars

01 Feb 1997-Monthly Notices of the Royal Astronomical Society (Oxford University Press)-Vol. 284, Iss: 4, pp 839-858
About: This article is published in Monthly Notices of the Royal Astronomical Society.The article was published on 1997-02-01 and is currently open access. It has received 115 citations till now. The article focuses on the topics: T Tauri star & Stars.
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Journal ArticleDOI
TL;DR: Recent results for classical Be stars are reviewed and links to general astrophysics are presented in this article, where the authors show that the evidence that Be stars do not form a homogeneous group with respect to disk formation is growing or the short-term periodic variability is less important than previously thought.
Abstract: Recent results for classical Be stars are reviewed and links to general astrophysics are presented. Classical Be stars are B-type stars close to the main sequence that exhibit line emission over the photospheric spectrum. The excess is attributed to a circumstellar gaseous component that is commonly accepted to be in the form of an equatorial disk. Since 1988, when the last such review was published, major progress has been made. The geometry and kinematics of the circumstellar environment can be best explained by a rotationally supported relatively thin disk with very little outflow, consistent with interferometric observations. The presence of short-term periodic variability is restricted to the earlier type Be stars. This variation for at least some of these objects has been shown to be due to nonradial pulsation. For at least one star, evidence for a magnetic field has been observed. The mechanisms responsible for the production and dynamics of the circumstellar gas are still not constrained. Observations of nonradial pulsation beating phenomena connected to outbursts point toward a relevance of pulsation, but this mechanism cannot be generalized. Either the evidence that Be stars do not form a homogeneous group with respect to disk formation is growing or the short-term periodic variability is less important than previously thought. The statistics of Be stars investigated in open clusters of the Milky Way and the Magellanic Clouds has reopened the question of the evolutionary status of Be stars. The central B star is a fast rotator, although theoretical developments have revived the question of how high rotational rates are, so the commonly quoted mean value of about 70%-80% of the critical velocity may just be a lower limit. Be stars are in a unique position to make contributions to several important branches of stellar physics, e.g., asymmetric mass-loss processes, stellar angular momentum distribution evolution, astroseismology, and magnetic field evolution.

645 citations


Cites methods from "Spectroscopic modelling of non-radi..."

  • ...Townsend (1997) published a modeling code applicable to NRP in rapidly rotating stars in general, i.e., not only to Be stars, the BRUCE/KYLIE package....

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Journal ArticleDOI
TL;DR: In this article, the authors present line-profile calculations that emphasize the insensitivity of line width to rotation for fast rotators and suggest that the observational parameter v sin i may systematically underestimate the true projected equatorial rotation velocity, v e sin i by some tens of per cent for rapid rotators.
Abstract: We argue that, in general, observational studies of Be-star rotation have paid insufficient attention to the effects of equatorial gravity darkening. We present new line-profile calculations that emphasize the insensitivity of line width to rotation for fast rotators. Coupled with a critical review of observational procedures, these calculations suggest that the observational parameter v sin i may systematically underestimate the true projected equatorial rotation velocity, v e sin i, by some tens of per cent for rapid rotators. A crucial implication of this work is that Be stars may be rotating much closer to their critical velocities than is generally supposed, bringing a range of new processes into contention for the elusive physical mechanism responsible for the circumstellar disc thought to be central to the Be phenomenon.

319 citations

Journal ArticleDOI
TL;DR: This paper showed that the observational parameter v sin(i) may systematically underestimate the true projected equatorial rotation velocity by tens of per cent for rapid rotators for Be-star rotation.
Abstract: We argue that, in general, observational studies of Be-star rotation have paid insufficient attention to the effects of equatorial gravity darkening. We present new line-profile calculations that emphasize the insensitivity of line width to rotation for fast rotators. Coupled with a critical review of observational procedures, these calculations suggest that the observational parameter v sin(i) may systematically underestimate the true projected equatorial rotation velocity, ve sin(i), by some tens of per cent for rapid rotators. The crucial implication of this work is that Be stars may be rotating much closer to their critical velocities than is generally supposed, bringing a range of new processes into contention for the elusive physical mechanism responsible for the circumstellar disk thought to be central to the Be phenomenon.

239 citations


Cites methods from "Spectroscopic modelling of non-radi..."

  • ...The calculations use the bruce code (Townsend 1997), which is readily adapted from its original intended application in modeling nonradial pulsation by simply setting the pulsation amplitudes to zero....

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Journal ArticleDOI
TL;DR: In this paper, the authors derived the θ-dependence of the displacement vector of rotationally modulated low-frequency nonradial oscillations by numerically integrating Laplace's tidal equation as an eigenvalue problem with a relaxation method.
Abstract: We obtain the θ-dependence of the displacement vector of rotationally modulated low-frequency nonradial oscillations by numerically integrating Laplace's tidal equation as an eigenvalue problem with a relaxation method. This method of calculation is more tractable than our previous method in which the θ-dependence was represented by a truncated series of associated Legendre functions. Laplace's tidal equation has two families of eigenvalues. In one of these families, an eigenvalue λ coincides with l(l + 1) when rotation is absent, where l is the latitudinal degree of the associated Legendre function, Pml(cos θ). The value of λ changes as a function of ν ≡ 2Ω/ω, where Ω and ω are the angular frequencies of rotation and of oscillation (seen in the corotating frame), respectively. These eigenvalues correspond to rotationally modulated g-mode oscillations. In the domain of | ν | > 1, another family of eigenvalues exists. Eigenvalues belonging to this family have negative values for prograde oscillations, while they change signs from negative to positive for retrograde oscillations as | ν | increases. Negative λ's correspond to oscillatory convective modes. The solution associated with a λ that has a small positive value after changing its sign is identified as an r-mode (global Rossby wave) oscillation. Amplitudes of g-mode oscillations tend to be confined to the equatorial region as | ν | increases. This tendency is stronger for larger λ. On the other hand, amplitudes of oscillatory convective modes are small near the equator.

192 citations

Journal ArticleDOI
TL;DR: In this paper, the angular dependence of pulsation modes in uniformly rotating stars has been analyzed through the solution of Laplace's tidal equations, approximated to describe equatorially trapped wave propagation, and four classes of asymptotic solution are found, corresponding to g (gravito-inertial), r (Rossby), Kelvin and Yanai modes.
Abstract: Through the solution of Laplace's tidal equations, approximated to describe equatorially trapped wave propagation, analytical expressions are obtained for the angular dependence of pulsation modes in uniformly rotating stars. As the ratio between rotation and pulsation frequencies becomes large, these expressions approach the exact solutions of the governing low-frequency pulsation equations. Four classes of asymptotic solution are found, corresponding to g (gravito-inertial), r (Rossby), Kelvin and Yanai modes. The Kelvin modes arise through the conservation of specific vorticity, much like the r modes, but propagate in the same sense as the rotation; they are found to be the equivalents of prograde sectoral modes. The prograde Yanai modes behave like g modes, as do the retrograde ones if the rotation is sufficiently rapid; otherwise, the latter exhibit the character of r modes. Comparison between asymptotic and numerical solutions to the tidal equations reveals that the former converge rapidly towards the latter, for g and Yanai modes. The convergence is slower for Kelvin and r modes, as these become equatorially trapped only when the rotation is very rapid. It is argued that the utility of the asymptotic solutions does not rest on their accuracy alone, but also on the valuable physical insights that they are capable of providing.

145 citations


Cites background or methods from "Spectroscopic modelling of non-radi..."

  • ...The ( , m) pair of indices is often used to classify the Hough functions (e.g. Townsend 1997a,b), as it provides a clear indication of their nonrotating progenitors....

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  • ...Such an ordering is always possible, because the eigenvalues of the tidal equation are guaranteed never to be degenerate (see, e.g. Townsend 1997a,b)....

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  • ...…applied in many areas of stellar pulsation, from modelling the nrp-originated line-profile variations seen in early-type stars (Lee & Saio 1990; Townsend 1997b), to examining tidal forcing in massive binary systems (Papaloizou & Savonije 1997), to investigating what role gravity modes might…...

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