Sensitivity of five minute eigenfrequencies to the structure of the sun

Berthomieu, G.; Cooper, Adam J.; Gough, D. O.; Osaki, Yoji; Provost, J.; Rocca, Alessandro Della

doi:10.1007/3-540-09994-8_29

Cited by 73 publications

(61 citation statements)

References 11 publications

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“…In a next step, we plan to compare our complete computations with the so-called traditional approximation, which is also extensively used to determine g-mode frequencies (e.g Berthomieu et al 1978;Lee & Saio 1997). We will also analyze how rotation affects the regularities of the spectrum -such as the period spacing -and compare it to the predictions of the perturbative and traditional methods.…”

Section: Resultsmentioning

confidence: 99%

Gravity modes in rapidly rotating stars

Ballot¹,

Lignières²,

Reese

et al. 2010

A&A

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Context. CoRoT and Kepler missions are now providing high-quality asteroseismic data for a large number of stars. Among intermediate-mass and massive stars, fast rotators are common objects. Taking the rotation effects into account is needed to correctly understand, identify, and interpret the observed oscillation frequencies of these stars. A classical approach is to consider the rotation as a perturbation. Aims. In this paper, we focus on gravity modes, such as those occurring in γ Doradus, slowly pulsating B (SPB), or Be stars. We aim to define the suitability of perturbative methods. Methods. With the two-dimensional oscillation program (TOP), we performed complete computations of gravity modes -including the Coriolis force, the centrifugal distortion, and compressible effects -in 2D distorted polytropic models of stars. We started with the modes = 1, n = 1−14, and = 2−3, n = 1−5, 16−20 of a nonrotating star, and followed these modes by increasing the rotation rate up to 70% of the break-up rotation rate. We then derived perturbative coefficients and determined the domains of validity of the perturbative methods. Results. Second-order perturbative methods are suited to computing low-order, low-degree mode frequencies up to rotation speeds ∼100 km s −1 for typical γ Dor stars or ∼150 km s −1 for B stars. The domains of validity can be extended by a few tens of km s −1 thanks to the third-order terms. For higher order modes, the domains of validity are noticeably reduced. Moreover, perturbative methods are inefficient for modes with frequencies lower than the Coriolis frequency 2Ω. We interpret this failure as a consequence of a modification in the shape of the resonant cavity that is not taken into account in the perturbative approach.

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Section: Resultsmentioning

confidence: 99%

Gravity modes in rapidly rotating stars

Ballot¹,

Lignières²,

Reese

et al. 2010

A&A

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“…To achieve this aim, the Coriolis acceleration has first been treated using the traditional approximation, that can be applied in stellar radiation zones in the super-inertial regime where 2Ω < σ N in the case of uniform rotation (N is the Brunt-Väisälä frequency) (see for example Berthomieu et al 1978;Friedlander 1987;Talon 1997;. First numerical results using a stellar evolution code have been obtained (cf.…”

Section: Article Published By Edp Sciencesmentioning

confidence: 99%

Transport by gravito-inertial waves in differentially rotating stellar radiation zones

Mathis

2009

A&A

113

172

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Context. We examine the dynamics of low-frequency waves in differentially rotating stellar radiation zones, the angular velocity being taken as generally as possible depending both on radius and on latitude in stellar interiors. The associated induced transport of angular momentum, which plays a key role in the evolution of rotating stars, is derived. Aims. We focus on the wave-induced transport of angular momentum, taking into account the Coriolis acceleration in the case of strong radial and latitudinal differential rotation. We thus go beyond the "weak differential rotation" approximation, where rotation is almost a solid-body one plus a residual radial differential rotation. As has been shown in previous works, the Coriolis acceleration modifies such transport. Methods. We built analytically a complete formalism that allows the study of rotational transport in stellar radiation zones taking into account the wave action modified by a general strong differential rotation. Results. The different approximations possible for low-frequency waves in a differentially rotating stably stratified radiative region, namely the traditional and the JWKB approximations, are examined and discussed. The complete bidimensional structure of regular elliptic gravito-inertial waves, which verify these approximations, is derived and compared to those in the "weak differential rotation" case. Next, associated transport of energy and of angular momentum in the vertical and in the horizontal directions and the dynamical equations, respectively for the mean radial differential rotation and the latitudinal one, are obtained. Conclusions. The complete formalism, which takes into account low-frequency wave action, is derived and can be used for the study of secular hydrodynamics of radiative regions and of the associated mixing. The modification of waves due to general strong differential rotation and their feed-back on the angular momentum transport are treated rigourously. In a forthcoming paper (Paper II), this formalism will be applied to the case of solar differential rotation. However, the case of hyperbolic gravito-inertial waves should be carefully studied.

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“…This is known as the traditional approximation, which is well known in geophysics (see e.g. Eckart 1960), and it was used for the first time in an astrophysical context by Berthomieu et al (1978). In this case, wave eigenfunctions can be separated into radial and horizontal components.…”

Section: The Traditional Approximationmentioning

confidence: 99%

Angular momentum transport by internal gravity waves

Pantillon¹,

Talon²,

Charbonnel³

2007

A&A

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Context. This is the third in a series of papers that deal with angular momentum transport by internal gravity waves. We concentrate on the waves excited by core convection in a 3 M , Pop I main sequence star. Aims. Here, we want to examine the role of the Coriolis acceleration in the equations of motion that describe the behavior of waves and to evaluate its impact on angular momentum transport. Methods. We use the so-called traditional approximation of geophysics, which allows variable separation in radial and horizontal components. In the presence of rotation, the horizontal structure is described by Hough functions instead of spherical harmonics. Results. The Coriolis acceleration has two main effects on waves. It transforms pure gravity waves into gravito-inertial waves that have a larger amplitude closer to the equator, and it introduces new waves whose restoring force is mainly the conservation of vorticity. Conclusions. Taking the Coriolis acceleration into account changes the subtle balance between prograde and retrograde waves in nonrotating stars. It also introduces new types of waves that are either purely prograde or retrograde. We show in this paper where the local deposition of angular momentum by such waves is important.

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Sensitivity of five minute eigenfrequencies to the structure of the sun

Cited by 73 publications

References 11 publications

Gravity modes in rapidly rotating stars

Gravity modes in rapidly rotating stars

Transport by gravito-inertial waves in differentially rotating stellar radiation zones

Angular momentum transport by internal gravity waves

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