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

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

^{1}, Katholieke Universiteit Leuven

^{2}, Radboud University Nijmegen

^{3}, Aarhus University

^{4}, Centre national de la recherche scientifique

^{5}, Las Cumbres Observatory Global Telescope Network

^{6}, National Center for Atmospheric Research

^{7}, Max Planck Society

^{8}, University of Liège

^{9}, University of Central Lancashire

^{10}, Imperial College London

^{11}, Université libre de Bruxelles

^{12}, Heidelberg University

^{13}, University of Sheffield

^{14}

135 citations

98 citations

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

...A particularly illustrative study in this respect is the one by Schrijvers et al. (1997), where the predicted variability of line-profiles due to adiabatic non-radial pulsations in rotating stars is shown for a large variety of oscillation and rotation parameters....

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...…(1) where 〈3 n 〉 = ∫ ∞ −∞ (3 − 〈3〉)n(1− F(3))d3 ∫ ∞ −∞ (1− F(3))d3 for n = 2, 3 (2) are the second and third normalized central moments of a spectral line denoted as (3, F(3)), adopting the definition used in Schrijvers et al. (1997), and 〈3〉 = ∫ ∞ −∞ 3 (1− F(3))d3 ∫ ∞ −∞ (1− F(3))d3 ....

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...An interesting work in this respect is the one by Schrijvers et al. (1997), where line-profile asymmetry due to a long lifetime oscillation mode of degreeℓ and azimuthal order m in rotating stars is shown for a large variety of oscillation and rotational parameters (the latter quantified in t rms…...

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...We refer the reader to the works by Schrijvers et al. (1997) Article number, page 8 of 17 and Telting & Schrijvers (1997) for a comprehensive illustration of predicted line-profile variations originated by adiabatic non-radial pulsations in rotating stars....

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...The velocity moments of the line-profile (Balona 1986; Aerts et al. 1992; Schrijvers et al. 1997) have been proven to be powerful tools to characterize the temporal behavior of line asymmetry independently of the physical cause that is originating it....

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95 citations

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### Additional excerpts

...To refine the period we used the formula suggested by Schrijvers et al. (1997), who performed a similar time series analysis of the line profile variations of pulsating stars, Iobsij ¼ I ð0Þ i þ X3 k¼1 I ðkÞ i sin k Tj T0 P þ ðkÞi ; ð1Þ where Iobsij is the observed flux in the ith wavelength bin of…...

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##### References

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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