Line-profile variations due to adiabatic non-radial pulsations in rotating stars. I. Observable characteristics of spheroidal modes
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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TL;DR: In this article, the results of the mode identification for a sample of 7 bright southern slowly pulsating B stars showing one-pulsation frequency in the XX 413 nm Si II profiles were combined with the results from photometric amplitudes, moment method, and amplitude and phase variation across the profile to search for the l and m values of the modes best fitting the data.
Abstract: We present the results of the mode identification for a sample of 7 bright southern slowly pulsating B stars showing onepulsation frequency in the XX 413 nm Si II profiles. We combined the results from (1) the method of photometric amplitudes; (2) the moment method; and (3) the amplitude and phase variation across the profile to search for the l and m values of the modes best fitting the data. It is the first time that the applicability of these techniques is tested to a sample of main-sequence g-mode pulsators. Combining the moment method with the amplitude and phase variations across the observed line profile gives an improvement in spectroscopic identification of low degree I g-mode pulsations. Using the variations of the higher order even moments (v4> and (v6> of the moment method solutions can also help. For HD 181558, HD 24587, HD 140873 and HD 177863, the photometric and spectroscopic results are compatible and point towards (I, m) = (1, +1) sectoral modes. For HD 215573, HD 53921 and HD 92287, the results are inconclusive. Our proposed methodology for mode identification is also applicable to y Doradus stars.
45 citations
Cites methods from "Line-profile variations due to adia..."
...Next, we calculated the “IPS diagnostics”, i.e. the amplitudes and phases of variations with ν j,obs and 2ν j,obs across the line profile (cf. Schrijvers et al. 1997; Telting & Schrijvers 1997; Telting et al. 1997)....
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TL;DR: In this paper, the authors presented the first line-based analysis of pulsating red giants, taking into account the small line-profile variations and the pre-dicted short damping and re-excitation times.
Abstract: Observatoire de Gene`ve, 51 chemin de Maillettes, 1290 Sauverny, SwitzerlandReceived idate?; accepted idate?ABSTRACTContext. So far, red giant oscillations have been studied from radial velocity and/or light curve variations, which reveal frequencies of theoscillation modes. To characterise radial and non-radial oscillations, line profile variations are a valuable diagnos tic. Here we present for thefirst time a line profile analysis of pulsating red giants, tak ing into account the small line profile variations and the pre dicted short damping andre-excitation times. We do so by modelling the time variations in the cross correlation profiles in terms of oscillation t heory.Aims.The performance of existing diagnostics for mode identifica tion is investigated for known oscillating giants which have very small lineprofile variations. We modify these diagnostics, perform si mulations, and characterise the radial and non-radial modes detected in the crosscorrelation profiles.Methods.Moments and line bisectors are computed and analysed for four giants. The robustness of the discriminant of the moments againstsmall oscillations with finite lifetimes is investigated. I n addition, line profiles are simulated with short damping an d re-excitation times andtheir line shapes are compared with the observations.Results.For three stars, we find evidence for the presence of non-radial pulsation modes, while for ξHydrae perhaps only radial modes arepresent. Furthermore the line bisectors are not able to distinguish between different pulsation modes and are an insufficient diagnostic todiscriminate small line profile variations due to oscillati ons from exoplanet motion.Key words. stars: oscillations – stars: individual: ǫOphiuchi, ηSerpentis, ξHydrae, δEridani – Techniques: spectroscopic – Line: profiles
42 citations
Cites methods from "Line-profile variations due to adia..."
...The amplitude and phase for each velocity in the cross correlation profile are determined by fitting a harmonic function, with the dominant frequencies of〈v〉, to the flux values at each velocity pixel of the time series of spectra (Schrijvers et al. 1997)....
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TL;DR: The first confirmed detection of a dipolar magnetic field in an upper main-sequence pulsating star was reported in this article, where the authors applied the least square deconvolution method on the Stokes V spectra and derived the longitudinal component of the integrated magnetic field over the visible hemisphere of the star.
Abstract: Context. Although the star itself is not helium enriched, the periodicity and the variability in the UV wind lines of the pulsating B1 IV star β Cephei are similar to what is observed in magnetic helium-peculiar B stars, suggesting that β Cep is magnetic. Aims. We searched for a magnetic field using high-resolution spectropolarimetry. From UV spectroscopy, we analysed the wind variability and investigated the correlation with the magnetic data. Methods. We used 130 time-resolved circular polarisation spectra that were obtained from 1998 (when β Cep was discovered to be magnetic) to 2005, with the MuSiCoS echelle spectropolarimeter at the 2 m Telescope Bernard Lyot. We applied the least-square deconvolution method on the Stokes V spectra and derived the longitudinal component of the integrated magnetic field over the visible hemisphere of the star. We performed a period analysis on the magnetic data and on equivalent-width measurements of UV wind lines obtained over 17 years. We also analysed the short- and long-term radial velocity variations, which are due to the pulsations and the 90-year binary motion, respectively. Results. β Cep hosts a sinusoidally varying magnetic field with an amplitude 97 ± 4Ga nd an average value−6 ± 3G . From the UV wind line variability, we derive a period of 12.00075(11) days, which is the rotation period of the star, and is compatible with the observed magnetic modulation. Phases of maximum and minimum field match those of maximum emission in the UV wind lines, strongly supporting an oblique magnetic-rotator model. We discuss the magnetic behaviour as a function of pulsation behaviour and UV line variability. Conclusions. This paper presents the analysis of the first confirmed detection of a dipolar magnetic field in an upper main-sequence pulsating star. Maximum wind absorption originates in the magnetic equatorial plane. Maximum emission occurs when the magnetic north pole points to the Earth. Radial velocities agree with the ∼90-year orbit around its Be-star binary companion.
39 citations
Cites methods from "Line-profile variations due to adia..."
...The velocity was measured using the first moment of the profile with respect to the barycentric restframe, which is normalised by the equivalent width (we followed Schrijvers et al. 1997)....
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References
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Book•
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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