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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01 Jan 2000
TL;DR: In this paper, the Telting and Schrijvers' method was used to estimate the mode degree I and azimuthal order | m | with reasonably high accuracy, using the CLEAN and CLEANEST algorithms.
Abstract: Abstract. £ Ophiuchi and 77 Centauri are hot, rapidly rotating, southern Be stars showing multi-mode nonradial pulsations (nrp). We use high resolution, high signal-to-noise ratio spectroscopic observations of these objects to test the Telting and Schrijvers' method (TS) of mode degree I and azimuthal order | m | estimation. In this method, these quantum numbers are calculated from the blue-to-red phase difference of the corresponding main frequency and its first harmonic, respectively. The phase differences were obtained withe the help of the CLEAN and CLEANEST algorithms. Quantum numbers calculated with TS are compatible with those obtained with the Fourier Doppler method within the estimated errors. In the absence of other tools, the TS method can thus be used to estimate I and | m | with reasonably accuracy.
3 citations
TL;DR: In this article, a search for and analysis of line-profile variations in the spectrum of the star ι Her was carried out with the 1.8 m telescope of the Bohyunsan Optical Astronomy Observatory (Republic of Korea) in May-June 2004.
Abstract: We present the results of a search for and analysis of line-profile variations in the spectrum of the star ι Her. The observations were acquired with the 1.8 m telescope of the Bohyunsan Optical Astronomy Observatory (Republic of Korea) in May–June 2004. We obtained 69 spectra of the star with signal-to-noise ratios ≈300 and a time resolution of 5–7 min. Profile variability was revealed for six lines of HI, HeI, and SiIII, in the central parts of the lines. The variability amplitude is ≈(1–2)% in units of the intensity of the adjacent continuum. Evidence was found for cyclic variations of the lines, with periods from ≈7h to ≈2.9d. We conclude that ι Her belongs to the group of slowly pulsating stars.
3 citations
Dissertation•
01 Mar 2018
TL;DR: In this paper, two candidate γ Doradus stars, HD 103257 and HD 109799, were analysed using the HERCULES spectrograph at the University of Canterbury Mt John Observatory.
Abstract: Two candidate γ Doradus stars are analysed: HD 103257 and HD 109799. Over 250 spectra were gathered for analysis using the HERCULES spectrograph at the University of Canterbury Mt John Observatory. The spectra for each star were cross-correlated with synthetic spectra to produce line profiles and augmented with photometric data from the WASP archive and HIPPARCOS catalogue for frequency and mode analysis.
Three pulsation frequencies were identified for HD 103257: 1.22496 ± 0.00001 d^(-1), 1.14569 ± 0.00002 d^(-1) and 0.67308 ± 0.00004 d^(-1), explaining 66.6% of the variation across the line profiles. The frequencies were characterised with best-fit modes of (l, m) = (1, 1), (1, 1) and (3, -2) respectively. The inclination of the rotation axis and the radius were best-fit to i = 86.4° and R = 2.6 R_⊙, while a zero-point fit yielded a vsini of 71.5 km s^(-1).
Three pulsation frequencies were identified for HD 109799: 1.48679 ± 0.00002 d^(-1), 1.25213 ± 0.00002 d^(-1) and 0.92184 ± 0.00004 d^(-1) , explaining 39.3% of the variation across the line profiles. The frequencies yielded individual mode fits of modes (l, m) = (1, 1), (1, 1) and (3, 2). The rotational axis for HD 109799 to the range i = 65° - 70° with a zero-point fitted vsini of 40.2 km s^(-1).
Based on observations of frequencies and modes characteristic of the class, HD 103257 and HD 109799 can now be categorised as bona fide γ Doradus stars. The results within this thesis will be of service in the future development of theoretical models pertaining to the interiors of γ Doradus stars.
3 citations
TL;DR: In this article, the problem of modeling the surface of stars undergoing non-radial pulsation is reviewed and linear-approximation expressions for the surface radius, temperature, velocity and geometry of a pulsating star are derived and discussed using both the Lagrangian and Eulerian formalisms.
Abstract: The problem of modelling the surface of stars undergoing non-radial pulsation is reviewed. Linear-approximation expressions for the surface radius, temperature, velocity and geometry of a pulsating star are derived and discussed using both the Lagrangian (fixed-element) and Eulerian (fixed-position) formalisms. In each case, small numerical discrepancies are found between the perturbed states predicted by these alternative approaches. These discrepancies are shown to scale quadratically with the pulsation amplitude, and are therefore attributed to a transgression of the linear-approximation limits.
Singled out for particular attention are the expressions for the surface geometry perturbations predicted by each formalism. Marked differences are apparent between these expressions: terms containing the horizontal fluid displacement appear explicitly in the Lagrangian result, but are absent from the corresponding Eulerian one. By examining the physical origin of these terms, it is demonstrated that the two formalisms are, in fact, perfectly consistent with regard to the geometry perturbations, and – as with all other perturbations – simply furnish alternative representations of the same physical processes. The conclusion is that either formalism is an appropriate choice when modelling the surface of a pulsating star.
3 citations
TL;DR: In this paper, the CLEAN algorithm was used to search for harmonic components in the variation of the Hβ line profile in spectra of the triple star δ Ori A obtained in 2004 with the BTA telescope at the Special Astrophysical Observatory of the Russian Academy of Sciences.
Abstract: This is an analysis of certain aspects of using the CLEAN algorithm for Fourier analysis of short segments of time series and of time series consisting of short segments of length ΔT separated by very long irregular gaps. It is assumed that the time series contain a harmonic component of amplitude A with a period longer than the length of the longest of the segments of the time series plus white noise with dispersion N2. Reliability plots are constructed for determining the ranges of the parameters (ν, ϕ) for which the CLEAN procedure can be used to determine the values of ν, the frequency, and ϕ, the phase of the harmonic component, with a given accuracy. The results of this analysis are used to search for harmonic components in the variation of the Hβ line profile in spectra of the triple star δ Ori A obtained in 2004 with the BTA telescope at the Special Astrophysical Observatory of the Russian Academy of Sciences.
3 citations
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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