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 paper, the variability of the Hg ii � 3984 line in the primary of the binary star was discovered through the examination of high-dispersion spectra with signal-to-noise ratios greater than 500.
Abstract: The variability of the Hg ii � 3984 line in the primary of the binary starAnd was discovered through the examination of high-dispersion spectra with signal-to-noise ratios greater than 500. This first definitively identified spectrum variation in any mercury-manganese star is not due to the orbital motion of the compan- ion. Rather, the variation is produced by the combination of the 2.38236 day period of rotation of the pri- mary that we determined and a nonuniform surface distribution of mercury that is concentrated in its equatorial region. If the surface mercury distribution exhibits long-term stability, then it is likely that a weak magnetic field operates in its atmosphere, but if changes are observed in the line profile over a period of a few years, then these would constitute direct evidence for diffusion. Subject headings: binaries: general — binaries: spectroscopic — stars: chemically peculiar — stars: individual (� Andromedae)
76 citations
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...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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TL;DR: In this paper, a numerical version of the moment method for the identification of non-radial pulsation modes was presented, allowing users to consider all the information contained in the first three moments of a multi-periodic star and to identify multiple modes simultaneously.
Abstract: We present a numerical version of the moment method for the identification of non-radial pulsation modes. The new version requires less computation time than the previous one, allowing users to consider all the information contained in the first three moments of a multiperiodic star and to identify multiple modes simultaneously. This, together with the use of a new discriminant that considers the moments calculated at each time of observation, increases considerably the feasibility and the accuracy of the mode identification for multiperiodic stars. Moreover, the technique is extended to rotating pulsating stars. We apply the new version to three B stars showing multiperiodicity.
71 citations
Cites background from "Line-profile variations due to adia..."
...One can do this for the profiles themselves, or else for their variation of amplitude and phase across the profile (for a definition of the latter diagnostic values, we refer to Schrijvers et al. 1997)....
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TL;DR: In this article, the authors investigated the geometrical distortion and the stellar and circumstellar activity of a Eri (HD 10144), the brightest Be star in the sky, using high resolution and high S/N spectroscopic observations of He 1 and Mg II lines.
Abstract: We explore the geometrical distortion and the stellar and circumstellar activity of a Eri (HD 10144), the brightest Be star in the sky. We present a thorough discussion of the fundamental parameters of the object for an independent determination of its rotational distortion. We used stellar atmosphere models and evolutionary tracks calculated for fast rotating early-type stars. If the star is a rigid rotator, its angular velocity rate is Ω/Ω c ≃ 0.8, so that its rotational distortion is smaller than the one inferred from recent interferometric measurements. We then discuss the stellar surface activity using high resolution and high S/N spectroscopic observations of He 1 and Mg II lines, which concern a period of Ha line emission decline. The variations in the He I lines are interpreted as due to non-radial pulsations. Time series analysis of variations was performed with the CLEANEST algorithm, which enabled us to detect the following frequencies: 0.49, 0.76, 1.27 and 1.72 c/d and pulsation degrees l ∼ (3-4) for v = 0.76 c/d; l ∼ (2-3) for v = 1.27 c/d and l ∼ (3-4) for v = 1.72 c/d. The study of the absolute deviation of the He I λ6678 A spectral line revealed mass ejection between 1997 and 1998. We conclude that the lowest frequency found, v = 0.49 c/d, is due to the circumstellar environment, which is present even at epochs of low emission in the wings of He I λ6678 A and Mg II λ4481 A line profiles, as well as during nearly normal aspects of the Hα line. This suggests that there may be matter around the star affecting some spectral regions, even though the object displays a B-normal like phase. The long-term changes of the Ha line emission in a Eri are studied. We pay much attention to the Ha line emission at the epoch of interferometric observations. The Ha line emission is modeled and interpreted in terms of varying structures of the circumstellar disc. We conclude that during the epoch of interferometric measurements there was enough circumstellar matter near the star to produce λ2.2 μm flux excess, which could account for the overestimated stellar equatorial angular diameter. From the study of the latest B?Be phase transition of a Eri we concluded that the Ha line emission formation regions underwent changes so that: a) the low Ha emission phases are characterized by extended emission zones in the circumstellar disc and a steep outward matter density decline; b) during the strong Hα emission phases the emitting regions are less extended and have a constant density distribution. The long-term variations of the Ha line in a Eri seem to have a 14-15 year cyclic B?Be phase transition. The disc formation time scales, interpreted as the periods during which the Ha line emission increases from zero to its maximum, agree with the viscous decretion model. On the other hand, the time required for the disc dissipation ranges from 6 to 12 years which questions the viscous disc model.
69 citations
TL;DR: In this paper, the authors presented a mode identification based on new high-resolution time-series spectra of the non-radially pulsating delta Scuti star FG Vir (HD 106384, V = 6.57, A5V).
Abstract: Aims. We present a mode identification based on new high-resolution time-series spectra of the non-radially pulsating delta Scuti star FG Vir (HD 106384, V = 6.57, A5V). From 2002 February to June a global Delta Scuti Network (DSN) campaign, utilizing high-resolution spectroscopy and simultaneous photometry has been conducted for FG Vir in order to provide a theoretical pulsation model. In this campaign we have acquired 969 Echelle spectra covering 147 h at six observatories. Methods. The mode identification was carried out by analyzing line profile variations by means of the Fourier parameter fit method, where the observational Fourier parameters across the line are fitted with theoretical values. This method is especially well suited for determining the azimuthal order m of non-radial pulsation modes and thus complementary with the method of Daszynska-Daszkiewicz (2002) which does best at identifying the degree l. Results. 15 frequencies between 9.2 and 33.5 d(-1) were detected spectroscopically. We determined the azimuthal order m of 12 modes and constrained their harmonic degree l. Only modes of low degree (l <= 4) were detected, most of them having axisymmetric character mainly due to the relatively low projected rotational velocity of FG Vir. The detected non-axisymmetric modes have azimuthal orders between -2 and 1. We derived an inclination of 19 degrees, which implies an equatorial rotational rate of 66 km s(-1).
68 citations
Cites methods from "Line-profile variations due to adia..."
...Such a description has also been applied by Aerts & Waelkens (1993) in the case of the MM and by Schrijvers et al. (1997)....
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TL;DR: In this article, a spectroscopic monitoring campaign of the OB-star companions to the eclipsing X-ray pulsars SMC X-1, LMC X-4 and Cen X-3 is presented.
Abstract: We present the results of a spectroscopic monitoring campaign of the OB-star companions to the eclipsing X-ray pulsars SMC X-1, LMC X-4 and Cen X-3. High-resolution optical spectra obtained with UVES on the ESO Very Large Telescope are used to determine the radial-velocity orbit of the OB (super)giants with high precision. The excellent quality of the spectra provides the opportunity to measure the radial-velocity curve based on individual lines, and to study the effect of possible distortions of the line profiles due to e.g. X-ray heating on the derived radial-velocity amplitude. Several spectral lines show intrinsic variations with orbital phase. The magnitude of these variations depends on line strength, and thus provides a criterion to select lines that do not suffer from distortions. The undistorted lines show a larger radial-velocity amplitude than the distorted lines, consistent with model predictions. Application of our line-selection criteria results in a mean radial-velocity amplitude K(Opt) of 20.2 +/- 1.1, 35.1 +/- 1.5, and 27.5 +/- 2.3 km/s (1 sigma errors), for the OB companion to SMC X-1, LMC X-4 and Cen X-3, respectively. Adding information on the projected rotational velocity of the OB companion (derived from our spectra), the duration of X-ray eclipse and orbital parameters of the X-ray pulsar (obtained from literature), we arrive at a neutron star mass of 1.06^{+0.11}_{-0.10}, 1.25^{+0.11}_{-0.10} and 1.34^{+0.16}_{-0.14} M{sun} for SMC X-1, LMC X-4 and Cen X-3, respectively. The mass of SMC X-1 is near the minimum mass (~1 M{sun}) expected for a neutron star produced in a supernova. We discuss the implications of the measured mass distribution on the neutron-star formation mechanism, in relation to the evolutionary history of the massive binaries.
66 citations
Cites methods from "Line-profile variations due to adia..."
...Such computationally demanding techniques have been successfully explored in stellar pulsation studies (e.g. Schrijvers et al. 1997) and in modeling photome ric lightcurves of HMXBs (e.g. Heemskerk & Van Paradijs 1989)....
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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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