Non-radial Pulsation Modes Research Articles

The VELOCE modulation zoo I. Spectroscopic detection of non-radial modes in the first-overtone Cepheids BG Crucis, QZ Normae, V0391 Normae, and V0411 Lacertae

The photometric observations from the recent decade revolutionized our view on classical pulsators. Low-amplitude signals have been detected photometrically in addition to the dominant high-amplitude radial mode pulsations in many RR Lyrae stars and classical Cepheids. First-overtone pulsators with an additional low-amplitude signal at a period ratio of around 0.61 with the main mode, the so-called 0.61 stars, form the most populous group among these stars. The nature of this signal has been attributed to non-radial pulsations. Another mysterious group are stars in which the additional signal forms a period ratio of around 0.68. These are the 0.68 stars. The origin of the signal remains unknown. Here, we search for similar phenomena in spectroscopic observations of first-overtone classical Cepheids collected as part of the project. We performed a frequency analysis of several parameters derived from cross-correlation functions (CCFs), including radial velocity, the full width at half maximum, the bisector inverse span, and the CCF depth (contrast). Using standard pre-whitening, we searched for additional low-amplitude signals. We identified the location of these stars in various sequences of the Petersen diagram. We detect additional signals in four first-overtone classical Cepheids: BG Cru, QZ Nor, V0391 Nor, and V0411 Lac. We classified BG Cru, QZ Nor, and V0391 Nor as 0.61 stars based on their period ratios. V0411 Lac, however, exhibits a ratio of 0.68 between the two modes, and the additional signal has a longer period. This type of multi-periodicity remains unexplained. CCFs yield the first spectroscopic detections of non-radial pulsation modes in classical Cepheids. This opens an asteroseismic window for pursuing a more detailed understanding of these important stars. While the 0.61 signal of BG Cru, QZ Nor, and V0391 Nor is understood to originate from non-radial modes of moderate degrees, the 0.68 signal of V0411 Lac still lacks a physical explanation.

Frequency analysis of OGLE-IV photometry for classical Cepheids in Galactic fields: non-radial modes and modulations

ABSTRACT We analyse photometry of ∼2000 Galactic Cepheids available in the OGLE Collection of Variable Stars. We analyse both Galactic disc and Galactic bulge fields; stars classified both as single- and multiperiodic. Our goal was to search for additional low-amplitude variability. We extend the sample of multimode radial pulsators by identifying 10 new candidates for double mode and 6 new candidates for triple-mode pulsation. In the first overtone OGLE sample, we found 12 Cepheids with additional periodicity having period ratio $P_{\rm x}/P_{\rm 1O}\in (0.60,\, 0.65)$. These periodicities do not correspond to any other radial mode. While such variables are abundant in the Magellanic Clouds, only one Cepheid of this class was known in the Galaxy before our analysis. Comparing our sample with the Magellanic Cloud Cepheids, we note a systematic shift towards longer pulsation periods for more metal rich Galactic stars. Moreover, in 11 stars we find one more type of additional variability, with characteristic frequencies close to half of that reported in the group with (0.60, 0.65) period ratios. Two out of the above inventory show simultaneous presence of both signals. Most likely, origin of these signals is connected to excitation of non-radial pulsation modes. We report three Cepheids with low-amplitude periodic modulation of pulsation: two stars are single-mode fundamental and first overtone Cepheids and one is a double-mode Cepheid pulsating simultaneously in fundamental and in first overtone modes. Only the former mode is modulated. It is a first detection of periodic modulation of pulsation in this type of double-mode Cepheids.

New Beta Cephei Stars from the KELT Project

Abstract We present the results of a search for Galactic β Cephei stars, which are massive pulsating stars with both pressure modes and mixed modes. Thus, these stars can serve as benchmarks for seismological studies of the interiors of massive stars. We conducted the search by performing a frequency analysis on the optical light curves of known O- and B-type stars with data from the Kilodegree Extremely Little Telescope exoplanet survey. We identify 113 β Cephei stars, of which 86 are new discoveries, which altogether represent a 70% increase in the number currently known. An additional 97 candidates are identified. Among our targets, we find five new eclipsing binaries and 22 stars with equal frequency spacings suggestive of rotational splitting of nonradial pulsation modes. Candidates for runaway stars among our targets and a number of interesting individual objects are discussed. Most of the known and newly discovered β Cephei stars will be observed by the Transiting Exoplanet Survey Satellite mission, providing by far the most comprehensive observational data set of massive main-sequence pulsating stars of sufficient quality for detailed asteroseismic studies. Future analysis of these light curves has the potential to dramatically increase our understanding of the structure of stellar interiors and the physical processes taking place therein.

The census of non-radial pulsation in first-overtone RR Lyrae stars of the OGLE Galactic bulge collection

ABSTRACT We analysed photometry for the up-to-date collection of the first-overtone RR Lyrae stars (RRc; 11 415 stars) and double-mode RR Lyrae stars (RRd; 148 stars) towards the Galactic bulge from the Optical Gravitational Lensing Experiment (OGLE). We analysed frequency spectra of these stars in search for additional, low-amplitude signals, beyond the radial modes. We focused on stars from two groups: RR0.61 and RR0.68. In the first group, additional low-amplitude signals have periods shorter than the first-overtone period; period ratios fall in the 0.60–0.64 range. In the second group, additional low-amplitude signals have periods longer than the first-overtone period; period ratios tightly cluster around 0.68. Altogether we have detected 960 and 147 RR Lyrae stars that belong to RR0.61 and RR0.68 groups, respectively, which yield the incidence rates of 8.3 and 1.3 per cent of the considered sample. We discuss statistical properties of RR Lyrae stars with additional periodicities. For RR0.61 group we provide strong arguments that additional periodicities are connected to non-radial pulsation modes of degrees ℓ = 8 and ℓ = 9, as proposed by Dziembowski. We have also detected two double-periodic variables, with two close periodicities, similar to RR Lyrae variable V37 in NGC 6362. Properties of these peculiar variables, which may form a new group of double-mode pulsators, are discussed.

Short-term variability and mass loss in Be stars

Context. In early-type Be stars, groups of nonradial pulsation (NRP) modes with numerically related frequencies may be instrumental for the release of excess angular momentum through mass-ejection events. Difference and sum/harmonic frequencies often form additional groups.Aims. The purpose of this study is to find out whether a similar frequency pattern occurs in the cooler third-magnitude B7-8 IIIe shell starνPup.Methods. Time-series analyses were performed of space photometry with BRITE-Constellation (2015, 2016/17, and 2017/18), SMEI (2003–2011), and HIPPARCOS(1989–1993). Two IUE SWP and 27 optical echelle spectra spanning 20 years were retrieved from various archives.Results. The optical spectra exhibit no anomalies or well-defined variabilities. A magnetic field was not detected. All three photometry satellites recorded variability near 0.656 c/d which is resolved into three features separated by ∼0.0021 c/d. Their first harmonics and two combination frequencies form a second group, whose features are similarly spaced by 0.0021 c/d. The frequency spacing is very nearly but not exactly equidistant. Variability near 0.0021 c/d was not detected. The long-term frequency stability could be used to derive meaningful constraints on the properties of a putative companion star. The IUE spectra do not reveal the presence of a hot subluminous secondary.Conclusions.νPup is another Be star exhibiting an NRP variability pattern with long-term constancy and underlining the importance of combination frequencies and frequency groups. This star is a good target for efforts to identify an effectively single Be star.

Spectroscopic time-series analysis of R Canis Majoris

R Canis Majoris is the prototype of a small group of Algol-type stars showing short orbital periods and low mass ratios. A previous detection of short-term oscillations in its light curve has not yet been confirmed. We investigate a new time series of high-resolution spectra with the aim to derive improved stellar and system parameters, to search for the possible impact of a third component in the observed spectra, to look for indications of activity in the Algol system, and to search for short-term variations in radial velocities. We disentangled the composite spectra into the spectra of the binary components. Then we analysed the resulting high signal-to-noise spectra of both stars. Using a newly developed program code based on an improved method of least-squares deconvolution, we were able to determine the radial velocities of both components also during primary eclipse. This allowed us to develop a better model of the system including the Rossiter–McLaughlin effect and to derive improved orbital parameters. Combining the results with those from spectrum analysis, we obtain accurate stellar and system parameters. We further deduce at least one oscillation frequency of 21.38 c d−1. It could be detected during primary eclipses only and confirms a previous photometric finding. Results point to an amplitude amplification of non-radial pulsation modes due to the eclipse mapping effect. The presence of a He I line in the spectra indicates mass transfer in the R CMa system. Calculations of its Roche geometry give evidence that the cool secondary component may fill its Roche lobe. No evidence of a third body in the system could be found in the observed spectra.

Short-term variability and mass loss in Be stars

Context. Be stars are important reference laboratories for the investigation of viscous Keplerian discs. In some cases, the disc feeder mechanism involves a combination of non-radial pulsation (NRP) modes. Aims. We seek to understand whether high-cadence photometry can shed further light on the role of NRP modes in facilitating rotation-supported mass loss. Methods. The BRITE-Constellation of nanosatellites obtained mmag photometry of 28 Cygni for 11 months in 2014–2016. We added observations with the Solar Mass Ejection Imager (SMEI) in 2003–2010 and 118 Hα line profiles, half of which were from 2016. Results. For decades, 28 Cyg has exhibited four large-amplitude frequencies: two closely spaced frequencies of spectroscopically confirmed g modes near 1.5 c/d, one slightly lower exophotospheric (Štefl) frequency, and at 0.05 c/d the difference (Δ) frequency between the two g modes. This top-level framework is indistinguishable from η Cen (Paper I), which is also very similar in spectral type, rotation rate, and viewing angle. The circumstellar (Štefl) frequency alone does not seem to be affected by the Δ frequency. The amplitude of the Δ frequency undergoes large variations; around maximum the amount of near-circumstellar matter is increased and the amplitude of the Štefl frequency grows by a factor of a few. During such brightenings dozens of transient spikes appear in the frequency spectrum; these spikes are concentrated into three groups. Only 11 frequencies were common to all years of BRITE observations. Conclusions. Be stars seem to be controlled by several coupled clocks, most of which are not very regular on timescales of weeks to months but function for decades. The combination of g modes to the slow Δ variability and/or the atmospheric response to it appears significantly non-linear. As in η Cen, the Δ variability seems to be mainly responsible for the modulation of the star-to-disc mass transfer in 28 Cyg. A hierarchical set of Δ frequencies may reach the longest known timescales of the Be phenomenon.

Ap stars with resolved magnetically split lines: Magnetic field determinations from StokesIandVspectra

We present the results of a systematic study of the magnetic fields and other properties of the Ap stars with resolved magnetically split lines. This study is based on new measurements of the mean magnetic field modulus, the mean longitudinal magnetic field, the crossover, the mean quadratic magnetic field, and the radial velocity of 43 stars, complemented by magnetic data from the literature for 41 additional stars. Stars with resolved magnetically split lines represent a significant fraction, of the order of several percent, of the whole population of Ap stars. Most of them are genuine slow rotators, whose consideration provides new insight into the long-period tail of the distribution of the periods of the Ap stars. Emerging correlations between rotation periods and magnetic properties provide important clues for the understanding of the braking mechanisms that have been at play in the early stages of stellar evolution. The geometrical structures of the magnetic fields of Ap stars with magnetically resolved lines appear in general to depart slightly, but not extremely, from centred dipoles. However, there are a few remarkable exceptions, which deserve further consideration. We suggest that pulsational crossover can be observed in some stars; if confirmed, this would open the door to the study of non-radial pulsation modes of degree $\ell$ too high for photometric or spectroscopic observations. How the lack of short orbital periods among binaries containing an Ap component with magnetically resolved lines is related with their (extremely) slow rotation remains to be fully understood, but the very existence of acorrelation between the two periods lends support to the merger scenario for the origin of Ap stars.

Pulsating low-mass white dwarfs in the frame of new evolutionary sequences

We present a theoretical assessment of the expected temporal rates of change of periods ($\dot{\Pi}$) for low-mass ($M_{\star}/M_{\sun} \lesssim 0.45$) and extremely low-mass (ELM, $M_{\star}/M_{\sun} \lesssim 0.18-0.20$) white-dwarf stars, based on fully evolutionary low-mass He-core white dwarf and pre-white dwarf models. Our analysis is based on a large set of adiabatic periods of radial and nonradial pulsation modes computed on a suite of low-mass He-core white dwarf and pre-white dwarf models with masses ranging from $0.1554$ to $0.4352 M_{\sun}$. We compute the secular rates of period change of radial ($\ell= 0$) and nonradial ($\ell= 1, 2$) $g$ and $p$ modes for stellar models representative of ELMV and pre-ELMV stars, as well as for stellar objects that are evolving just before the occurrence of CNO flashes at the early cooling branches. We found that the theoretically expected magnitude of $\dot{\Pi}$ of $g$ modes for pre-ELMVs are by far larger than for ELMVs. In turn, $\dot{\Pi}$ of $g$ modes for models evolving before the occurrence of CNO flashes are larger than the maximum values of the rates of period change predicted for pre-ELMV stars. Regarding $p$ and radial modes, we found that the larger absolute values of $\dot{\Pi}$ correspond to pre-ELMV models. We conclude that any eventual measurement of a rate of period change for a given pulsating low-mass pre-white dwarf or white dwarf star could shed light about its evolutionary status. Also, in view of the systematic difficulties in the spectroscopic classification of stars of the ELM Survey, an eventual measurement of $\dot{\Pi}$ could help to confirm that a given pulsating star is an authentic low-mass white dwarf and not a star from another stellar population.

Mass-ejection events in Be stars triggered by coupled nonradial pulsation modes

AbstractBe stars (for an in-depth review see Rivinius, Carciofi & Martayan 2013) rotate at ⩾80% of the critical velocity and are multi-mode nonradial pulsators. Magnetic dipole fields are not detected, and binaries with periods less than 30 days are rare. The name-giving emission lines form in a Keplerian decretion disk, which is viscously re-accreted and also radiatively ablated unless replenished by outburts of unknown origin.Months-long, high-cadence space photometry with the BRITE-Constellation nanosatellites (Pablo et al. 2016) of about 10 early-type Be stars reveals the following (cf. Baade et al. 2016a, Baade et al. 2016b): ○Many Be stars exhibit 1 or 2 so-called Δ frequencies, which are differences between two nonradial-pulsation (NRP) frequencies and much lower (mostly less than 0.1 c/d) than the parent frequencies. The associated light curves are roughly sinusoidal. The amplitudes can exceed that of the sum of the parent amplitudes.○Conventional beat patterns also occur.○Amplitudes of both Δ and beat frequencies can temporarily be enhanced. Around phases of maximal amplitude the mean brightness is in- or decreased, and the scatter can be enhanced.○During high-activity phases (outbursts), broad and dense groups of numerous spikes arise in the power spectra. The two strongest groups often have a frequency ratio near 2. The phase coherence seems to be low.○Time coverage (less than half a year) is not yet sufficient to infer whether two Δ or beat frequencies can combine to cause long-lasting (years) superoutbursts (cf. Carciofi et al. 2012).From these observations it is concluded: •The variable mean brightness and the increased Δ-frequency amplitude and scatter trace the amount of near-circumstellar matter.•Increase or decrease of mean brightness is aspect-angle dependent (pole-on vs. equator-on).•Increased amounts of near-circumstellar matter are due to rotation-assisted mass ejections caused by coupled NRP modes.•Observations do not constrain the location of the coupling (atmosphere or stellar interior).•Broad frequency groups do not represent stellar pulsation modes but circumstellar variability.•Be stars later than B5 are less active and may in some cases even behave differently.

Spectral modelling of theαVirginis (Spica) binary system

Context: The technique of matching synthetic spectra computed with theoretical stellar atmosphere models to the observations is widely used in deriving fundamental parameters of massive stars. When applied to binaries, however, these models generally neglect the interaction effects present in these systems Aims: The aim of this paper is to explore the uncertainties in binary stellar parameters that are derived from single-star models Methods: Synthetic spectra that include the tidal perturbations and irradiation effects are computed for the binary system alpha Virginis (Spica) using our recently-developed CoMBiSpeC model. The synthetic spectra are compared to S/N~2000 observations and optimum values of Teff and log(g) are derived. Results: The binary interactions have only a small effect on the strength of the photospheric absorption lines in Spica (<2% for the primary and <4% for the secondary). These differences are comparable to the uncertainties inherent to the process of matching synthetic spectra to the observations and thus the derived values of Teff and log(g) are unaffected by the binary perturbations. On the other hand, the interactions do produce significant phase-dependent line profile variations in the primary star, leading to systematic distortions in the shape of its radial velocity curve. Migrating sub-features ("bumps") are predicted by our model to be present in the same photospheric lines as observed, and their appearance does not require any a priori assumptions regarding non-radial pulsation modes. Matching the strength of lines in which the most prominent "bumps" occur requires synthetic spectra computed with larger "microturbulence" than that required by other lines.

HUBBLE SPACE TELESCOPEAND OPTICAL DATA ON SDSSJ0804+5103 (EZ Lyn) ONE YEAR AFTER OUTBURST

We present an ultraviolet spectrum and light curve of the short orbital period cataclysmic variable EZ Lyn obtained with the Cosmic Origins Spectrograph on the Hubble Space Telescope 14 months after its dwarf nova outburst, along with ground-based optical photometry. The UV spectrum can be fit with a 13,100K, log g=8 white dwarf using 0.5 solar composition, while fits to the individual lines are consistent with solar abundance for Si and Al, but only 0.3 solar for C. The Discrete Fourier Transforms of the UV and optical light curves at 14 months following outburst show a prominent period at 256 sec. This is the same period reported by Pavlenko in optical data obtained 7 months and one year after outburst, indicating its long term stability over several months, but this period is not evident in the pre-outburst data and is much shorter than the 12.6 min period that was seen in observations obtained during an interval from 8 months to 2.5 years after the 2006 outburst. In some respects, the long and short periods are similar to the behavior seen in GW Lib after its outburst but the detailed explanation for the appearance and disappearance of these periods and their relation to non-radial pulsation modes remain to be explored with theoretical models.

The pulsations of the B5IVe star HD 181231 observed with CoRoT and ground-based spectroscopy

Context. HD 181231 is a B5IVe star, which has been observed with the CoRoT satellite during ∼5 consecutive months and simultaneously from the ground in spectroscopy and spectropolarimetry. Aims. By analysing these data, we aim to detect and characterize as many pulsation frequencies as possible, to search for the presence of beating effects possibly at the origin of the Be phenomenon. Our results will also provide a basis for seismic modelling. Methods. The fundamental parameters of the star are determined from spectral fitting and from the study of the circumstellar emission. The CoRoT photometric data and ground-based spectroscopy are analysed using several Fourier techniques: Clean-ng ,P asper ,a nd Tisaft, as well as a time-frequency technique. A search for a magnetic field is performed by applying the LSD technique to the spectropolarimetric data. Results. We find that HD 181231 is a B5IVe star seen with an inclination of ∼45 degrees. No magnetic field is detected in its photosphere. We detect at least 10 independent significant frequencies of variations among the 54 detected frequencies, interpreted in terms of non-radial pulsation modes and rotation. Two longer-term variations are also detected: one at ∼14 days resulting from a beating effect between the two main frequencies of short-term variations, the other at ∼116 days due either to a beating of frequencies or to a zonal pulsation mode. Conclusions. Our analysis of the CoRoT light curve and ground-based spectroscopic data of HD 181231 has led to the determination of the fundamental and pulsational parameters of the star, including beating effects. This will allow a precise seismic modelling of this star.

A 3D study of the photosphere of HD 99563 - I. Pulsation analysis

We have used high-speed spectroscopy of the rapidly oscillating Ap (roAp) star HD 99563 to study the pulsation amplitude and phase behaviour of elements in its stratified atmosphere over one 2.91-d rotation cycle. We identify spectral features related to patches in the surface distribution of chemical elements and study the pulsation amplitudes and phases as the patches move across the stellar disc. The variations are consistent with a distorted non-radial dipole pulsation mode. We measure a 1.6 km s−1 rotational variation in the mean radial velocities of Hα and argue that this is the first observation of Hα abundance spots caused by He settling through suppression of convection by the magnetic field on an oblique rotator, in support of a prime theory for the excitation mechanism of roAp star pulsation. We demonstrate that HD 99563 is the second roAp star to show aspect dependence of blue-to-red running wave line profile variations in Nd iii spots.

A new method for the spectroscopic identification of stellar non-radial pulsation modes

Aims. We present the Fourier parameter fit method, a new method for spectroscopically identifying stellar radial and non-radial pulsation modes based on the high-resolution time-series spectroscopy of absorption-line profiles. In contrast to previous methods this one permits a quantification of the statistical significance of the computed solutions. The application of genetic algorithms in seeking solutions makes it possible to search through a large parameter space. Methods. The mode identification is carried out by minimizing Χ 2 , using the observed amplitude and phase across the line profile and their modeled counterparts. Computations of the theoretical line profiles are based on a stellar displacement field, which is described as superposition of spherical harmonics and that includes the first order effects of the Coriolis force. Results. We made numerical tests of the method on a grid of different mono- and multi-mode models for 0 ≤ l ≤ 4 in order to explore its capabilities and limitations. Our results show that whereas the azimuthal order m can be unambiguously identified for low-order modes, the error of l is in the range of ±1. The value of m can be determined with higher precision than with other spectroscopic mode identification methods. Improved values for the inclination can be obtained from the analysis of non-axisymmetric pulsation modes. The new method is ideally suited to intermediatley rotating 6 Scuti andβ Cephei stars.

TW Dra: NRP mode identification with FAMIAS

Die Serie Communications in Asteroseismology (CoAst) stellt eine international gefragte Plattform für wissenschaftliche Publikationen der neuesten Forschungsergebnisse auf dem Gebiet der Asteroseismologie dar. Forschungsgegenstand der Asteroseismologie sind veränderliche und pulsierende Sterne. Neben den halbjährlich erscheinenden regulären Ausgaben mit Beiträgen aus der laufenden Forschung werden auch Sonderausgaben für Konferenzberichte bzw. Programmhandbücher herausgegeben. JENAM (Joint European and National Astronomy Meeting) ist die größte jährliche Zusammenkunft der europäischen Berufsastronomen, die diesmal im September 2008 in Wien stattfand. Die Konferenz beherbergte neun Minisymposien, wobei eines der Asteroseismologie gewidmet war. Die neuesten Entwicklungen auf diesem Gebiet sind im vorliegenden Band im Rahmen von Übersichts- und Detailartikeln zusammengefasst.

Towards mode selection in δ Scuti stars: regularities in observed and theoretical frequency spectra

Only a fraction of the theoretically predicted nonradial pulsation modes have so far been observed in Delta Scuti stars. Nevertheless, the large number of frequencies detected in recent photometric studies of selected Delta Scuti stars allow us to look for regularities in the frequency spacing of modes. Mode identifications are used to interpret these results. Statistical analyses of several Delta Scuti stars (FG Vir, 44 Tau, BL Cam and others) show that the photometrically observed frequencies are not distributed at random, but that the excited nonradial modes cluster around the frequencies of the radial modes over many radial orders. The observed regularities can be partly explained by modes trapped in the stellar envelope. This mode selection mechanism was proposed by Dziembowski & Krolikowska (1990) and shown to be efficient for l = 1 modes. New pulsation model calculations confirm the observed regularities. We present the s-f diagram, which compares the average separation of the radial frequencies (s) with the frequency of the lowest-frequency unstable radial mode (f). This provides an estimate for the log g value of the observed star, if we assume that the centers of the observed frequency clusters correspond to the radial mode frequencies. This assumption is confirmed by examples of well-studied Delta Scuti variables in which radial modes were definitely identified.

MOST photometry of the RRd Lyrae variable AQ Leo: two radial modes, 32 combination frequencies and beyond

Highly precise and nearly uninterrupted optical photometry of the RR Lyrae star AQ Leo was obtained with the MOST (Microvariability & Oscillations of STars) satellite over 34.4 days in February-March 2005. AQ Leo was the first known double-mode RR Lyrae pulsator (RRd star). Three decades after its discovery, MOST observations have revealed that AQ Leo oscillates with at least 42 frequencies, of which 32 are linear combinations (up to the sixth order) of the radial fundamental mode and its first overtone. Evidence for period changes of these modes is found in the data. The other intrinsic frequencies may represent an additional nonradial pulsation mode and its harmonics (plus linear combinations) which warrant theoretical modeling. The unprecedented number of frequencies detected with amplitudes down to millimag precision also presents an opportunity to test nonlinear theories of mode growth and saturation in RR Lyrae pulsators.

A new method for the spectroscopic identification of stellar non-radial pulsation modes

We present the Fourier parameter fit method, a new method for spectroscopically identifying stellar radial and non-radial pulsation modes based on the high-resolution time-series spectroscopy of absorption-line profiles. In contrast to previous methods this one permits a quantification of the statistical significance of the computed solutions. The application of genetic algorithms in seeking solutions makes it possible to search through a large parameter space. The mode identification is carried out by minimizing chi-square, using the observed amplitude and phase across the line profile and their modeled counterparts. Computations of the theoretical line profiles are based on a stellar displacement field, which is described as superposition of spherical harmonics and that includes the first order effects of the Coriolis force. We made numerical tests of the method on a grid of different mono- and multi-mode models for 0 <= l <= 4 in order to explore its capabilities and limitations. Our results show that whereas the azimuthal order m can be unambiguously identified for low-order modes, the error of l is in the range of pm 1. The value of m can be determined with higher precision than with other spectroscopic mode identification methods. Improved values for the inclination can be obtained from the analysis of non-axisymmetric pulsation modes. The new method is ideally suited to intermediatley rotating Delta Scuti and Beta Cephei stars.

A new method for the spectroscopic identification of stellar non-radial pulsation modes

Aims.We present a mode identification based on new high-resolution time-series spectra of the non-radially pulsating δ Scuti star FG Vir (HD 106384, , 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.