Slowly Pulsating B Stars Research Articles

Non-linear three-mode coupling of gravity modes in rotating slowly pulsating B stars

Context. Slowly pulsating B (SPB) stars display multi-periodic variability in the gravito-inertial mode regime with indications of non-linear resonances between modes. Several have undergone asteroseismic modeling in the past few years to infer their internal properties, but only in a linear setting. These stars rotate fast, so that rotation is typically included in the modeling by means of the traditional approximation of rotation (TAR). Aims. We aim to extend the set of tools available for asteroseismology, by describing time-independent (stationary) resonant non-linear coupling among three gravito-inertial modes within the TAR. Such coupling offers the opportunity to use mode amplitude ratios in the asteroseismic modeling process, instead of only relying on frequencies of linear eigenmodes, as has been done so far. Methods. Following observational detections, we derive expressions for the resonant stationary non-linear coupling between three gravito-inertial modes in rotating stars. We assess selection rules and stability domains for stationary solutions. We also predict non-linear frequencies and amplitude ratio observables that can be compared with their observed counterparts. Results. The non-linear frequency shifts of stationary couplings are negligible compared to typical frequency errors derived from observations. The theoretically predicted amplitude ratios of combination frequencies match with some of their observational counterparts in the SPB targets. Other, unexplained observed ratios could be linked to other saturation mechanisms, to interactions between different modes, or to different opacity gradients in the driving zone. Conclusions. For the purpose of asteroseismic modeling, our non-linear mode coupling formalism can explain some of the stationary amplitude ratios of observed resonant mode couplings in single SPB stars monitored during 4 years by the Kepler space telescope.

Characterizing B stars from Kepler /K2 Campaign 11. Optical analysis and seismic diagnostics

In this study, we analyze 122 B-type star candidates observed during Campaign 11 of the Kepler /K2 mission to investigate their variability and pulsation characteristics. A subset of 45 B star candidates was observed during the Kepler /K2 mission's Campaign 11 between September and December 2016. Our analyses aim to gain a deeper understanding of the physical characteristics of these massive stars. Our methods involve both spectroscopy and seismology. The spectroscopic analysis was performed through medium-resolution blue spectra, which also allowed us to perform a spectral classification of the objects. Our results will contribute to the ongoing effort to expand our knowledge of variable B stars and the processes that drive their variability. We used the iterative prewhitening and wavelet frequency searching algorithms to analyze the light curves to identify the different types of variability in the data. The frequencies were carefully chosen based on the signal-to-noise ratio and the magnitude of errors. We applied spectroscopic analysis techniques to enhance our understanding of the observed stars, including sme and mesa algorithms. A spectral classification was performed based on the observed spectra. The resulting astrophysical parameters were compared to Gaia mission data. Additionally, a seismology technique was applied to determine the average internal rotation frequency ($ rot $) and buoyancy travel time ($P_0$) for selected stars in the sample. We detected several types of variability among the B-type stars, including slowly pulsating B (SPB) stars, hybrid pulsators showing both beta Cep and SPB pulsations, stars with stochastic low-frequency (SLF) variability, Maia variables, and SPB/Maia hybrids. Their positions in our Gaia and classical HR diagrams are compatible with the theoretical expectations. We also found stars exhibiting variability attributed to binarity and rotation. We determined the physical characteristics for 45 of our targets and conducted a seismic analysis for 14 objects. Two SPB/Maia stars show internal velocities comparable to those of fast SPB stars. The derived average rotation frequencies, $ rot $, for these 14 stars lie between the critical $ crit Roche $ and the minimal frequency values of $ lim rot $ implied by the $ i $ measured from the spectra. Our analysis classified 41 stars as SPB stars and attributed the primary variability of 53 objects to binarity, rotation, or both. We identified five stars as Maia/fast-rotating SPB variables. Two stars were classified as hybrid SPB/beta Cep pulsators, and one as a beta Cep binary. Thirteen stars exhibited prominent, low-frequency power excess, indicating SLF variability. Additionally, we found a positive correlation between the dominant $ f g $ frequency and the internal average rotation frequency.

Mode coupling coefficients between the convective core and radiative envelope of γ Doradus and slowly pulsating B stars

Context. Signatures of coupling between an inertial mode in the convective core and a gravito-inertial mode in the envelope have been found in four-year Kepler light curves of 16 rapidly rotating γ Doradus (γ Dor) stars. This makes it possible to obtain a measurement of the rotation frequency in their convective core. Despite their similar internal structure and available data, inertial modes have not yet been reported for slowly pulsating B (SPB) stars. Aims. We aim to provide a numerical counterpart of the recently published theoretical expressions for the mode-coupling coefficients, ε and ε̃. These coefficients represent the two cases of a continuous and a discontinuous Brunt-Väisälä frequency profile at the core-envelope interface, respectively. We consider γ Dor and SPB stars to shed light on the difference between these two classes of intermediate-mass gravito-inertial mode pulsators in terms of core and envelope mode coupling. Methods. We used asteroseismic forward models of two samples consisting of 26 SPB stars and 37 γ Dor stars to infer their numerical values of ε and ε̃. For both samples, we also computed: the linear correlation coefficients between ε or ε̃ and the near-core rotation frequency, the chemical gradient, the evolutionary stage, the convective core masses and radii, and the Schönberg-Chandrasekhar limiting mass representing the maximum mass of an inert helium core at central hydrogen exhaustion that can still withstand the pressure of the overlaying envelope. Results. The asteroseismically inferred values of ε and ε̃ for the two samples are between 0.0 and 0.34. While ε is most strongly correlated with the near-core rotation frequency for γ Dor stars, the fractional radius of the convective core instead provides the tightest correlation for SPB stars. We find ε to decrease mildly as the stars evolve. For the SPB stars, ε and ε̃ have similar moderate correlations with respect to the core properties. For the γ Dor stars, ε̃ reveals systematically lower and often no correlation to the core properties; their ε is mainly determined by the near-core rotation frequency. The Schönberg-Chandrasekar limit is already surpassed by the more massive SPB stars, while none of the γ Dor stars have reached it yet. Conclusions. Our asteroseismic results for the mode coupling support the theoretical interpretation and reveal that young, fast-rotating γ Dor stars are most suitable for undergoing couplings between inertial modes in the rotating convective core and gravito-inertial modes in the radiative envelope. The phenomenon has been found in 2.4% of such pulsators with detected period spacing patterns, whereas it has not been seen in any of the SPB stars so far.

Observational Properties of 155 O- and B-type Massive Pulsating Stars

O- and B-type (OB-type) pulsating stars are important objects for studying the structure and evolution of massive stars through asteroseismology. A large amount of data from various sky surveys provides an unprecedented opportunity to search for and study this kind of variable star. We identify 155 OB-type pulsating stars or candidates, including 38 Oe/Be stars or candidates, from the data observed by TESS, LAMOST, and Gaia, which are almost new. Among the 155 objects, 87 samples are identified as slowly pulsating B (SPB) stars including 37 objects with pure low-frequency and 50 objects with both low- and high-frequency pulsation, and 14 samples are identified as β Cephei pulsating variable (BCEP) stars with both low- and high-frequency pulsation. An H-R diagram shows that these SPB and BCEP stars are mainly located in their instability regions and in the evolutionary stage of the main sequence with mass ranges of 2.5–20 M ⊙ and 7–20 M ⊙, respectively. Two special objects show Fourier spectra similar to BCEP stars but with different positions in H-R, period–temperature (P-T), and period–luminosity (P-L) diagrams. Meanwhile, 52 other targets are identified as candidates of OB-type pulsating stars. We also derive the preliminary results of the P-L relation for SPB and BCEP stars, respectively. This work also indicates that in addition to the H-R diagram, the P-T and P-L diagrams are also very useful for the classification of SPB and BCEP stars. Further detailed analysis of these objects can dramatically increase our understanding of the theories of evolution and structure for massive OB-type pulsating stars.

Detecting deep axisymmetric toroidal magnetic fields in stars

Context. Asteroseismology has revealed small core-to-surface rotation contrasts in stars in the whole Hertzsprung–Russell diagram. This is the signature of strong transport of angular momentum (AM) in stellar interiors. One of the plausible candidates to efficiently carry AM is magnetic fields with various topologies that could be present in stellar radiative zones. Among them, strong axisymmetric azimuthal (toroidal) magnetic fields have received a lot of interest. Indeed, if they are subject to the so-called Tayler instability, the accompanying triggered Maxwell stresses can transport AM efficiently. In addition, the electromotive force induced by the fluctuations of magnetic and velocity fields could potentially sustain a dynamo action that leads to the regeneration of the initial strong axisymmetric azimuthal magnetic field. Aims. The key question we aim to answer is whether we can detect signatures of these deep strong azimuthal magnetic fields. The only way to answer this question is asteroseismology, and the best laboratories of study are intermediate-mass and massive stars with external radiative envelopes. Most of these are rapid rotators during their main sequence. Therefore, we have to study stellar pulsations propagating in stably stratified, rotating, and potentially strongly magnetised radiative zones, namely magneto-gravito-inertial (MGI) waves. Methods. We generalise the traditional approximation of rotation (TAR) by simultaneously taking general axisymmetric differential rotation and azimuthal magnetic fields into account. Both the Coriolis acceleration and the Lorentz force are therefore treated in a non-perturbative way. Using this new formalism, we derive the asymptotic properties of MGI waves and their period spacings. Results. We find that toroidal magnetic fields induce a shift in the period spacings of gravity (g) and Rossby (r) modes. An equatorial azimuthal magnetic field with an amplitude of the order of 105 G leads to signatures that are detectable in period spacings for high-radial-order g and r modes in γ Doradus (γ Dor) and slowly pulsating B (SPB) stars. More complex hemispheric configurations are more difficult to observe, particularly when they are localised out of the propagation region of MGI modes, which can be localised in an equatorial belt. Conclusions. The magnetic TAR, which takes into account toroidal magnetic fields in a non-perturbative way, is derived. This new formalism allows us to assess the effects of the magnetic field in γ Dor and SPB stars on g and r modes. We find that these effects should be detectable for equatorial fields thanks to modern space photometry using observations from Kepler, TESS CVZ, and PLATO.

Detection of non-linear resonances among gravity modes of slowly pulsating B stars: Results from five iterative pre-whitening strategies

Context. Slowly pulsating B (SPB) stars are main-sequence multi-periodic oscillators that display non-radial gravity modes. For a fraction of these pulsators, 4-year photometric light curves obtained with the Kepler space telescope reveal period spacing patterns from which their internal rotation and mixing can be inferred. In this inference, any direct resonant mode coupling is usually ignored. Aims. We re-analyse the light curves of a sample of 38 known Kepler SPB stars. For 26 of them, the internal structure, including rotation and mixing, was recently inferred from their dipole prograde oscillation modes. Our aim is to detect direct non-linear resonant mode coupling among the largest-amplitude gravity modes. Methods. We extract up to 200 periodic signals per star with five different iterative pre-whitening strategies based on linear and non-linear regression applied to the light curves. We then identify candidate coupled gravity modes by verifying whether they fulfil resonant phase relations. Results. For 32 of the 38 SPB stars we find at least one candidate resonance that is detected in both the linear and the best non-linear regression model fit to the light curve and involves at least one of the two largest-amplitude modes. Conclusions. The majority of the Kepler SPB stars reveal direct non-linear resonances based on the largest-amplitude modes. These stars are thus prime targets for the non-linear asteroseismic modelling of intermediate-mass dwarfs to assess the importance of mode couplings in probing their internal physics.

BRITE photometry and STELLA spectroscopy of bright stars in Auriga: Rotation, pulsation, orbits, and eclipses

Context. Knowing rotational and pulsational periods across the Hertzsprung-Russell diagram is of top priority for understanding stellar activity as a function of time. Aims. We aim to determine periods for bright stars in the Auriga field that are otherwise not easily accessible for ground-based photometry. Methods. Continuous photometry with up to three BRITE satellites was obtained for 12 targets and subjected to a period search. Contemporaneous high-resolution optical spectroscopy with STELLA was used to obtain radial velocities through cross correlation with template spectra as well as to determine astrophysical parameters through a comparison with model spectra. Results. The Capella red light curve was found to be constant over 176 days with a root mean square of 1 mmag, but the blue light curve showed a period of 10.1 ± 0.6 d, which we interpret to be the rotation period of the G0 component. From STELLA we obtained an improved orbital solution based on 9600 spectra from the previous 12.9 yr. We derive masses precise to ≈0.3% but 1% smaller than previously published. The BRITE light curve of the F0 supergiant ε Aur suggests 152 d as its main pulsation period, while the STELLA radial velocities reveal a clear 68 d period. An ingress of an eclipse of the ζ Aur binary system was covered with BRITE and a precise timing for its eclipse onset derived. A possible 70 d period fits the proposed tidal-induced, nonradial pulsations of this ellipsoidal K4 supergiant. η Aur is identified as a slowly pulsating B (SPB) star with a main period of 1.29 d and is among the brightest SPB stars discovered so far. The rotation period of the magnetic Ap star θ Aur is detected from photometry and spectroscopy with a period of 3.6189 d and 3.6177 d, respectively, likely the same within the errors. The radial velocities of this star show a striking non-sinusoidal shape with a large amplitude of 7 km s−1. Photometric rotation periods are also confirmed for the magnetic Ap star IQ Aur of 2.463 d and for the solar-type star κ1 Cet of 9.065 d, and also for the B7 HgMn giant β Tau of 2.74 d. Revised orbital solutions are derived for the eclipsing SB2 binary β Aur, which replaces the initial orbit dating from 1948 for the 27-year eclipsing SB1 ε Aur, and for the RS CVn binary V711 Tau, for which a spot-corrected orbital solution was achieved. The two stars ν Aur and ι Aur are found to be long-term, low-amplitude RV and brightness variables, but provisional orbital elements based on a period of 20 yr and an eccentricity of 0.7 could only be extracted for ν Aur. The variations of ι Aur are due to oscillations with a period of ≈4 yr.

Asteroseismic Analyses of Slowly Pulsating B Star KIC 8324482: Ultraweak Element Mixing beyond the Central Convective Core

Abstract Asteroseismology is a powerful tool for probing the inner structure and determining the evolutionary status and the fundamental parameters of stars. The oscillation spectra of slowly pulsating B (SPB) stars show almost uniform period spans, whose pattern is sensitive to the structure of the μ-gradient shell beyond the central convective core and hence can be used to efficiently describe their shapes and constrain the convective core. The SPB star KIC 8324482 was observed by Kepler for over 1470 days with a long-cadence pattern. Nearly equidistant period spacing patterns are found for the 14 connective dipolar modes that are extracted from the oscillation spectrum by Zhang et al. In the present work, we analyze them in depth with the χ 2-matching method and determine their χ 2-minimization models (CMMs). Based on those calculated CMMs, we find that KIC 8324482 is a young ( Myr), metal-poor ( dex), and intermediate-mass ( ) star with a convective core of in mass and in radius and with a surface rotation velocity . The central hydrogen abundance is of . Asteroseismic analyses indicate that the “propagation time” of g-mode in KIC 8324482 is of μHz. To well match with the observed period spacing pattern, an extra diffusion mixing ( ) should be considered, but the normal core overshooting f ov must be fixed as zero in the best-fitting model. Such ultraweak mixing beyond the convective core corresponds to a fast rotation that is about 20–30 times the asteroseismic suggested rotation Ωrot ≃ 0.2 μHz, if it is thought of as shear mixing induced completely by differential rotation.

Pulsational properties of ten new slowly pulsating B stars

Context. Slowly pulsating B (SPB) stars are upper main-sequence multi-periodic pulsators that show non-radial g-mode oscillations driven by the κ mechanism acting on the iron bump. These multi-periodic pulsators have great asteroseismic potential and can be employed for the calibration of stellar structure and evolution models of massive stars. Aims. We collected a sample of ten hitherto unidentified SPB stars with the aim of describing their pulsational properties and identifying pulsational modes. Methods. Photometric time series data from various surveys were collected and analyzed using diverse frequency search algorithms. We calculated astrophysical parameters and investigated the location of our sample stars in the log Teff vs. log L/L⊙ diagram. Current pulsational models were calculated and used for the identification of pulsational modes in our sample stars. An extensive grid of stellar models along with their g-mode eigenfrequencies was calculated and subsequently cross-matched with the observed pulsational frequencies. The best-fit models were then used in an attempt to constrain stellar parameters such as mass, age, metallicity, and convective overshoot. Results. We present detected frequencies, corresponding g-mode identifications, and the masses and ages of the stellar models producing the best frequency cross-matches. We partially succeeded in constraining stellar parameters, in particular concerning mass and age. Where applicable, rotation periods have been derived from the spacing of triplet component frequencies. No evolved SPB stars are present in our sample. We identify two candidate high-metallicity objects (HD 86424 and HD 163285), one young SPB star (HD 36999), and two candidate young SPB stars (HD 61712 and HD 61076). Conclusions. We demonstrate the feasibility of using ground-based observations to perform basic asteroseismological analyses of SPB stars. Our results significantly enlarge the sample of known SPB stars with reliable pulsational mode identifications, which provides important input parameters for modeling attempts aiming to investigate the internal processes at work in upper main-sequence stars.

Angular momentum transport by heat-driven g-modes in slowly pulsating B stars

Motivated by recent interest in the phenomenon of waves transport in massive stars, we examine whether the heat-driven gravity (g) modes excited in slowly-pulsating B (SPB) stars can significantly modify the stars' internal rotation. We develop a formalism for the differential torque exerted by g modes, and implement this formalism using the GYRE oscillation code and the MESASTAR stellar evolution code. Focusing first on a $4.21$ $M_\odot$ model, we simulate 1,000 years of stellar evolution under the combined effects of the torque due to a single unstable prograde g mode (with an amplitude chosen on the basis of observational constraints), and diffusive angular momentum transport due to convection, overshooting, and rotational instabilities. We find that the g mode rapidly extracts angular momentum from the surface layers, depositing it deeper in the stellar interior. The angular momentum transport is so efficient that by the end of the simulation the initially non-rotating surface layers are spun in the retrograde direction to $\approx30\%$ of the critical rate. However, the additional inclusion of magnetic stresses in our simulations, almost completely inhibits this spin-up. Expanding our simulations to cover the whole instability strip, we show that the same general behavior is seen in all SPB stars. After providing some caveats to contextualize our results, we hypothesize that the observed slower surface rotation of SPB stars (as compared to other B-type stars) may be the direct consequence of the angular momentum transport that our simulations demonstrate.

Beyond the Kepler/K2 bright limit: variability in the seven brightest members of the Pleiades

The most powerful tests of stellar models come from the brightest stars in the sky, for which complementary techniques, such as astrometry, asteroseismology, spectroscopy, and interferometry can be combined. The K2 Mission is providing a unique opportunity to obtain high-precision photometric time series for bright stars along the ecliptic. However, bright targets require a large number of pixels to capture the entirety of the stellar flux, and bandwidth restrictions limit the number and brightness of stars that can be observed. To overcome this, we have developed a new photometric technique, that we call halo photometry, to observe very bright stars using a limited number of pixels. Halo photometry is simple, fast and does not require extensive pixel allocation, and will allow us to use K2 and other photometric missions, such as TESS, to observe very bright stars for asteroseismology and to search for transiting exoplanets. We apply this method to the seven brightest stars in the Pleiades open cluster. Each star exhibits variability; six of the stars show what are most-likely slowly pulsating B-star (SPB) pulsations, with amplitudes ranging from 20 to 2000 ppm. For the star Maia, we demonstrate the utility of combining K2 photometry with spectroscopy and interferometry to show that it is not a 'Maia variable', and to establish that its variability is caused by rotational modulation of a large chemical spot on a 10 d time scale.

A comprehensive study of young B stars in NGC 2264

Space photometric time series of the most massive members of the young open cluster NGC 2264 allow us to study their different sources of variability down to the millimagnitude level and permits a search for Slowly Pulsating B (SPB) type pulsation among objects that are only a few million years old. Our goal is to conduct a homogeneous study of young B type stars in the cluster NGC 2264 using photometric time series from space in combination with high-resolution spectroscopy and spectropolarimetry obtained from the ground. The latter will be presented in a separate follow-up article. We performed frequency analyses for eleven B stars in the field of the young cluster NGC 2264 using photometric time series from the MOST, CoRoT and Spitzer space telescopes and the routines Period04 and SigSpec. We employ the MESA stellar evolution code in combination with the oscillation code GYRE to identify the pulsation modes for two SPB stars which exhibit short period spacing series. From our analysis we identify four objects that show SPB pulsations, five stars that show rotational modulation of their light curves caused by spots, one star that is identified to be a binary, and one object in the field of the cluster that is found to be a non-member Be star. In two SPB stars we detect a number of regularly spaced pulsation modes that are compatible with being members of a g mode period series. Despite NGC 2264's young age, our analysis illustrates that its B type members have already arrived on the zero-age main sequence (ZAMS). Our asteroseismic analysis yields masses between 4 and 6 Msun and ages between 1 and 6 million years, which agree well to the overall cluster age.

Signatures of internal rotation discovered in theKeplerdata of five slowly pulsating B stars

Massive stars are important building blocks of the Universe, and their stellar structure and evolution models are fundamental cornerstones of various fields in modern astrophysics. The precision of these models is limited by our lack of understanding of various internal mixing processes that significantly influence the lifetime of these objects (e.g. core overshoot, chemical mixing, or the internal differential rotation). Our goal is to calibrate models by extending the sample of available seismic studies of slowly pulsating B (SPB) stars, providing input for theoretical modelling efforts that will deliver precise constraints on the parameters describing the internal mixing processes in these objects. We used spectral synthesis and disentangling techniques to derive fundamental parameters and to determine precise orbital parameters from high-resolution spectra. We employed custom masks to construct light curves from the Kepler pixel data and used standard time-series analysis tools to construct a set of significant frequencies for each target. These sets were first filtered from combination frequencies, and then screened for period spacing patterns. We detect gravity mode period series of modes of the same degree l with consecutive radial order n in four new and one revisited SPB star. These predominantly prograde dipole series (covering ~10-40 radial orders) are influenced by rotation and carry signatures of chemical mixing processes. Our spectroscopic analysis, in addition to placing each object inside the SPB instability strip and identifying KIC 4930889 as an SB2 binary, reveals that KIC 11971405 is a fast rotator that shows very weak Be signatures. Together with the observed photometric outbursts this illustrates that this Be star is a fast rotating SPB star. We hypothesise that the outbursts might be connected to its very densely compressed oscillation spectrum.

Pulsation-driven mean zonal and meridional flows in rotating massive stars

Zonal and meridional axisymmetric flows can deeply impact the rotational and chemical evolution of stars. Therefore, momentum exchanges between waves propagating in stars, differential rotation, and meridional circulation must be carefully evaluated. In this work, we study axisymmetric mean flows in rapidly and initially uniformly rotating massive stars driven by small amplitude non-axisymmetric $\kappa$-driven oscillations. We treat them as perturbations of second-order of the oscillation amplitudes and derive their governing equations as a set of coupled linear ordinary differential equations. This allows us to compute 2-D zonal and meridional mean flows driven by low frequency $g$- and $r$-modes in slowly pulsating B (SPB) stars and $p$-modes in $\beta$ Cephei stars. Oscillation-driven mean flows usually have large amplitudes only in the surface layers. In addition, the kinetic energy of the induced 2-D zonal rotational motions is much larger than that of the meridional motions. In some cases, meridional flows have a complex radial and latitudinal structure. For SPB stars, we find that there are low frequency retrograde $g$-modes and $r$-modes that drive mean flows with positive velocity components in the radial and azimuthal directions at the stellar surface. This suggests that low frequency retrograde modes can transport angular momentum to the surface layers, which may help to form a circumstellar gaseous disc. Moreover, pulsation-driven and rotation-driven meridional flows can have similar amplitudes. These results show the importance of taking wave-- mean flow interactions into account when studying the evolution of massive stars.

A unifying explanation of complex frequency spectra of γ Dor, SPB and Be stars: combination frequencies and highly non-sinusoidal light curves

There are many Slowly Pulsating B (SPB) stars and gamma Dor stars in the Kepler Mission data set. The light curves of these pulsating stars have been classified phenomenologically into stars with symmetric light curves and with asymmetric light curves. In the same effective temperature ranges as the gamma Dor and SPB stars, there are variable stars with downward light curves that have been conjectured to be caused by spots. Among these phenomenological classes of stars, some show `frequency groups' in their amplitude spectra that have not previously been understood. While it has been recognised that nonlinear pulsation gives rise to combination frequencies in a Fourier description of the light curves of these stars, such combination frequencies have been considered to be a only a minor constituent of the amplitude spectra. In this paper we unify the Fourier description of the light curves of these groups of stars, showing that many of them can be understood in terms of only a few base frequencies, which we attribute to g mode pulsations, and combination frequencies, where sometimes a very large number of combination frequencies dominate the amplitude spectra. The frequency groups seen in these stars are thus tremendously simplified. We show observationally that the combination frequencies can have amplitudes greater than the base frequency amplitudes, and we show theoretically how this arises. Thus for some gamma Dor and SPB stars combination frequencies can have the highest observed amplitudes. Among the B stars are pulsating Be stars that show emission lines in their spectra from occasional ejection of material into a circumstellar disk. Our analysis gives strong support to the understanding of these pulsating Be stars as rapidly rotating SPB stars, explained entirely by g mode pulsations.

Are the stars of a new class of variability detected in NGC 3766 fast rotating SPB stars?

AbstractA recent photometric survey in the NGC 3766 cluster led to the detection of stars presenting an unexpected variability. They lie in a region of the Hertzsprung-Russell (HR) diagram where no pulsation are theoretically expected, in between the δ Scuti and slowly pulsating B (SPB) star instability domains. Their variability periods, between ~0.1–0.7 d, are outside the expected domains of these well-known pulsators. The NCG 3766 cluster is known to host fast rotating stars. Rotation can significantly affect the pulsation properties of stars and alter their apparent luminosity through gravity darkening. Therefore we inspect if the new variable stars could correspond to fast rotating SPB stars. We carry out instability and visibility analysis of SPB pulsation modes within the frame of the traditional approximation. The effects of gravity darkening on typical SPB models are next studied. We find that at the red border of the SPB instability strip, prograde sectoral (PS) modes are preferentially excited, with periods shifted in the 0.2–0.5 d range due to the Coriolis effect. These modes are best seen when the star is seen equator-on. For such inclinations, low-mass SPB models can appear fainter due to gravity darkening and as if they were located between the δ Scuti and SPB instability strips.

DISCOVERY OF 14 NEW SLOWLY PULSATING B STARS IN THE OPEN CLUSTER NGC 7654

We carried out time-series BV CCD photometric observations of the open cluster NGC 7654 (Messier 52) to search for variable stars. Eighteen slowly pulsating B (SPB) stars have been detected, among which 14 candidates are newly discovered, three known ones are confirmed, and a previously found delta Scuti star is also identified as an SPB candidate. Twelve SPBs are probable cluster members based on membership analysis. This makes NGC 7654 the richest galactic open cluster in terms of SPB star content. It is also a new discovery that NGC 7654 hosts three gamma Dor star candidates. We found that all these stars (18 SPB and 3 gamma Dor stars) have periods longer than their corresponding fundamental radial mode. With such a big sample of g-mode pulsators in a single cluster, it is clear that multi-mode pulsation is more common in the upper part of the main sequence than in the lower part. All the stars span a narrow strip on the period-luminosity plane, which also includes the gamma Dor stars at the low-luminosity extension. This result implies that there may be a single period-luminosity relation applicable to all g-mode main-sequence pulsators. As a by-product, three EA-type eclipsing binaries and an EW-type eclipsing binary are also discovered.

FIRST MAGNETIC FIELD MODELS FOR RECENTLY DISCOVERED MAGNETIC β CEPHEI AND SLOWLY PULSATING B STARS

In spite of recent detections of magnetic fields in a number of beta Cephei and slowly pulsating B (SPB) stars, their impact on stellar rotation, pulsations, and element diffusion is not sufficiently studied yet. The reason for this is the lack of knowledge of rotation periods, the magnetic field strength distribution and temporal variability, and the field geometry. New longitudinal field measurements of four beta Cephei and candidate beta Cephei stars, and two SPB stars were acquired with FORS2 at the VLT. These measurements allowed us to carry out a search for rotation periods and to constrain the magnetic field geometry for four stars in our sample.

On the incidence of magnetic fields in slowly pulsating B, β Cephei and B-type emission-line stars

We have obtained 40 high-resolution circular spectropolarimetric measurements of 12 slowly-pulsating B (SPB) stars, 8 Beta Cephei stars and two Be stars with the ESPaDOnS and NARVAL spectropolarimeters. The aim of these observations is to evaluate recent claims of a high incidence of magnetic field detections in stars of these types obtained using low-resolution spectropolarimetry by Hubrig (2006), Hubrig (2007) and Hubrig (2009). The precision achieved is generally comparable to or superior to that obtained by Hubrig et al., although our new observations are distinguished by their resolution of metallic and He line profiles, and their consequent sensitivity to magnetic fields of zero net longitudinal component. In the SPB stars we confirm the detection of magnetic field in one star (16 Peg), but find no evidence of the presence of fields in the remaining 11. In the Beta Cep stars, we detect a field in xi^1 CMa, but not in any of the remaining 7 stars. Finally, neither of the two B-type emission line stars shows any evidence of magnetic field. Based on our results, we conclude that fields are not common in SPB, Beta Cep and B-type emission line stars, consistent with the general rarity of fields in the broader population of main sequence B-type stars.

Confirmation of simultaneous p and g mode excitation in HD 8801 and γ Peg from time-resolved multicolour photometry of six candidate ‘hybrid’ pulsators

We carried out a multi-colour time-series photometric study of six stars claimed as "hybrid" p and g mode pulsators in the literature. Gamma Peg was confirmed to show short-period oscillations of the Beta Cep type and simultaneous long-period pulsations typical of Slowly Pulsating B (SPB) stars. From the measured amplitude ratios in the Stromgren uvy passbands, the stronger of the two short period pulsation modes was identified as radial; the second is l=1. Three of the four SPB-type modes are most likely l=1 or 2. Comparison with theoretical model calculations suggests that Gamma Peg is either an 8.5 solar mass radial fundamental mode pulsator or a 9.6 solar mass first radial overtone pulsator. HD 8801 was corroborated as a "hybrid" Delta Sct Gamma Dor star; four pulsation modes of the Gamma Dor type were detected, and two modes of the Delta Sct type were confirmed. Two pulsational signals between the frequency domains of these two known classes of variables were confirmed and another was newly detected. These are either previously unknown types of pulsation, or do not originate from HD 8801. The O-type star HD 13745 showed small-amplitude slow variability on a time scale of 3.2 days. This object may be related to the suspected new type of supergiant SPB stars, but a rotational origin of its light variations cannot be ruled out at this point. 53 Psc is an SPB star for which two pulsation frequencies were determined and identified with low spherical degree. The behaviour of 53 Ari and Iota Her is consistent with non-variability during our observations, and we could not confirm light variations of the comparison star 34 Psc previously suspected. The use of signal-to-noise criteria in the analysis of data sets with strong aliasing is critically discussed.