Β Cephei Stars Research Articles

Polarimetric detection of non-radial oscillation modes in the β Cephei star β Crucis

Here we report the detection of polarization variations due to nonradial modes in the beta Cephei star beta Crucis. In so doing we confirm 40-year-old predictions of pulsation-induced polarization variability and its utility in asteroseismology for mode identification. In an approach suited to other beta Cep stars, we combine polarimetry with space-based photometry and archival spectroscopy to identify the dominant nonradial mode in polarimetry, f2, as l = 3, m = -3 (in the m-convention of Dziembowski) and determine the stellar axis position angle as 25 (or 205) +/- 8 deg. The rotation axis inclination to the line of sight was derived as approx. 46 deg. from combined polarimetry and spectroscopy, facilitating identification of additional modes and allowing for asteroseismic modelling. This reveals a star of 14.5 +/- 0.5 Solar masses and a convective core containing approx. 28% of its mass -- making beta Crucis the most massive star with an asteroseismic age.

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.

Time-resolved multicolour photometry of bright B-type variable stars in Scorpius

The first two of a total of six nano-satellites that will constitute the BRITE-Constellation space photometry mission have recently been launched successfully. In preparation for this project, we carried out time-resolved colour photometry in a field that is an excellent candidate for BRITE measurements from space. We acquired 117 h of Stromgren uvy data during 19 nights. Our targets comprised the Beta Cephei stars Kappa and Lambda Sco, the eclipsing binary Mu 1 Sco, and the variable super/hypergiant Zeta 1 Sco. For Kappa Sco, a photometric mode identification in combination with results from the spectroscopic literature suggests a dominant (l, m) = (1, -1) Beta Cephei-type pulsation mode of the primary star. The longer period of the star may be a rotational variation or a g-mode pulsation. For Lambda Sco, we recover the known dominant Beta Cephei pulsation, a longer-period variation, and observed part of an eclipse. Lack of ultraviolet data precludes mode identification for this star. We noticed that the spectroscopic orbital ephemeris of the closer pair in this triple system is inconsistent with eclipse timings and propose a refined value for the orbital period of the closer pair of 5.95189 +/- 0.00003 d. We also argue that the components of the Lambda Sco system are some 30% more massive than previously thought. The binary light curve solution of Mu 1 Sco requires inclusion of the irradiation effect to explain the u light curve, and the system could show additional low amplitude variations on top of the orbital light changes. Zeta 1 Sco shows long-term variability on a time scale of at least two weeks that we prefer to interpret in terms of a variable wind or strange mode pulsations.

Understanding the dynamical structure of pulsating stars: The center-of-mass velocity and the Baade-Wesselink projection factor of theβCephei starαLupi

High-resolution spectroscopy of pulsating stars is a powerful tool to study the dynamical structure of their atmosphere. Lines asymmetry is used to derive the center-of-mass velocity of the star, while a direct measurement of the atmospheric velocity gradient helps determine the projection factor used in the Baade-Wesselink method of distance determination. We aim at deriving the center-of-mass velocity and the projection factor of the beta-Cephei star alpha-Lup. We present HARPS high spectral resolution observations of alpha-Lup. We calculate the first-moment radial velocities and fit the spectral line profiles by a bi-Gaussian to derive line asymmetries. Correlations between the gamma-velocity and the gamma-asymmetry (defined as the average values of the radial velocity and line asymmetry curves respectively) are used to derive the center-of-mass velocity of the star. By combining our spectroscopic determination of the atmospheric velocity gradient with a hydrodynamical modelof the photosphere of the star, we derive a semi-theoretical projection factor for alpha Lup. We find a center-of-mass velocity of Vgamma = 7.9 +/- 0.6 km/s and that the velocity gradient in the atmosphere of alpha Lup isnull. We apply to alpha Lup the usual decomposition of the projection factor into three parts, p = p0 fgrad fog (originally developed for Cepheids), and derive a projection factor of p = 1.43 +/-0.01. By comparing our results with previous HARPS observations of classical Cepheids, we also point out a linear relation between the atmospheric velocity gradient and the amplitude of the radial velocity curve. Moreover, we observe a phase shift (Van Hoof effect), whereas alpha Lup has no velocity gradient.

Chaos in large-amplitude pulsators: application to the β Cep star HD 180642

The CoRoT observations of the beta Cephei star HD180642 uncover an unexpectedly rich frequency spectrum, in addition to several heat-driven modes. So far, two processes have been proposed to explain this behaviour: the presence of stochastic oscillations, and the excitation of time-dependent frequencies by nonlinear resonance. I argue for a third explanation for the observations, in the form of chaos due to the nonlinear behaviour of the dominant radial mode. The long-term frequency stability of the dominant radial mode is studied using archival data spanning roughly 20 years. Nonlinear time series analysis techniques are applied to the CoRoT observations, and the observations are compared with simulations of a simple nonlinear oscillator. I show that chaos offers one single explanation for many of the observed features, such as the structure in the autocorrelation of the power spectrum, the long-term frequency shift, the power excess and the wide range of frequencies in the power spectrum. However, the mixture of opacity-driven linear oscillations and nonlinear oscillations complicate the nonlinear time series analysis techniques.

THE ROLE OF θ OPH IN THE FORMATION AND EVOLUTION OF THE PIPE NEBULA—IS STAR FORMATION EVER ISOLATED?

We propose that the Pipe Nebula is an HII region shell swept up by the B2 IV beta Cephei star theta Ophiuchi. After reviewing the morphological evidence by recent observations, we perform a series of analytical calculations. We use realistic HII region parameters derived with the radiative transfer code Cloudy from observed stellar parameters. We are able to show that the current size, mass and pressure of the region can be explained in this scenario. We investigate the configuration today and come to the conclusion that the Pipe Nebula can be best described by a three phase medium in pressure equilibrium. The pressure support is provided by the ionized gas and mediated by an atomic component to confine the cores at the observed current pressure. In the future, star formation in these cores is likely to be either triggered by feedback of the most massive, gravitationally bound cores as soon as they collapse or by the supernova explosion of theta Ophiuchi itself.

Newβ Cephei stars in the young open cluster NGC 637

Studying stellar pulsations in open clusters offers the possibility to perform ensemble asteroseismology. The reasonable assumption that the cluster members have the same age, distance, and overall metallicity aids in the seismic modelling process and tightly constrains it. Therefore it is important to identify open clusters with many pulsators. New pulsating stars of the Beta Cephei type were searched for among the members of the open cluster NGC 637. Thirty-one hours of time resolved V filter CCD photometry were obtained. The measurements confirmed two previously known variables, and revealed three new Beta Cephei stars plus one more candidate. All four pulsators have amplitudes high enough for easy mode identification and are multiperiodic. With four certain pulsating members, NGC 637 is now among the six open clusters richest in Beta Cephei stars. It is thus an excellent target for ensemble asteroseismology, and to tackle the question what separates pulsating from apparently constant stars in the Beta Cephei domain.

The strong magnetic field of the large-amplitudeβ Cephei pulsator V1449 Aquilae

Only for very few beta Cephei stars has the behaviour of the magnetic field been studied over the rotation cycle. During the past two years we have obtained multi-epoch polarimetric spectra of the beta Cephei star V1449 Aql with SOFIN at the Nordic Optical Telescope to search for a rotation period and to constrain the geometry of the magnetic field. The mean longitudinal magnetic field is measured at 13 different epochs. The new measurements, together with the previous FORS1 measurements, have been used for the frequency analysis and the characterization of the magnetic field. V1449 Aql so far possesses the strongest longitudinal magnetic field of up to 700G among the beta Cephei stars. The resulting periodogram displays three dominant peaks with the highest peak at f=0.0720d^-1 corresponding to a period P=13.893d. The magnetic field geometry can likely be described by a centred dipole with a polar magnetic field strength B_d around 3kG and an inclination angle beta of the magnetic axis to the rotation axis of 76+-4deg. As of today, the strongest longitudinal magnetic fields are detected in the beta Cephei stars V1449 Aql and xi^1 CMa with large radial velocity amplitudes. Their peak-to-peak amplitudes reach ~90km/s and ~33km/s, respectively. Concluding, we briefly discuss the position of the currently known eight magnetic beta Cephei and candidate beta Cephei stars in the Hertzsprung-Russell (H-R) diagram.

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.

Rotation and convective core overshoot inθOphiuchi

(abridged) Recent work on several beta Cephei stars has succeeded in constraining both their interior rotation profile and their convective core overshoot. In particular, a recent study focusing on theta$ Oph has shown that a convective core overshoot parameter of alpha = 0.44 is required to model the observed pulsation frequencies, significantly higher than for other stars of this type. We investigate the effects of rotation and overshoot in early type main sequence pulsators, and attempt to use the low order pulsation frequencies to constrain these parameters. This will be applied to a few test models and theta Oph. We use a 2D stellar evolution code and a 2D linear adiabatic pulsation code to calculate pulsation frequencies for 9.5 Msun models. We calculate low order p-modes for models with a range of rotation rates and convective core overshoot parameters. Using these models, we find that the convective core overshoot has a larger effect on the pulsation frequencies than the rotation, except in the most rapidly rotating models considered. When the differences in radii are accounted for by scaling the frequencies, the effects of rotation diminish, but are not entirely accounted for. We find that increasing the convective core overshoot decreases the large separation, while producing a slight increase in the small separations. We created a model frequency grid which spanned several rotation rates and convective core overshoot values. Using a modified chi^2 statistic, we are able to recover the rotation velocity and core overshoot for a few test models. Finally, we discuss the case of the beta Cephei star theta Oph. Using the observed frequencies and a fixed mass and metallicity, we find a lower overshoot than previously determined, with alpha = 0.28 +/- 0.05. Our determination of the rotation rate agrees well with both previous work and observations, around 30 km/s.

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.

Ground-based observations of the β Cephei CoRoT main target HD 180 642: abundance analysis and mode identification

The known beta Cephei star HD 180642 was observed by the CoRoT satellite in 2007. From the very high-precision light curve, its pulsation frequency spectrum could be derived for the first time (Degroote and collaborators). In this paper, we obtain additional constraints for forthcoming asteroseismic modeling of the target. Our results are based on both extensive ground-based multicolour photometry and high-resolution spectroscopy. We determine T_eff = 24 500+-1000 K and log g = 3.45+-0.15 dex from spectroscopy. The derived chemical abundances are consistent with those for B stars in the solar neighbourhood, except for a mild nitrogen excess. A metallicity Z = 0.0099+-0.0016 is obtained. Three modes are detected in photometry. The degree l is unambiguously identified for two of them: l = 0 and l = 3 for the frequencies 5.48694 1/d and 0.30818 1/d, respectively. The radial mode is non-linear and highly dominant with an amplitude in the U-filter about 15 times larger than the strongest of the other modes. For the third frequency of 7.36673 1/d found in photometry, two possibilities remain: l = 0 or 3. In the radial velocities, the dominant radial mode presents a so-called stillstand but no clear evidence of the existence of shocks is observed. Four low-amplitude modes are found in spectroscopy and one of them, with frequency 8.4079 1/d, is identified as (l,m)=(3,2). Based on this mode identification, we finally deduce an equatorial rotational velocity of 38+-15 km/s.

Multimode Radiative beta Cephei and delta Cephei Models

As a by-product of beta Cephei and delta Cephei radiative model surveys we have found interesting cases of multimode pulsation. In case of beta Cephei stars, we found two multimode domains with two or three modes being involved. The origin of the multimode pulsation can be traced to one of the two different mechanisms: either to the non-resonant coupling of the two excited modes (double-mode pulsation) or to the 2omega_1 = omega_0 + omega_2 parametric resonance (triple-mode pulsation). In case of delta Cephei models, a triple-mode pulsation domain, connected with the 2:1 resonance, 2omega_0 = omega_2, is found. These models are of theoretical interest only, since they do not obey a proper mass-luminosity relation.

SEISMOLOGY OF β CEPHEI STARS: DIFFERENTIALLY ROTATING MODELS FOR INTERPRETING THE OSCILLATION SPECTRUM OF ν ERIDANI

A method for the asteroseismic analysis of beta Cephei stars is presented and applied to the star nu Eridani. The method is based on the analysis of rotational splittings, and their asymmetries using differentially-rotating asteroseismic models. Models with masses around 7.13 M_sun, and ages around 14.9 Myr, were found to fit better 10 of the 14 observed frequencies, which were identified as the fundamental radial mode and the three L=1 triplets g, p, and p. The splittings and aymmetries found for these modes recover those provided in the literature, except for p. For this last mode, all its non-axysimmetric components are predicted by the models. Moreover, opposite signs of the observed and predicted splitting asymmetries are found. If identification is confirmed, this can be a very interesting source of information about the internal rotation profile, in particular in the outer regions of the star. In general, the seismic models which include a description for shellular rotation yield slightly better results as compared with those given by uniformly-rotating models. Furthermore, we show that asymmetries are quite dependent on the overshooting of the convective core, which make the present technique suitable for testing the theories describing the angular momentum redistribution and chemical mixing due to rotationally-induced turbulence.

Third order effect of rotation on stellar oscillations of a β-Cephei star

Here the effect of rotation up to third order in the angular velocity of a star on the p, f and g modes is investigated. To do this, the third-order perturbation formalism presented by Soufi et al. (Astron. Astrophys. 334:911, 1998) and revised by Karami (Chin. J. Astron. Astrophys. 8:285, 2008), was used. I quantify by numerical calculations the effect of rotation on the oscillation frequencies of a uniformly rotating β-Cephei star with 12 M⊙. For an equatorial velocity of 90 km s−1, it is found that the second- and third-order corrections for (l,m)=(5,−4), for instance, are of order of 0.07% of the frequency for radial order n=−3 and reaches up to 0.6% for n=−20.

Pulsating variables in NGC 3293, the open cluster with the most β Cephei stars known

Inhalt (u.a.): M. BREGER: Delta Scuti stars: Observational aspects; M.S. Cunha: Theory of rapidly oscillating Ap stars; M. SACHKOV et al.: Vertical structure of pulsations in roAp stars; G. HOUDEK: Theoretical asteroseismology of solar-like oscillations; B.L. POPIELSKI: Core modes as a seismic probe of mixing beyond the convective core; M. GODART: Temperature gradients in the core overshooting region; W.A. DZIEMBOWSKI – J. DASZYŃSKA-DASZKIEWICZ – A.A. PAMYATNYKH: Interpretation of the Be star HD 163868 oscillation spectrum based on the MOST observations; D. KILKENNY: Pulsating Hot Subdwarfs – An Observational Review; M.H. MONTGOMERY: Mapping Convection using Pulsating White Dwarf Stars; M. ROTH: The Network Activities in HELAS; I. KUDZEJ et al.: A New Slovak Observatory 500 km from Vienna; W.W. WEISS: Microsatellites; G. KOPACKI – S. FRANDSEN: RR Lyrae stars in M4

An asteroseismic study of the β Cephei star β Canis Majoris

We present a spectroscopic study of the beta Cephei star beta Canis Majoris. Hundreds of high-resolution spectra were gathered during 4.5 years and the Si III line profiles centered on 4560 A were subjected to a detailed line profile analysis. We searched for oscillation frequencies in different line diagnostics, compared them with those known from photometric studies and concluded the presence of three frequencies in our dataset: f_1 = 3.97933 c/d, f_2 = 3.99959 c/d and f_3= 4.1832 c/d, which were already found earlier from photometric data. By means of the moment method and from amplitude and phase variations across the profiles we could identify two of the modes as (l_1,m_1)=(2,2) and (l_2,m_2)=(0,0$. We present our first results of modelling based on the oscillation frequencies and place constraints on the mass, age and core overshooting of this massive evolved beta Cephei star.

Amplitude Saturation in β Cephei Models - Preliminary Results

Using nonlinear hydrocodes we have calculated single mode saturation amplitudes for beta Cephei models. Predicted saturation amplitudes are systematically higher than amplitudes observed in beta Cephei variables, even in monoperiodic ones. We argue that collective saturation of the pulsation instability by a dozen or so acoustic modes brings the theoretical amplitudes to the observed level.

A spectroscopic study of the β Cephei star 12 (DD) Lacertae

Inhalt (u.a.): M. BREGER: Delta Scuti stars: Observational aspects; M.S. Cunha: Theory of rapidly oscillating Ap stars; M. SACHKOV et al.: Vertical structure of pulsations in roAp stars; G. HOUDEK: Theoretical asteroseismology of solar-like oscillations; B.L. POPIELSKI: Core modes as a seismic probe of mixing beyond the convective core; M. GODART: Temperature gradients in the core overshooting region; W.A. DZIEMBOWSKI – J. DASZYŃSKA-DASZKIEWICZ – A.A. PAMYATNYKH: Interpretation of the Be star HD 163868 oscillation spectrum based on the MOST observations; D. KILKENNY: Pulsating Hot Subdwarfs – An Observational Review; M.H. MONTGOMERY: Mapping Convection using Pulsating White Dwarf Stars; M. ROTH: The Network Activities in HELAS; I. KUDZEJ et al.: A New Slovak Observatory 500 km from Vienna; W.W. WEISS: Microsatellites; G. KOPACKI – S. FRANDSEN: RR Lyrae stars in M4

Nitrogen excess in slowly-rotating β Cephei stars: deep mixing or diffusion?

We present the results of an NLTE abundance study of a small sample of beta Cephei stars, which point to the existence of a population of slowly-rotating B-type pulsators exhibiting a significant amount of nitrogen-enriched material at their surface. Although the origin of this nitrogen excess remains unclear, an overabundance preferentially occurring in stars with a detected magnetic field seems to emerge at this stage. Full details can be found in Morel et al. (2006).