Rotational Splitting Research Articles

First Kepler results on compact pulsators - V. Slowly pulsating subdwarf B stars in short-period binaries

The survey phase of the Kepler Mission includes a number of hot subdwarf B (sdB) stars to search for non-radial pulsations. We present our analysis of two sdB stars that are found to be g-mode pulsators of the V1093 Her class. These two stars also display the distinct irradiation effect typical of sdB stars with a close M-dwarf companion with orbital periods of less than half a day. Because the orbital period is so short, the stars should be in synchronous rotation, and if so, the rotation period should imprint itself on the multiplet structure of the pulsations. However, we do not find clear evidence for such rotational splitting. Though the stars do show some frequency spacings that are consistent with synchronous rotation, they also display multiplets with splittings that are much smaller. Longer-duration time series photometry will be needed to determine if those small splittings are in fact rotational splitting, or caused by slow amplitude or phase modulation. Further data should also improve the signal-to-noise ratio, perhaps revealing lower-amplitude periodicities that could confirm the expectation of synchronous rotation. The pulsation periods seen in these stars show period spacings that are suggestive of high-overtone g-mode pulsations.

Core properties ofαCentauri A using asteroseismology

A set of long and nearly continuous observations of alpha Centauri A should allow us to derive an accurate set of asteroseismic constraints to compare to models, and make inferences on the internal structure of our closest stellar neighbour. We intend to improve the knowledge of the interior of alpha Centauri A by determining the nature of its core. We combined the radial velocity time series obtained in May 2001 with three spectrographs in Chile and Australia: CORALIE, UVES, and UCLES. The resulting combined time series has a length of 12.45 days and contains over 10,000 data points and allows to greatly reduce the daily alias peaks in the power spectral window. We detected 44 frequencies that are in good overall agreement with previous studies, and found that 14 of these show possible rotational splittings. New values for the large and small separations have been derived. A comparison with stellar models indicates that the asteroseismic constraints determined in this study allows us to set an upper limit to the amount of convective-core overshooting needed to model stars of mass and metallicity similar to those of alpha Cen A.

Algol-Type Eclipsing Binaries with δ Scuti-Type Pulsating Components: IV Cas

We present the results of photometric and spectroscopic observations of the Algol-type eclipsing binary with a δ Scuti-type pulsating component IV Cas. This is the first comprehensive study of the absolute properties of the binary system and also of the pulsation characteristics of the primary component. The high-resolution spectroscopic data have enabled us to estimate the atmospheric parameters of the primary component. Our BV light-curve analysis has revealed that the binary system is in a semidetached configuration, consisting of a detached main-sequence primary of spectral type A3 and an evolved secondary of early-K spectral type, which fills its inner Roche lobe completely. We found that the two components are too close to each other to form an accretion disk. Spectroscopic results without an emission feature supported the nonexistence of noticeable disk. The rotation of the primary turned out to be nearly synchronized with the revolution, giving a hint that IV Cas is in the middle or late stage of the slow mass transfer phase. This coincides well with a slow mass transfer rate deduced from the fact that there was no secular parabolic change of the orbital period for the past ∼100 yr. Using residuals subtracted from synthetic eclipsing curves of photometric data, we examined the pulsation properties of the primary component. A multiple-frequency analysis was applied to the residuals in the out-of-primary eclipsing phases and this resulted in the detection of four frequencies: f1 = 32.69236 cycles day-1, f2 = 36.65999 cycles day-1, f3 = 20.71649 cycles day-1, and f4 = 30.66072 cycles day-1. We tentatively identified their pulsation modes on the basis of pulsation constants, frequency spacing, mode visibility in eclipsing binaries, phase differences, and amplitude ratios; f1 and f4 (or f1 and f2) appeared to be rotational splitting frequencies. The observational properties of IV Cas well matched the empirical relations for Algol-type eclipsing binaries with δ Scuti-type pulsating components.

Modelling the autocovariance of the power spectrum of a solar-type oscillator

Asteroseismology is able to conduct studies on the interiors of solar-type stars from the analysis of stellar acoustic spectra. However, such an analysis process often has to rely upon subjective choices made throughout. A recurring problem is to determine whether a signal in the acoustic spectrum originates from a radial or a dipolar oscillation mode. In order to overcome this problem, we present a procedure for modelling and fitting the autocovariance of the power spectrum which can be used to obtain global seismic parameters of solar-type stars, doing so in an automated fashion without the need to make subjective choices. From the set of retrievable global seismic parameters we emphasize the mean small frequency separation and, depending on the intrinsic characteristics of the power spectrum, the mean rotational frequency splitting. Since this procedure is automated, it can serve as a useful tool in the analysis of the more than one thousand solar-type stars expected to be observed as part of the Kepler Asteroseismic Investigation (KAI). We apply the aforementioned procedure to simulations of the Sun. Assuming different apparent magnitudes, we address the issues of how accurately and how precisely we can retrieve the several global seismic parameters were the Sun to be observed as part of the KAI.

MULTI-SITE OBSERVATIONS OF PULSATION IN THE ACCRETING WHITE DWARF SDSS J161033.64–010223.3 (V386 Ser)

Nonradial pulsations in the primary white dwarfs of cataclysmic variables can now potentially allow us to explore the stellar interior of these accretors using stellar seismology. In this context, we conducted a multi-site campaign on the accreting pulsator SDSS J161033.64-010223.3 (V386 Ser) using seven observatories located around the world in May 2007 over a duration of 11 days. We report the best fit periodicities here, which were also previously observed in 2004, suggesting their underlying stability. Although we did not uncover a sufficient number of independent pulsation modes for a unique seismological fit, our campaign revealed that the dominant pulsation mode at 609s is an evenly spaced triplet. The even nature of the triplet is suggestive of rotational splitting, implying an enigmatic rotation period of about 4.8 days. There are two viable alternatives assuming the triplet is real: either the period of 4.8 days is representative of the rotation period of the entire star with implications for the angular momentum evolution of these systems, or it is perhaps an indication of differential rotation with a fast rotating exterior and slow rotation deeper in the star. Investigating the possibility that a changing period could mimic a triplet suggests that this scenario is improbable, but not impossible. Using time-series spectra acquired in May 2009, we determine the orbital period of SDSS J161033.64-010223.3 to be 83.8 +/- 2.9 min. Three of the observed photometric frequencies from our May 2007 campaign appear to be linear combinations of the 609s pulsation mode with the first harmonic of the orbital period at 41.5min. This is the first discovery of a linear combination between nonradial pulsation and orbital motion for a variable white dwarf.

On the efficiency of azimuthal and rotational splitting for Monte Carlo simulation of clinical linear accelerators

This article presents rotational splitting as a modification to the sampling process of the azimuthal angle used in the variance-reduction technique of azimuthal particle redistribution, with the goal to improve the efficiency of this variance-reduction technique for the Monte Carlo simulation of radiation transport in clinical linear accelerators. Using a constant azimuthal angle, instead of a random one, in the azimuthal particle redistribution technique, increases the efficiency of the simulation of a clinical linear accelerator by about 30% and reduces the latent variance of a 10×10 cm 2 phase space by about 40%.

Effect of stellar rotation on oscillation frequencies

We investigate whether the rotational splittings of β Cephei stars can give some clue about the existence of a differential rotation in latitude, and if they are contaminated by the cubic order effects of rotation on oscillation frequencies. We also study some properties of splitting asymmetries and axisymmetric mode frequencies which provide seismic constrains on the distortion of the star. We find that only non-perturbative methods are able to reproduce those two seismic characteristics within 0.01% error bars for stars when they rotate faster than 3.3%Ω k . If error bars of 1% are acceptable, the threshold of validity of perturbative methods is extended to 10%Ω k .

Effects of rotation on the evolution and asteroseismic properties of red giants

The influence of rotation on the properties of red giants is studied in the context of the asteroseismic modelling of these stars. While red giants exhibit low surface rotational velocities, we find that the rotational history of the star has a large impact on its properties during the red giant phase. In particular, for stars massive enough to ignite He burning in non-degenerate conditions, rotational mixing induces a significant increase of the stellar luminosity and shifts the location of the core helium burning phase to a higher luminosity in the HR diagram. This of course results in a change of the seismic properties of red giants at the same evolutionary state. As a consequence the inclusion of rotation significantly changes the fundamental parameters of a red giant star as determined by performing an asteroseismic calibration. In particular rotation decreases the derived stellar mass and increases the age. Depending on the rotation law assumed in the convective envelope and on the initial velocity of the star, non-negligible values of rotational splitting can be reached, which may complicate the observation and identification of non-radial oscillation modes for red giants exhibiting moderate surface rotational velocities. By comparing the effects of rotation and overshooting, we find that the main-sequence widening and the increase of the H-burning lifetime induced by rotation (Vini=150 km/s) are well reproduced by non-rotating models with an overshooting parameter of 0.1, while the increase of luminosity during the post-main sequence evolution is better reproduced by non-rotating models with overshooting parameters twice as large. This is due to the fact that rotation not only increases the size of the convective core but also changes the chemical composition of the radiative zone.

A fresh look at the seismic spectrum of HD49933: analysis of 180 days of CoRoT photometry

Solar-like oscillations have now been observed in several stars, thanks to ground-based spectroscopic observations and space-borne photometry. CoRoT, which has been in orbit since December 2006, has observed the star HD49933 twice. The oscillation spectrum of this star has proven difficult to interpret. Thanks to a new timeseries provided by CoRoT, we aim to provide a robust description of the oscillations in HD49933, i.e., to identify the degrees of the observed modes, and to measure mode frequencies, widths, amplitudes and the average rotational splitting. Several methods were used to model the Fourier spectrum: Maximum Likelihood Estimators and Bayesian analysis using Markov Chain Monte-Carlo techniques. The different methods yield consistent result, and allow us to make a robust identification of the modes and to extract precise mode parameters. Only the rotational splitting remains difficult to estimate precisely, but is clearly relatively large (several microHz in size).

The solar-like oscillations of HD 49933: a Bayesian approach

<i>Context. <i/>Asteroseismology has entered a new era with the availability of continuous observations from space-borne missions such as MOST, CoRoT and Kepler. However, the low amplitude and the complexity of the observed spectrum make the exploitation of these data sets difficult. <i>Aims. <i/>The use of robust methods to estimate the parameters of stellar oscillation eigenmodes is necessary to fully exploit these new data sets. These parameters include in particular the frequency, the width and the energy of the eigenmodes, all being required for a seismic interpretation of the stellar internal structure or excitation of the eigenmodes.<i>Methods. <i/>A Bayesian approach, coupled with a Markov chain Monte Carlo (MCMC) algorithm, is presented. Such a method allows the use of a priori knowledge to improve the parameter estimation. It also provides complete information on the probability distribution of the fitted parameters. The method is tested on simulated time series and then applied to CoRoT observations of HD 49933.<i>Results. <i/>The simulated time series allow the validation of the method for conditions similar to those of the observations in terms of spectral complexity and signal-to-noise ratio. However, a very important problem in the analysis of the HD 49933 mode spectrum is the <i>l<i/> degree identification of the modes. The degree identification has little impact on the large frequency separation, rotational splitting, energy and width estimation, whereas individual frequencies and the star inclination angle evaluation are strongly affected. From a statistical point of view, we provide a quantitative ranking of the four models considered. The most probable model includes only modes of degree 0 and 1. Two other models include modes with degree up to 2 and have a non negligible level of significance. The last model includes modes of degree 0 and 1 but has an alternate degree identification and can be definitively rejected. In conclusion, the significance of the resulting probabilities is not sufficient to draw a definite conclusion.

WHAT MAGNETAR SEISMOLOGY CAN TEACH US ABOUT MAGNETIC FIELDS

The effect of magnetic fields on the frequencies of toroidal oscillations of neutron stars is derived to lowest order. We suggest that the fine structure in the quasiperiodic oscillation power spectrum of magnetars following giant flares reported by Strohmayer & Watts is magnetic splitting of degenerate toroidal modes, and we estimate a corresponding crustal magnetic field on the order of 1015 Gauss or more. We suggest that residual m, –m symmetry following such splitting, together with nonaxisymmetric or rotational splitting of the residual symmetry, might allow beating of individual frequency components that is slow enough to be observed.

Solar-like oscillations in HD 181420: data analysis of 156 days of CoRoT data

Context. The estimate of solar-like oscillation properties, such as their frequencies, amplitudes and lifetimes, is challenging because of their low amplitudes and will benefit from long and uninterrupted observing runs. The space telescope CoRoT allows us to obtain high-performance photometric data over a long and quasi continuous period. Among its main targets are stars for which we expect solar-like oscillations. Aims. HD 181420, an F2 main sequence star, has been observed by CoRoT during its first long run covering about 156 days. With this unprecedently high-quality set of data, our aim is to derive the p-mode parameters that can be used to probe the stellar interior. Methods. The CoRoT data obtained on HD 181420 is analysed using a classical Fourier approach for the search for the p mode signature. The p-mode parameters are then derived using global fitting of the power spectrum by a Lorentzian model, as used widely in the solar case. Results. From the p-mode frequencies, the mean value of the large spacing is estimated to be 75 μHz. The p-mode amplitudes are slightly less than 4 ppm with a line width of about 8 μHz at the maximum of the p modes. The inclination angle is estimated to be around 45 ◦ . The large mode line-width combined with the observed mode spacing make it difficult to identify the � = 2 modes and to estimate the rotational splitting. We explore two scenarios for the identification of the modes.

Coupled Translation−Rotation Eigenstates of H2, HD, and D2 in the Large Cage of Structure II Clathrate Hydrate: Comparison with the Small Cage and Rotational Raman Spectroscopy

We report fully coupled quantum five-dimensional calculations of the translation-rotation (T-R) energy levels of one H(2), HD, and D(2) molecule confined inside the large hexakaidecahedral (5(12)6(4)) cage of the structure II clathrate hydrate. Highly converged T-R eigenstates have been obtained for excitation energies beyond the j = 2 rotational levels of the guest molecules, in order to allow comparison with the recent Raman spectroscopic measurements. The translationally excited T-R states are assigned with the quantum numbers n and l of the 3D isotropic harmonic oscillator. However, the translational excitations are not harmonic, since the level energies depend not only on n but also on l. For l > 1, the T-R levels having the same n,l values are split into groups of almost degenerate levels. The splitting patterns follow the predictions of group theory for the environment of T(d) symmetry, which is created by the configuration of the oxygen atoms of the large cage. The 2j + 1 degeneracy of the j = 1 and 2 rotational levels of the encapsulated hydrogen molecule is lifted entirely by the angular anisotropy of the H(2)-cage interaction potential. The patterns and magnitudes of the j = 1, 2 rotational level splittings, and the energies of the sublevels, in the large cage are virtually identical with those calculated for the small cage. This is in agreement with, and sheds light on, the observation that the S(0)(0) (j = 0-->2) bands in the rotational Raman spectra measured for simple H(2) hydrate and the binary hydrate of H(2) with tetrahydrofuran are remarkably similar with respect to their frequencies, widths, shapes, and internal structure, when the H(2) occupancy of the large cage of simple H(2) hydrate is low.

Oscillations of rapidly rotating superfluid stars

Using time evolutions of the relevant linearized equations, we study non-axisymmetric oscillations of rapidly rotating and superfluid neutron stars. We consider perturbations of Newtonian axisymmetric background configurations and account for the presence of superfluid components via the standard two-fluid model. Within the Cowling approximation, we are able to carry out evolutions for uniformly rotating stars up to the mass-shedding limit. This leads to the first detailed analysis of superfluid neutron star oscillations in the fast rotation regime, where the star is significantly deformed by the centrifugal force. For simplicity, we focus on background models where the two fluids (superfluid neutrons and protons) corotate, are in β-equilibrium and co-exist throughout the volume of the star. We construct sequences of rotating stars for two analytical model equations of state. These models represent relatively simple generalizations of single fluid, polytropic stars. We study the effects of entrainment, rotation and symmetry energy on non-radial oscillations of these models. Our results show that entrainment and symmetry energy can have a significant effect on the rotational splitting of non-axisymmetric modes. In particular, the symmetry energy modifies the inertial mode frequencies considerably in the regime of fast rotation.

Direct observations of the viscosity of Earth's outer core and extrapolation of measurements of the viscosity of liquid iron

Estimates vary widely as to the viscosity of Earth's outer fluid core. Directly observed viscosity is usually orders of magnitude higher than the values extrapolated from high-pressure high-temperature laboratory experiments, which are close to those for liquid iron at atmospheric pressure. It turned out that this discrepancy can be removed by extrapolating via the widely known Arrhenius activation model modified by lifting the commonly used assumption of pressure-independent activation volume (which is possible due to the discovery that at high pressures the activation volume increases strongly with pressure, resulting in 102 Pa s at the top of the fluid core, and in 1011 Pa s at its bottom). There are of course many uncertainties affecting this extrapolation process. This paper reviews two viscosity determination methods, one for the top and the other for the bottom of the outer core, the former of which relies on the decay of free core nutations and yields 2371 ± 1530 Pa s, while the other relies on the reduction in the rotational splitting of the two equatorial translational modes of the solid inner core oscillations and yields an average of 1.247 ± 0.035 Pa s. Encouraged by the good performance of the Arrhenius extrapolation, a differential form of the Arrhenius activation model is used to interpolate along the melting temperature curve and to find the viscosity profile across the entire outer core. The viscosity variation is found to be nearly log-linear between the measured boundary values.

Mechanism of Collisional Spin Relaxation inΣ3Molecules

We measure and theoretically determine the effect of molecular rotational splitting on Zeeman relaxation rates in collisions of cold 3Sigma molecules with helium atoms in a magnetic field. All four stable isotopomers of the imidogen (NH) molecule are magnetically trapped and studied in collisions with 3He and 4He. The 4He data support the predicted 1/B_{e};{2} dependence of the collision-induced Zeeman relaxation rate coefficient on the molecular rotational constant B_{e}. The measured 3He rate coefficients are much larger than the 4He coefficients, depend less strongly on B_{e}, and theoretical analysis indicates they are strongly affected by a shape resonance. The results demonstrate the influence of molecular structure on collisional energy transfer at low temperatures.

Time-resolved spectroscopy of the planet-hosting sdB pulsator V391 Pegasi

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.

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.

The Pulsating White Dwarf Stars

ABSTRACTWe present a summary of what is currently known about the three distinct families of isolated pulsating white dwarfs. These are the GW Vir stars (He/C/O-atmosphere stars with Teff ≃ 120,000 K), the V777 Her stars (He-atmosphere, Teff ≃ 25,000 K), and the ZZ Ceti stars (H-atmosphere, Teff ≃ 12,000 K), all showing multiperiodic luminosity variations caused by low-order and low-degree g-mode instabilities. We also provide, in an , a very brief overview of the newly found evidence in favor of the existence of a fourth category of oscillating white dwarfs bearing strong similarities with these families of pulsators. We begin our survey with a short historical introduction, followed by a general discussion of pulsating white dwarfs as compact pulsators. We then discuss the class properties of these objects, including an updated census. We next focus on the instability domains for each family of pulsators in the log g - Teff diagram, and present their time-averaged properties in more detail. This is followed by a section on excitation physics, i.e., the causes of the pulsational instabilities, with emphasis on the common properties of the different types of pulsator. We then discuss the time-dependent properties of the pulsating white dwarfs featuring, among other things, a brief “picture tour” across the ZZ Ceti instability strip. We next review the methods used to infer or constrain the angular geometry of a pulsation mode in a white dwarf. These include multicolor photometry and time-resolved spectroscopy, the exploitation of the nonlinear features in the observed light curves, and rotational splitting. We also consider basic adiabatic asteroseismology starting with a discussion of the reaction of the period spectrum to variations of model parameters. We next review the various asteroseismological inferences that have so far been claimed for white dwarfs. We also discuss the potential of exploiting the rates of period change. We finally provide some concluding remarks, including a list with several suggestions for future progress in the field.

The β Cephei star HD 167743

The β Cephei star HD 167743 was observed from three different observatories in the years 2006 and 2007. The data sets were collected through the filters Johnson UBV and Strömgren uvy. First analyses show six independent and five combination frequencies. We present mode identifications, which are simplified by the rather high amplitudes of the star. No evidence for rotational splitting was found yet.