Amplitude variations in pulsating sdB stars

Frequency analyses over two or more seasons are presented for several pulsating sdB stars. These results indicate that amplitude variations in sdBV stars might be common and occur on timescales from less than a day to years. It is not clear whether such variations are a result of real amplitude modulation or of the fact that very close frequencies have not all been resolved. In either case, it would appear to be necessary to carry out reasonably extensive studies before one can claim to have resolved “all” frequencies, and to exhibit care before selecting frequencies for ‘ $\dot{P}$ ’ studies.     

Three new pulsating sdB stars from the Edinburgh–Cape survey

We report the discovery of very rapid pulsations in three sdB stars from the Edinburgh–Cape blue object survey. The short periods, small amplitudes and multi-periodicity clearly establish these stars as members of the EC 14026 class. EC 11583−2708 has pulsation periods near 149, 144 and 114 s, though evidence is presented that the 149-s period is resolved into two periods at 148.87 and 148.55 s by the full photoelectric data set. The amplitudes of the detected variations are in the range 0.002–0.006 mag. The light variation of EC 20338−1925 is dominated by a period near 147 s with a very large amplitude for a variable sdB star (0.025 mag), though four other frequencies are detected with periods near 168, 151, 141 and 135 s and amplitudes in the range 0.002–0.005 mag. The third star, EC 09582−1137, displays a light curve which is virtually a textbook example of frequency beating, being produced by two pulsations of almost equal amplitude (∼0.008 mag) and periods near 136.0 and 151.2 s.     

The NOT pulsating sdB search programme

A search program for pulsating sdBs was conducted with the Nordic Optical Telescope in the years 1999–2001. Possible candidates were selected from the HS, HE and PG surveys. In total 10 pulsators were found, some quite bright. In addition one more was found from a small SDSS sample observed in Oct. 2002.     

Colour and radial velocity variations in pulsating subluminous B stars

The utility of pulsations for the investigation of the structure and evolution of subdwarf B stars is considerable. However, the small number of detected modes generally limits the potential for a traditional seismological analysis such as that carried out for the Sun. Therefore, it is crucial to acquire additional primary data to characterise the stellar oscillations more completely. We review recent studies of radial velocity amplitudes and introduce new multi-colour photometry of small-amplitude sdBV stars. We also discuss a set of models for radial velocity and colour variations and demonstrate how these may be used to infer the spherical and azimuthal degrees of observed pulsations.     

Photometric determination of variations in the surface conditions for pulsating stars

Two sets of model atmosphere spectra have been used to determine variations of effective temperature, surface gravity, and radius from multicolour indices measured for pulsating stars. The two model atmosphere sets led to surface parameters that differ by consideraby more than the measurement uncertainties.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984.     

Abundance analyses of three helium-rich sdB stars

We present some preliminary results based on the CoRoT observations of the young distant cluster Dolidze 25. The light curve for the 28 stars observed by the satellite have been analyzed and the relevant periodogram presented. As a result we have found two binary, three Pulsating Be, three SPB, two Spotted and one ellipsoidal variables. Noteworthy, we have also identified one PMS δ Scuti candidate.     

The masses of sdB and sdO stars

Mass is a fundamental parameter, but the masses are not well known for most hot subdwarfs. We propose a method of determining the masses of hot subdwarfs. Using this method, we studied the masses of hot subdwarfs from the ESO supernova Ia progenitor survey and the Hamburg quasar survey. The study shows that most of the subdwarf B stars have masses between 0.42 and 0.54 M _⊙, whilst most sdO stars are in the range 0.40～0.55 M _⊙. Comparing our study to the theoretical mass distributions of Han et al. (Mon. Not. R. Astron. Soc. 341:669, 2003), we found that sdO stars with mass less than ～0.5 M _⊙ may evolve from sdB stars, whilst most high-mass (>0.5 M _⊙) sdO stars result from mergers directly.     

Radial velocity curves of nine sdB binary stars

Radial velocity curves have been measured for nine sdB stars from high resolution optical spectra and are found to be sinusoidal indicating that they are binary stars with circular orbits. Their periods range from ≈12 h to more than 8 days. The companions are invisible in optical light. Minimum companion masses are derived from the mass functions, assuming the mass of the sdB primary to be half a solar mass. We argue that the companions to UVO 1735+22, Feige 108, HD 188112, and HD 171858 are white dwarfs, since their (statistically) most likely mass is above ≈0.7M _⊙. Five of the systems have not been investigated before, for the others our results agree with previously published ones.     

Population I pulsating stars

Evolutionary masses corresponding to various evolutionary phases of Population I pulsating stars (89 Delta Scuti variables and 155 classical cepheids) are interpolated in the systems of tracks of Iben (1967) and Paczyski (1970). The evolutionary masses are larger in the latter system than in the former one. The uncertainty of the evolutionary mass of a star is estimated, when various evolutionary phases are possible for this star (a smaller evolutionary mass corresponds to a later phase). Semi-empirical period-evolutionary mass-colour (P-M _e -C) and period-evolutionary mass (P-M _e ) relations are derived for various modes, groups of stars, colour indices (and effective temperature), and evolutionary phases. For Delta Scuti stars, the uncertainty of evolutionary masses calculated from theP-M _e relations for different modes, is estimated. The improvement of the evolutionary mass accuracy is estimated, when aP-M _e -C relation is used instead of the correspondingP-M _e relation. The theoretical and semi-empirical period ratios of radial pulsations derived from theP-M _e relations for Delta Scuti stars, are compared. There is a relatively good agreement between theP-M _e relations for the two types of Population I pulsating stars, but a gap exists between them. The evolutionary masses of these stars are closer in the two systems of tracks and are derived with a relatively higher accuracy in comparison with their ages.     

Population i pulsating stars

Six ways for obtaining approximate period-luminosity (P-L) relations for classical cepheids and Delta Scuti variables are presented. Three out of these ways were earlier schematically considered by J.P. Cox (1980, 1985). It was proceeded from certain results derived from the study of stellar pulsation and evolution, by using some simple considerations and simplifying assumptions. The expressions obtained for the coefficients of these approximate P-L relations, were used to estimate the slopes and the zero-points. In addition, it was evaluated the influence of both different modes of radial pulsations and variations of Population I chemical composition on the zero-points. The results satisfactorily agree with those derived from observations or accurate theoretical calculations.     

Population I pulsating stars

Luminosities of Population I pulsating stars (Delta Scuti variables and classical cepheids) are investigated. From data for 80 Delta Scuti stars, semi-empirical period-luminosity-colour (P-L-C) relations and period-luminosity (P-L) relations are obtained for the four lowest modes of radial pulsations. The improvement of the accuracy of the stellar luminosity is determined when a P-L-C relation is used instead of the corresponding P-L relation. From data for 155 classical cepheids, empirical P-L relations are derived for short-period stars (logP1.1), long-period stars (logP>1.1), and s-cepheids. The comparison of the P-L relations for the two types of variable stars shows good agreement, but between them there is a gap with a dim nature.     

Population i pulsating stars

On the basis of our age estimations of Population I pulsating stars in our Galaxy (Tsvetkov, 1986a), the mean ages of 6 open star clusters containing 21 Delta Scuti-variables and of 8 star clusters and associations containing 13 classical cepheids, have been evaluated. These mean cluster age estimations weighted according to the probabilities for different evolutionary phases of the pulsating stars, are obtained in the evolutionary track systems of Iben (1967) and Paczyski (1970); the cluster ages are larger in the former system. Our results are compared with those obtained from various methods by other authors. Clusters with classical cepheids and with Delta Scuti-stars have ages, respectively, in the ranges 10⁷–10⁸ years and 10⁶–10⁹ years. It is shown that the use of simple period-age(-colour) relations for Population I pulsating stars gives sufficiently accurate cluster age estimations. By use of our period-age relations for classical cepheids (Tsvetkov, 1986a), the mean ages of 56 other star clusters and associations in our Galaxy, the Magellanic Clouds, and M 31 galaxy have been estimated in both systems of tracks. The results are generally in agreement with those obtained from various methods by other authors. The use of Population I pulsating stars in star clusters and associations is one of the simplest and most easily applied methods for determining cluster ages; but there are some limitations in its application.     

A search for magnetic fields in cool sdB stars

Hot cluster horizontal branch (HB) stars and field subdwarf B (sdB) stars are core helium burning stars that exhibit abundance anomalies that are believed to be due to atomic diffusion. Diffusion can be effective in these stars because they are slowly rotating. In particular, the slow rotation of the hot HB stars (T_eff > 11000 K), which show abundance anomalies, contrasts with the fast rotation of the cool HB stars, where the observed abundances are consistent with those of red giants belonging to the same cluster. The reason why sdB stars and hot HB stars are rotating slowly is unknown. In order to assess the possible role of magnetic fields on abundances and rotation, we investigated the occurrence of such fields in sdB stars with T_eff < 30 000 K, whose temperatures overlap with those of the hot HB stars. We conclude that large‐scale organised magnetic fields of kG order are not generally present in these stars but at the achieved accuracy, the possibility that they have fields of a few hundred Gauss remains open. We report the marginal detection of such a field in SB 290; further observations are needed to confirm it (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The slowly pulsating sdB star EC 21324−1346

We present results from a two-week, single-site photometric campaign on the slowly pulsating sdB star, EC 21324−1346. Nine frequencies are detected between about 333 and 125 μHz (periods between 3000 and 8000 s) with amplitudes ranging from 0.003 to 0.001 mag; large for this class of star. Comparison with sparser, earlier data indicates that some of these oscillations are persistent, though at least one shows clear evidence of substantial amplitude variation.     

Population I pulsating stars

The radiiR and surface gravitiesg of Population I pulsating stars (89 Delta Scuti-variables and 155 classical cepheids) have been investigated. Semi-empirical period-radius (P-R) and period-gravity (P-g) relations are obtained for Delta Scuti-stars (for the four lowest modes of radial pulsations) and for classical cepheids. For Delta Scuti-stars, the uncertainties of radius and gravity estimations calculated from theP-R andP-g relations for different modes, are evaluated. There is a good agreement both between theP-R relations and between theP-g relations for Delta Scuti-stars and for classical cepheids, but a gap exists between the two types of variables. From models of Delta Scuti-stars, theoreticalP-R andP-g relations for the four lowest modes of radial pulsations are obtained, in a good agreement with the corresponding semi-empirical relations. There is an excellent agreement between the theoretical and semi-empirical period ratios of radial pulsations as derived from theP-R andP-g relations for Delta Scuti-stars. It is not necessary to take into account the colours (in addition to the periods), in order to estimate the radii and gravities of the variables under study.     

RAT0455+1305: another pulsating hybrid sdB star

RAT0455+1305 was discovered during the Rapid Temporal Survey which aims in finding any variability on timescales of a few minutes to several hours. The star was found to be another sdBV star with one high amplitude mode and relatively long period. These features along with estimation of T _eff and log?g makes this star very similar to Balloon?090100001. Encouraged by prominent results obtained for the latter star we have decided to perform white light photometry on RAT0455+1305. In 2009 we used the 1.5 m telescope located in San Pedro Martir Observatory in Mexico. Fourier analysis confirmed the dominant mode found in the discovery data, uncovered another peak close to the dominant one, and three peaks in the low frequency region. This shows that RAT0455+1305 is another hybrid sdBV star pulsating in both p- and g-modes.     

Periodic motions around pulsating stars

The periodic motion of a test particle (dust, grain, or a larger body) around a pulsating star with a luminosity oscillation of small amplitude (featured by a small parameterB) is being studied. The perturbations of all orbital elements are determined to first order inB, by using Delaunay-type canonical variables and a method whose bases were put forth by von Zeipel. According to the value of the ratio oscillation frequency/dynamic frequency, three possible situations are pointed out: nonresonant (NR), quasi-resonant (QR), and resonant (R). The solution of motion equations shows that only in the (QR) and (R) cases there are orbital parameters (argument of periastron and mean anomaly) affected by secular perturbations. These solutions (which indicate a secularly stable motion in a first approximation) are valid over prediction times of orderB ^–1 in the (NR) case andB ^–1/2 in the (QR) and (R) cases. The theory may be applied to various astronomical situations.     

MSST observations of the pulsating sdB star PG 1605+072

We present the first results from the MultiSite Spectroscopic Telescope (MSST) observations of the sdBV star PG 1605+072. Pulsating sdB stars (also known as EC 14026 stars) offer the chance to gain new insights into the formation and evolution of extreme Horizontal Branch stars using the tools of asteroseismology. PG 1605+072 is an outstanding object in its class, with the richest frequency spectrum, the longest periods, and the largest variations. The MSST campaign took place in May/June 2002 immediately following the Whole Earth Telescope Xcov22 run, which observed PG 1605+072 as an alternate target. We will first give an overview of the project and its feasibility, after which we will present the massive data set, made up of 399 h of photometry and 151 h of spectroscopy. The overall aims of the project are to examine light/velocity amplitude ratios and phase differences, changes in equivalent width/line index, and λ-dependence of photometric amplitudes, and to use these properties for mode identification.