Amplitude ratios of several groups of variable stars

The observed positions of classical cepheids, RR Lyrae stars, Scuti stars and dwarf cepheids in the logg-logT _e plane form a continuous sequence, thereby defining the location of maximum instability. The amplitude ratio (the ratio of radial velocity amplitude to light amplitude) is small for variables at the upper end of the instability strip and increases almost linearly towards the lower end of the strip. The theory of radial pulsation predicts the trend of this correlation.     

Theoretical rates of pulsation period change in the Galactic Cepheids

Theoretical estimates of the rates of radial pulsation period change in Galactic Cepheids with initial masses 5.5 M _⊙ ≤ M _ZAMS ≤ 13 M _⊙, chemical composition X = 0.7, Z = 0.02 and periods 1.5 day ≤ Π ≤ 100 day are obtained from consistent stellar evolution and nonlinear stellar pulsation computations. Pulsational instability was investigated for three crossings of the instability strip by the evolutionary track in the HR diagram. The first crossing occurs at the post-main sequence helium core gravitational contraction stage which proceeds in the Kelvin-Helmholtz timescale whereas the second and the third crossings take place at the evolutionary stage of thermonuclear core helium burning. During each crossing of the instability strip the period of radial pulsations is a quadratic function of the stellar evolution time. Theoretical rates of the pulsation period change agree with observations but the scatter of observational estimates of \(\dot \Pi\) noticeably exceeds the width of the band \(\left( {\delta \log \left| {\dot \Pi } \right| \leqslant 0.6} \right)\) confining evolutionary tracks in the period-period change rate diagram. One of the causes of the large scatter with very high values of \(\dot \Pi\) in Cepheids with increasing periods might be the stars that cross the instability strip for the first time. Their fraction ranges from 2% for M _ZAMS = 5.5 M _⊙ to 9% for M _ZAMS = 13 M _⊙ and variables α UMi and IX Cas seem to belong to such objects.     

Evolution and Period Change in RR Lyr Variables of the Globular Cluster M 3

The grid of evolutionary tracks of population II stars with initial masses 0.81 M_⊙ ≤ M_ZAMS ≤ 0.85 M_⊙ and chemical composition of the globular cluster M3 is computed. Selected models of horizontal branch stars were used as initial conditions for solution of the equations of radiation hydrodynamics and time–dependent convection describing radial stellar oscillations. The boundaries of the instability strip on the Herztsprung–Russel diagram were determined using ≈100 hydrodynamic models of RR Lyr pulsating variables. For each evolutionary track crossing the instability strip the pulsation period was determined as a function of evolutinary time. The rate of period change of most variables is shown to range within ?0.02 ≤ \(\dot{\Pi}\) ≤ 0.05 day/10⁶ yr. Theoretical estimate of the mean period change rate obtained by the population synthesis method is 〈\(\dot{\Pi}\)〉 = 6.0 × 10^?3 day/10⁶ yr and agrees well with observations of RR Lyr variables of the globular cluster M3.     

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.     

On the intrinsic colours of cepheids

Some consequences from new data on the photometrically obtained intrinsic colours are considered. It is shown that the small amplitude and almost sinusoidal light-curve cepheids (Cs-subtype) increase their pulsation amplitude towards the red instability strip edge, differing from the other galactic cepheids. This feature is discussed in connection with Efremov's (1968) hypothesis that the Cs-cepheids first cross the instability strip from left to right. The galactic cepheid period-colour relation obtained by Dean, Warren and Cousins (1978) satisfies rather well the LMC cepheid observations and, consequently, considerations for the period-luminosity relations are made. The residuals from the PL relation proposed by us (AA line instead of Gascoigne's BB line in Figure 3) correlate with the colour residuals from the DWC period-colour relation V/(B–V) being equal to 2.7 (Figure 4). The luminosity effect as a possible cause of the descrepancy between the spectroscopic cepheid colours and the photometric colours is briefly discussed.     

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.     

Rapid extreme horizontal branch pulsators in ω Centauri

We present the first results of an observational campaign aimed at detecting rapid extreme horizontal branch (EHB) pulsators in globular clusters. So far, we have observed multi-frequency luminosity variations for three EHB stars in ω Cen, with typical periods in the 100–120 s range. This is towards the short end, but comparable to, the periodicities measured for rapidly pulsating subdwarf B (sdB) stars in the field. Given that the effective temperatures of the variables discovered seem to be compatible with the instability strip for fast sdB pulsators, we believe we have uncovered the first such variables in a globular cluster.     

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.     

Spectrophotometric study of the cepheids DT Cyg and SZ Tau

The effective temperatures of the cepheids DT Cyg and SZ Tau have been determined from a comparison of their spectral scans with appropriate stellar model atmospheres. Using these temperatures and an independent Wesselink radius determination, the luminosities of the stars have been determined. The pulsation masses and the evolutionary masses of the stars have been discussed.     

Secular Perion Changes and Fundamental Parameters of Long–Period Cepheids

Hydrodynamic computations of nonlinear Cepheid pulsation models with periods from 20 to 100 day on the evolutionary stage of core helium burning were carried out. Equations of radiation hydrodynamics and time–dependent convection were solved with initial conditions obtained from selected models of evolutionary sequences of population I stars with initial masses from 8 M_⊙ to 12.5 M_⊙. For each crossing of the instability strip the pulsation period Π and the rate of period change \(\dot \prod \) were derived as a function of evolutionary time. Comparing results of our computations with observational estimates of Π and \(\dot \prod \) we determined fundamental parameters (the age, the mass, the luminosity and the radius) of seven long–period Cepheids. Theoretical estimates of the stellar radius are shown to agree with radius measurements by the Baade–Wesselink technique within 3% for RS Pup and GY Sge whereas for SV Vul the disagreement between theory and observations does not exceed 10%.     

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.     

Constraints for cataclysmic binary evolution as derived from space distributions

Space densities and galacticz-distributions of novae, recurrent novae, dwarf novae and symbiotic stars are newly determined and discussed in the context of earlier determinations. The data are then compared with the distributions of single and binary stars of possibly related types (late type giants, Mira variables, Algol systems, W UMa systems).Novae and dwarf novae have similar distributions, those of fairly young stellar populations. The observed space density of potential novae (novalike objects) indicates that the mean recurrence time of novae might be as small as a few hundred years, which leads, with given nova shell masses and mass transfer rates in the minimum stage, to a secular decrease of the masses of the components undergoing nova outbursts.Recurrent novae and symbiotic stars have distributions of older stellar populations, similar to those of late type giants and Mira variables.On the basis of galactic distribution, novae and dwarf novae are closely related and may be final stages of W UMa systems, as well as progenitors of supernovae of type I. A small fraction of W UMa systems seems to belong to an older population. If evolutionary transitions between these types of stars can be substantiated, the presence of a minority of novae and dwarf novae in globular clusters and of supernovae I in elliptical galaxies can be explained.Due to the lack of sufficiently well determined space distributions of Algol binaries, the suggestion that long-period Algol systems might be the progenitors of cataclysmic binaries can as yet neither be substantiated nor refuted. A very high space density of long-period Algol systems in the solar neighbourhood is derived. The observed space density of cataclysmic binaries could be explained by the transformation of a small percentage of the long-period Algol systems by common envelope evolution.Paper presented at the Lembang-Bamberg IAU Colloquium No. 80 on Double Stars: Physical Properties and Generic Relations, held at Bandung, Indonesia, 3–7 June, 1983.     

Optical monitoring of the central region of the globular cluster M 15 = NGC 7078: New variable stars

We obtained a series of more than two hundred R-band CCD images for the crowded central (115″×77″) region of the metal-poor globular cluster M 15 with an angular resolution of \(0\mathop .\limits^{''} 5 - 0\mathop .\limits^{''} 9\) in most images. Optimal image subtraction was used to identify variable stars. Brightness variations were found in 83 stars, 55 of which were identified with known cluster variables and the remaining 28 are candidates for new variables. Two of them are most likely SX Phe variables. The variability type of two more stars is uncertain. The remaining stars were tentatively classified as RR Lyrae variables. A preliminary analysis of published data and our results shows that the characteristics of RR Lyrae variables in the densest part (r<35″) of the cluster probably change. More specifically, the maximum of the period distribution of first-and second-overtone (RR1, RR2) pulsating stars shifts toward shorter periods; i.e., there is an increase in the fraction of stars pulsating with periods \( < 0\mathop .\limits^d 3\) and a deficiency of stars with \(0\mathop .\limits^d 35 - 0\mathop .\limits^d 40\). The ratio of the number of these short-period RR Lyrae variables to the number of fundamental-tone (RR0) pulsating variables changes appreciably. We found and corrected the error of transforming the coordinates of variables V128–155 in M 15 into the coordinate system used in the catalog of variable stars in globular clusters.     

Non-adiabatic oscillations of red giants

Using our non-local time-dependent theory of convection, the linear non-adiabatic oscillations of 10 evolutionary model series with masses of  1–3 M_⊙  are calculated. The results show that there is a red giant instability strip in the lower temperature side of the Hertzsprung–Russell diagram which goes along the sequences of the red giant branch and the asymptotic giant branch. For red giants of lower luminosities, pulsation instability is found at high order overtones; the lower order modes from the fundamental to the second overtone are stable. Towards higher luminosity and lower effective temperature, instability moves to lower order modes, and the amplitude growth rate of oscillations also grows. At the high luminosity end of the strip, the fundamental and the first overtone become unstable, while all the modes above the fourth order become stable. The excitation mechanisms have been studied in detail. It is found that turbulent pressure plays a key role for excitation of red variables. The frozen convection approximation is unavailable for the low temperature stars with extended convective envelopes. In any case, this approximation can explain neither the red edge of the Cepheid instability strip, nor the blue edge of the pulsating red giant instability strip. An analytic expression of a pulsation constant as a function of stellar mass, luminosity and effective temperature is presented from this work.     

δ Scuti Pulsations in Pre-main Sequence Stars

Intermediate mass pre-main sequence stars (1.5 to 5 M )cross the instability strip on their way to the main sequence.They are therefore expected to be pulsating in a similar way as the Scuti stars. In this review, I present the status of observational studies ofpulsations in these stars, and comment on prospects for futureinvestigations of these pulsations from the ground and from space.     

The delta scuti-star HD 220392: a possible component of a binary system

Physical parameters and distances are determined for the stars HD 220391 and HD 220392, which possibly form a physical pair. Ages and evolutionary masses in the new track system of Schalleret al. (1992) as well as gravitational masses of both stars are evaluated. Distance and age estimates of this possible binary system are obtained: 128(±12) pc and 7.9(±0.8) × 10⁸ yr. Both stars are located within the Delta Scuti instability strip on the H-R diagram, but a variability was only detected in HD 220392 by Lampens (1992). The pulsation mode(s) and the pulsation mass of this variable star cannot be determined at the present time.     

The early-type variables

We review the observational status of several different kinds of intrinsic variables among the early-type stars and attempt to interpret the variations in terms of our current understanding of stellar pulsation. Four distinct types of intrinsic variable can be defined: the Cep, 53 Per, Oph and Eri stars. A simple observational classification scheme, which is readily interpreted in terms of pulsation properties, is proposed. The limits of the instability strip and pulsation constants for the Cep and 53 Per stars is discussed. Problems with the interpretation of Eri stars in terms of pulsation are pointed out. The observations are consistent with rotational modulation. A problem with mode identification in Eri stars is discussed.     

Close binary systems in multiple stars: II. Eclipsing variables in visual binary and multiple systems

Eclipsing variables in visual binary and multiple stars are searched using data from GCVS, WDS, and CCDM catalogs. The list of 421 eclipsing variables is obtained. The masses of components of multiple systems from the list are estimated using the mass-luminosity relation for the main sequence stars. It is shown that, for 85% multiple systems from the list, the mass of visual components is smaller by a factor of 2 than the total mass of close binary systems. The distributions of orbital elements of visual binary systems are constructed and used for calculation of orbit semi-major axes for star from the list. The distributions of orbit semi-major axes and periods obtained from observations are approximated by Gaussian curves. The maxima of the curves correspond to a = 800 a.u. and P = 7600 years, respectively. The distribution of orbit semi-major axes larger than 800 a.u. is better described by Opik’s law; it is expected that this law describes the real a distribution in the region of small values as well. The frequency of eclipsing variables in multiple stars makes 12% of the total number of stars of this type in GCVS.     

Period-finding methods,techniques and applications to variable stars observations

The problem of finding periods of variable stars is considered and it's main methods are generally reviewed. Special attention has been devoted to three methods based on Fourier transform. These methods have been coded in Fortran and have been applied to data of three eclipsing binaries (AD Cnc, UZ Pup and Per), three Scuti stars (HR 1170, HR 1223 and RY Lep) and one spectroscopic binary (RS Sag). The methods have been tested, compared and evaluated concerning their speed, resolution and sensitivity. It has been found that data exhibiting irregular variations lead to erroneous periods. To save computing time and to avoid any spurious period a practical procedure for period finding is proposed with an effective approach for period refinement. The revised and refined periods for the above stated variables have been discussed with comparison to the ones given in literatures and they can be adopted for future work. Some of these variables have been found to show variations in both their periods and amplitudes.     

The comparable analysis of the Cepheids and non-variable supergiants from the instability strip.I

The elemental abundances, temperatures, gravities and microturbulence velocities were derived for 14 non-variable supergiants from the Cepheids' instability strip and two hotter supergiants. For 8 stars the abundances were determined for the first time. The comparable analysis of the program stars' chemical composition and that of the small-amplitude Cepheids has shown that there is no essential differences in the elemental abundances for two stellar groups. Some discussion of the phenomenon of non-variable supergiants in the instability strip is given.