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.     

Masses and ages of delta scuti stars in eclipsing binary systems

By using data mainly from Frolovet al. (1982) for four Delta Scuti stars in eclipsing binary systems, AB Cas, Y Cam, RS Cha, and AI Hya, their physical parameters, distances, and radial pulsation modes are determined. The evolutionary track systems of Iben (1967), Paczyski (1970), and Maeder and Meynet (1988) are interpolated, in order to estimate evolutionary massesM _eand agest of these variables. Their pulsation massesM _Qare estimated from the fitting formulae of Faulkner (1977) and Fitch (1981). Our estimates of evolutionary massesM _eand pulsation massesM _Qare close to the massesM determined by Frolovet al. (1982) from the star binarity. The only exception is AB Cas, for which there is no agreement between certain star parameters.Another, independent approach is also applied to the stars RS Cha and AI Hya: by using their photometric indicesb — y andc ₁ from the catalogue of López de Cocaet al. (1990) and appropriate photometric calibrations, other sets of physical parameters, distances, modes, ages, evolutionary and pulsation masses of both variables are obtained.     

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.     

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.     

Ages and masses of delta scuti stars in the praesepe cluster

Physical parameters and radial pulsation modes are determined for three Delta Scuti stars in the Praesepe cluster: HD 73345, HD 73712, and HD 73746. Their agest and evolutionary massesM _eare interpolated in the track systems of Iben (1967) and Paczyski (1970). By combining these age estimates with our previous results for nine other Delta Scuti-stars in the Praesepe cluster (Tsvetkov, 1989), the following weighted mean age estimates of this cluster are obtained: (14.2 ± 1.3) × 10⁸ yr (Iben) and (5.4 ± 0.4) × 10⁸ yr (Paczyski). Age and evolutionary mass estimates of the twelve cluster variables are also obtained in the modern track system of Maeder and Meynet (1988), in which the weighted mean cluster age is (15.3 ± 1.0) × 10⁸ yr.Pulsation massesM _Qcalculated from the fitting formulae of Faulkner (1977) and Fitch (1981) as well as massesM _g=gR ² / G were evaluated for the twelve cluster variables by Tsvetkov (1990) or in the present paper. In most cases there is a satisfactory agreement between our estimates of massesM _e,M _g, andM _Q.Due to a large disagreement between the long period and low luminosity of the star HD 73746, its radial pulsation mode and pulsation massM _Qcannot be evaluated.     

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.     

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.     

Mass loss in semi-detached binaries

Pre-Main-Sequence contracting objects, post-Main-Sequence expanding stars and mass-losing components of semi-detached systems all occupy more or less the same region in the conventional H-R-diagram. We make a transformation to variables (logL) and (logT _e), where is the difference between the observed quantity, logL or logT _e, and the value of that quantity which a star of the same mass would have on the empirical Main Sequence. It is demonstrated that a plot between the new variables clearly separates the mass-losing stars from other objects which is essentially an effect of the increasing abundance of helium relative to hydrogen.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.     

Coalescing neutron stars as gamma ray bursters?

We investigate the dynamics and evolution of coalescing neutron stars. The three-dimensional Newtonian equations of hydrodynamics are integrated by the Piecewise Parabolic Method on an equidistant Cartesian grid. The code is purely Newtonian, but does include the emission of gravitational waves and their back-reaction. The properties of neutron star matter are described by the equation of state of Lattimer and Swesty (1991). Energy loss by all types of neutrinos and changes of the electron fraction due to the emission of electron neutrinos and antineutrinos are taken into account by an elaborate neutrino leakage scheme. We simulate the coalescence of two identical, cool neutron stars with a baryonic mass of 1.6M and a radius of 15 km and with an initial center-to-center distance of 42 km. The initial distributions of density and electron concentration are given from a model of a cold neutron star in hydrostatic equilibrium. We investigate three cases which differ by the initial velocity distribution in the neutron stars. The orbit decays due to gravitational-wave emission and after one revolution the stars are so close that dynamical instability sets in. Within 1 ms the neutron stars merge into a rapidly spinning (P 1 ms), high-density body ( 10¹⁴ g/cm³) with a surrounding thick disk of material with densities 10¹⁰ – 10¹² g/cm³ and orbital velocities of 0.3-0.5 c. The peak emission of gravitational waves has a maximum luminosity of a few times 10⁵⁵ erg/s and is reached for about 1 ms. The amplitudes of the gravitational waves are close to 3 10^–23 at a distance of 1 Gpc and the typical frequency is near the dynamical value of the orbital motion of the merging neutron stars of 2 KHz. In a post-processing step, the rate of neutrino-antineutrino annihilation is calculated from the neutrino luminosities generated during the hydrodynamical simulations. We find the integral annihilation rate to be a few 10⁵⁰ erg/s during the phase of strongest neutrino emission, which is too small to generate the observed bursts considering the fact that the merged object of about 3M will most likely collapse to a black hole within milliseconds.     

The effect of metallicity on the empirical relations for RR Lyrae stars

It has empirically been shown that, for a given value of the effective temperature, the correction in (B-V) due to line blanketing varies linearly with the metallicity parameter S. Next, on the basis of considerations different from those used to obtain a similar result by Sturch (1966), a relation between reciprocal effective temperature _e (=5040/T _e ) and intrinsic line-free colour index(B-V) _o,c has been obtained based on the _e and (B-V) values for five RR Lyr variables. Relations between _e and intrinsic colour(B-V) _o for different groups of stars having a S parameter in the range 0S11 have also been obtained.     

Trapping of test particles in static and spherical space-time geometries

Estimates of the pulsation massesM _Q and of massesM _g=gR²/G (g is the surface gravity;R, the mean stellar radius; andG, the gravitational constant) of 89 Delta Scuti-variables have been obtained. An intercomparison of three kinds of masses —M _e, M_g, andM _Q — is performed; the evolutionary massesM _e of the same variables were estimated in a previous paper (Tsvetkov, 1986). It is pointed out that within the limits of the accuracy of determination, the three kinds of masses agree for the majority of the stars under study. For several varaibles, however, there is a considerable discrepancy between the estimates of the pulsation massesM _Q and the estimates of the massesM _e andM _g. Arguments are represented, which may alleviate or even remove this mass discrepancy for some of these stars. It is shown that the results from the comparison between the three kinds of masses of the considered Delta Scuti-stars are not very sensitive to the choice of the system of evolutionary tracks and the adopted chemical composition as well as to the evolutionary phases of the variables (core or shell hydrogen burning). The variations of the chemical composition in most of the stars under study are probably not very large.     

Structural Properties of Pulsating Star Light Curves Through Fuzzy Divisive Hierarchical Clustering

The aim of this paper is to explore the possibility of using a fuzzy divisive clustering technique to the classification of pulsating stars according to the shape of their light curves. The considered sample contains Cepheides, RR Lyrae stars, and high amplitude Scuti and SX Phoenicis stars. Our investigations proved the ability of this method to identify morphological groups in a given class of pulsating stars. The method is also useful for establishing the membership of an unknown variable star in a given class.     

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.     

On the possibility of constructing a radiative sunspot model in magnetohydrostatic equilibrium

It is currently believed that it is impossible to construct a radiative sunspot model in magnetohydrostatic equilibrium unless magnetic fields below the surface are excessively large (> 100 kG). This belief is based on results obtained using the mixing length theory of convection. We wish to point out that by using a different theory of convection, due to Öpik (1950), it is possible to compute a radiative sunspot model in which the field becomes no greater than 9000 G. By applying two boundary conditions, (i) depth of spot equals depth of convection zone, (ii) magnetic field has zero gradient at the base of the spot, we show that a radiative spot has a unique effective temperature for a given Wilson depression, . For = 650 km, we find T _e = 3800K ; for = 150 km, T _e = 3950K. According to our model, spots having T _e cooler than these values should not exist.     

Period distributions in pulsating and binary stars

We analyze the hypothesis of quantization in bands for the angular momenta of binary systems and for the maount of actionA _c in stable and pulsating stars. This parameter isA _c=Mv _eff R _eff, where the effective velocity corresponds to the kinetic energy in the stellar interior and the effective radius corresponds to the potential energyGM ²/R _eff. Analogous parameters can be defined for a pulsating star withm=M where is the rate of the massm participating in the oscillation to the total massM andv _osc,R _osc the effective velocity and oscillation radius.From an elementary dimensional analysis one has thetA _c (energy x time) (period)^1/3 independently ifA _c corresponds to the angular momentum in a binary system, or to the oscillation in a pulsating star or the inner energy and its time-scaleP _eff in a stable star.From evolving stellar models one has that P _effP _eff(solar)1.22 hr a near-invariant for the Main Sequence and for the range of masses 0.6M <M<1.6M .With this one can give scalesn _k=kn ₁ withk integers andn ₁=(P/P ₁)^1/3 withP ₁=P _eff1.22 hr. In these scales proportional toA _c, one sees that the periods in binary and pulsating stars are clustered in discrete unitsn ₁,n ₂,n ₃, etc.This can be seen in pulsating Scuti, Cephei, RR Lyrae, W Virginis, Cephei, semi-regular variables, and Miras and in binary stars as cataclysmic binaries, W Ursa Majoris, Algols, and Lyrae with the corresponding subgroups in all these materials. Phase functions (n _k) in RR Lyrae and Cephei are also associated with discrete levelsn _k.the suggested scenario is that the potential energies and the amounts of actionE _p(t), A_c(t) are indeed time-dependent, but the stars remain more time in determinated most proble states. The Main Sequence itself is an example of this. These most probable states in binary systems, or pulsating or stable stars, must be associated with velocities sub-multiplesc/ _F , given by the velocity of light and the fine structure constant.Additional tests for such a hypothesis are suggested when the sufficient amount of observational data are available. They can made with oscillation velocities in pulsating stars and velocity differences of pairs of galaxies.     

Initial mass functions of Wolf-Rayet stars

On the basis of evolutionary tracks on the HR diagram the lower limit of initial mass functions for Wolf-Rayet stars are estimated. The lower limit to the initial masses of the Wolf-Rayet stars seems to be 20M and in this respect there is no significant difference between the WN and WC stars.     

Recent progress in CP star detection and classification

Chemically peculiar (CP) stars are mainly found among B and A stars. Present theories are not able to account fully for the observed spectrum anomalies, suggesting that in the atmospheres of stars in the range ofT _e , where mass loss is no longer very large and convection is still not very important, the present theoretical approach needs further refinement. Moreover, the lack of laboratory data is responsible, at least partly, for the discrepancies between observed and computed stellar energy distributions.The choice for quick detection of CP stars among faint objects is reviewed; the measure of the flux depression at 5200 appears to be very powerful, and the identification of this complex feature is urgently needed.The need to separate the various subclasses of the He abnormal stars in a standard way is underlined and further analyses of the characteristics of the Boo stars are required.The problem of the determination ofT _e and consequently of realistic atmospheric abundance anomalies of CP stars is discussed.     

Gravity Modes in Delta Scuti Stars

This paper examines the observational evidence for the detectionof gravity modes in Scuti stars, which are p-mode pulsators.Low-order gravity modes have also been found in at least one star (FG Vir).Some reports of gravity modes may be due to systematic errors in theabsolute magnitude calibrations for slowly rotating stars. Furthermore,many detected low frequencies are not high-order gravity modes, but linear combinations,f _i -f _j , of the main pulsation modes. Other low frequencies are caused bya close binary companion leading to tidal deformation as well as tidallyexcited gravity modes.     

The mass-ratio distribution of spectroscopic binary stars

In order to determine the mass-ratio distribution of spectroscopic binary stars, the selection effects that govern the observations of this class of binary systems are investigated. The selection effects are modelled numerically and analytically. The results of the models are compared to the data inThe Eighth Catalogue of the Orbital Elements of Spectroscopic Binary Stars (DAO8) compiled by Battenet al. (1989). The investigations involve binary systems with Main-Sequence primary components only, in order to avoid confusion of evolutionary and selection effects.For single-lined spectroscopic binaries (SBI) it is found that the mass ratios (q=M _sec/M _prim) in general adhere to a distribution _q q ^-2 forq>q ₀, withq ₀=0.3. The observations are consistent with a distribution that is flat forq<q ₀. The turn-over value varies fromq ₀=0.3 for systems with B-type primaries, toq ₀=0.55 for systems with K-type primaries. The semi-major axesa ₁ are distributed according to _a (a ₁)a ₁ ^-a with an average value of _a =1.3. The power varies from _a =1.7 for systems with B-type primaries to _a =0 for systems with K-type primaries. The eccentricitiese of the orbits of SBI systems are distributed according to _e (e)e ^-1.For double-lined spectroscopic binary stars (SBII) it is found that the shape of theq-distribution, as derived from observations, is almost entirely determined by selection effects. It is shown that the distribution is compatible with theq-distribution found for SBI systems. A sub-sample, consisting of the SBII systems from DAO8 with magnitudesm _V 5 ^m , is less hampered by selection effects, and shows the same shape of theq-distribution as the SBI systems, at theq-interval (0.67, 1).It is estimated that 19–45% of the stars in the solar neighbourhood are spectroscopic binary systems.     

Recent Observations of PMS δ Scuti Stars

We present time series observations of the intermediate mass Pre-Main Sequence star H254 belonging to the young star cluster IC 348 and of the Herbig Ae star V351 Ori.Both these stars present light variation on short time scale (a few hours) typical of the Scuti pulsation. The new data are briefly described together with the plan for future observational campaigns on PMS Scuti stars.