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.     

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.     

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.     

Delta Scuti stars in the Praesepe cluster observed by the MOST satellite

The Praesepe cluster contains a number of δ Sct and γ Dor pulsators. Asteroseismology of cluster stars is simplified by the common distance, age and stellar abundances. Since asteroseismology requires a large number of known frequencies, the small pulsation amplitudes of these stars require space satellite campaigns. The present study utilizes photometric MOST satellite measurements in order to determine the pulsation frequencies of two evolved (EP Cnc, BT Cnc) and two main‐sequence (BS Cnc, HD 73872) δ Sct stars in the Praesepe cluster. The frequency analysis of the 2008 and 2009 data detected up to 34 frequencies per star with most amplitudes in the submillimag range. In BS Cnc, two modes showed strong amplitude variability between 2008 and 2009. The frequencies ranged from 0.76 to 41.7 cd^–1. After considering the different evolutionary states and mean stellar densities of these four stars, the differences and large ranges in frequency remain (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The empirical upper limit for mass loss of cool main sequence stars

The knowledge of mass loss rates due to thermal winds in cool dwarfs is of crucial importance for modeling the evolution of physical parameters of main sequence single and binary stars. Very few, sometimes contradictory, measurements of such mass loss rates exist up to now. We present a new, independent method of measuring an amount of mass lost by a star during its past life. It is based on the comparison of the present mass distribution of solar type stars in an open cluster with the calculated distribution under an assumption that stars with masses lower than M_lim have lost an amount of mass equal to ΔM. The actual value of ΔM or its upper limit is found from the best fit. Analysis of four clusters: Pleiades, NGC 6996, Hyades and Praesepe gave upper limits for ΔM in three of them and the inconclusive result for Pleiades. The most restrictive limit was obtained for Praesepe indicating that the average mass loss rate of cool dwarfs in this cluster was lower than 6 × 10^–11 M_⊙/yr. With more accurate mass determinations of the solar type members of selected open clusters, including those of spectral type K, the method will provide more stringent limits for mass loss of cool dwarfs. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

V792 Her=HD 155638: A totally eclipsing RS CVn binary

Photometry of HD 155638=V792 Her has been analyzed to determine the elements of this totally eclipsing RS CVn binary. The light variation outside eclipse was found to have a period of 27^d.07±0^d.07, which is slightly different from the 27^d.5384±0^d.0045 orbital period. Analysis of the eclipses was achieved by a modification of the Russell-Merrill technique. With the aid of radial velocity measures, absolute elements were obtained for the hot and cool stars, respectively;R _h=2.58R ,R _c=12.28R ,M _h=1.40M ,M _c=1.46M ,i=80^o.61 and velocity semi-amplitudesK _c=48.36 km s^–1±0.79 km s^–1, andK _h=50.50 km s^–1±0.33 km s^–1. The apparent magnitudes areV _h=9 ^m .73 andV _c=8 ^m .48. The distance to HD 155638 was estimated to be 310 parsecs.     

The circumstellar shells of carbon miras

The relation between mass loss rate and pulsation period in carbon Miras is discussed. The dust mass loss rate is very low (about 2 × 10^–10 M/yr) up to aboutP = 380 days, where there is a sudden increase. ForP > 400 days there is a linear relation between logM andP. The change in the mass loss rate near 380 days may be related to radiation pressure on dust becoming effective in driving the outflow.     

The Cepheid impostor HD 18391 and its anonymous parent cluster

New and existing photometry for the G0 Ia supergiant HD 18391 is analyzed in order to confirm the nature of the variability previously detected in the star, which lies off the hot edge of the Cepheid instability strip. Small‐amplitude variability at a level of δV = 0.016 ± 0.002 is indicated, with a period of P = 123^d.04 ± 0^d.06. A weaker second signal may be present at P = 177^d.84 ± 0^d.18 with δV = 0.007 ± 0.002, likely corresponding to fundamental mode pulsation if the primary signal represents overtone pulsation (123.04/177.84 = 0.69). The star, with a spectroscopic reddening of E_B–V = 1.02 ± 0.003, is associated with heavily‐reddened B‐type stars in its immediate vicinity that appear to be outlying members of an anonymous young cluster centered ∼10′ to the west and 1661 ± 73 pc distant. The cluster has nuclear and coronal radii of r_n = 3.5′ and R_c = 14′, respectively, while the parameters for HD 18391 derived from membership in the cluster with its outlying B stars are consistent with those implied by its Cepheid‐like pulsation, provided that it follows the semi‐period‐luminosity relation expected of such objects. Its inferred luminosity as a cluster member is M_V = –7.76 ± 0.10, its age (9 ± 1) × 10⁶ years, and its evolutionary mass ∼19 M_⊙. HD 18391 is not a classical Cepheid, yet it follows the Cepheid period‐luminosity relation closely, much like another Cepheid impostor, V810 Cen (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Bimodality and the Hale cycle

Because of the bimodal distribution of sunspot cycle periods, the Hale cycle (or double sunspot cycle) should show evidence of modulation between 20 and 24 yr, with the Hale cycle having an average length of about 22 yr. Indeed, such a modulation is observed. Comparison of consecutive pairs of cycles strongly suggests that even-numbered cycles are preferentially paired with odd-numbered following cycles. Systematic variations are hinted in both the Hale cycle period and R _sum (the sum of monthly mean sunspot numbers over consecutively paired sunspot cycles). The preferred even-odd cycle pairing suggests that cycles 22 and 23 form a new Hale cycle pair (Hale cycle 12), that cycle 23 will be larger than cycle 22 (in terms of R _M, the maximum smoothed sunspot number, and of the individual cycle value of R _sum), and that the length of Hale cycle 12 will be longer than 22 yr. Because of the strong correlation (r = 0.95) between individual sunspot cycle values of R _sum and R _M, having a good estimate of R _Mfor the present sunspot cycle (22) allows one to predict its R _sum, which further allows an estimation of both R _Mand R _sum for cycle 23 and an estimation of R _sum for Hale cycle 12. Based on Wilson's bivariate fit (r = 0.98), sunspot cycle 22 should have an R _Mequal to 144.4 ± 27.3 (at the 3- level), implying that its R _sum should be about 8600 ± 2200; such values imply that sunspot cycle 23 should have an R _sum of about 10500 ± 2000 and an R _Mof about 175 ± 40, and that Hale cycle 12 should have an R _sum of about 19100 ± 3000.     

Gravitational potential energy of a pair of overlapping galaxies

The interaction of the gravitational potential energy of a pair of overlapping Plummer-model galaxies is determined exactly for various separationsr of their centres. It is shown that the results can be well represented by the simple relationW(r)=–GM ₁ M ₂/(r ²+ ²)^1/2, where 1/ is the average reciprocal distance between the stars of two galaxies of massesM ₁ andM ₂ when they have zero separation.     

Nonlinear pulsations of a very luminous star

The radial nonlinear pulsations of a model withM=0.8M ,M _bol=–6 mag andT _eff=5500 K have been studied. The pulsations are shown to exist in the form of the standing wave only in the innermost layers withR<0.2R _ph. In the outer layers, the standing wave transforms into running waves, the frequency of which decreases with an increasingR. the pulsation period at the photosphere is found to be twice as long as the pulsation period atR<0.2R _ph. The difference between the pulsation periods causes alternation of deep and shallow minima in the temporal dependences of the kinetic energy and radii and can be used to explain the nature of RV Tau variables. It is shown that at the distanceR>3R _ph, the time-independent mass flux caused by shocks takes place. The rate of mass loss is found to beM10^–4 M yr^–1.     

Photographicuvby photometry of the open cluster M52

Photographicuvby photometry of 15 stars in the open cluster M52 (NGC 7654) has been obtained. The distance modulusV _o–M _v=11.3±0.1 and mean cluster reddeningE(B–V)=0.57 are determined. Some basic physical characteristics of 30 stars with observeduvby values are obtained as well as a numerical estimation of the open cluster age 9.6×10⁷ yr is made.     

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.     

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.     

Hydrogen and Helium under high pressure: A case for a classical theory of dense matter

When subject to high pressure, H₂ and ³He are expected to undergo phase transitions, and to become metallic at a sufficiently high pressure. Using a semiclassical theory of dense matter proposed by Savi and Kaanin, calculations of phase transition and metallisation pressure have been performed for these two materials. In hydrogen, metallisation occurs at p _M= (3.0 ± 0.2) Mbar, while for helium the corresponding value is p _M= (106 ± 1) Mbar. A phase transition occurs in helium at p _tr= (10.0 ± 0.4) Mbar. These values are close to the results obtainable by more rigorous methods. Possibilities of experimental verification of the calculations are briefly discussed.     

Stellar pulsation: (I) analysis of stability of envelope

The life-time of the star on AGB is approximately 6 × 10⁴ yr. We divide it into front half and back half of AGB (including to optical Mira variable and OH/IR star) according to their evolution character. The observations show that the star has non-pulsation, but constant mass loss rate ( 5 × 10^–7 M yr^–1) on front half of AGB. Its circumstellar envelope is formed. When the star has pulsation on back half of AGB, its mass loss rate is relative with time, and increases gradually. In this time the star is on the stage of optical Mira variable. When the mass loss rate reaches the value of 3 × 10^–6 M yr^–1, the star evoluted from the stage of optical variable into the stage of radio bright OH/IR star. On the end of AGB the mass loss rate reaches 10^–4 M yr^–1. (Band and Habing 1983, Hermen and Habing 1985).     

Estimating the Luminosity Function of M51-Type Galaxies

A new sample of M51-type galaxies consisting of 46 systems is used to estimate the B-band luminosity function. The luminosity function for the primary components of the systems can be described by a Schechter function with the parameters _* = (1.4±0.3)×10^-5 Mpc^-3, = -1.3^+0.4 _-0.3, and M _* = -20.3^+0.2 _-0.1. The values of the latter two parameters are comparable to those for isolated galactic pairs. The resulting estimate of the average density of M51-type galaxies is (4±3)% of the average density of isolated pairs for luminosities in the range -22^m.0<M<-16^m.0     

Light-time orbit and apsidal motion of the eclipsing binary U Ophiuchi

A comprehensive period study of the times of minima observed from 1881 to 1985 has been performed. Previous interpretations of the O–C diagram based on light-time effect are confirmed. The light-time orbit of U Oph has been revised using a differential corrections procedure. We get an eccentric orbit withe=0.22±0.06,P=38.7±0.2 yr, and a mass function . In addition, our analysis has revealed short-period apsidal motion (U/P=4515±75) in a slightly eccentric close orbit (e=0.0031±0.0003), allowing a reliable determination of the density concentration coefficient,k ₂=0.0059±4. A comparison with stellar evolutionary models calculated by Jeffery (1984) yields the helium contentY=0.28±0.05 and an age of 3×10⁷ yr for the components of U Oph.     

The core evolution of a globular cluster containing massive black holes

In this paper we consider effects of the general relativity and an accreting black hole in a globular cluster by studying the evolution of a globular cluster core as a whole, i.e., without the partition of the core into the so-called cusp and isothermal core regions. The globular cluster core is assumed to contain a massive black hole at its center. We show that the final fate of the evolution of a globular cluster core depends on the mass of the black hole at its center. When the massM of the black hole is greater than 3×10³ M , there will be a contraction of the core. On the other hand, if the mass of the black hole is smaller (10² M M3×10³ M ) in the center, the core will expand until complete dissolution.