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1.
The results of calculations of graphite grain formation in the atmospheres of R CrB stars are given. The parameters for the models wereM=1M ,M bol=?6 mag. The effective temperature ranged from 5300K to 8300K. The chemical composition corresponded to the hydrogen-deficient carbon rich mixture:X=0,Y=0.9,Z c=0.1. The results obtained show the existence of a critical mass loss rate which is ranged fromM *≈10?6 M yr?1 forT eff=5300 K toM *≈10?5 M yr?1 forT eff=8300 K. As soon as the rate of mass loss exceedsM * by 3–5 times the degree of condensation of carbon changes from 0 to 0.7. The finite radii of grains are about from 0.01 μm to 0.6 μm depending on the density near the condensation point, the velocity of matter outflow, and the stellar effective temperature. The duration of grain growth should amount to some dozens of days. It is supposed that the most probable explanation of dust-shell formation around R CrB stars is graphite condensation behind a shock wave arising from nonlinear stellar pulsation.  相似文献   

2.
The stars in the Main Sequence are seen as a hierarchy of objects with different massesM and effective dynamical radiiR eff=R/ given by the stellar radii and the coefficients for the inner structure of the stars.As seen in a previous work (Paper I), during the lifetime in the Main SequenceR eff(t) remains a near invariant when compared to the variation in the time ofR(t) and (t).With such an effectiveR eff one obtains the amounts of actionA c(M), the effective densities eff(M)=(M)3(M), the densities of action and of energy (or mean presures in the stellar interior)a c(M),e c(M), and the potential energiesE p(M).The amounts of action areA cM k withk1.87 for the M stars,k5/3 for the KGF stars, andk1.83 for the A and earlier stars, representing very simples conditions for the other dynamical parameters. For instancek5/3 means a near invariant effective density eff for the KGF stars, while for such stars the mean densities and coefficients present the strongest variations with masses (M)M –1.81, (M)M0.6.The cases for the M stars (e c(M)M –1) and for the A and earlier stars (betweena c(M)=constant and eff(M)M –1) and also discussed. These conditions for the earlier stars also represent reasonable mean values for the whole stellar hierarchy in the range of masses 0.2M M25M .With all this, one can build dynamical HR diagrams withA c(M), Ep(M), eff M p , etc., whose characteristics are analogous to these in the photometrical HR diagram. A comparison is made betweenA c(M) from the models here and the HR diagram with the best known stars of luminosity classes IV, V, and white dwarfs.The comparison of the potential energiesE p(M)M –p according to the stellar models used here and the observed frequency function (MM –q (number of stars in a given interval of masses) from different authors suggests the possibility that the productE p(M)(M) is a constant, but this must be confirmed with further studies of the function (M) and its fine structure.There are analogies between the formulation used here for the stellar hierarchy and other physical processes, for instance, in modified forms of the Kolmogorov law of turbulence and in the formulation used for the hierarchy of molecular clouds in gravitational equilibrium. Besides, the function of actionA c(M) for the stars has analogous properties to the relations of angular momenta and massesJ(M) for different types of objects. The cosmological implications of all this are discussed.  相似文献   

3.
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), Ac(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.  相似文献   

4.
With the available data in planets, stars and galaxies, it is studied the functions of angular momentaJ(M) and amounts of actionA c(M) (associated to the non rotational terms in the kinetic energy). The results indicate that independently of how are these functionsJ(M),A c(M) their ratioA c/J remains a near invariant. It is independent also from the type of angular momenta: intrinsic spins of the bodies or the total angular (orbital) momenta of the bodies forming a system; for instance, the Solar System and the planets.The relationA c(M) for the Solar System are analogous to these in the FGK stars of the main sequence, and the relationJ(M) (also for the Solar System) is analogous to the lower possible limit for binary stars.The different types of binary stars from the short period, detached systems to contactary systems, gives a range of functionsJ(M),A c(M) that are the same that one can expect in stars with planetary systems. According to the detection limits given for planetary companions by Campbell, Walker and Yang (1988) (masses of less than 9 Jupiter masses and orbital periods of less than 50 years) we calculate the limits forJ(M) andA c(M) This gives a lower limitA c/J 1 associated to stars with planetary systems as 61 Cygni and to short period detached binaries. The upper limitA c/J 16 correspond to planetary systems as the ours and probably to cataclysmic binaries. There are reasons to suspect that systems as the ours and in range 4 A c/J 16 (with a lower limit analogous to contactary binaries as Algols and W Ursa Majoris) must be the most common type of planetary systems. The analogies with the functionsJ(M)A c(M) for galaxies suggest cosmogonical conditions in the stellar formation.Independently of this, one can have boundary conditions for the Jacobi problem when applied to a collapsing cloud. Namely, from the initial stage (a molecular cloud) to the final stage (a formed stellar system: binary or planetary) the angular momenta and amounts of action decayed to 10~4 the initial values, but in such a form thatA c(t)/J(t) remains a near invariant.  相似文献   

5.
We show that hydrostatically equilibrium models for the thin photospheres of helium stars based on new opacities κR (OPAL and OP) can be constructed only for masses M<5M . The parameter Г=κL/4πGMc, defined as the ratio of light pressure to gravity, exceeds a critical value of 1.0 for larger masses, which must result in mass outflow under light pressure. This mass limit matches the observed lower limit for the masses of Wolf-Rayet stars (M WR>5M )), which is an additional argument that the Wolf-Rayet stellar cores are actually helium stars. By solving the equation of radiative transfer in extended atmospheres, we construct a semiempirical model for a WN5 star (M WN5=10M )) with a helium core and an expanding envelope, whose physical and geometric parameters are known mainly from light-curve solution for the eclipsing binary V444 Cyg (WN5+06): outflow rate $\dot M \approx 1.0 \times 10^{ - 5} M_ \odot yr^{ - 1} $ , terminal velocity V ≈2000 km s?1, and expanding-envelope optical depth τenv≈25. The temperature at the outer boundary of the photosphere of a helium star surrounded by such an envelope is approximately 130 kK higher than that in the absence of an envelope, being T ph≈240 kK. Because of the high temperatures, the absorption coefficients at the corresponding photospheric levels are smaller than those in models with no envelope; therefore, the photosphere turns out to be in hydrostatic equilibrium and stable against light pressure (Гmax≈0.9). As a way out of this conflicting situation (an expanding envelope together with a hydrostatically equilibrium photosphere), we propose a model of discrete mass outflow, which is also supported by the observed cloudy structure of the envelopes in this type of stars. To quantitatively estimate parameters of the nonuniform outflow model requires detailed gas-dynamical calculations.  相似文献   

6.
We consider the problem of dust grain survival in the disk winds from T Tauri and Herbig Ae stars. For our analysis, we have chosen a disk wind model in which the gas component of the wind is heated through ambipolar diffusion to a temperature of ~104 K. We show that the heating of dust grains through their collisions with gas atoms is inefficient compared to their heating by stellar radiation and, hence, the grains survive even in the hot wind component. As a result, the disk wind can be opaque to the ultraviolet and optical stellar radiation and is capable of absorbing an appreciable fraction of it. Calculations show that the fraction of the wind-absorbed radiation for T Tauri stars can be from 20 to 40% of the total stellar luminosity at an accretion rate ? a = 10?8-10?6 M yr?1. This means that the disk winds from T Tauri stars can play the same role as the puffed-up inner rim in current accretion disk models. In Herbig Ae stars, the inner layers of the disk wind (r ≤ 0.5 AU) are dust-free, since the dust in this region sublimates under the effect of stellar radiation. Therefore, the fraction of the radiation absorbed by the disk wind in this case is considerably smaller and can be comparable to the effect from the puffed-up inner rim only at an accretion rate of the order of or higher than 10?6 M yr?1. Since the disk wind is structurally inhomogeneous, its optical depth toward the observer can be variable, which should be reflected in the photometric activity of young stars. For the same reason, moving shadows from gas and dust streams with a spiral-like shape can be observed in high-angular-resolution circumstellar disk images.  相似文献   

7.
The model of a presupernova’s carbon-oxygen (C-O) core with an initial mass of 1.33 M , an initial carbon abundance X C (0) =0.27, and a mean rate of increase in mass of 5 × 10?7 M yr?1 through accretion in a binary system evolved from the central density and temperature ρc=109 g cm?3 and T c=2.05 × 108K, respectively, by forming a convective core and its subsequent expansion to an explosive fuel ignition at the center. The evolution and explosion equations included only the carbon burning reaction 12C+12C with energy release corresponding to the complete conversion of carbon and oxygen (at the same rate as that of carbon) into 56Ni. The ratio of mixing length to convection-zone size αc was chosen as the parameter. Although the model assumptions were crude, we obtained an acceptable (for the theory of supernovae) pattern of explosion with a strong dependence of its duration on αc. In our calculations with sufficiently large values of this parameter, αc=4.0 × 10?3 and 3.0×10?3, fuel burned in the regime of prompt detonation. In the range 2.0×10?3≥αc≥3.0×10?4, there was initially a deflagration with the generation of model pulsations whose amplitude gradually increased. Eventually, the detonation regime of burning arose, which was triggered from the model surface layers (with m ? 1.33 M ) and propagated deep into the model up to the deflagration front. The generation of model pulsations and the formation of a detonation front are described in detail for αc=1.0 × 10?3.  相似文献   

8.
We determined the spatial structure of the scattered concentration of galaxies in the Canes Venatici constellation. We redefined the distances for 30 galaxies of this region using the deep images from the Hubble Space Telescope archive with the WFPC2 and ACS cameras.We carried out a high-precision stellar photometry of the resolved stars in these galaxies, and determined the photometric distances by the tip of the red giant branch (TRGB) using an advanced technique and modern calibrations. High accuracy of the results allows us to distinguish the zone of chaotic motions around the center of the system. A group of galaxies around M94 is characterized by the median velocity V LG = 287 km/s, distance D = 4.28 Mpc, internal velocity dispersion σ = 51 km/s and total luminosity L B = 1.61 × 1010 L ?. The projection mass of the system amounts to M p = 2.56 × 1012 M ?, which corresponds to the mass-luminosity ratio of (M/L) p = 159 (M/L)?. The estimate of the mass-luminosity ratio is significantly higher than the typical ratio M/L B ~ 30 for the nearby groups of galaxies. The CVn I cloud of galaxies contains 4–5 times less luminous matter compared with the well-known nearby groups, like the Local Group, M81 and CentaurusA. The central galaxy M94 is at least 1m fainter than any other central galaxy of these groups. However, the concentration of galaxies in the Canes Venatici may have a comparable total mass.  相似文献   

9.
We present the results of our hydrodynamic calculations of radial pulsations in helium stars with masses 1 MM ≤ 10 M, luminosity-to-mass ratios 1 × 103L/ML/M ≤ 2 × 104L/M, and effective temperatures 2 × 104 K ≤ Teff ≤ 105 K for mass fractions of helium Y=0.98 and heavy elements Z=0.02. We show that the lower boundary of the pulsation-instability region corresponds to L/M ~ 103L/M and that the instability region for L/M ? 5 × 103L/M is bounded by effective temperatures Teff ? 3 × 104 K. As the luminosity rises, the instability boundary moves into the left part of the Hertzsprung-Russell diagram and radial pulsations can arise in stars with effective temperatures Teff ? 105 K at L/M ? 7 × 103L/M. The velocity amplitude for the outer boundary of the hydrodynamic model increases with L/M and lies within the range 200 ? ΔU ? 700 km s?1 for the models under consideration. The periodic shock waves that accompany radial pulsations cause a significant change of the gas-density distribution in the stellar atmosphere, which is described by a dynamic scale height comparable to the stellar radius. The dynamic instability boundary that corresponds to the separation of the outer stellar atmospheric layers at a superparabolic velocity is roughly determined by a luminosity-to-mass ratio L/M ~ 3 × 104L/M.  相似文献   

10.
We performed hydrodynamic computations of nonlinear stellar pulsations of population I stars at the evolutionary stages of the ascending red giant branch and the following luminosity drop due to the core helium flash. Red giants populating this region of the Hertzsprung–Russel diagram were found to be the fundamental mode pulsators. The pulsation period is the largest at the tip of the red giant branch and for stars with initial masses from 1.1 M to 1.9 M ranges from ∏ ≈ 254 day to ∏ ≈ 33 day , respectively. The rate of period change during the core helium flash is comparable with rates of secular period change in Mira type variables during the thermal pulse in the helium shell source. The period change rate is largest (∏?/∏ ≈ ?10?2 yr?1) in stars with initial mass M ZAMS = 1.1 M and decreases to ∏?/∏ ~ ?10?3 yr?1 for stars of the evolutionary sequence M ZAMS = 1.9 M . Theoretical light curves of red giants pulsating with periods ∏ > 200 day show the presence of the secondary maximum similar to that observed in many Miras.  相似文献   

11.
This paper describes the STAROX stellar evolution code for the calculation of the evolution of a model of a spherical star. The code calculates a model at time t k , that is the run of pressure, density, temperature, radius, energy flux and related variables on a mesh in mass M i , given the distribution of chemical elements X j (i) at t k and the model at the previous time step t k?1. It then advances the chemical composition to the next time step t k+1 and calculates a new model at time t k+1. This process is iterated to convergence. The model equations are solved by Newton–Raphson relaxation; the chemical equations are solved by an iterative procedure, each element being advanced in turn, and the process repeated to convergence. Convection is modelled by a mixing length model and convective mixing is treated as a diffusive process; chemical overshooting can be incorporated in parametric form. The equation of state is taken from OPAL tables and the opacity from a blend of OPAL and Alexander tables. Nuclear reaction rates are from NACRE but only cover the pp chain and CNO cycle. The atmospheric layers are incorporated in the model by applying the surface boundary condition at small optical depth (τ≈0.001). The mesh in mass M i is usually taken as fixed except that there is a moveable mesh point at the boundary of a convective core. Results are given for models of mass 0.9 and 5.0M with initial composition X=0.7,Z=0.02 evolved to a state where the central hydrogen abundance is X c =0.35, and for a model of mass 2.0M with initial X=0.72,Z=0.02, evolved to X c =0.01 and with core overshooting. In this latter case we compute two models one with and one without a moveable mesh point at the boundary of the convective core to illustrate the importance of having such a moveable mesh point for the determination of the Brunt–Väisälä frequency in the layers outside the core.  相似文献   

12.
We present the results of a statistical study of the star formation rates (SFR) derived from the Galaxy Evolution Explorer (GALEX) observations in the ultraviolet continuum and in the Hα emission line for a sample of about 800 luminous compact galaxies (LCGs). Galaxies in this sample have a compact structure and include one or several regions of active star formation. Global galaxy characteristics (metallicity, luminosity, stellar mass) are intermediate between ones of the nearby blue compact dwarf (BCD) galaxies and Lyman-break galaxies (LBGs) at high redshifts z>2–3. SFRs were corrected for interstellar extinction which was derived from the optical Sloan Digital Sky Survey (SDSS) spectra. We find that SFRs derived from the galaxy luminosities in the far ultraviolet (FUV) and near ultraviolet (NUV) ranges vary in a wide range from 0.18 M ?yr?1 to 113 M ?yr?1 with median values of 3.8 M ?yr?1 and 5.2 M ?yr?1, respectively. Simple regression relations are found for luminosities L(Hα) and L(UV) as functions of the mass of the young stellar population, the starburst age, and the galaxy metallicity. We consider the evolution of L(Hα), L(FUV) and L(NUV) with a starburst age and introduce new characteristics of star formation, namely the initial Hα, FUV and NUV luminosities at zero starburst age.  相似文献   

13.
We report the discovery of a binary, HS 2233 + 3927, consisting of an sdB star with a faint companion. From its lightcurve the orbital period of 14,844 s, the mass ratio, the inclination, and other system parameters are derived. The companion does not contribute to the optical light of the system except through a strong reflection effect. The semi-amplitude of the radial velocity curve K 1= 89.6 km/s?1 and a mass function of f(m) = 0.013 M are determined. A preliminary spectroscopic analysis of the blue spectra using NLTE model atmospheres results in Teff= 36 500 K, log g= 5.70, and log(n He/n H) =?2.15. These parameters are typical for sdB stars, the companion is probably an M dwarf.  相似文献   

14.
We study relation between stellar mass and halo mass for high-mass halos using a sample of galaxy clusters with accurate measurements of stellar masses from optical and ifrared data and total masses from X-ray observations. We find that stellar mass of the brightest cluster galaxies (BCGs) scales as M*,BCG ∝ M 500 αBCG with the best fit slope of αBCG ≈ 0.4 ± 0.1. We measure scatter of M*,BCG at a fixed M500 of ≈0.2 dex. We show that stellar mass-halo mass relations from abundance matching or halo modelling reported in recent studies underestimate masses of BCGs by a factor of ~2?4. We argue that this is because these studies used stellar mass functions (SMF) based on photometry that severely underestimates the outer surface brightness profiles of massive galaxies. We show that M*?M relation derived using abundance matching with the recent SMF calibration by Bernardi et al. (2013) based on improved photometry is in a much better agreement with the relation we derive via direct calibration for observed clusters. The total stellar mass of galaxies correlates with total mass M500 with the slope of ≈0.6 ± 0.1 and scatter of 0.1 dex. This indicates that efficiency with which baryons are converted into stars decreases with increasing cluster mass. The low scatter is due to large contribution of satellite galaxies: the stellar mass in satellite galaxies correlates with M500 with scatter of ≈0.1 dex and best fit slope of αsat ≈ 0.8 ± 0.1. We show that for a fixed choice of the initial mass function (IMF) total stellar fraction in clusters is only a factor of 3?5 lower than the peak stellar fraction reached in M ≈ 1012M halos. The difference is only a factor of ~1.5?3 if the IMF becomes progressively more bottom heavy with increasing mass in early type galaxies, as indicated by recent observational analyses. This means that the overall efficiency of star formation in massive halos is only moderately suppressed compared to L* galaxies and is considerably less suppressed than previously thought. The larger normalization and slope of the M*?M relation derived in this study shows that feedback and associated suppression of star formation in massive halos should be weaker than assumed in most of the current semi-analytic models and simulations.  相似文献   

15.
Evolutionary tracks from the zero age main sequence to the asymptotic giant branch were computed for stars with initial masses 2 M M ZAMS ≤ 5 M and metallicity Z = 0.02. Some models of evolutionary sequences were used as initial conditions for equations of radiation hydrodynamics and turbulent convection describing radial stellar pulsations. The early asymptotic giant branch stars are shown to pulsate in the fundamental mode with periods 30 day ? Π ? 400day. The rate of period change gradually increases as the star evolves but is too small to be detected (Π?/Π < 10?5 yr?1). Pulsation properties of thermally pulsing AGB stars are investigated on time intervals comprising 17 thermal pulses for evolutionary sequences with initial masses M ZAMS = 2 M and 3 M and 6 thermal pulses for M ZAMS = 4 M and 5 M . Stars with initial masses M ZAMS ≤ 3 M pulsate either in the fundamental mode or in the first overtone, whereas more massive red giants (M ZAMS ≥ 4 M ) pulsate in the fundamental mode with periods Π ? 103 day. Most rapid pulsation period change with rate ?0.02 yr?1 ? Π?/Π ? ?0.01 yr?1 occurs during decrease of the surface luminosity after the maximum of the luminosity in the helium shell source. The rate of subsequent increase of the period is Π?/Π ? 5 × 10?3 yr?1.  相似文献   

16.
The main results of a study of a catalogue of physical parameters of 1041 spectroscopic binaries are presented. The distribution of spectroscopic binaries over all main parametersM 1, a, e, M1/M2, P, and certain dependencies between some of them have been found.
  1. It appears that among bright (m v?3 m –5 m ) stars withM?1M , about 40% are apparently spectroscopic binaries with comparable masses of components.
  2. The majority of spectroscopic binaries with the ratio of the large semiaxis of the orbit to the radius of the primarya/R 1?20, have eccentricities close to zero. This is probably a consequence of the tidal circularization of orbits of close binaries by viscous friction.
  3. The discovery of duplicity of double-line spectroscopic binaries is possible only if the semiamplitude of radial velocityK 1 is almost 10 times higher than the semiamplitude of the radial velocity of a single-line spectroscopic binary of the same mass.
  4. Double-line spectroscopic binaries witha/R ?6(M 1/M )1/3,M 1M 2?1.5M are almost almost absent, and the number of stars witha/R ?6(M 1/M )1/3,M 1≈1.5M is relatively low.
  5. The distribution of unevolved SB stars over the large semiaxis may be described by the expression d(N d/Nt)≈0.2 d loga for 6(M 1/M )1/3?a/R ?100.
  6. The intial mass-function for primaries of spectroscopic binaries is the same Salpeter function dN d≈M 1 ?2.35 dM 1 for 1?M 1/M ?30.
  7. It is possible to explain the observed ratio of the number of single-line spectroscopic binaries to the number of double-line binaries if one assumes that the average initial mass ratio is close to 1 and that the mass of the postmass-exchange remnant of the primary exceeds the theoretical one and/or that half of the angular momentum of the system is lost during mass-exchange.
  8. The above-mentioned distributions ofM 1 anda and assumptions on the mass of remnant and/or momentum loss also allow us to explain the observed shapes of dN/dM, dN/dq, and dN/da distributions after some selection effects are taken into account.
  相似文献   

17.
We present the results of Monte Carlo mass-loss computations for hot low-mass stars, specifically for subdwarf B (sdB) stars. It is shown that the mass-loss rates on the Horizontal Branch (HB) computed from radiative line-driven wind models are not high enough to create sdB stars. We argue, however, that mass loss plays a role in the chemical abundance patterns observed both in field sdB stars, as well as in cluster HB stars. The derived mass loss recipe for these (extremely) hot HB stars may also be applied to other groups of hot low-mass stars, such as post-HB (AGB-manqué, UV-bright) stars, over a range in effective temperatures between ?10 000 and 50 000 K. Finally, we present preliminary spectral synthesis on the more luminous sdB stars for which emission cores in Hα have been detected (Heber, U., et al.: 2003, in:Stellar Atmosphere Modeling, ASP Conference Proceedings, p. 251). We find that these line profiles can indeed be interpreted as the presence of a stellar wind with mass loss on the order of 10?11?M yr ?1.  相似文献   

18.
We perform a kinematic analysis of the Hipparcos and TRC proper motions of stars by using a linear Ogorodnikov-Milne model. All of the distant (r>0.2 kpc) stars of the Hipparcos catalog have been found to rotate around the Galactic y axis with an angular velocity of M 13 ? =?0.36±0.09 mas yr?1. One of the causes of this rotation may be an uncertainty in the lunisolar precession constant adopted when constructing the ICRS. In this case, the correction to the IAU (1976) lunisolar precession constant in longitude is shown to be Δp1=?3.26±0.10 mas yr?1. Based on the TRC catalog, we have determined the mean Oort constants: A=14.9±1.0 and B=?10.8±0.3 km s?1 kpc?1. The component of the model that describes the rotation of all TRC stars around the Galactic y axis is nonzero for all magnitudes, M 13 ? =?0.86±0.11 mas yr?1.  相似文献   

19.
20.
The grid of evolutionary tracks of population II stars with initial masses 0.81 MMZAMS ≤ 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.  相似文献   

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