Main sequence for rotating stars of intermediate mass

We have investigated the evolutionary behaviour of intermediate mass (2, 3, 4, 5, and 7M ) Population I stars, assuming two different rates of rotation at the threshold of stability.In the first part of the study, stars are assumed to start with a critical rotation (fast rotation model) and to progress to the point of rotational instability. The stars evolve by losing mass and become rotationally unstable before they reach the zero-age Main Sequence. It is argued that multiple star systems might be formed through the evolution of rapidly rotating stars. An expression for the rotational mass loss rate is derived as a function of the physical parameters of stars.In the second part of the study, stars are assumed to rotate at a rate below the critical value (slow rotation model). The evolution of slowly rotating stars is followed as far as zero-age Main Sequence on the theoretical Hertzsprung-Russell diagram and compared with that of normal stars. The evolutionary paths are found to be more or less similar to those of normal stars; but their positions on the Main Sequence are characterized by effective temperatures and luminosities lower than those of normal stars. The zero-age Main-Sequence times of these stars are longer than those of normal stars. The rotational rates obtained for the zero-age Main Sequence are in good agreement with observed values.     

Pregalactic-primordial low-mass stars

The Main-Sequence positions as well as the evolutionary behavior of Population III stars up to an evolution age of 2×10¹⁰ yr, taking this time as the age of the Universe, have been investigated in the mass range 0.2 and 0.8M . While Population III stars with masses greater than 0.3M develop a radiative core during the approach to the Main Sequence, stars with masses smaller than 0.3M reach the Main Sequence as a wholly convective stars. Population III stars with masses greater than 0.5M show a brightening of at most 2.2 in bolometric magnitude when the evolution is terminated as compared to the value which corresponds to zero-age Main Sequence. The positions of stars with masses smaller than 0.5M remain almost the same in the H-R diagram.If Population III stars have formed over a range of redshifts, 6相似文献   

Theoretical evolution of a hydrogen-helium star of 3M ⊙ from the pre-Main Sequence to the core helium-exhaustion phase

The evolution of a first-generation 3M star from the threshold of stability through the stage of helium exhaustion in the core has been studied. The total time elapsed is 4.174×10⁸ yr and most of this time is spent in the blue-giant region of theH-R diagram. Hydrogen-burning near the Main Sequence occurs at a high central temperature via the proton-proton chain until the triplealpha reactions generate a small amount of C¹² toward the end of the hydrogen-burning phase. The corresponding evolution time is longer than that of a normal population I star with the same mass. The ignition of the triple-alpha processes begins in a mildly degenerate, small convective core while the star still has a high surface temperature. Helium-burning in the core, coupled with hydrogenburning in the shell, occupies a period of about 1.8×10⁷ yr, which is only one-third that of a normal star. The mass of the star interior to the hydrogen shell source has increased to a value of 0.50M near the end of core helium exhaustion. This region maintains an inhomogenous composition composed of helium, carbon and oxygen.     

Evolutionary considerations involving the internal density concentration parameter of binary stars

The evolutionary changes that occur in the internal density concentration parameterk ₂ (called the apsidal constant for brevity) for a star of given mass and initial composition are examined in detail. The purpose is to ascertain whether or not such an approach leads to a reduction in the differences now noted between the theoretically derived values ofk ₂ and the observed values derived from the secular advance of the periastron in close eclipsing binary systems.A series of stellar models of mass 2.0, 5.0, 10.0 and 20.0M were employed, with an initial compositional mixture ofX=0.739,Y=0.24 andZ=0.021. These models cover an evolutionary range from a point in time where the star has just completed the Hayashi phase of its pre-Main Sequence contraction through its entire Main Sequence phase to the point where hydrogen depletion in the core is complete.For each model, a value ofk ₂ is determined by numerically integrating Radau's equation and using the values of , the ratio of the star's density at pointa to its mean density, as taken from the models. The result is the time history ofk ₂ for each stellar mass over the evolutionary range of interest. The results are then summarized in the (logk ₂, logT _e) plane which, for the first time, quantitatively indicates the variation ink ₂ as a function of the evolutionary state of the star.A comparison between these theoretically derived values ofk ₂ and a selected set of observationally determined ones immediately indicates that the secular variation ink ₂ plays an extremely important part in any comparison between theory and observation. For most of the cases studied, the difference between the theoretically and observationally determined values ofk ₂ can be reconciled in terms of the evolutionary history of the binary system.While tentatively providing a satisfactory explanation for the previously noted differences in the determination ofk ₂, there now exists the problem of accurately pinpointing the evolutionary state of the observed binary system.     

Convective shells and the core He-burning phase of massive stars

In this paper we briefly discuss the effect of complete homogenization in the intermediate unstable layers of massive stars on the effective temperature of the core He-burning models. To this end, a 20M star of Population I chemical composition (X=0.700,Z=0.020) has been allowed to evolve from the Main Sequence into the core He-exhaustion stage without taking into account semiconvective mixing. The results show that the models are systematically bluer than those computed with the same physical parameters but with the inclusion of semiconvection.     

Physical conditions in the convective envelope of stars

Summary The mechanical flux originating in the convective envelope of stars is shown to depend critically by the treatment of convection. In particular, in the framework of the mixing-length theory, in passing from a mixing lengthl=H _P to a mixing lengthl=H the presence of mechanical fluxes shifts from being a marginal phenomenon to a dominant one.Possible implications concerning atmospheric microturbulence in Main Sequence stars, as so asA _p andA _m stars, several types of variables and mass loss are briefly discussed.

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Sommario Si mostra come il flusso cinetico originato negli inviluppi convettivi di una stella dipenda criticamente dalle assunzioni fatte nel trattamento della convezione superadiabatica. In particolare, sulla base della teoria della lunghezza di rimescolamento, a seconda che si assumal=H _P o l=H i flussi cinetici passano dall'essere un fenomeno marginale a contributi determinanti.E' discussa una serie di possibili implicazioni riguardanti la microturbolenza atmosferica in stelle di sequenza principale, le stelleA _p eA _m, diversi tipi di variabili e la perdita di massa in fase di gigante.

     

Pre-Main-Sequence evolution of rotating low-mass stars

The evolutionary behaviour of rotating low-mass stars in the mass range 0.2 and 0.9M has been investigated during the pre-Main-Sequence phase. The angular momentum is conserved locally in radiative regions and totally in convective regions, according to a predetermined angular velocity distribution depending on the structure of the star. As the stars contract toward the zero-age Main Sequence, they spin up under the assumption that the angular momentum is conserved during the evolution of the stars. When the stars have differential rotations, their inner regions rotate faster than the outer regions. The effective temperatures and luminosities of rotating low-mass stars are obtained lower than those of non-rotating stars. They have lower central temperature and density values compared to those of non-rotating stars.     

Visual binary systems in the solar neighbourhood: The mass-ratio distribution

Nearby visual binaries, with both components on the Main Sequence, have been considered in order to obtain information about the distribution of their mass ratios. These systems have their primary components ranging from A0 to G9. The data have been corrected for selection effects and the differences V of the visual magnitudes have been transformed into mass-ratio values.The frequency distribution of the mass ratios appears to be bimodal, with a peak around unity and a maximum at about 0.25. It is suggested that this feature may be indicative of different mechanisms of formation for wide binaries.     

Equivalent width of molecular lines in stars

We have calculated the expected equivalent widths of the individual rotational lines of the Lyman band of H₂ and (A-X) band of CO and SiO for Main Sequence stars. The results indicate that the lines of H₂ should be observable in absorption up toT _e9000 K. The lines of CO are found to be much weaker than those of H₂ lines. A discussion of these results is presented.     

The effect of increasing helium content and disk dwarfs evolution on the chemical enrichment of the Galaxy

This paper deals with two main effects: First the empirical metal abundance distribution in Main Sequence disk dwarfs of the solar neighbourhood, and second, the theoretical possibility of (i) an increased helium content as the Galaxy evolves, and (ii) the presence of evolutionary effects in disk dwarfs (i.e., the age of some or all stars considered up to the subgiant phase is not necessarily longer than the age of the galactic disk). We take into account a linear increase of helium content with metal content, and we impose some constraints relative to initial, solar and present-day observed values ofY andZ, and to observed relative helium to heavy element enrichment, Y/Z. In this way, little influence is found on the empirical metal abundance distribution in the range 0Y/Z3, while larger values of Y/Z would lead to a more significant influence. Evolved and unevolved theoretical metal abundance distributions are derived by accounting for a two-phase model of chemical evolution of galaxies and for a linear mass dependence of star lifetimes in the spectral range G2V–G8V, and are compared with the empirical distribution. All are in satisfactory agreement due to systematic shift data by different observations; several values o collapse timeT _c and age of the GalaxyT are also considered. Finally, models of chemical evolution invoking homogeneous collapse without infall and inhomogeneous collapse with infall, are briefly discussed relative to the empirical metal abundance distribution in Main Sequence disk dwarfs of the solar neighbourhood.     

The evolution of massive stars with mass loss

The evolution of massive stars is investigated in the phases of hydrogen and helium burning, taking into account the mass-loss due to light pressure in optically thick media. The evolution in the stage of hydrogen burning near the Main Sequence occurs without mass loss. The large inverse density gradient appears in the outer layers of a 30 M star after it goes into the domain of red super-giants in the helium-burning stage. This effect appears as a consequence of an excess of luminosity of the star the ciritical one in sufficiently extensive outer layer, where convection is not so effective. In this way, the conditions for outflow of matter are formed. The sequence of selfconsistent models is constructed, with the core in hydrostatic equilibrium and hydrodynamically outflowing envelope. The amount of mass loss is not a given parameter, but it is found during the calculations as a characteristic number of the problem. The amount of mass loss is very high, of the order of 0.5M yr, the velocity of the flow is 20 km s^–1. The star loses about 7.2M during 15 yr. The amount of mass loss must rapidly decrease or finish altogether when matter near the hydrogen-burning layer begins to flow out, and a transformation of stellar structure must occur.The evolution of a 9M star is calculated. The density in the envelope of this star is sufficiently large and the outer convective zone, which develops on the red giant stage, prevents the outflow of matter. The intensive mass outflow from such star can take place at the carbon burning, or heavier element burning stages. The formation of infrared stars and Wolf-Rayet stars can be possibly explained by such a mechanism of mass loss, so that the infrared stage must precede the Wolf-Rayet stage.     

The evolutionary behaviour of population III intermediate mass stars

Assuming the Big-Bang nucleosynthesis was responsible for the formation of helium, the evolution of first-generation intermediate-mass stars of 5, 7, and 9M with no metals have been studied from the threshold of stability through the stage of helium exhaustion in the cores of the stars. Hydrogen Main-Sequence positions are marked at effective temperatures higher than those of normal stars. The evolutionary tracks during the hydrogen burning phase start to be similar to those of normal stars when the CN-cycle reactions, which are controlled by the triple-alpha reactions, become operative for hydrogen depletion. Helium Main Sequence of Population III stars of intermediate mass occurs at the high effective temperature region of the H-R diagram and stars stay as blue stars until the end of the core helium exhaustion phase. The total time elapsed is in the range of 3×10⁷ and 10⁸yr. The stars with the initial masses of 5, 7, and 9M developed a moderately electron degenerate complete hydrogen-exhausted region with masses of 0.77, 1.06, and 1.42M , respectively, in which the most abundant element is carbon.     

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.     

Hidden mass in the solar neighborhood

It is suggested that the minimum mass of a star at the time of its formation is approximately 0.01M . Making use of this fact and the stellar mass functionF(M) M ^–, it is found that the hidden mass (or the missing mass) in the solar neighborhood may be explained by the presence of a large number of invisible stars of very low mass (0.01M M<0.07M ).     

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.     

Asymmetric supernova explosions and the origin of binary pulsars

We investigate the effect of asymmetric supernova explosions on the orbital parameters of binary systems with a compact component. We relate such explosions to the origin of binary pulsars. The degree of asymmetry of the explosion is represented by the kick velocity gained by the exploding star due to the asymmetric mass ejection. The required kick velocity to produce the observed parameters of the binary pulsar PSR 1913+16 should be larger than 80 km s^–1 if the mass of the exploding star is larger than 4M . We examine the mean survival probability of the binary system (<f>) for various degrees of asymmetry in the explosion. The rare occurrence of a binary pulsar does not necessarily imply that such a probability is low since not all pulsars have originated in a binary system. Assuming the birth rate of pulsars derived by Taylor and Manchester (1977), we derive that <f> would be as high as 0.25. Such values of <f> can be obtained if the mass of the exploding stars is, in general, not large (10M ).     

Stellar 5 min oscillations

Estimates are given for the amplitudes of stochastically excited oscillations in Main Sequence stars and cool giants; these were obtained using the equipartition between convective and pulsational energy which was originally proposed by Goldreich and Keeley. The amplitudes of both velocity and luminosity perturbation generally increase with increasing mass along the Main Sequence as long as convection transports a major fraction of the total flux, and the amplitudes also increase with the age of the model. The 1.5 M _⊙ ZAMS model, of spectral type F0, has velocity amplitudes ten times larger than those found in the Sun. For very luminous red supergiants luminosity amplitudes of up to about 0 ^m .1 are predicted, in rough agreement with observations presented by Maeder.     

Spectrophotometric studies of Am stars

The relationships among the various physical parameters-namely, the effective temperatures, radii and bolometric magnitudes, determined on the basis of the energy distribution curves of 25 Am stars — have been studied. Their effective temperatures are in the range of 7200 K to 9700 K; the radii, 1.5R to 2.5R ; the bolometric magnitudes, 0.75 mag. to 2.25 mag.; and the masses, 1.5M to 2.25M . The Am stars in general, appear redder than their normal counterparts, the blanketing in the blue andUV regions being the major cause. For the relatively cooler stars, the (B-V) colours are found to be less affected by blanketing. They are located in the neighbourhood of the upper edge of the zero-age Main Sequence band and show a fairly wide range in the evolutionary status among themselves. The bolometric corrections which are independent of the uncertainties in the parallax measurements, follow the same trend as that of the Ap stars, with reference to the temperature.     

Supernova remnants and content in high mass stars of the giant Hii region NGC 604

An optical survey of NGC 604, the brightestHII complex in M33, has lead to the discovery of a single supernova remnant, in agreement with the predominantly thermal radio spectrum of the region. For the same NGC 604, we have derived from the H flux and the evolutionary tracks of the stars, the population and the birth-rates of Main Sequence, high-mass stars. The computation is in agreement with the observations of the upper part of the stellar luminosity function. From the stellar population one predicts in the region a number of remnants significantly larger than 1. To explain this discrepancy, it is suggested the presence in NGC 604 of at least one overluminous, hot star (M _B9), which contributes to a large fraction of the ionizations.On leave from the Asiago Observatory.On leave from Istituto di Fisica Generale, Università di Torino.     

Very low mass stars,black dwarfs and planets

Hydrogen-rich stars of very low mass (M 0.08M ) never go through hydrogenburning thermonuclear reactions and, in a time scale much shorter than the age of the Galaxy, become completely degenerate objects or black dwarfs. The number of the very-low-mass (VLM) black dwarfs is expected to be very large and they are likely to make a significant contribution to the total mass of the Galaxy. Processes of star and planet formation are discussed and it is concluded that the luminous and dark objects of mass 0.001M -0.08M beyond the solar system are not likely to be planets. Formation of Jupiter is discussed and it is suggested that the mass of Jupiter at the time of formation was smaller than its present mass.Paper presented at the Conference on Planetary Systems: Formation, Evolution, and Detection held 7–10 December, 1992 at CalTech, Pasadena, California, U.S.A.