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).     

Steady mass-loss from supermassive stars

Structures of Newtonian super-massive stars are calculated with the opacity for Comptor effectK ₀/(1 + T), whereK ₀=0.21(1 +X and =2.2×10^–9K^–1. The track of the Main-Sequence is turned right in the upper part of the HR diagram. Mass loss will occur in a Main-Sequence stage for a star with mass larger than a critical mass. The cause of mass loss and the expansion of the radius is continuum radiation pressure. The critical mass for mass loss is 1.02×10⁶ M for a Population I star, and 1.23×10⁵ M for Population III star. Mass loss rates expected in these stars are 3.3×10^–3 and 4.0×10^–3 M yr^–1, respectively.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984.     

An expanding circumstellar cloud of Zeta Aurigae

Strong absorption satellite lines of CaI 6572 were found on spectrograms taken on three successive days just after the fourth contact of the 1971–72 eclipse of Zeta Aurigae. The radial velocities of the satellite lines are –88 km s^–1, –74 km s^–1, and –180 km^–1, respectively, relative to the K-type primary star (K4 Ib). These absorptions should be due to a circumstellar cloud in which the column density of neutral calcium atoms is 1×10¹⁷ cm^–2 and the turbulent velocities come to 20–50 km s^–1. It is suggested that the cloud may be formed by the rocket-effect of the Lyman quanta of the B-type component (B6 V). We estimate the density in the cloud to be 2×10¹¹ atoms cm^–3 fors=10R _K and 2×10¹⁰ atoms cm^–3 fors=10² R _K, wheres denotes the distance of the cloud from the K star andR _K the K star's radius. The mass loss rate of the K-type component is also estimated to be about 10^–7 M yr^–1, assuming that the expansion of the K star occurs isotropically.     

Mass transfer in TV Cassiopeiae

The period variations of TV Cassiopeiae between 1901 and 1977 are discussed in the light of the period change model proposed by Biermann and Hall. During each period decrease 4.0×10^–6 M of mass is transferred from the secondary star to the primary. The average observable mass transfer rate is found to be 4.3×10^–7 M yr^–1. This average rate corresponds to the thermal time-scale of the mass-losing star.     

On steady-state nuclear burning in accreting neutron stars

The properties of the hydrogen burning shell in the envelope of an accreting neutron star have been studied for a range of mass accretion rates, neutron star radii, and metal abundances of the accreted matter. It is found that the hydrogen burning shells lie at densities ranging from 10⁵–6×10⁶ gm cm^–3. For mass accretion rates in excess ofM _c2 hydrogen and helium burn together. ForM _c1MM _c2, the hydrogen burning shell is stabilized by the limited CNO cycle. Implications of these results to the X-ray burst phenomena are briefly discussed.     

The Wolf-Rayet stars and mass loss

Wolf-Rayet stars are defined, a summary is given of the properties of Wolf-Rayet stars, and a qualitative model of a Wolf-Rayet star is sketched. It is incontrovertible that Wolf-Rayet stars are losing mass, a typical rate of mass loss being near 10^–5 M per year. The outward directed velocity of the expanding shell has been estimated for 10 stars. The largest value found is 2500 km/sec; most values lie between 1000 and 1500 km/sec. Two outstanding problems are to understand how the observed high velocities are generated and to demonstrate quantitatively the effect of these velocities on the observed spectrum. Five questions raised by the fact that mass loss is observed to take place from Wolf-rayet stars are discussed briefly in Section 5.Presented at the Trieste Colloquium on Mass Loss from Stars, September 12–16, 1968.     

The angular momentum loss of low-mass close binary systems

The detailed evolution of low-mass main-sequence stars (M < 1M ) with a compact companion is studied. For angular momentum loss associated with magnetic braking it is found that about 10^–11–10^–12 M yr^–1 in stellar wind loss would be required. This wind is 10²–10³ times stronger than the solar wind, so we believe here magnetic stellar wind is insufficient. It is well known that there is mass outflow in low-mass close binary systems. We believe here that these outflows are centrifugal driven winds from the outer parts of the accretion disks. The winds extract angular momentum from these systems and therefore drive secular evolution. Disk winds are preferred to winds from the secondary, because of the lower disk surface gravity.     

Axisymmetrical models for the origin and shaping of proto-planetary nebulae

Axisymmetrical models for protoplanetary nebulae are produced. We discuss the mechanism for mass loss from evolved cool stars and the characteristics of the gas outflow. By using two-dimensional magnetohydrodynamics, we find that the gas is preferentially ejected in a so-called equatorial plane. For a grid of models, the expansion velocities are found to be of the order ofv _escape/2 and the mass loss rates tilde 10^–5-10^–4 M /year which appear consistent with the available observational data. Magnetic fields intensities in the 10^–4 to 10^–3 gauss range are obtained in circumstellar envelopes, in good agreement with observations (Nedoluha and Bowers, 1992).     

High-dispersion spectroscopy of the symbiotic star AX Per: A binary model with rapid mass accretion

Results of high-dispersion spectroscopy (10 Å mm^–1) of the symbiotic star AX Per carried out in the years from 1979 to 1987 are reported. The emission line [FeVII] 6086 consists of a narrow and a broad component; the radial velocity of the narrow one varies according to the photometric period 681.6 days. This variation (K=30.6±1.5 km s^–1) seems to be due to the orbital motion of the hot star. The radial velocity of absorption lines varies with an inverse phase dependence and a much smaller amplitude (K=5.6±2 km s^–1), which may reflect the orbital motion of the red giant. The variation of the radial velocity of the emission lines of FeII, ect. (K=6.7±1.5 km s^–1) might be due to the rotation of the red giant. The profile of H emission line suddenly changed around the phase of the photometric minimum, which could be explained as a result of an eclipse of the emitting region by the red giant. On the other hand, some problems remain open in the behaviour of the radial velocities of H and HeI 5876.The observed results support a binary model of AX Per consisting of a rather massive (3M ) M-type giant and a Main-Sequence star (0.6M ). AX Per seems to be in an early stage of the Case C mass transfer, and the estimated very high mass accretion rate (10^–4 M yr^–1) is consistent with the theoretical models. The narrow component of the emission line of [FeVII] 6086 might be emitted in radiatively driven polar jets on the hot star of which luminosity is close to the Eddington limit.A new identification as ZrII at 6106.47 Å is proposed for the emission line at 6106 Å.     

Massive fluid spheres with isothermal cores

We can define some adiabatic exponents for neutron star cores. The equality of and ₃ leads to an equation of stateE=P ln(K/P) orP=K exp(–E/P). This equation has been solved alongwith equations for hydrostatic equilibrium for different physical conditions at the centre. The parameters of isothermal neutron star cores have been computed by taking surface densityE _a=2×10¹⁴ g cm^–3. ForP ₀=E ₀ the maximum mass and radius of neutron star core are 3.25M and 17.14 km, respectively.     

UIT observations of NGC 1275

We present the results from UV imagery of NGC 1275 obtained using the Goddard Ultraviolet Imaging Telescope (UIT). We are able to study the UV morphology down to_µ249 ~ 25 mag arcsec^–2. There are significant non-axisymmetric structures in the UV continuum associated with the low-velocity filament system. Continuum from the high-velocity system may also be present. The large aperture UV colors indicate that although the mass function extends to ~5M , more massive objects are not present. This implies either a cessation of star formation during the last 50–100 Myr or a truncated initial mass function.     

On the interior of the neutron star (II)

With the assumption, the physical 3-spacet = constant in a superdense star is spheroidal and the matter-density on the boundary surface of the configurationa = 2 × 10¹⁴ g cm^–3( the average matter density in a neutron star) Vaidya and Tikekar (1982) proposed an exact relativistic model for a neutron star. They suggested that their model can describe the hydrostatic equilibrium conditions in such a superdense star with densities in the range of 10¹⁴-10¹⁶ g cm^–3. Based on this model Parui and Sarma (1991) estimated the maximum limit of the density variation parameter for a stable neutron star (both for charged and uncharged) which is equal to 0.68, i.e. _max = 0.68.In this paper we have shown variation of central density per unit equilibrium radius (0/a), variation of mass, upper limit of density variation parameter both for charged and uncharged neutron stars at densities 10¹⁵ and 10¹⁶ g cm^–3, respectively. We have obtained _max = 0.68, i.e. the same as before. The important is that the duration of stability among the neutron star's constituents around _max will be shorter and shorter at higher densities as we proceed near the centre of the neutron star. In case of a charged neutron star, once stability among the constituents has been established, then unstability appears gradually maintaining linear relation between change in central density per unit equilibrium radius and change in mass whereas in case of uncharged neutron star, linear relation does not maintain.     

The case of the fastest stellar wind in central stars of planetary nebulae

An exceptionally fast wind (8500 km/s) was suggested to occur in the central star of the planetary nebula K1-16, belonging to the class of the PG 1159 H-deficient pre-white dwarfs. To ascertain the reality of such a fast wind this star has been observed with the HST telescope using the GHRS in the zone of theCiv 155.0 nm doublet. The HST data and tests made using synthetic stellar spectra support the existence of a stellar wind with a terminal velocity of 3800 km/s and a mass loss rate lower thanM<2 · 10^–11 M per year. Possibly it is no longer the fastest stellar wind so far observed but it is still among the fastest.     

The neutrino radiation of collapsing stellar cores and the neutrino burst detected from SN 1987 A

The properties of the neutrino burst generated by massive 1.5–2M collapsing stellar iron-oxygen cores are discussed. Special attention is given to the neutrino heat conductivity theory which allows us to calculate the transport of neutrinos through the collapsing stellar core up to the formation and during the first seconds of cooling of a hot hydrostatic neutron star. The theoretical predictions seem to be in good agreement with both the KAMIOKANDE II and IMB data on the neutrino burst detected from SN 1987A. The most reliable constraint on the neutrino rest mass is shown to bem _v <20–30eV, while the safest upper limit on the neutrino magnetic moment, µ _v < 10^–11 Bohr magnetons, results rather from the cooling of white dwarfs than from the SN 1987A neutrino data.Presented to the 13th International Conference Neutrino-88, Boston, U.S.A., 5–11 June, 1988.     

Rapidly rotating supermassive stars in the first post-Newtonian approximation to general relativity

The structure and stability of rapidly uniformly rotating supermassive stars is investigated using the full post-Newtonian equations of hydrodynamics. The standard model of a supermassive star, a polytrope of index three, is adopted. All rotation terms up to and including those of order ⁴, where is the angular velocity, are retained. The effects of rotation and post-Newtonian gravitation on the classical configuration are explicitly evaluated and shown to be very small. The dynamical stability of the model is treated by using the binding energy approach. The most massive objects are found to be dynamically unstable when =1/c ².p _c / _c 2.2 × 10^–3, wherep _c and _c are the central pressure and density, respectively. Hence, the higher-order terms considered in this analysis do not appreciably alter the previously known stability limits.The maximum mass that can be stabilized by uniform rotation in the hydrogen-burning phase is found to be 2.9×10⁶ M , whereM is the solar mass. The corresponding nuclear-generated luminosity of 6×10⁴⁴ erg/sec^–1 is too small for the model to be applicable to the quasi-stellar objects. The maximum kinetic energy of a uniformly rotating supermassive star is found to be 3×10^–5 Mc ², whereM is the mass of the star. Masses in excess of 10¹⁰ M are required if an adequate store of kinetic energy is to be made available to a pulsar like QSO. However such large masses have rotation periods in excess of 100 yr and thus could not account for any short term periodic variability. It is concluded then that the uniformly rotating supermassive star does not provide a suitable base for a model of a QSO.     

The variability of the light curve of the WR-eclipsing binary CV serpentis

Two sets of observations of the WR-eclipsing binary CV Ser were carried out in 1982 and 1983 in the standard photometric systemUBV. Since 1982, the depth of the atmospheric eclipse has changed and does not show in theV data obtained in 1983. There is significant intrinsic variability (0 _. ^m 05) in the light curves of CV Ser over both sets of observations and it is suggested that this is due to the changing mass-loss rate from the envelope of the WC8 star on time-scales from days to months. The observed mass-loss rate can change the mass by some 10^–5 M y^–1. An orbital inclinationi=72±2° is obtained.     

Expansion of neutron star matter and its final nuclear composition

The final nuclear composition of the matter expanding from the density of a neutron star is investigated. It is assumed that starquakes cause the cracks which penetrate the neutron star crust and that the neutron star fluid can flow out through the cracks into space. The change with time of the nuclear composition of this matter is calculated by use of the compressible nuclear mass formula, and the hydrodynamics of the system is followed by the effect of nuclear transformation with time of the second fission of heavy neutron-rich nuclei, which is followed by a rapid rise to above 10⁹ K. If the value of the -strength function exceeds about 10^–5.5 MeV^–1 s^–1, the system proceeds to a state of nuclear equilibrium in the later expansion stage and the nuclear composition is reshuffled, finally to be transformed into neutron-excess, stable nuclei within the atomic mass region 80A120. It also becomes clear that if the strength function has a value smaller than the above critical value, then the neutron-rich nuclides withA[200, 400] are copiously produced. These results will also be applied in the cases of a neutron-star-black-hole collision and the explosion of a neutron star associated with the catastrophic phase transition within the neutron star core. The astrophysical implications are briefly discussed.     

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.     

Gravitational collapse of cosmic gas clouds and formation of star clusters

In this paper the gravitational collapse of cosmic gas clouds and formation of star clusters has been considered. Hoyle's view of successive fragmentation has been taken as the basic mechanim in the present work. The initial masses of protostars have been estimated as the function of their distances from the centre of the cluster and the intensity of the magnetic field of the medium. It has been shown that the fragmentation process is greatly inhibited by the presence of a strong magnetic field. A model has been constructed showing how a protostar grows in mass by accretion from the surrounding medium, on the basis of the assumption that as the star moves at random in the cluster it picks up a fraction of the material through which it passes. It has been estimated that a protostar of initial mass of about 0.1M grows to one of 1.0M in a time period which ranges from a few multiples of 10⁵ to a few multiples of 10⁷ yr, depending on the parameters involved in the accretion process. The number of stars per unit mass range has also been estimated; it is found to be proportional tom ^–3.3,m being the mass of the star.     

Evolution of low-mass close binaries and the problem of orbital period gap in cataclysmic variables

Evolution of close binary composed of a white dwarf primary and a Main-Sequence secondary has been calculated. Angular-momentum loss via gravitational radiation and magnetic stellar wind have been taken into account. We have found that magnetic stellar wind with a rate greater than (10^–10–10^–9)M yr^–1 is able to drive the evolution with mass exchange. If the time-scale of switch-off of wind when the primary becomes fully convective is not longer than 10⁶ yr, mass exchange interrupts due to a contraction of the secondary and the system becomes unobservable. Mass exchange resumes when components approach one another due to loss of momentum via gravitational radiation. The location and width of the thus-arising gap in the orbital periods are comparable to those observed.