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.     

The parameters of planetary nebulae and their central stars derived from observations

On the basis of data on planetary nebula (PN) central star temperatures obtained by measurements in the ultraviolet (UV) range, the empirical calibration dependence between the number of Lyman photons emitted by a central starS and PN diameterD, is constructed. The temperatures of 118 PN central stars are estimated with this dependence. It is shown that the central star masses are distributed in a wide interval from 0.5 to 1.2M . About 60% of all stars have masses <0.6M , about 25% have masses >0.6M and the remainder have masses 0.6M . The averaged empirical tracks of evolution of low-mass (<0.6M ) and massive (>0.6M ) central stars differing considerably from each other are constructed. It is shown that the majority of central stars may possess hot chromospheres (T>2×10⁵ K) which spread for several tens of radii of the central star. The PN originates as a result of ionization of the matter ejected by a red giant at the superwind stage. The cause for this ionization is the UV radiation of the PN central star.     

Evolution of massive close binaries

The evolution of a binary system with components of 10M and 8M is computed through a case B of mass exchange. It is found that after the end of core helium burning, a second stage of mass transfer from the primary occurs. Carbon ignition is prohibited by the large neutrino losses in the degenerated core. The primary remnant, a 1.12M star, ends as a white dwarf. A comparison with the 10M single evolution is made.This research is supported by the National Foundation of Collective Fundamental Research of Belgium (F.K.F.O.) under No. 10303.     

Planetary nebulae in planetary and binary systems

The problem of the survival of a low-mass secondary orbiting a primary that becomes a planetary nebula is studied. The values of the mass of the primary are 1.0, 1.5, and 2.0M ; the values of the mass of the secondary 0.001M , 0.01M and 0.1M . The orbital decay and mass of the secondary due to accretion and gravitational drag in the common envelope are presented. The possible application of the results to V471 Tau, UU Sge, WZ Sge and the Sun-Jupiter system are discussed.     

Identification of a collapsing protostar

The globular molecular cloud B335 contains a single, deeply embedded, far-infrared source. Our recent observations of H₂CO and CS lines toward this source provide direct kinematic evidence for collapse. Both the intensity and detailed shape of the line profiles match those expected from inside-out collapse inside a radius of 0.036 pc. The collapse began about 1.5 × 10⁵ years ago, similar to the onset of the outflow. The mass accretion rate is about 10 times the outflow rate, and about 0.4M should have now accumulated in the star and disk. Because B335 rotates only very slowly, any disk would still be very small (about 3 AU). The accretion luminosity should be adequate to power the observed luminosity. Consequently, we believe that B335 is indeed a collapsing protostar.Paper presented at the Conference onPlanetary Systems: Formation, Evolution, and Detection held 7–10 December, 1992 at CalTech, Pasadena, California, U.S.A.     

On the formation of Jupiter

Arguments are presented to show that Jupiter could not have been formed as a star of mass 0.001M and that the observed excess energy is not due to gravitational contraction from an extended, gaseous state.     

Non-stationary atmospheres of supergiants

A model of 5M hydrogen-helium star with no metals has been considered. The properties of the adiabatic oscillations were obtained, and the vibrational instability of the model has been investigated. The model is a double-shell burning star. Calculations were done for the fundamental mode as well as the first and the second harmonics. The model has been found vibrationally unstable against radial adiabatic pulsations.     

On the pre-supernova parameters of the Hercules X-1 system

On the assumption that, at the moment of the supernova explosion, the presently nondegenerate companion of Her X-1 was a Main-Sequence star with polytropic indexn=3, it is found that the effects of impact and ablation cannot have removed more than about 10% of its pre-supernova mass. A remnant mass for a neutron star of 1.4M was adopted. The effects of impact and ablation were calculated in the manner given by Wheeleret al. (1975). Depending on the ejection velocity of the SN shell, it is found that with a pre-SN mass of 2.2M (i.e., the maximum possible value) for the non-degenerate component, the initial binary period was in the range 2–4 days.     

Neutron stars and general equation of nuclear matter

It has been shown that the mass of neutron stars obtained from equations of state based on nuclear theory depend upon the number of baryons assembled in it but not on the type of interactions considered. On examining the behaviour of different equations of state based on nuclear theories, a simple polytropic equation of state,P = (K/N)(p –p _s)^N is proposed. The results obtained forN=1.75 cover the entire range of neutron star masses obtained from the equations of state based on nuclear theories and give a maximum mass of 2.8M . Depending upon various mechanisms for energy output the mass of Crab pulsar is estimated to range from 0.32M to 1.5M . The relation connecting the coordinate mass,M, and the rest mass,M ₀, may be written asM/M 0.93 (M ₀/M)^0.9.     

The product of the globular cluster collapse

In this paper we calculate the number of close binaries formed during the evolution process of a globular cluster core. The globular cluster core is assumed to contain a massive black hole at its center. We show that the central black hole can drive binaries formation in the core and the rate of binaries formation depends on the mass of the black hole at its center. When the massM of the black hole is between 10² M and 3×10³ M , there will be a few binaries formed. When the mass of the black hole is 4×10³ M M6×10³ M , the number of binary star formation will suddenly increase with a jump to the maximum value 58. When the mass of the black hole is 7×10³ M M9×10³ M , the number of binary star will immediately decrease. Whether cluster X-ray is produced mainly by the central black hole or by binaries in the core depends on the mass of the central black hole. Therefore, two cases arise: namely, black hole accretion domination and binaries radiation domination. We do think that we cannot exclude the possibility of the existence of a central black hole even when binary radiation characteristics have been observed in globular cluster X-ray sources.     

A full cycle in the evolution of a classical nova

A classical nova model was evolved through a complete cycle, i.e. accretion leading to cutburst, mass loss and again accretion, ending in another outburst, by means of an implicit Lagrangian hydrodynamic code, which included diffusion (concentration, pressure and thermal terms), as well as an extensive nuclear reactions network between 28 isotopes of C, N, O, F, Ne, Na, Mg and Al. The initial model was a 1.25 M C–O white dwarf (WD) and the accretion rate assumed was 10^–11 M/yr. For more details of this calculation, see Prialnik (1986).The accreted matter was assumed to have normal composition (X=0.70, Z=0.03). Nevertheless, due to diffusion and convection, a significant amount of core material was mixed into the accreted matter, raising Z by a factor of 10. The model's evolution closely resembled that of a fast nova eruption, with a peak bolometric luminosity of 2.9×10⁵ L, a time of decline by 3^m of 25 days, an ejected mass of 6.5×10^–6 M and a maximum velocity of 3800 km/sec.Paper presented at the IAU Colloquium No. 93 on Cataclysmic Variables, Recent Multi-Frequency Observations and Theoretical Developments, held at Dr. Remeis-Sternwarte Bamberg, F.R.G., 16–19 June, 1986.     

Study of the X-ray selected BL Lac object 1727+502

In this paper, accretion disc and synchrotron emission models have been used to analyse simultaneous IR-optical-UV data of the BL Lac object 1727+502. In the following, some of its properties have been discussed. It is shown that the temperature of the disc is about 19, 000°k, the mass of the central black hole isM ₈ 5.4, and the accretion ratio is 10^–3 M /yr.     

The relation between molecular clouds and stellar kinematics

The relation between molecular clouds, star clusters, and the stellar component of the galactic disk is investigated. According to Elmegreen (1985) bound stellar systems, e.g., open star clusters, can be formed from molecular cloud of mass 10⁴ M . A close encounter with a giant molecular cloud or massive black hole disrupts such stellar systems and forms superclusters. This explains why some open star clusters are so mass-deficient. Unbound stellar systems, e.g., expanding OB associations, are formed from molecular clouds of mass 10⁵ M . When disruptive O-type stars appear the star formation is halted and the cloud is destroyed. An example of the relict of GMC disruption in the solar vicinity is Gould's belt. The velocity dispersion-versus-age relation is also investigated and explained as a consequence of gravitational scattering of stars on GMC, or massive black holes, or as due to recurrent transient spirals.Paper presented at a Workshop on The Role of Dust in Dense Regions of Interstellar Matter, held at Georgenthal, G.D.R., in March 1986.     

Preliminary study of light variations of the eclipsing binary AB Cassiopeiae

Preliminary study of the eclipsing binary AB Cas is presented here by using the photometric observational data. The primary component is one of the Sct variables with period of 0^d.054, and whether the oscillation is of a radial mode or of a non-radial one is discussed. Two colour indices (B-V andU-B) data and the light curve analysis suggest that this binary system is a typical Algol type binary system, in which the primary component is near the ZAMS with about 2.3M and the secondary one is a subgiant star with about 0.5M .     

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.     

Maximal red shifts of neutron stars

It has been recently established that there exists a maximal red shiftz _max for a homogeneous star of given massM. The relationshipz _max(M) is obtained for neutron stars in the mass range 0.71M/M 12.06.     

The accretion of matter by a collapsing star in the presence of a magnetic field. II. Selfconsistent stationary picture

The stationary two-dimensional magnetohydrodynamic solution for the accretion of the matter without pressure into a gravitating centre of a black hole is obtained. It is assumed that the magnetic field far from the collapsed star is homogeneous and its influence on the flow is negligible. Around the star, at the plane perpendicular to the direction of the magnetic field, the dense quasistationary disc is formed, the structure of which in a large extent is determined by dissipation processes. The structure is calculated for (a) a laminar disc with the Coulomb mechanism of dissipation; and (b) a turbulent disc.The estimations of the parameters of the shock which result from the infall of the matter onto the disc are given. In the last section the numerical estimation and approximate character of the radiation spectrum of the disc and the shock are obtained for two cases of 10M and 10⁵ M . The luminosity of collapsed objects withM=10M appears to be about solar, thus its observation is possibly only at the distances less than 300–1000 pc. The collapsed objects in the Galaxy withM=10⁵ M could constitute very bright sources in spectral regions from optical up to X-ray. The spectra of a laminar and a turbulent disc for 10M black hole are very different. The laminar disc radiates primarily in the ultraviolet. The turbulent disc radiates a large part of its flux in the infrared. Therefore, one cannot exclude the possibility that some of the galactic infrared star-like sources are individual black holes in the accretion state.     

On the X-ray source SCO XR-1

If the assumption of a catastrophic explosion during the formation of a neutron star is correct, the parent systems for klovsky's model of SCO XR-1 seem to have been very short-period white-dwarf binaries. A white dwarf originally in contact with its Roche limit is forced to lose mass. During the ejection of matter the primary may pass the white-dwarf mass limit and become a neutron star. The mass transfer time-scale can change from pulsational to thermal, and a mass flow of 10^–9 M per year needed for SCO XR-1 can be understood, while at the same time the orbital period will increase.     

Advanced evolutionary phase of a first-generation star

The theoretical evolution of a first-generation star of 3M after the core helium-exhaustion phase has been investigated. The star displays the character of a double shell burning model. Shell hydrogenburning produces energy mostly by the p-p chain reaction. CN-cycle reaction is only operating in the inner edge regions where sufficient amount of carbon is formed by the 3-reactions. Hence, the shell burning time of the star is longer than that of normal stars, thus lengthening the total evolutionary lifetime of the first-generation stars.Prior to carbon-burning phase, the mass of the complete hydrogen-exhausted region is 1.14M and that of complete helium-exhausted region is 0.83M . A carbon-oxygen core of about 0.87M has developed within the star in which the ratio of carbon to oxygen is about 0.85, but decreases down to a value of 0.50 near the boundary of the core.     

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.