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.     

Evolution through mass exchange in close binary systems of total mass 2.5M ⊙

Calculations show that the observed semi-detached binary systems of massM ₁+M ₂2.5M can be explained in terms of a mass exchange which starts after the central hydrogen in the original primary has been exhausted.Presented at the Trieste Colloquium on Mass Loss from Stars, September 12–16, 1968.     

Evolution of binaries with ultra-short periods: Systematic study

A detailed investigation of the evolution of low-mass binaries is performed for the case when the secondary fills its Roche lobe at the stage of core hydrogen exhaustion. The obtained results are compared with observational data for ultra-short periodic X-ray systems MXB 1820-30 and MXB 1916-05. In the frame of the proposed evolutionary scenario it is possible to obtain for MXB 1820-30 its periodP=11.4 min twice (see Figure 2). In the first case the parameters of the system are:M ₂ 0.13–0.15M ,X0.05–0.13, |P/P| (3.6–6.2) } 10^–7 yr^–1, M₂ (4.1–9.6) } 10^–9 M yr^–1, for the second:M ₂ 0.08–0.09M ,X= 0, |P/P| (1.3–1.5) } 10^–7 yr^–1, M₂ (1.4–1.8) } 10^–8 M yr^–1. It is suggested that MXB 1916-05 is the progenitor of the system MXB 1820-30 (M ₂ = 0.1M,X 0.221,M ₂ 1.8 × 10^–10 M yr^–1).     

Evolution of a binary system consisting of a helium star and a white dwarf

Results of evolutionary calculations for a close binary system with a central helium burning He-star filling its Roche lobe and an accreting white dwarf are presented. Values for the mass of the components and the degree of central helium exhaustion before the filling of the Roche lobe are varied. It is shown that in such a system the mass accretion rate will remain for a long time (2–4) Ö 10^–8 yr^–1 ifq<1 (q=M _He,2/M _CO,1). The obtained results are discussed in connection with pre-supernova I phenomenon.     

The angular momentum-vs-mass relation and the distribution of mass ratios for visual binary systems

The investigation of the angular momentum vs mass relation for binary stars is completed with a study of the 847 systems contained in theFourth Catalog of Orbits of Visual Binary Stars. Because bothJ andM of a visual binary depend steeply on the distance to the system (5th and 3rd powers, respectively), and many of the distances are not well known, the study makes use of an auxiliary parameterR which is independent of distance and proportional toJM ^–5/3.R appears to be uncorrelated withM for the 789 systems for which both can be determined. The non-correlation implies thatJ M ^5/3, expected from Kepler's third law, provides a better fit to the visual binaries than doesJ M ², predicted by some more complex considerations.The distribution functionf(q=M ₂/M₁) of mass ratios for the visual binaries results as a byproduct of the investigation. It peaks extremely sharply towardq=1.0 (much more so than for spectroscopic binaries). Because most visual binaries are wide enough to consist of stars that condensed independently (and so that can be thought of as chosen at random from an initial mass function), one expects the realf(q) to rise toward low ratios. Observational selection against the discovery and study of systems with large magnitude differences between the components must be very large indeed to account for the discrepancy between expectation and observation. The alternative is a mechanism for formation of wide binaries that favours equal components. The distribution of mass ratios for eclipsing binaries is given in an appendix. It peaks strongly atq=0.6–0.75 and largely reflects processes of angular momentum, mass, and energy exchange between the stars in contact systems.     

Structure of close binaries

Internal models have been obtained for uniformly rotating synchronous close binary systems using a modified double approximation scheme. We have considered primaries of 10M , 5M , and 2M with mass ratios of 0.0 to 1.0 in steps of 0.1, and some results are given for a 1M primary with a mass ratio of 1.0. A maximum luminosity reduction of 2.3% was found for a 10M primary with a mass ratio of 1.0 and 7.7% for a mass ratio of 0.0. The corresponding values for 5M are 2.0% and 7.0%, and for 2M they are 1.6% and 5.3%, respectively. These values were not found to be sensitive to small changes in composition. The maximum equatorial velocity varies from 399 km s^–1 for 2M to 567 km s^–1 for 10M when the mass ratio is zero, but these velocities decrease by 200–300 km s^–1 if the mass ratio is unity. The effect of gravity darkening on the apparent position of the primary in the theoretical H-R diagram was investigated. It was determined that an unresolved close binary of unit mass ratio can lie up to 0.9 magnitudes (depending on inclination) above the main sequence, whereas if the effects of distortion are ignored this number is at most 0.75 magnitudes. There seems to be some observational support for the larger value. Two models of the secondaries are given and their dimensions are compared with their critical Roche lobes.     

Evolution of close binaries and origin of Algol-type systems

The evolution of close binary systems was followed for ten systems with the initial mass of the primary in the range 1–4M and with different initial mass ratios and initial separations. A brief discussion of the evolution of the contact component is presented for two separate cases: when the primary reaches its Roche lobe during central hydrogen burning (case A) and after the exhaustion of hydrogen in the center (case B).The models obtained are compared with observed semi-detached systems separately for massive (with total mass greater than 5M ) and low mass (with total mass below 4M ) binaries. It is shown that the contact components of the observed massive binaries are probably burning hydrogen in the core. On the contrary, the majority of contact components of the observed low-mass binaries are burning hydrogen in the shell. The observed distribution of such binaries as a function of different luminosity excesses of contact components seems to indicate that their origin is connected with case A rather than with case B.     

Mass accretion onto massive white dwarfs

We have studied the thermonuclear runaways which develop on white dwarfs of 1.205M and 1.358M accreting hydrogen rich material at 10^–10 M yr^–1. It is found that ignition of this material occurs at densities in excess of about 10⁴ gm cm^–3 and that the critical accumulated mass required to initiate the runaway is 0.7(1.5)×10^–4 M for a 1.358(1.205)M white dwarf.     

Astron observations of the Rapid Burster MXB 1730-335 and constraints on burster parameters from spectra of trailing bursts

We report on eight X-ray bursts detected by ASTRON from the Rapid Burster (RB) on 13 and 28 April and 16 August, 1983. Six of them (trailing bursts), with durations of 1.5–2 min, rise times of 5–10 s and intervals of 1–1.5 hours, exhibit spectral softening during the burst decay and may be related to the type I bursts. Two of the bursts (triangle bursts) observed on 28 April at interval of 28 min with much longer rise times (30–50 s) and longer durations (3 min), do not show distinct spectral softening. Persistent flux from RB on 16 August was estimated asF _p(2.0–2.4)×10^–9 erg cm^–2 s^–1. Spectral evolution of two trailing bursts was investigated by fitting their spectra in consecutive time intervals with the blackbody (BB), isothermal scattering photosphere (SP) and thermal bremsstrahlung (TB) models. Around the burst maxima the SP model fits the data best whereas in the burst tails the TB model is generally better. The BB model is worse than at least one of the two others. Interpretation of the burst spectra in terms of the BB radiation leads to improbably small neutron star mass and radius (M<0.86M ,R _NS<5 km) if the peak luminosity does not exceed the Eddington limit. Interpretation of the spectra around the burst maxima (3–15 s from the burst onset) in terms of an isothermal SP yields reasonable constraints onM,R _NS, and distanceD. For instance, for the hydrogen photosphere we obtainedM=(1.0–2.1)M R _NS=(7.1–16.4) km ifD=11 kpc. If one postulatesM=1.4M , thenD=(8.5–13) kpc for hydrogen photosphere; if, besides,D=11 kpc, thenR _NS=(8.1–13.3) km. It follows also from the SP-interpretation that the photosphere radius may increase up to 20–30 km in maxima of the trailing bursts when the luminosity becomes close to the Eddington luminosity.     

A mechanism for the production of planetary nebulae

C¹² stars in the range 1.04–1.55M are evolved to simulate the core evolution of the possible precursors of planetary nebulae. The nuclear shell burning in stars above 1.2M advances to within about 0.2M of the surface, where the intense radiation interacts with the surface matter and causes mass loss. Comparison between our theoretical results and observations suggests that this may be a mechanism by which planetary nebulae are formed.Presented at the Trieste Colloquium on Mass Loss from Stars, September 12–16, 1968.     

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.     

A study of weak molecular and atomic lines in the photospheric spectrum

An attempt is made to detect the lines of Mg²⁵H and Mg²⁶H in the photospheric spectrum, using calculated isotope shifts. From comparisons with the Mg²⁴H lines of the ² –² transition in the (0, 0) band the ratios Mg²⁵/Mg²⁴ = 0.12 ± 0.04 and Mg²⁶/Mg²⁴ = 0.12 ± 0.02 are derived. These are essentially the same as the terrestrial ratios. The profile of one line of Mgi confirms these values.The wavelengths of MgH and C₂ lines, when corrected for the gravitational red shift, indicate that macroturbulent (or streaming) velocities die out near log ₀ = – 1.0. From the equivalent widths of the MgH lines a rotational temperature of 5132 ± 200 K is obtained and compared to predictions from various model atmospheres. The band oscillator strength is found to be 0.024 ± 0.002, in serious disagreement with the single laboratory determination.The profiles of MgH, C₂, CN and some weak atomic lines are used to derive the variation of the radial component of microturbulence with optical depth, on the assumption of streaming velocities of 2.5–3.0 km/sec. A slow increase with increasing height in the photosphere is found, over the range –1.5 < log₀< 0.2.The center-limb variation of the equivalent widths of MgH and C₂ lines for a wholly inhomogeneous model is found to be the same as for a model which is homogeneous above log ₀ = - 1.0. With such a model as the latter, the center-limb variation of the profiles of the selected molecular and atomic lines is moderately-well reproduced by an anisotropic microturbulent velocity with a tangential component of 3 km/sec which seems to be constant with height over the range considered.     

Models of pulsating low-massive yellow supergiants

The nonlinear self-excited oscillations of the envelopes of low-massive highly luminous stars are described. The parameters for these models wereM=0.8M ,M _bol=–5.5, –5.84 mag,T _eff=4500, 5000, 5500 K. The oscillations have been found to consist of the standing wave pulsation near the envelope bottom and running waves in outer layers. The ratio of the standing wave frequency _s to the average frequency of the running waves _r increases with the stellar luminosity: _s / _r =1.7 whenM _bol=–5.5 mag and _s / _r =2.4 whenM _bol=–5.84 mag. The frequency of oscillations near the photosphere is found to be in close agreement with the critical frequency for running waves. Mass loss from these stars is caused by shocks. It has been shown that agreement between FG Sge's period change observed during the last decade and the period-luminosity relation for double shell stars takes place when FG Sge's luminosity isM _bol=–5.96 mag.     

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 ).     

The post-RLOF structure of the secondary components in close binary systems,with an application to masses of Wolf-Rayet stars

The post-RLOF structure of the secondary after relaxation towards thermal equilibrium is calculated for a large grid of massive close binaries evolving through an early caseB of mass transfer. The initial primary masses range between 15 and 30M _o, the initial mass ratio between 0.3 and 0.9. The possibility that matter leaves the system during RLOF is included using an additional free parameter . The calculations are based on the accretion and relaxation properties of massive accretion stars. Conclusions on the post-RLOF secondaries are presented in function of , M1i, andq _i , in the form of tables and figures on the post-RLOF positions in the HR diagram, the final masses, mass ratios, chemical profiles and the remaining core-hydrogen burning lifetime. It is found that all systems starting from initial conditions in the grid specified above evolve sequentially, i.e. the primary evolves into a supernova before the end of core H burning of the secondary. No WR+WR systems are encountered. The results are used to determine the masses of ten double lined spectroscopic WR+OB binaries. Most of the WR masses are in the range 8–14M _o, although the sample is subject to some important selection effects. One WR+OB binary has a WR mass between 4 and 5M _o. It is argued that mass determinations based only on the spectral type of the secondary yield WR masses that are too high up to a factor two.     

Strömgren photometry of a-stars: A test of physical parameter determination

By use of known published values forT _eff, logg, andM _v, a check on our procedure for determining the physical parameters of A v-type stars from Strömgren photometry has been performed. External errors for our calculated physical parameters have been obtained.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

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.     

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.     

Nature of the symbiotic binary V 1329 Cyg

The published photometric and spectroscopic data of the symbiotic binary V 1329 Cyg are interpreted. It is shown, that V 1329 Cyg is an eclipsing binary with an elliptical orbit orbit (e=0.28). The cooler component fills up the Roche-lobe at periastron. A model of moving gaseous structures in the system is proposed and their influence on the radial velocity curve is shown. The following characteristics of the system are derived: the cooler component is an M6 giant with mass 7.9M , radius 339R and luminosityM _bol=–5.42, the hot component is a white dwarf surrounded by an accretion disk. The mean distance between the components is 842R and in periastron it decreases to 605R .     

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.