Non-conservative evolution of low-mass,close binaries with gravitational radiation and systemic mass losses

The evolution of a low mass, close binary system driven primarily by gravitational radiation is followed with the assumption that the mass-losing component obeys an empirical mass-radius relation and continuously fills its Roche lobe. The possibility that some mass may be lost from the system carrying off various amounts of angular momentum is incorporated in the formulation. In addition, we make allowance for the uncertainty in the Landau-Lifshitz formula for gravitational quadrupole radiation. The simplicity of the formulation allows the effects of the various parameters describing the mass-radius relation, the modes of mass and angular momentum losses, etc., to be fully explored. We also discuss the condition for the Roche-lobe to be continuously filled and the possibility of estimating the minimum period.     

The evolution of massive close binaries

The results of evolutionary computations for massive binary systems (initial masses of the primary 10M ) with mass ratios between 0.3 and 0.8 are summarized and compared with observations in order to verify how far one can go with the conservative assumption of mass exchange. It is found that conservative mass exchange leads to acceptable first-order models of W-R and massive X-ray binaries. However, the comparison between this theory and observation reveals that for the observed systems (W-R and X-ray binaries) a preference exists for low intial mass ratios; moreover, the X-ray luminosities of the theoretical models are systematically too low, though this may be due to the adopted wind model. In addition, the influences of several parameters (distance between the components, chemical composition, primary mass, mass ratio and atmosphere) are examined. These parameters influence the remnant mass and any further evolution only marginally. Attention is also given to the effect on the system parameters of a supernova explosion of the remnant of the mass-losing component. For a large range of systems a disruption probability smaller than 25% is found.     

The evolution of massive close binaries

The final state of the primaries of binary systems with initial massesM _1i=10M to 15M is derived from the mass of their C/O-cores. The possibility of a second stage of mass transfer towards the secondary is considered. It turns out that the critical mass for the bifurcation is about 14M : stars with larger masses in this range are the progenitors of neutron stars, while the lower mass stars are the ancestors of white dwarfs.Research supported by the National Foundation of Collective Fundamental Research of Belgium (F.K.F.O.) under No. 10303.     

The evolution of massive close binaries

The influence of tidal, interaction on the periods of massive X-ray binaries during the postsupernova evolution is investigated. It is assumed that after a certain time the orbit has become circular and synchronous. The tidal effects of subsequent evolutionary changes in the moment of inertia of the massive component are calculated. It is shown that, as is already suggested by Sparks and Stecher (1974), for small mass ratios and short binary periods a tidal instability may occur resulting in an accelerating inward spiral motion. Before the onset of the instability the tidal forces maintain a nearly synchronous orbit. Possibly the orbits of Cen X-3 and 3 U 1700-37 are already unstable at present.     

Double-core evolution and the formation of neutron star binaries with compact companions

We present the results of a systematic exploration of an alternative evolutionary scenario to form double neutron star (DNS) binaries, first proposed by Brown (1995) , which does not involve a neutron star passing through a common envelope. In this scenario, the initial binary components have very similar masses, and both components have left the main sequence before they evolve into contact; preferably the primary has already developed a CO core. We have performed population synthesis simulations to study the formation of DNS binaries via this channel and to predict the orbital properties and system velocities of such systems. We obtain a merger rate for DNSs in this channel in the range of 0.1–12 Myr⁻¹. These rates are still subject to substantial uncertainties such as the modelling of the contact phase.     

Accretion and evolution in close binaries

The discovery of X-ray binary systems in the 1960's opened up stellar evolution theory by revealing further endpoints in addition to white dwarfs. This review summarises recent progress in studies of stellar-evolutionary processes that lead to X-ray binaries themselves, the mass transfer rates that power them, and the accretion processes which convert this into electromagnetic radiation. Particular attention is paid to the topics of mass transfer fluctuations and of the accretion by magnetic compact stars.     

On estimates of lower and upper limits for the masses of compact components in close binaries

A method of determination of limits for a compact component mass on the base of disk emission lines parameters is described. Lower limit of the mass depends upon the distance between maxima in double peaked lines, the upper the full width of the line. The method is tested for some cataclysmic variables with well known masses of compact components. We obtain a lower limit for the mass of the compact object in the close binary SS433 is 4.9M . This component is apparently a black hole.     

Disk wind in young binaries with low-mass secondary components: Optical observational manifestations

We consider a model of a young binary with a low-mass secondary component. Mass accretion from the remnants of the protostellar cloud onto the binary components is assumed to take place in accordance with current models; i.e., it proceeds mainly onto the low-mass component. The accretion is accompanied by mass outflow (disk wind), whose low-velocity component can be partially captured by the primary component. As a result, an asymmetric common envelope is formed. Its densest part is involved in the orbital motion of the secondary and can periodically shield the primary component of the binary from the observer. Assuming a standard dust-to-gas ratio for the disk wind (1: 100), we calculated the possible photometric effects from such eclipses and showed that they could be observed even at moderate accretion rates onto the low-mass binary component, ∼10⁻⁸–10⁻⁹ M _⊙ per year. In this case, the parameters of the minima depend on the model of the disk wind, on the ratio of its characteristic velocity to the orbital velocity of the secondary, and on its orbital inclination to the line of sight. These results can form the basis for interpreting a wide range of phenomena observed in young stars, such as the activity cycles in UX Ori stars, the unusually broad minima in some young eclipsing systems, etc., and for searching for substellar objects and massive protoplanets. In addition, the peripheral parts of the gas and dust disk around a young binary can fall within the shadow zone produced by the opaque part of the common envelope. In such cases, a shadow from the common envelope must be observed on the disk; this shadow must move over the disk following the orbital motion of the low-mass component. Detection and investigation of such structures in the images of protoplanetary disks may become a method of searching for protoplanets and studying binaries at early stages of their evolution.     

Late stages of the evolution of close binaries

Close binaries can evolve through various ways of interaction into compact objects (white dwarfs, neutron stars, black holes). Massive binary systems (mass of the primaryM ₁ larger than 14 to 15M ₀) are expected to leave, after the first stage of mass transfer a compact component orbiting a massive star. These systems evolve during subsequent stages into massive X-ray binaries. Systems with initial large periode evolve into Be X-ray binaries.Low mass X-ray sources are probably descendants of lower mass stars, and various channels for their production are indicated. The evolution of massive close binaries is examined in detail and different X-ray stages are discussed. It is argued that a first X-ray stage is followed by a reverse extensive mass transfer, leading to systems like SS 433, Cir X1. During further evolution these systems would become Wolf-Rayet runaways. Due to spiral in these system would then further evolve into ultra short X-ray binaries like Cyg X-3.Finally the explosion of the secondary will in most cases disrupt the system. In an exceptional case the system remains bound, leading to binary pulsars like PSR 1913+16. In such systems the orbit will shrink due to gravitational radiation and finally the two neutron stars will coalesce. It is argued that the millisecond pulsar PSR 1937+214 could be formed in this way.A complete scheme starting from two massive ZAMS stars, ending with a millisecond pulsar is presented.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.     

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.     

Populating the Galaxy with low-mass X-ray binaries

We perform binary population-synthesis calculations to investigate the incidence of low-mass X-ray binaries (LMXBs) and their birth rate in the Galaxy. We use a binary-evolution algorithm that models all the relevant processes including tidal circularization and synchronization. Parameters in the evolution algorithm that are uncertain and may affect X-ray binary formation are allowed to vary during the investigation. We agree with previous studies that under standard assumptions of binary evolution the formation rate and number of black hole (BH) LMXBs predicted by the model are more than an order of magnitude less than what is indicated by observations. We find that the common-envelope process cannot be manipulated to produce significant numbers of BH LMXBs. However, by simply reducing the mass-loss rate from helium stars adopted in the standard model, to a rate that agrees with the latest data, we produce a good match to the observations. Including LMXBs that evolve from intermediate-mass systems also leads to favourable results. We stress that constraints on the X-ray binary population provided by observations are used here merely as a guide as surveys suffer from incompleteness and much uncertainty is involved in the interpretation of results.     

The structure of close binaries

A method for calculating the structure of a close binary component is presented. It is seen that the effect of binary distortion is to shift the zero age main sequence to the right. Attempts to construct contact systems with these models confirm the results of earlier workers that this is not possible.     

Magnetic and spin evolution of neutron stars in close binaries

The evolution of neutron stars in close binary systems with a low-mass companion is considered, assuming the magnetic field to be confined within the solid crust. We adopt the standard scenario for the evolution in a close binary system, in which the neutron star passes through four evolutionary phases ('isolated pulsar'–'propeller'– accretion from the wind of a companion – accretion resulting from Roche-lobe overflow). Calculations have been performed for a great variety of parameters characterizing the properties of both the neutron star and the low-mass companion. We find that neutron stars with more or less standard magnetic field and spin period that are processed in low-mass binaries can evolve to low-field rapidly rotating pulsars. Even if the main-sequence life of a companion is as long as 10¹⁰ yr, the neutron star can maintain a relatively strong magnetic field to the end of the accretion phase. The model that is considered can account well for the origin of millisecond pulsars.     

Bifurcation points in close binary evolution: Medium-mass binaries

The remaining core hydrogen burning lifetime after case B of mass transfer of the secondary (mass gaining) component in a medium mass close binary star is estimated, for mediummass binaries with primaries in the mass range 5M to 9M . From the comparison of this quantity with the helium burning time-scale of the remnant primary a critical mass ratioq _c is derived such that for larger values ofq, mass transfer from the secondary towards the primary starts before the latter has evolved into a white dwarf. Consequences for the advanced stages of medium mass binaries are discussed.     

The luminosity function of low-mass X-ray binaries in galaxies

The X-ray luminosity function of low-mass binaries constructed from the observations of point like X-ray sources in galactic bulges can be explained in terms of the main evolutionary relations for the rate of mass transfer onto a compact object. The observed scatter of luminosities for individual low-mass X-ray sources in our Galaxy is shown to be satisfactorily described by a symmetric quasi-Lorentz curve with a dispersion proportional to the mean luminosity. Such a form of the mean luminosity function for individual sources does not affect the power-law pattern of the luminosity function for the entire population of sources that is expected for a power-law dependence of the mass transfer rate in a close binary on the mass of the Roche lobe—filling optical component.