Common envelope evolution of binary stars

We discuss the common envelope phase in the evolution of binary systems. The problem of the efficiency of energy deposition into envelope ejection is treated in some detail. We describe the implications of common envelope evolution for the shaping of planetary nebulae with close binary nuclei and for double white dwarf systems, considered to be the progenitors of Type I supernovae.     

A gentle process for the formation of Algols

This work is concerned with binary systems that we call ‘moderately close’. These are systems in which the primary (by which we mean the initially more massive star) fills its Roche lobe when it is on the giant branch with a deep convective envelope but before helium ignition (late case B). We find that if the mass ratio q(= M ₁/M ₂) < q _crit = 0.7 when the primary fills its Roche lobe positive feedback will lead to a rapid hydrodynamic phase of mass transfer which will probably lead to common envelope evolution and thence to either coalescence or possibly to a close binary in a planetary nebula. Although most Algols have probably filled their Roche lobes before evolving off the main-sequence we find that some could not have and are therefore ‘moderately close’. Since rapid overflow is unlikely to lead to an Algol-like system there must be some way of avoiding it. The most likely possibility is that the primary can lose sufficient mass to reduce q below q _crit before overflow begins. Ordinary mass loss rates are insufficient but evidence that enhanced mass loss does take place is provided by RS CVn systems that have inverted mass ratios but have not yet begun mass transfer. We postulate that the cause of enhanced mass loss lies in the heating of the corona by by magnetic fields maintained by an α — ω dynamo which is enhanced by tidal effects associated with corotation. In order to model the the effects of enhanced mass loss we ignore the details and adopt an empirical approach calibrating a simple formula with the RS CVn system Z Her. Using further empirical relations (deduced from detailed stellar models) that describe the evolution of red giants we have investigated the effect on a large number of systems of various initial mass ratios and periods. These are notable in that some systems can now enter a much gentler Algol-like overflow phase and others are prevented from transferring mass altogether. We have also investigated the effects of enhanced angular momentum loss induced by corotation of the wind in the strong magnetic fields and consider this in relation to observed period changes. We find that a typical ‘moderately close’ Algol-like system evolves through an RS CVn like system and then possibly a symbiotic state before becoming an Algol and then goes on through a red giant-white dwarf state which may become symbiotic before ending up as a double white dwarf system in either a close or wide orbit depending on how much mass is lost before the secondary fills its Roche lobe.     

The evolution of moderately close and moderately wide binaries

We discuss evolutionary processes in binaries where the primary becomes a red giant with a deep convective envelope before it fills its Roche lobe. Such binaries (late Case B or late Case C, if they evolve conservatively) ought to suffer drastic mass transfer, on a hydrodynamic timescale. In some circumstances this may lead to a common envelope, spiral-in, and finally either a very short-period binary or coalescence. But there appear to be other circumstances in which the outcome is an ordinary Algol, or a wide binary with a white dwarf companion as in Barium stars and some symbiotics. We try to demonstrate that stellar-wind mass loss, enhanced one or two orders of magnitude by tidal interaction with a companion, can vitally affect the approach to RLOF, and indeed may prevent RLOF in binaries with periods over 1000 d. Such mass loss is probably accompanied by angular momentum loss, by magnetic braking combined with tidal friction. The result is that it will not be easy to predict definitively the outcome of evolution in a given zero-age binary.     

The evolution of moderately close and moderately wide binaries

We discuss evolutionary processes in binaries where the primary becomes a red giant with a deep convective envelope before it fills its Roche lobe. Such binaries (late Case B or late Case C, if they evolve conservatively) ought to suffer drastic mass transfer, on a hydrodynamic timescale. In some circumstances this may lead to a common envelope, spiral-in, and finally either a very short-period binary or coalescence. But there appear to be other circumstances in which the outcome is an ordinary Algol, or a wide binary with a white dwarf companion as in Barium stars and some symbiotics. We try to demonstrate that stellar-wind mass loss, enhanced one or two orders of magnitude by tidal interaction with a companion, can vitally affect the approach to RLOF, and indeed may prevent RLOF in binaries with periods over 1000 d. Such mass loss is probably accompanied by angular momentum loss, by magnetic braking combined with tidal friction. The result is that it will not be easy to predict definitively the outcome of evolution in a given zero-age binary.     

SN 1987A and SN 1993J: Testing stellar evolution theory?

Nearby supernovae like SN 1987A and SN 1993J provide valuable constraints on the late evolution of massive stars. For this purpose, we review evolutionary models for the progenitor of SN 1987A and confront them with five observational/theoretical tests we devised. We show that single-star models (with the possible exception of rapid-rotation models) fail at least two of these tests, while two binary models (accretion and merger models) are consistent with all available constraints. We conclude that it is most likely that the progenitor of SN 1987A had a binary companion, either at the time of the explosion or at least in the not-too-distant past, and that SN 1987A should therefore not be used to calibrate single stellar evolution theory. For SN 1993J, we infer from the presupernova photometry and the early light curve that its progenitor was a 15M star that lost almost all of its hydrogen-rich envelope prior to the supernova. This seems to require that the progenitor underwent stable case C mass transfer. We discuss future observational tests of binary models for both supernovae.     

The evolution of massive stars to explosion

We review the possible evolutionary paths from massive stars to explosive endpoints as various types of supernovae associated with Population I and hence with massive stars: Type II-P, Type II-L, Type Ib, Type Ic, and the hybrid events SN 1987K and SN 1993J. We identify SN 1954A as another hybrid event from the evidence for both H and He in its spectrum with velocities nearly the same as SN 1983J. Evidence for ejected⁵⁶Ni mass of 0.07 M suggests that SN II-P underwent standard iron core collapse, not collapse of an O–Ne–Mg core nor thermonuclear explosion of a C–O core. Most SN II-P presumably arise in single stars or wide binaries of 10–20 M. There may be indirect evidence for duplicity in some cases in the form of strong Ba II lines, such as characterized SN 1987A. SN II-L are recognizably distinct from typical SN II-P and must undergo a significantly different evolution. Despite indications that SN II-L have small envelopes that may be helium enriched, they are also distinct from events like SN 1993J that must have yet again a different evolution. The SN II-L that share a common Luminosity seem to have ejected a small nickel mass and hence may come from stars with O–Ne–Mg cores. The amount of nickel ejected by the exceptionally bright events, SN 1980K and SN 1979C, remains controversial. SN Ib require the complete loss of the H envelope, either to a binary companion or to a wind. The few identified have relatively large ejecta masses. It is not clear what evolutionary processes distinguish SN Ib's evolving in binary systems from hybrid events that retain some H in the envelope. SN Ic events are both H and He deficient. Binary models that can account for transfer of an extended helium envelope from low mass helium cores, 2 to 4 M, imply C–O core masses that are roughly consistent with that deduced from the ejecta mass plus a neutron star, 2 to 3 M. It is possible that the hybrid events are the result of Roche lobe overflow and that the pure events, SN Ib or SN Ic, result from common envelope evolution.     

Highly evolved close binary stars

Recent progress on observational and theoretical investigations of close binary systems of stars allows one to understand the origin and evolution of peculiar objects in close binary systems: Wolf-Rayet stars, white dwarfs, neutron stars and black holes. The prediction made by Gamov (1943) about the Wolf-Rayet stars as stars displaying at their surfaces products of thermo-nuclear processing is now confirmed by observations of Wolf-Rayet stars in binary systems. The Catalogue of Close Binary Stars on Late Evolutionary Stages has been published by our group in 1989 in Moscow University Press. An improved version of this Catalogue is now in preparation and will be published in 1995 by Gordon and Breach.     

Two centuries of study of Algol systems

The periodicity of the light variation of Algol, discovered just over 200 years ago, may be regarded as the beginning of the study of eclipsing binary systems, especially those of the Algol type. Such studies, however, gained no real momentum until Vogel, 100 years ago, demonstrated by spectroscopy that the binary hypothesis of Algol's light changes is, in its essentials, correct. Three elements were needed to give us our modern notions of evolution by mass-transfer, namely: (i) results of combined analysis of light-curves and velocity-curves, (ii) evidence of circumstellar matter within binary systems and (iii) the notion that at least one component of an Algol system was near the limit of dynamical stability. All three entered the literature within about a decade, approximately halfway through the second century of eclipsing-binary studies; but it is the computational and instrumental developments of the last 25 years that have made real progress possible. We still lack commensurate theoretical developments, and the whole question of the contribution of Algol systems to the development of the Galaxy has barely been considered.     

Two centuries of study of Algol systems

The periodicity of the light variation of Algol, discovered just over 200 years ago, may be regarded as the beginning of the study of eclipsing binary systems, especially those of the Algol type. Such studies, however, gained no real momentum until Vogel, 100 years ago, demonstrated by spectroscopy that the binary hypothesis of Algol's light changes is, in its essentials, correct. Three elements were needed to give us our modern notions of evolution by mass-transfer, namely: (i) results of combined analysis of light-curves and velocity-curves, (ii) evidence of circumstellar matter within binary systems and (iii) the notion that at least one component of an Algol system was near the limit of dynamical stability. All three entered the literature within about a decade, approximately halfway through the second century of eclipsing-binary studies; but it is the computational and instrumental developments of the last 25 years that have made real progress possible. We still lack commensurate theoretical developments, and the whole question of the contribution of Algol systems to the development of the Galaxy has barely been considered.     

A gentle process for the formation of Algols

This work is concerned with binary systems that we call moderately close. These are systems in which the primary (by which we mean the initially more massive star) fills its Roche lobe when it is on the giant branch with a deep convective envelope but before helium ignition (late case B). We find that if the mass ratio q(= M ₁/M ₂) < q _crit = 0.7 when the primary fills its Roche lobe positive feedback will lead to a rapid hydrodynamic phase of mass transfer which will probably lead to common envelope evolution and thence to either coalescence or possibly to a close binary in a planetary nebula. Although most Algols have probably filled their Roche lobes before evolving off the main-sequence we find that some could not have and are therefore moderately close. Since rapid overflow is unlikely to lead to an Algol-like system there must be some way of avoiding it. The most likely possibility is that the primary can lose sufficient mass to reduce q below q _crit before overflow begins. Ordinary mass loss rates are insufficient but evidence that enhanced mass loss does take place is provided by RS CVn systems that have inverted mass ratios but have not yet begun mass transfer. We postulate that the cause of enhanced mass loss lies in the heating of the corona by by magnetic fields maintained by an — dynamo which is enhanced by tidal effects associated with corotation. In order to model the the effects of enhanced mass loss we ignore the details and adopt an empirical approach calibrating a simple formula with the RS CVn system Z Her. Using further empirical relations (deduced from detailed stellar models) that describe the evolution of red giants we have investigated the effect on a large number of systems of various initial mass ratios and periods. These are notable in that some systems can now enter a much gentler Algol-like overflow phase and others are prevented from transferring mass altogether. We have also investigated the effects of enhanced angular momentum loss induced by corotation of the wind in the strong magnetic fields and consider this in relation to observed period changes. We find that a typical moderately close Algol-like system evolves through an RS CVn like system and then possibly a symbiotic state before becoming an Algol and then goes on through a red giant-white dwarf state which may become symbiotic before ending up as a double white dwarf system in either a close or wide orbit depending on how much mass is lost before the secondary fills its Roche lobe.     

The long term variability of 4U 1258-61 (GX304-1)

We present optical spectroscopy and photometry of 4U 1258-61 obtained over the course of six years. Evidence for the evolution of a circumstellar envelope throughout the course of the observations is presented.     

A Comparison of Binary Delay-Lock Tracking-Loop Implementations

The delay-lock loop is a device for tracking the delay difference between two correlated waveforms. It is used as a synchronizing loop for binary communications and tracking. The delay tracking performance is derived for various radio-frequency implementations of the binary delay-lock loop. Amplitude and biphase modulation by pseudorandom sequences are considered. Three types of receivers are analyzed for each modulation: envelope correlation, phase-coherent correlation, and phase-lock demodulation followed by video correlation.     

On the Acquisition Behavior of Binary Delay-Lock Loops

The acquisition problem for binary delay-lock loops is re-examined. Previous results obtained by Spilker and Gill on the maximum allowable search rate are shown to be in error. New results are given for the 2-? loop with video correlation and the 1-? loop with video and envelope correlation.     

TeV emission from close binaries

It is commonly accepted that candidates for very high energy -ray sources are neutron stars, binary systems, black holes etc. Close binary systems containing a normal hot star and a neutron star (or a black hole) form an important class of very high energy -ray sources. Such systems are variable in any region of the electromagnetic spectrum and they enable us to study various stages of stellar evolution, accretion processes, mechanisms of particle acceleration, etc. Phenomena connected with this class of very high energy -ray sources are discussed. Particular emphasis has been placed on the TeV energy region.     

Evolution of massive close binaries

This paper briefly reviews the competition between massive single star and massive close binary evolution the last two decades. The status of the binary evolutionary model is summarized, the assumptions and simplifications are critically discussed. Using all computations performed since 1970, general conclusions are drawn and a comparison with massive single star evolution is presented. Special attention is given at the assumptions behind the commonly accepted model for the mass gainer and a new accretion model is proposed. The binary results in combinarion with single star evolution are compared with observations of massive stars with emphasis on the HR diagram, star number counts, WR stars, SN 1987A, OBN and OBC stars.     

The evolution of binary stars into contact states

Good-quality empirical results on 62 short-period binary stars recently summarised by Hilditch & Bell (1987) and Hilditch, King & McFarlane (1988) are discussed in terms of evolutionary paths from detached to semi-detached and contact states. These data suggest two evolutionary paths to the contact binaries — from detached systems directly into contact to form initially shallow-contact systems, and via case A mass transfer to semi-detached states, thence to contact systems. These empirical results support previous arguments based on evolutionary models and less detailed observational data.Concern is expressed about the paucity of high-quality spectroscopic data, particularly for low-mass systems displaying EB-type light curves and the resultant limitations on analyses of those light curves. Such systems provide tests of evolution into contact for the first time, or of broken-contact phases for WUMa-type binaries. The crucial importance of long-term monitoring (decades) of times of minima as indicators of mass transfer rates amongst these interacting binaries is also noted.     

The evolution of binary stars into contact states

Good-quality empirical results on 62 short-period binary stars recently summarised by Hilditch & Bell (1987) and Hilditch, King & McFarlane (1988) are discussed in terms of evolutionary paths from detached to semi-detached and contact states. These data suggest two evolutionary paths to the contact binaries — from detached systems directly into contact to form initially shallow-contact systems, and via case A mass transfer to semi-detached states, thence to contact systems. These empirical results support previous arguments based on evolutionary models and less detailed observational data. Concern is expressed about the paucity of high-quality spectroscopic data, particularly for low-mass systems displaying EB-type light curves and the resultant limitations on analyses of those light curves. Such systems provide tests of evolution into contact for the first time, or of broken-contact phases for WUMa-type binaries. The crucial importance of long-term monitoring (decades) of times of minima as indicators of mass transfer rates amongst these interacting binaries is also noted.     

Reverse Algols

An Algol is a binary system having a semidetached configuration where the less massive component is in contact with the critical equipotential surface. A reverse Algol is a binary system having a semidetached configuration where the more massive component is in contact with the critical equipotential surface. In 1985, Leung suggested 5 reverse Algol systems at the Beijing Colloquium. Two more such systems have been discovered recently. The spectral types of these systems range from early B to mid G. There is also a wide spread in mass ratio among these systems. There appear to be two types of reverse Algols, hot and cool systems. The hot systems have their more massive components as the hotter stars and the cool systems their more massive components as the cooler stars. The mass-radius relation of the reverse Algols is very similar to that of the contact and near-contact systems. It is believed that reverse Algols represent the pre-mass-reversal semidetached phase of close binary evolution. Since selection effects apply to both the regular Algols and reversed Algols in a similar manner, the evolutionary time scale between them would be simply the ratio of the number of confirmed systems of these two types of Algols.     

Evolution into contact of the low-mass close binary systems

We investigated the effect of mass accretion on the secondary components in close binomy systems (M _total ≤ 2.5 M _⊙ M _2,0 ≤ 0.75 M _⊙) exchanging mass in the case A. The evolution of the low-mass close binary systems (M _total ≤ 2.5 M _⊙) exchanging the mass in the case A depends on the three main factors:

-the initial mass ratio (q ₀ = M _2,0/M _1,0), which determines the rate of mass transfer between components;

-the inital mass of the secondary component (M _2,0) and

-the effectiveness of the heating of the photosphere of the secondary component, by infalling matter.

The second factor allows to divide all systems into two essentially different groups:

1. systems in which the secondary component is a star with a radiative envelope, or with a thin convection zone in the uppermost layers;
2. and systems in which secondary component has a thick convective envelope or is fully convective.

The systems from the first group evolve into contact in a characteristic time scale 10⁵ – 10⁷ years, and reach contact after transfering of 0.03 – 0.3 M _⊙. The mass exchange proceeds only in a thermal time scale. For the systems from the group b the effectiveness of the heating of the stellar surface is the most important. In the case when the entropy of the newly accreted matter is the same as the surface entropy of the secondary, a convective star should shrink upon accretion. Then contact binaries are not formed. In the case when the entropy of the infalling matter is greater then that on the surface, the reaction of the secondary is different. The radius of the secondary component grows rapidly in response to accretion, and the systems reaches contact after the 10³ – 3 10⁶ years, and after transfer of 0.002 – 0.2. M _⊙. The reaction of the secondary is determined by the formation of the temperature inversion layer below the stellar surface. Full references in: Sarna, M.J. and Fedorova, A.V. (1988) “Evolutionary status of W UMa-type Binaries — Evolution into contact”, Astron. Astrophys., in press.     

能量包线随机平均法在双线性迟滞系统随机响应分析中的应用

 本文将能量包线随机平均法应用于分析单自由度双线性迟滞系统对白噪声激励的随机响应,详细分析了位移、速度及总能量的平稳响应各统计量随系统粘性阻尼、次斜率及激励强度的变化。解析结果与数字模拟结果比较表明,该方法优于迄今为止用于双线性迟滞系统随机响应分析的其他近似方法。