Evolution of binary stars and the effect of tides on binary populations

We present a rapid binary-evolution algorithm that enables modelling of even the most complex binary systems. In addition to all aspects of single-star evolution, features such as mass transfer, mass accretion, common-envelope evolution, collisions, supernova kicks and angular momentum loss mechanisms are included. In particular, circularization and synchronization of the orbit by tidal interactions are calculated for convective, radiative and degenerate damping mechanisms. We use this algorithm to study the formation and evolution of various binary systems. We also investigate the effect that tidal friction has on the outcome of binary evolution. Using the rapid binary code, we generate a series of large binary populations and evaluate the formation rate of interesting individual species and events. By comparing the results for populations with and without tidal friction, we quantify the hitherto ignored systematic effect of tides and show that modelling of tidal evolution in binary systems is necessary in order to draw accurate conclusions from population synthesis work. Tidal synchronism is important but, because orbits generally circularize before Roche lobe overflow, the outcome of the interactions of systems with the same semilatus rectum is almost independent of eccentricity. It is not necessary to include a distribution of eccentricities in population synthesis of interacting binaries; however, the initial separations should be distributed according to the observed distribution of semilatera recta rather than periods or semimajor axes.     

Close binary system GO Cyg

In this study, we present long term photometric variations of the close binary system GO Cyg. Modelling of the system shows that the primary is filling Roche lobe and the secondary of the system is almost filling its Roche lobe. The physical parameters of the system are M₁ = 3.0 ± 0.2M_⊙, M₂ = 1.3 ± 0.1M_⊙, R₁ = 2.50 ± 0.12R_⊙, R₂ = 1.75 ± 0.09R_⊙, L₁ = 64 ± 9L_⊙, L₂ = 4.9 ± 0.7L_⊙, and a = 5.5 ± 0.3R_⊙. Our results show that GO Cyg is the most massive system near contact binary (NCB). Analysis of times of the minima shows a sinusoidal variation with a period of 92.3 ± 0.5 yr due to a third body whose mass is less than 2.3M_⊙. Finally a period variation rate of −1.4 × 10⁻⁹ d/yr has been determined using all available light curves.     

Magnetic interaction in ultra-compact binary systems

This article reviews the current works on ultra-compact double-degenerate binaries in the presence of magnetic interaction, in particular, unipolar induction. The orbital dynamics and evolution of compact white-dwarf pairs are discussed in detail. Models and predictions of electron cyclotron masers from unipolar-inductor compact binaries and unipolar-inductor white-dwarf planetary systems are presented. Einstein-Laub effects in compact binaries are briefly discussed.     

Galaxy activity in merging binary galaxy clusters

We present the results of a study of galaxy activity in two merging binary clusters (A168 and A1750) using the Sloan Digital Sky Survey (SDSS) data supplemented with the data in the literature. We have investigated the merger histories of A168 and A1750 by combining the results from a two-body dynamical model and X-ray data. In A168, two subclusters appear to have passed each other and to be coming together from the recent maximum separation. In A1750, two major subclusters appear to have started interaction and to be coming together for the first time. We find an enhanced concentration of the galaxies showing star formation (SF) or active galactic nuclei (AGN) activity in the region between two subclusters in A168, which were possibly triggered by the cluster merger. In A1750, we do not find any galaxies with SF/AGN activity in the region between two subclusters, indicating that two major subclusters are in the early stage of merging.     

Microlensing of close binary stars

The gravity due to a multiple-mass system has a remarkable gravitational effect: the extreme magnification of background light sources along extended so-called caustic lines. This property has been the channel for some remarkable astrophysical discoveries over the past decade, including the detection and characterization of extrasolar planets, the routine analysis of limb darkening, and, in one case, limits set on the apparent shape of a star several kiloparsec distant. In this paper, we investigate the properties of the microlensing of close binary star systems. We show that in some cases it is possible to detect flux from the Roche lobes of close binary stars. Such observations could constrain models of close binary stellar systems.     

The double-lined spectroscopic binary HR 6046

HR 6046 has long been known as a single-lined binary system, for which preliminary orbital solutions were given in the 1930s, but the nature of the secondary star in the system has to date appeared puzzling. The rather large masses which the component stars were once believed to possess caused much speculation that the secondary was a 'collapsed star', and the large mass function that was originally published encouraged determined, but unsuccessful, efforts to be made to resolve the system by optical interferometry. We have observed the system as a double-lined binary, and now present the orbit. We are unable to specify the exact nature of the secondary star, whose mass is only slightly less than that of the primary, but comparison with late-type standard spectra suggests that it is an evolved star, while the primary is a giant somewhat cooler than the published spectral type indicates. The Hipparcos parallax is consistent with such a model for the system, but it is possible that it is vitiated by the photocentric motion. Our new orbital elements and their improved level of precision show conclusively that the system is by no means as exotic as was once thought.     

An electrically powered binary star?

We propose a model for stellar binary systems consisting of a magnetic and a non-magnetic white dwarf pair which is powered principally by electrical energy. In our model the luminosity is caused by resistive heating of the stellar atmospheres arising from induced currents driven within the binary. This process is reminiscent of the Jupiter–Io system, but greatly increased in power because of the larger companion and stronger magnetic field of the primary. Electrical power is an alternative stellar luminosity source, following on from nuclear fusion and accretion. We find that this source of heating is sufficient to account for the observed X-ray luminosity of the 9.5-min binary RX J1914+24, and provides an explanation for its puzzling characteristics.     

The massive double-lined O-type binary HD 165052

We present a new optical spectroscopic study of the O-type binary HD 165052 based on high- and intermediate-resolution CCD observations. We re-investigated the spectral classification of the binary components, obtaining spectral types of O6.5 V and O7.5 V for the primary and secondary, respectively, finding that both stars display weak C  iii λ 5696 emission in their spectra. We also determined a radial-velocity orbit for HD 165052 with a period of  2.95510±0.00001 d  , and semi-amplitudes of 94.8 and  104.7±0.5 km s^-1  , resulting in a mass ratio   Q =0.9  . From a comparison with previous radial-velocity determinations, we found evidence of apsidal motion in the system. Several signatures of wind–wind collision, such as phase-locked variability of the X-ray flux and the Struve–Sahade effect, are also considered. It was also found that the reddening in the region should be normal, in contrast with previous determinations.     

Galactic X-ray binary jets

With their relatively fast variability time-scales, Galactic X-ray binaries provide an excellent laboratory to explore the physics of accretion and related phenomena, most notably outflows, over different regimes. After comparing the phenomenology of jets in black hole systems to that of neutron stars, here I discuss the role of the jet at very low Eddington ratios, and present preliminary results obtained by fitting the broadband spectral energy distribution of a quiescent black hole binary with a ‘maximally jet-dominated’ model. Chandra Fellow     

Mass transfer in eccentric binary stars

The concept of Roche lobe overflow is fundamental to the theory of interacting binaries. Based on potential theory, it is dependent on all the relevant material corotating in a single frame of reference. Therefore if the mass losing star is asynchronous with the orbital motion or the orbit is eccentric, the simple theory no longer applies and no exact analytical treatment has been found. We use an analytic approximation whose predictions are largely justified by smoothed particle hydrodynamic simulations (SPH). We present SPH simulations of binary systems with the same semi-major axis   a = 5.55 R_⊙  , masses   M ₁= 1 M_⊙, M ₂= 2 M_⊙  and radius   R ₁= 0.89 R_⊙  for the primary star but with different eccentricities   e = 0.4, 0.5, 0.6  and 0.7. In each case the secondary star is treated as a point mass. When   e = 0.4  no mass is lost from the primary while at   e = 0.7  catastrophic mass transfer, partly through the L₂ point, takes place near periastron. This would probably lead to common-envelope evolution if star 1 were a giant or to coalescence for a main-sequence star. In between, at   e ≥ 0.5  , some mass is lost through the L₁ point from the primary close to periastron. However, rather than being all accreted by the secondary, some of the stream appears to leave the system. Our results indicate that the radius of the Roche lobe is similar to circular binaries when calculated for the separation and angular velocity at periastron. Part of the mass loss occurs through the L₂ point.     

On rejuvenation in massive binary systems

We introduce a set of stellar models for massive stars whose evolution has been affected by mass transfer in a binary system, at a range of metallicities. As noted by other authors, the effect of such mass transfer is frequently more than just rejuvenation. We find that, whilst stars with convective cores which have accreted only H-rich matter rejuvenate as expected, those stars which have accreted He-rich matter (e.g. at the end stages of conservative mass transfer) evolve in a way that is qualitatively similar to rejuvenated stars of much higher metallicity. Thus, the effects of non-conservative evolution depend strongly on whether He-rich matter is amongst the portion accreted or ejected. This may lead to a significant divergence in binary evolution paths with only a small difference in initial assumptions. We compare our models to observed systems and find approximate formulae for the effect of mass accretion on the effective age and metallicity of the resulting star.     

Parametrization of single and binary stars

Stellar masses and ages are not directly observable parameters, and the methods used to determine them are based on the calibrating relations. In particular, the mass–luminosity relation, based on the masses of less than 200 well-studied binaries, is virtually the only way to estimate the mass of single stars. Thus, the development of methods for estimating stellar masses with accuracy comparable to direct methods is a problem of vital importance.
Here, we describe a method for estimating stellar masses and ages, which is based on the geometric similarity of evolutionary tracks for the stars at the same evolutionary stage in the Hertzsprung–Russell (HR) diagram. To examine the proposed approach, it has been applied to various test data sets. Application of the method, using synthetic stellar spectra Basel Stellar Library (of theoretical spectra; BaSeL), demonstrates that it allows determination of masses and ages of stars with a predictable distribution of uncertainties.
This statistical approach allows us to demonstrate the viability of the method using it on the set of double-lined eclipsing binaries with intermediate-mass and low-mass components which allows us to compare calculated characteristics with observational ones. As a result, the uncertainties of the stellar masses estimated with the proposed method are comparable with the accuracy of ones obtained from direct observations. This allows us to recommend the method for mass estimates of masses of single stars by the localization in the HR diagram.
As for the ages, the estimates for intermediate-mass stars are more reliable, while those obtained for low-mass stars are very uncertain, due both to slower movement of these stars in the HR diagram with age at stages close to the main sequence and to certain disagreements between theoretical models for this mass range.     

Evolution of massive binary black holes

Since many or most galaxies have central massive black holes (BHs), mergers of galaxies can form massive binary black holes (BBHs). In this paper we study the evolution of massive BBHs in realistic galaxy models, using a generalization of techniques used to study tidal disruption rates around massive BHs. The evolution of BBHs depends on BH mass ratio and host galaxy type. BBHs with very low mass ratios (say, ≲0.001) are hardly ever formed by mergers of galaxies, because the dynamical friction time-scale is too long for the smaller BH to sink into the galactic centre within a Hubble time. BBHs with moderate mass ratios are most likely to form and survive in spherical or nearly spherical galaxies and in high-luminosity or high-dispersion galaxies; they are most likely to have merged in low-dispersion galaxies (line-of-sight velocity dispersion ≲90 km s⁻¹) or in highly flattened or triaxial galaxies.
The semimajor axes and orbital periods of surviving BBHs are generally in the range  10^-3–10 pc  and  10–10⁵ yr;  they are also larger in high-dispersion galaxies than in low-dispersion galaxies, larger in nearly spherical galaxies than in highly flattened or triaxial galaxies, and larger for BBHs with equal masses than for BBHs with unequal masses. The orbital velocities of surviving BBHs are generally in the range  10²–10⁴ km s^-1  . The methods of detecting surviving BBHs are also discussed.
If no evidence of BBHs is found in AGNs, this may be either because gas plays a major role in BBH orbital decay or because nuclear activity switches on soon after a galaxy merger, and ends before the smaller BH has had time to spiral to the centre of the galaxy.     

SS Ari: a shallow-contact close binary system

Two CCD epochs of light minimum and a complete R light curve of SS Ari are presented. The light curve obtained in 2007 was analyzed with the 2003 version of the W-D code. It is shown that SS Ari is a shallow contact binary system with a mass ratio q=3.25 and a degree of contact factor f=9.4%(±0.8%). A period investigation based on all available data shows that there may exist two distinct solutions about the assumed third body. One, assuming eccentric orbit of the third body and constant orbital period of the eclipsing pair, results in a massive third body with M ₃=1.73M _⊙ and P ₃=87.0 yr. On the contrary, assuming continuous period changes of the eclipsing pair the orbital period of tertiary is 37.75 yr and its mass is about 0.278M _⊙. Both of the cases suggest the presence of an unseen third component in the system.     

The close binary system SU Ind

Photometric data on the southern mid‐F type close eclipsing binary system SU Ind from the Carter Observatory (NZ) were examined, together with a light curve obtained from the Hipparcos Epoch Photometry (HEP) database. The system appears detached, although appreciably evolved from the Zero Age Main Sequence. The HEP period must be accurate for its own epoch, but it is significantly different from the reference (Hoffmeister 1956) value. This is difficult to explain, given the uncomplicated nature of the light curve. The apparent discrepancy can be reconciled with a period that has remained almost constant over the 40 year interval between the epochs by assuming some confusion between the almost equal depth minima. The near‐equality of components raises issues of determinacy in light curve analysis, which are reviewed against the presentation of relevant numerical curve‐fitting details. The system is of physical interest, in that it is close to the start of the ‘active’ range of spectral types. Its stars have relatively rapid rotation speeds and probably shallow convective subphotospheric layers. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Irradiation pressure effects in close binary systems

We test an analytic model for the two-point correlations of galaxy clusters in redshift space using the Hubble volume N -body simulations. The correlation function of clusters shows no enhancement along the line of sight, owing to the lack of any virialized structures in the cluster distribution. However, the distortion of the clustering pattern arising from coherent bulk motions is clearly visible. The distribution of cluster peculiar motions is well described by a Gaussian, except in the extreme high-velocity tails. The simulations produce a small but significant number of clusters with large peculiar motions. The form of the redshift-space power spectrum is strongly influenced by errors in measured cluster redshifts in extant surveys. When these errors are taken into account, the model reproduces the power spectrum recovered from the simulation to an accuracy of 15 per cent or better over a decade in wavenumber. We compare our analytic predictions with the power spectrum measured from the APM cluster redshift survey. The cluster power spectrum constrains the amplitude of density fluctuations, as measured by the linear rms variance in spheres of radius 8  h ⁻¹ Mpc, denoted by σ ₈. When combined with the constraints on σ ₈ and the density parameter Ω derived from the local abundance of clusters, we find a best-fitting cold dark matter model with     and     , for a power spectrum shape that matches that measured for galaxies. However, for the best-fitting value of Ω and given the value of Hubble's constant from recent measurements, the assumed shape of the power spectrum is incompatible with the most readily motivated predictions from the cold dark matter paradigm.     

Modelling the binary progenitor of Supernova 1993J

We have developed a detailed stellar evolution code capable of following the simultaneous evolution of both stars in a binary system, together with their orbital properties. To demonstrate the capabilities of the code, we investigate potential progenitors for the Type IIb Supernova 1993J, which is believed to have been an interacting binary system prior to its primary exploding. We use our detailed binary stellar evolution code to model this system to determine the possible range of primary and secondary masses that could have produced the observed characteristics of this system, with particular reference to the secondary. Using the luminosities and temperatures for both stars (as determined by Maund et al.) and the remaining mass of the hydrogen envelope of the primary at the time of explosion, we find that if mass transfer is 100 per cent efficient, the observations can be reproduced by a system consisting of a  15 M_⊙  primary and a  14 M_⊙  secondary in an orbit with an initial period of 2100 days. With a mass transfer efficiency of 50 per cent, a more massive system consisting of a  17 M_⊙  primary and a  16 M_⊙  secondary in an initial orbit of 2360 days is needed. We also investigate some of the uncertainties in the evolution, including the effects of tidal interaction, convective overshooting and thermohaline mixing.