Internal stellar rotation and orbital period modulation in close binary systems

The orbital period modulation, observed in close binary systems with late-type secondary stars, is considered in the framework of a general model that allows us to test the hypothesis proposed by Applegate. It relates the orbital period variation to the modulation of the gravitational quadrupole moment of their magnetically active secondary stars produced by angular momentum exchanges within their convective envelopes. By considering the case of RS CVn binary systems, it is found that the surface angular velocity variation of the secondary component required by Applegate's hypothesis is between 4 and 12 per cent, i.e. too large to be compatible with the observations and that the kinetic energy dissipated in its convection zone ranges from 4 to 43 times that supplied by the stellar luminosity along one cycle of the orbital period modulation. Similar results are obtained for other classes of close binary systems by applying a scaling relationship based on a simplified internal structure model. The effect of rapid rotation is briefly discussed finding that it is unlikely that the rotational quenching of the turbulent viscosity may solve the discrepancy. Therefore, the hypothesis proposed by Applegate is not adequate to explain the orbital period modulation of close binary systems with a late-type secondary.     

Evolutionary Processes in Low-Mass Binary Systems

We consider the evolution of certain low-mass binaries, incorporating models of (a) internal evolution, (b) tidal friction, (c) dynamo activity driven by an elementary α,Ω dynamo, (d) stellar wind driven by the activity, and (e) magnetic braking as a consequence of wind and poloidal dynamo-generated magnetic field. In some circumstances the stellar wind is found to remove mass on a nuclear timescale, as is necessary to explain some observed systems. We can hope that various uncertainties in the model may be clarified by a careful comparison of the models with such observed quantities as rotation periods. These are modified by processes (a), (b) and (e). Assuming that stellar evolution is slow, rotation rate should in some circumstances represent a balance between magnetic braking trying to slow the star down and tidal friction trying to spin it up. Preliminary attempts are promising, but indicate that some fine tuning is necessary. When there is a third body present, in an orbit which is inclined but not necessarily of short period, the eccentricity of a close binary can be strongly modified by ‘Kozai cycles’. We show that this may complicate attempts to account for spin rates of stars in close binaries.     

Magnetic activity and evolution of Algol-type stars – II

We examine the possibility of probing dynamo action in mass-losing stars, components of Algol-type binaries. Our analysis is based on the calculation of non-conservative evolution of these systems. We model the systems U Sge and β Per where the more massive companion fills its Roche lobe at the main sequence (case AB) and where it has a small helium core (early case B) respectively. We show that to maintain evolution of these systems at the late stages which are presumably driven by stellar 'magnetic braking', an efficient mechanism for producing large-scale surface magnetic fields in the donor star is needed. We discuss the relevance of dynamo operation in the donor star to the accelerated mass transfer during the late stages of evolution of Algol-type binaries. We suggest that the observed X-ray activity in Algol-type systems may be a good indicator of their evolutionary status and internal structure of the mass-losing stellar components.     

Stability of magnetic flux tubes in close binary stars

Photometric and Doppler imaging observations of active binaries indicate the existence of starspots at preferred longitudes (position angles with respect to the companion star). We investigate the stability of magnetic flux tubes in the convection zone of close, fast‐rotating binary stars and explore whether the observed preferred longitudes could be caused by tidal forces and the deformation of the active star. We assume a synchronized binary system with spin axes perpendicular to the orbital plane and a rotation period of a few days. The tidal force and the deviation from spherical structure are considered in lowest‐order perturbation theory. The magnetic field is in the form of toroidal magnetic flux rings, which are stored in mechanical equilibrium within the stably stratified overshoot region beneath the convection zone until the field has grown sufficiently strong for the undulatory instability to initiate the formation of rising loops. Frequencies and geometry of stable as well as growth rates of unstable eigenmodes are determined by linear stability analysis. Particular consideration is given to the question whether the effects of tidal forces and perturbations of the stellar structure can force a rising flux loop to enter the convection zone at specific longitudes.     

ROSAT observations of V471 Tauri, showing that stellar activity is determined by rotation, not age

I present pointed ROSAT PSPC observations of the pre-cataclysmic binary V471 Tauri. The hard X-ray emission (>0.4 keV) is not eclipsed by the K star, demonstrating conclusively that this component cannot be emitted by the white dwarf. Instead I show that its spectrum and luminosity are consistent with coronal emission from the tidally spun-up K star. The star is more active than other K stars in the Hyades, but equally active as K stars in the Pleiades with the same rotation periods, demonstrating that rotation — and not age — is the key parameter in determining the level of stellar activity.   The soft X-ray emission (<0.4 keV) is emitted predominately by the white dwarf and is modulated on its spin period. I find that the pulse profile is stable on time-scales of hours and years, supporting the idea that it is caused by the opacity of accreted material. The profile itself shows that the magnetic field configuration of the white dwarf is dipolar and that the magnetic axis passes through the centre of the star.   There is an absorption feature in the light curve of the white dwarf, which occurs at a time when our line of sight passes within a stellar radius of the K star. The column density and duration of this feature imply a volume and mass for the absorber that are similar to those of coronal mass ejections of the Sun.   Finally I suggest that the spin–orbit beat period detected in the optical by Clemens et al. may be the result of the interaction of the K-star wind with the magnetic field of the white dwarf.     

Spot signatures of a solar‐type dynamo in close binary stars

Magnetic activity signatures in the atmosphere of active stars can be used to place constrains on the underlying processes of flux transport and dynamo operation in its convective envelope. The ‘solar paradigm’ for magnetic activity suggests that the magnetic field is amplified and stored at the base of the convection zone. Once a critical field strength is exceeded, perturbations initiate the onset of instabilities and the growth of magnetic flux loops, which rise through the convection zone, emerge at the stellar surface, and eventually lead to the formation of starspots and active regions. In close binaries, the proximity of the companion star breaks the rotational symmetry. Although the magnitude of tidal distortions is rather small, non‐linear MHD simulations have nevertheless shown in the case of main‐sequence binary components that they can cause non‐uniform surface distributions of flux tube eruptions. The present work extends the investigation to post‐mainsequence components to explore the specific influence of the stellar structure on the surface pattern of erupting flux tubes. In contrast to the case of main‐sequence components, where the consistency between simulation results and observations supports the presumption of a solar‐like dynamo mechanism, the numerical results here do not recover the starspot properties frequently observed on evolved binary components. This aspect points out an insufficiency of the applied flux tube model and leads to the conclusion that additional flux transport and possibly amplification mechanisms have to be taken into account. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Massive stars

We describe the present state of massive star research seen from the viewpoint of stellar evolution, with special emphasis on close binaries. Statistics of massive close binaries are reasonably complete for the Solar neighbourhood. We defend the thesis that within our knowledge, many scientific results where the effects of binaries are not included, have an academic value, but may be far from reality. In chapter I, we summarize general observations of massive stars where we focus on the HR diagram, stellar wind mass loss rates, the stellar surface chemistry, rotation, circumstellar environments, supernovae. Close binaries can not be studied separately from single stars and vice versa. First, the evolution of single stars is discussed (chapter I). We refer to new calculations with updated stellar wind mass loss rate formalisms and conclusions are proposed resulting from a comparison with representative observations. Massive binaries are considered in chapter II. Basic processes are briefly described, i.e. the Roche lobe overflow and mass transfer, the common envelope process, the spiral-in process in binaries with extreme mass ratio, the effects of mass accretion and the merging process, the implications of the (asymmetric) supernova explosion of one of the components on the orbital parameters of the binary. Evolutionary computations of interacting close binaries are discussed and general conclusions are drawn. The enormous amount of observational data of massive binaries is summarized. We separately consider the non-evolved and evolved systems. The latter class includes the semi-detached and contact binaries, the WR binaries, the X-ray binaries, the runaways, the single and binary pulsars. A general comparison between theoretical evolution and observations is combined with a discussion of specially interesting binaries: the evolved binaries HD 163181, HD 12323, HD 14633, HD 193516, HD 25638, HD 209481, Per and Sgr; the WR+OB binary V444 Cyg; the high mass X-ray binaries Vela X-1, Wray 977, Cyg X-1; the low mass X-ray binaries Her X-1 and those with a black hole candidate; the runaway Pup, the WR+compact companion candidates Cyg X-3, HD 50896 and HD 197406. We finally propose an overall evolutionary model of massive close binaries as a function of primary mass, mass ratio and orbital period. Chapter III deals with massive star population synthesis with a realistic population of binaries. We discuss the massive close binary frequency, mass ratio and period distribution, the observations that allow to constrain possible asymmetries during the supernova explosion of a massive star. We focuss on the comparison between observed star numbers (as a function of metallicity) and theoretically predicted numbers of stellar populations in regions of continuous star formation and in starburst regions. Special attention is given to the O-type star/WR star/red supergiant star population, the pulsar and binary pulsar population, the supernova rates. Received 17 July 1998     

On the rotation–activity correlation for active binary stars

We present an investigation of rotation–activity correlations using International Ultraviolet Explorer ( IUE ) SWP measurements of the C  iv emission line at 1550Å for 72 active binary systems. We use a standard stellar evolution code to derive non-empirical Rossby numbers, R ₀, for each star in our sample and compare the resulting C  iv rotation–activity correlation to that found for empirically derived values of the Rossby number and that based on rotation alone. For dwarf stars our values of R ₀ do not differ greatly from empirical ones and we find a corresponding lack of improvement in correlation. Only a marginal improvement in correlation is found for evolved components in our sample. We discuss possible additional factors, other than rotation or convection, that may influence the activity levels in active binaries. Our observational data imply, in contrast to the theoretical predictions of convective motions, that activity is only weakly related to mass in evolved stars. We conclude that current dynamo theory is limited in its application to the study of active stars because of the uncertainty in the angular velocity-depth profile in stellar interiors and the unknown effects of binarity and surface gravity.     

Orbital period changes of contact binary systems: direct evidence for thermal relaxation oscillation theory

Orbital period changes of ten contact binary systems (S Ant, ε CrA, EF Dra, UZ Leo, XZ Leo, TY Men, V566 Oph, TY Pup, RZ Tau and AG Vir) are studied based on the analysis of their     curves. It is discovered that the periods of the six systems, S Ant, ε CrA, EF Dra, XZ Leo, TY Men and TY Pup, show secular increases. For UZ Leo, its secular period increase rate is revised. For the three systems, V566 Oph, RZ Tau and AG Vir, weak evidence is presented that a periodic oscillation (with periods of 20.4, 28.5 and 40.9 yr respectively) is superimposed on a secular period increase. The cyclic period changes can be explained by the presence of an unseen third body in the three systems. All the sample stars studied are contact binaries with     .
Furthermore, orbital period changes of 27 hot contact binaries have been checked. It is found that, apart from AW UMa with the lowest mass ratio     , none shows an orbital period decrease. The relatively weak magnetic activity in the hotter contact binaries means little angular momentum loss (AML) from the systems via magnetic stellar winds. The period increases of these W UMa binaries can be explained by mass transfer from the secondary to the primary components, which is in agreement with the prediction of the thermal relaxation oscillation (TRO) models. This suggests that the evolution of a hotter W UMa star is mainly controlled by TRO. On the other hand, for a cooler W UMa star     , its evolution may be TRO plus AML, which coincides with the recent results of Qian.     

Differential rotation on both components of the pre-main-sequence binary system HD 155555

We present the first measurements of surface differential rotation on a pre-main-sequence binary system. Using intensity (Stokes I) and circularly polarized (Stokes V) time-series spectra, taken over 11 nights at the Anglo-Australian Telescope (AAT), we incorporate a solar-like differential rotation law into the surface imaging process. We find that both components of the young, 18 Myr, HD 155555 (V824 Ara, G5IV + K0IV) binary system show significant differential rotation. The equator–pole lap times as determined from the intensity spectra are 80 d for the primary star and 163 d for the secondary. Similarly, for the magnetic spectra we obtain equator–pole lap times of 44 and 71 d, respectively, showing that the shearing time-scale of magnetic regions is approximately half of that found for stellar spots. Both components are therefore found to have rates of differential rotation similar to those of the same spectral-type main-sequence single stars. The results for HD 155555 are therefore in contrast to those found in other, more evolved, binary systems where negligible or weak differential rotation has been discovered. We discuss two possible explanations for this: first that at the age of HD 155555 binary tidal forces have not yet had time to suppress differential rotation and secondly that the weak differential rotation previously observed on evolved binaries is a consequence of their large convection zone depths. We suggest that the latter is the more likely solution and show that both temperature and convection zone depth (from evolutionary models) are good predictors of differential rotation strength. Finally, we also examine the possible consequences of the measured differential rotation on the interaction of binary star coronae.     

Activity cycle of the giant star of Z Andromedae and its spin period

We have re-analysed the long-term optical light curve (LC) of the symbiotic star Z Andromedae, covering 112 yr of mostly visual observations. Two strictly periodic cycles and one quasi-periodic cycle can be identified in this LC. A   P 1 = 7550  d quasi-periodicity characterizes the repetition time of the outburst episodes of this symbiotic star. Six such events have been recorded so far. During quiescence states of the system, that is, in time-intervals between outbursts, the LC is clearly modulated by a stable coherent period of   P 2 = 759.1  d. This is the well-known orbital period of the Z Andromedae binary system that has been measured also spectroscopically. A third coherent period of   P 3 = 658.4  d is modulating the intense fluctuations in the optical brightness of the system during outbursts. We attribute the trigger of the outburst phenomenon and the clock that drives it, to a solar-type magnetic dynamo cycle that operates in the convection and the outer layers of the giant star of the system. We suggest that the intense surface activity of the giant star during maximum phases of its magnetic cycle is especially enhanced in one or two antipode regions, fixed in the atmosphere of the star and rotating with it. Such spots could be active regions around the North Pole and the South Pole of a general magnetic dipole field of the star. The P3 periodicity is half the beat of the binary orbital period of the system and the spin period of the giant. The latter is then either 482 or 1790 d. If only one pole is active on the surface of the giant, P3 is the beat period itself, and the spin period is 352 d. It could also be 5000 d if the giant is rotating in a retrograde direction. We briefly compare these findings in the LC of Z Andromedae to similar modulations that were identified in the LC of two other prototype symbiotics, BF Cyg and YY Her.     

Magnetic activity and dynamics of close binaries

The connection between orbital period modulation and magnetic activity in close binaries is reviewed with an emphasis on the comparison between observational data for RS CVn systems and recently proposed theoretical models. The orbital period changes occurring on timescales of the order of a few decades can be accounted for by means of a standing torsional Alfven wave in the convection zone of the magnetically active components of such systems. Two resonant excitation mechanisms based on the coupling between the wave and an αΩ dynamo are discussed from a qualitative point of view. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optical, X-ray and radio observations of HD 61396: a probable new RS CVn-type binary

We have carried out BVR photometric and H spectroscopic observations of the star HD 61396 during 1998 March 20 to 1999 April 3. We have discovered regular optical photometric variability from this star, with an inferred period of 31.95±0.10 d, and an amplitude of 0.18 mag. A possible period of 35.34±0.12 d, as determined with Hipparcos , cannot be completely ruled out, however. Modelling of its photometric light curve with two circular spots indicates that 521 per cent of the stellar surface is covered by dark starspots which are 830 K cooler than the surrounding photosphere, and produce the observed rotational modulation of the optical flux. Optical spectroscopy reveals a variable H emission feature, indicating that it is an unusually active star.
In addition, we have analysed archival X-ray data of HD 61396, obtained from serendipitous observations with the ROSAT X-ray observatory, and we also discuss the radio properties of this star, based on both published Green Bank and unpublished VLA observations. The strong photometric variability and H emission, the relatively hard X-ray spectrum, and the high X-ray and radio luminosities imply that HD 61396 is most likely to be a member of the RS CVn class of evolved active binary stars. Its X-ray and radio luminosities place it among the five most luminous active binaries detected so far.     

Progenitors with enhanced rotation and the origin of magnetars

Among the dozen known magnetar candidates, there are no binary objects. Given that the fraction of binary neutron stars is estimated to be about 3–10 per cent, it is reasonable to address the question of solitarity of magnetars, to estimate theoretically the fraction of binary objects among them, and to identify the most probable companions. We present population synthesis calculations of massive binary systems. In this study, we adopt the hypothesis that magnetic field of a magnetar is generated at the protoneutron star stage due to a dynamo mechanism, so rapid rotation of the core of a progenitor star is essential. Our goal is to estimate the number of neutron stars originated from progenitors with enhanced rotation. In our calculations, the fraction of neutron stars originating from such progenitors is about 8–9 per cent. This should be considered as an upper limit to the fraction of magnetars, as some of the progenitors can lose momentum. Most of these objects are isolated due to coalescences of components prior to neutron star formation, or due to system disruption after the second supernova explosion. The fraction of such neutron stars in surviving binaries is about 1 per cent or lower. Their most numerous companions are black holes.     

大质量双星系统的非守恒演化

由于大质量双星系统有强大的星风物质损失,因而在研究其结构和演化时必须考虑星风物质损失,动量损失,物质交换以及由以上原因引起的轨道参量的变化,此外,天文观测又证实,一些大质量双星系统中存在星风冲击波,有Ｘ射线辐射以及有致密天体（白矮星,中子星）的存在,因此在研究大质量双星的演化时,又会遇到在星风冲击波理论及其对演化的影响,双星系统何时会演化成为公共外壳的系统,以及双星系统中如果发生超新星爆发,是否会     

On the time dependence of differential rotation in young late-type stars

A model for the angular momentum transfer within the convection zone of a rapidly rotating star is introduced and applied to the analysis of recent observations of temporal fluctuations of the differential rotation on the young late-type stars AB Doradus (AB Dor) and LQ Hydrae (LQ Hya). Under the hypothesis that the mean magnetic field produced by the stellar dynamo rules the angular momentum exchanges and that the angular velocity depends only on the distance s from the rotation axis and the time, the minimum azimuthal Maxwell stress  | B_sB _φ|  , averaged over the convection zone, is found to range from ∼0.04 to  ∼0.14 T²  . If the poloidal mean magnetic field   B _s   is of the order of 0.01 T, as indicated by the Zeeman–Doppler imaging maps of those stars, then the azimuthal mean field   B _φ  can reach an intensity of several teslas, which significantly exceeds equipartition with the turbulent kinetic energy. Such strong fields can account also for the orbital period modulation observed in cataclysmic variables and RS Canum Venaticorum systems with a main-sequence secondary component. Moreover, the model allows us to compute the kinetic energy dissipation rate during the maintenance of the differential rotation. Only in the case of the largest surface shear observed on LQ Hya may the dissipated power exceed the stellar luminosity, but the lack of a sufficient statistic on the occurrence of such episodes of large shear does not allow us to estimate their impact on the energy budget of the convection zone.     

X-ray binaries

Summary The various types and classes of X-ray binary are reviewed high-lighting recent results. The high mass X-ray binaries (HMXRBs) can be used to probe the nature of the mass loss from the OB star in these systems. Absorption measurements through one orbital cycle of the supergiant system X1700-37 are well modelled by a radiation driven wind and also require a gas stream trailing behind the X-ray source. In Cen X-3 the gas stream is accreted by the X-ray source via an accretion disk. Changes in the gas stream can cause the disk to thicken and the disk to obscure the X-ray source. How close the supergiant is to corotation seems to be as much a critical factor in these systems as how close it is to filling its Roche lobe. In the Be star X-ray binaries a strong correlation between the neutron stars rotation period and its orbital period has been explained as due to the neutron star being immersed in a dense, slow moving equatorial wind from the Be star. For the X-ray pulsars in the transient Be X-ray binaries a centrifugal barrier to accretion is important in determining the X-ray lightcurve and the spin evolution. The X-ray orbital modulations from the low mass X-ray binaries, LMXRBs, include eclipses by the companion and/or periodic dipping behaviour from structure at the edge of the disk. The corresponding optical modulations show a smooth sinusoidal like component and in some cases a sharp eclipse by the companion. The orbital period of the LMXRB XB1916-05 is 1% longer in the optical compared to that given by the X-ray dip period. The optical period has been interpreted as the orbital period, but this seems inconsistent with the well established view of the origin of the X-ray modulations in LMXRB. A new model is presented that assumes the X-ray dip period is the true orbital period. The 5.2 h eclipsing LMXRB XB2129+47 recently entered a low state and optical observations unexpectedly reveal an F star which is too big to fit into the binary. This is probably the first direct evidence that an X-ray binary is part of a hierarchical triple. Finally the class of X-ray binaries containing black hole candidates is reviewed focusing on the value of using X-ray signatures to identify new candidates.     

Imaging the cool stars in the interacting binaries AE Aqr,BV Cen and V426 Oph

It is well known that magnetic activity in late‐type stars increases with increasing rotation rate. Using inversion techniques akin to medical imaging, the rotationally broadened profiles from such stars can be used to reconstruct ‘Doppler images’ of the distribution of cool, dark starspots on their stellar surfaces. Interacting binaries, however, contain some of the most rapidly rotating late‐type stars known and thus provide important tests of stellar dynamo models. Furthermore, magnetic activity is thought to play a key role in their evolution, behaviour and accretion dynamics. Despite this, we know comparatively little about the magnetic activity and its influence on such binaries. In this review we summarise the concepts behind indirect imaging of these systems, and present movies of the starspot distributions on the cool stars in some interacting binaries. We conclude with a look at the future opportunities that such studies may provide. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Cataclysmic variable evolution: AM Her binaries and the period gap

AM Her variables – synchronized magnetic cataclysmic variables (CVs) – exhibit a different period distribution from other CVs across the period gap. We show that non-AM Her systems may infiltrate the longer-period end of the period gap if they are metal-deficient, but that the position and width of the gap in orbital period are otherwise insensitive to other binary parameters (except for the normalization of the braking rate). In AM Her binaries, magnetic braking is reduced as the wind from the secondary star may be trapped within the magnetosphere of the white dwarf primary. This reduced braking fills the period gap from its short-period end as the dipole magnetic moment of the white dwarf increases. The consistency of these models with the observed distribution of CVs, of both AM Her and non-AM Her type, provides compelling evidence supporting magnetic braking as the agent of angular momentum loss among long-period CVs, and its disruption as the explanation of the  2–3 h  period gap among non-magnetic CVs.     

The southern active-chromosphere star HD 6628

The star HD 6628, heretofore classified as a G5 subgiant, is shown to be a chromospherically active single-lined spectroscopic binary with a period of 27.332±0.008 d. From high-resolution spectra, the system is found to consist of a late F-type dwarf and an active G8–K1 bright subgiant, the latter having a rotation period of not more than 14.8±3.8 d derived from the width of metal lines. Further stellar and orbital parameters are derived and presented.