Orbital period modulation and magnetic cycles in close binaries

We discuss the observed orbital period modulations in close binaries, and focus on the mechanism proposed by Applegate relating the changes of the stellar internal rotation associated with a magnetic activity cycle with the variation of the gravitational quadrupole moment of the active component; the variation of this quadrupole moment in turn forces the orbital motion of the binary stars to follow the activity level of the active star. We generalize this approach by considering the details of this interaction, and develop some illustrative examples in which the problem can be easily solved in analytical form. Starting from such results, we consider the interplay between rotation and magnetic field generation in the framework of different types of dynamo models, which have been proposed to explain solar and stellar activity. We show how the observed orbital period modulation in active binaries may provide new constraints for discriminating between such models. In particular, we study the case of the prototype active binary RS Canum Venaticorum, and suggest that torsional oscillations — driven by a stellar magnetic dynamo — may account for the observed behaviour of this star. Further possible applications of the relationship between magnetic activity and orbital period modulation, related to the recent discovery of binary systems containing a radio pulsar and a convecting upper main-sequence or a late-type low-mass companion, are discussed.     

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.     

Observations of active-chromosphere stars – V. A photometric study of the RS CVn system CF Tuc (HD 5303)

The Wilson–Devinney program is used to model 27 light curves (our own and others) for CF Tuc. We find new parameters for the binary system, and estimate the longitudes and radii of the spots on the cooler secondary star. We also find a strong tendency for spots on the cooler star to appear in a limited range of longitudes, rather than to migrate fairly rapidly as for other RS CVn systems. There is evidence that the mean light level of the cooler star is varying cyclically.
The orbital period clearly changes discontinuously. We discuss this, and the apparently cyclic variations in mean light level, in relation to the model proposed by Applegate.     

Cyclic variations of the period and luminosity of SV Camelopardalis

New standardized V ‐band light curves (LCs) for the eclipsing binary SV Cam have been modeled using the PHOEBE program (v. 0.31a). Absolute parameters of the stellar components were then determined, enabling them to be positioned on the mass‐radius diagram. Analysis of eclipse minima timing data (O – C diagrams) indicated two cyclic periods of 48.0 and 23.3 yr. These cyclic variations of the orbital period are interpreted in terms of motion of a third body around the system and magnetic activity cycle modulating the orbital period of SV Cam via the Applegate (1992) mechanism. The use of the Applegate model for SV Cam has been checked by examining the long term brightness variation and calculating some important parameters of this system. The results of these calculations favor the modulation of the orbital period by the Applegate mechanism. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Composite spectra Paper 15: HD 216572, a triple system containing a short-period, double-lined secondary

We analyse 81 optical spectra of the composite-spectrum binary HD 216572, and show that the primary is a cool giant of type G8 III while the secondary is a double-lined binary consisting of two nearly identical B9 dwarfs in a 1.18-d orbit. The inner system undergoes partial eclipses, whose photometry we model to derive the physical parameters of both secondary stars. The outer system does not eclipse. We isolate the combined spectrum of the secondary by spectral subtraction, and from 48 separate radial-velocity measurements of both secondary components we obtain a triple-lined orbit solution from which we determine the individual masses of all three stars and the inclinations of both the inner and the outer orbits. The period of the outer system is 55 d, which is surprisingly short for a giant star, and our detection of small but non-negligible amounts of variable chromospheric emission in the Ca  ii K line is not unlike that detected in other systems with comparably short periods. The secondary components are in a circular orbit and are rotating at about  95 ± 10 km s⁻¹  ; although their surface-to-surface separation is only  4 R_⊙  the stars are not noticeably distorted geometrically by such close proximity. All three stars appear to be in synchronous rotation in their respective orbits. We derive fairly accurate Hertzsprung–Russell diagram positions for all three stars and compare them to evolutionary tracks calculated for the respective stellar masses, but cannot reconcile the age of the cool giant with that of the B stars.     

The Algol-type eclipsing binaries RW CrB and VZ Leo: new RI photometric study and search for pulsations

In this study we present the new R and I light curve solutions for the eclipsing binary systems RW CrB and VZ Leo, which for VZ Leo is the first one in the literature. Our new observations have been analyzed using the Wilson-Devinney code from which new geometric and photometric elements are derived. The geometry of both stars is that of a semi-detached binary system where the secondary component fills its Roche lobe while the primary component is well inside. In the case of RW CrB, asymmetry in the light curve was explained by a spot model. The orbital period changes of both systems were studied and the results indicated a period decrease which can be explained by angular momentum loss. We also investigated the possibility of pulsations of the primary components since these systems are mentioned as candidates of δ Sct type pulsation. However, a time-series analysis of the residual curves in the filter I does not indicate any evidence of periodic light variation for both systems. Finally, we compared the results obtained for both binary stars to those of similar systems.     

The role of tidal interactions in star formation

Nearly all of the initial angular momentum of the matter that goes into each forming star must somehow be removed or redistributed during the formation process. The possible transport mechanisms and the possible fates of the excess angular momentum are discussed, and it is argued that transport processes in discs are probably not sufficient by themselves to solve the angular momentum problem, while tidal interactions with other stars in forming binary or multiple systems are likely to be of very general importance in redistributing angular momentum during the star formation process. Most, if not all, stars probably form in binary or multiple systems, and tidal torques in these systems can transfer much of the angular momentum from the gas around each forming star to the orbital motions of the companion stars. Tidally generated waves in circumstellar discs may contribute to the overall redistribution of angular momentum. Stars may gain much of their mass by tidally triggered bursts of rapid accretion, and these bursts could account for some of the most energetic phenomena of the earliest stages of stellar evolution, such as jet-like outflows. If tidal interactions are indeed of general importance, planet-forming discs may often have a more chaotic and violent early evolution than in standard models, and shock heating events may be common. Interactions in a hierarchy of subgroups may play a role in building up massive stars in clusters and in determining the form of the upper initial mass function (IMF) . Many of the processes discussed here have analogues on galactic scales, and there may be similarities between the formation of massive stars by interaction-driven accretion processes in clusters and the buildup of massive black holes in galactic nuclei.     

The EC 14026 stars – VIII. PG 1336−018: a pulsating sdB star in an HW Vir-type eclipsing binary

The sdB star PG 1336−018 is found to be a very short-period eclipsing binary system, remarkably similar to the previously unique system HW Vir. In addition, and unlike HW Vir, the sdB star in the PG 1336 system shows rapid oscillations of the type found in the recently discovered sdB pulsators, or EC 14026 stars. The orbital period, 0.101 0174 d, is one of the shortest known for a detached binary. Analysis of photoelectric and CCD photometry reveals pulsation periods near 184 and 141 s, with semi-amplitudes of ∼0.01 and ∼0.005 mag respectively. Both oscillations might have variable amplitude, and it is probable that other frequencies are present with amplitudes ∼0.003 mag or less. The 184- and 141-s pulsations are in the range of periods predicted by models for hot horizontal-branch stars. Analysis of medium-dispersion spectrograms yields T _eff=33 000±1000 K and log g =5.7±0.1 for the sdB primary star, a radial velocity semi-amplitude K ₁=78±3 km s⁻¹ and a system velocity γ=6±2 km s⁻¹. Spectrograms from the IUE Final Archive give T _eff=33 000±3000 K and E ( B − V )=0.05 for log g =6.0 models. The derived angular radius leads to a distance of 710±50 pc for the system, and an absolute magnitude for the sdB star of +4.1±0.2. A preliminary analysis of U , V and R light curves indicates the orbital inclination to be near 81° and the relative radii to be r ₁=0.19 and r ₂=0.205. Assuming the mass of the sdB primary to be 0.5 M⊙ leads to a mass ratio q =0.3 for the system, and indicates that the secondary is a late-type dwarf of type ∼M5. As with HW Vir, it is necessary to invoke small limb-darkening coefficients and high albedos for the secondary star to obtain reasonable fits to the observed light curves.     

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.     

The dynamical stability of W Ursae Majoris-type systems

Theoretical study indicates that a contact binary system would merge into a rapidly rotating single star due to tidal instability when the spin angular momentum of the system is more than a third of its orbital angular momentum. Assuming that W Ursae Majoris (W UMa) contact binary systems rigorously comply with the Roche geometry and the dynamical stability limit is at a contact degree of about 70 per cent, we obtain that W UMa systems might suffer Darwin's instability when their mass ratios are in a region of about 0.076–0.078 and merge into the fast-rotating stars. This suggests that the W UMa systems with mass ratio   q ≤ 0.076  cannot be observed. Meanwhile, we find that the observed W UMa systems with a mass ratio of about 0.077, corresponding to a contact degree of about 86 per cent would suffer tidal instability and merge into the single fast-rotating stars. This suggests that the dynamical stability limit for the observed W UMa systems is higher than the theoretical value, implying that the observed systems have probably suffered the loss of angular momentum due to gravitational wave radiation (GR) or magnetic stellar wind (MSW).     

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.     

Orbital evolution with white-dwarf kicks

Recent observations of white dwarfs in globular clusters indicate that these stars may get a velocity kick during their time as giants. This velocity kick could originate naturally if the mass loss while on the asymptotic giant branch is slightly asymmetric. If white dwarfs get a kick comparable to the orbital velocity of the binary, the initial Runge–Lenz vector (eccentricity vector) of the orbit is damped to be replaced by a component pointing toward the cross-product of the initial angular momentum and the force. The final eccentricity may be of the order of unity and if the kick is sufficiently large, the system may be disrupted. These results may have important ramifications for the evolution of binary stars and planetary systems.     

Tidal Angular Momentum in Close Binary Systems in presence of Wind Driven Non-conservative Mass Transfer with Uniform Mass Accretion Rate

A very well-known property of close binary stars is that they usually rotate slowly than a similar type single star. Massive stars in close binary systems are supposed to experience an exchange of mass and angular momentum via mass transfer and tidal interaction, and thus the evolution of binary stars becomes more complex than that of individual stars. In recent times, it has become clear that a large number of massive stars interact with binary companions before they die. The observation also reveals that in close pairs the rotation tends to be synchronized with the orbital motion and the companions are naturally tempted to invoke tidal friction. We here introduce the effect of tidal angular momentum in the model of wind driven non-conservative mass transfer taking mass accretion rate as uniform with respect to time. To model the angular momentum evolution of a low mass main sequence companion star can be a challenging task. So, to make the present study more interesting, we have considered initial masses of the donor and gainer stars at the proximity of bottom-line main sequence stars and they are taken with lower angular momentum. We have produced a graphical profile of the rate of change of tidal angular momentum and the variation of tidal angular momentum with respect to time under the present consideration.     

Orbital Decay of a Binary System Consisting of Spin-Down Neutron Stars

{W}e consider the gravitational radiation from two time variable mass stars, orbiting around each other under the influence of gravity. The total rates of the variation of the energy, angular momentum, semimajor axis, eccentricity and orbital period are obtained. The results could be important for the understanding of general relativistic effects in the case of the variation of the gravitational mass due to spinning down of the compact stars, which sensitively depends on the equations of state. The cases of the binary systems PSR 1913+16 and PSR 1534+12 are analyzed in detail, and, for different equations of state of nuclear matter, the corrections to the orbital decay due to gravitational radiation and to the spinning down of the pulsars are calculated. The results show that a future significant improvement in the observational techniques could lead to the observation of the specific general relativistic effect of mass variation of pulsars due to spinning down, via the study of orbital decay, even in slowly rotating binary systems.     

HD 115781 and HD 116204—two RS CVn binaries

HD 115781 and HD 116204 (BL CVn and BM CVn) are shown to be RS CVn binaries with periods near 20 days. HD 115781 is double-lined; the primary type is about K1III, while the secondary is probably a late-type subgiant. The masses of the two components are equal within observational error. There is substantial photometric variability with a period half the orbital period; it is attributed to ellipsoidal variation. HD 116204 is also of type K1III. It shows exceptionally strong Ca II H and K emission, together with an emission-line spectrum typical of RS CVn stars in theIUE ultraviolet region, but Hα is an absorption line. The secondary star in the HD 116204 system has not been detected. The primary shows photometric variations, presumably due to starspots, with a period 5 per cent longer than the orbital period.     

Modelling the time variation of the surface differential rotation in AB Doradus and LQ Hydrae

Sequences of Doppler images of the young, rapidly rotating late-type stars AB Dor and LQ Hya show that their equatorial angular velocity and the amplitude of their surface differential rotation vary versus time. Such variations can be modelled to obtain information on the intensity of the azimuthal magnetic stresses within stellar convection zones. We introduce a simple model in the framework of the mean-field theory and discuss briefly the results of its application to those solar-like stars. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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     

An irradiation effect in Nova DN Gem 1912 and the significance of the period gap for classical novae

Continuous CCD photometry of the classical nova DN Gem during 52 nights in the years 1992–1998 reveals a modulation with a period of 0.127844 d. The semi-amplitude is about 0.03 mag. The stability of the variation suggests that it is the orbital period of the binary system. This interpretation makes DN Gem the fourth nova inside the cataclysmic variable (CV) period gap, as defined by Diaz & Bruch, and it bolsters the idea that there is no period gap for classical novae. However, the number of known nova periods is still too small to establish this idea statistically. We eliminate several possible mechanisms for the variation, and propose that the modulation is driven by an irradiation effect. We find that model light curves of an irradiated secondary star fit the data well. The inclination angle of the system is restricted by this model to 10°≲ i ≲65°. We also refine a previous estimate of the distance to the binary system, and find d =1.6±0.6 kpc.     

An Investigation of the Physical Mechanisms of Orbital Period Variations of the Semidetached Binary UW Vir

The orbital period variations of the Algol-type semidetached binary UW Vir are analyzed. It is shown that in addition to a long-term rapid increase (dP/dt = + 1.37 × 10⁻⁶ day/year), its orbit period has a variation with the period of 62.3 years. Based on the basic physical parameters given by Brancewicz and Dworak in 1980, the physical mechanisms causing the orbital period variations are investigated. The analysis indicates that the periodical variation of orbital period can be interpreted by the light-travel time effect due to the presence of a third body with the mass of M₃ ≥ 0.94 M. As no observational information has been reported for this tertiary component, it might be a compact object (e.g., a white dwarf). The long-term increase of orbital period can be explained in terms of the mass transfer from the secondary to the primary component (dM₂/dt = 1.43 × 10⁻⁷ M/year). This is in agreement with the semidetached configuration of the system with a lobe-filling secondary component. But according to the evolution theory of binaries, the Algol-type semidetached binary UW Vir should be at the evolutionary stage of slow mass transfer on the nuclear-reaction timescale of the secondary component. However, the analysis shows that the timescale for the periodical variation of orbital period is much shorter than the nuclear-reaction timescale of the secondary component, but close to the thermodynamic timescale of the secondary. This reveals that: (1) This binary system is at the evolutionary stage of rapid mass transfer on the thermodynamic timescale of the secondary component; or (2) The circumstellar matter of the system makes a contribution to the rapid increase of orbital period via the angular momentum transfer.