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.     

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.     

Model of the Magnetic Field of HD 187474

A model is constructed for the magnetic field of the star HD 187474, which has a very long axial rotation period P = 2345^d. It turns out that the structure of the magnetic field is best described by a model of a displaced (Δα = 0.1) dipole inclined to the axis of rotation by an angle β = 24°. The star is inclined to the line of sight by an angle i = 86°. Because of the displaced dipole the magnitude of the magnetic field differs at the poles: Bp = +6300 and 11600 G. A Mercator map of the distribution of the magnetic field over the surface is obtained. The 7 slowly rotating CP stars studied thus far have an average angle β = 62°, which equals the average value for a random orientation of dipoles. __________ Translated from Astrofizika, Vol. 48, No. 4, pp. 575–583 (November 2005).     

Magnetic braking of Ap/Bp stars: application to compact black-hole X-ray binaries

We examine the proposal that the subset of neutron-star and black-hole X-ray binaries that form with Ap or Bp star companions will experience systemic angular-momentum losses due to magnetic braking, not otherwise operative with intermediate-mass companion stars. We suggest that for donor stars possessing the anomalously high magnetic fields associated with Ap and Bp stars, a magnetically coupled, irradiation-driven stellar wind can lead to substantial systemic loss of angular momentum. Hence, these systems, which would otherwise not be expected to experience 'magnetic braking', evolve to shorter orbital periods during mass transfer. In this paper, we detail how such a magnetic braking scenario operates. We apply it to a specific astrophysics problem involving the formation of compact black-hole binaries with low-mass donor stars. At present, it is not understood how these systems form, given that low-mass companion stars are not likely to provide sufficient gravitational potential to unbind the envelope of the massive progenitor of the black hole during a prior 'common-envelope' phase. On the other hand, intermediate-mass companions, such as Ap and Bp stars, could more readily eject the common envelope. However, in the absence of magnetic braking, such systems tend to evolve to long orbital periods. We show that, with the proposed magnetic braking properties afforded by Ap and Bp companions, such a scenario can lead to the formation of compact black-hole binaries with orbital periods, donor masses, lifetimes and production rates that are in accord with the observations. In spite of these successes, our models reveal a significant discrepancy between the calculated effective temperatures and the observed spectral types of the donor stars. Finally, we show that this temperature discrepancy would still exist for other scenarios invoking initially intermediate-mass donor stars, and this presents a substantial unresolved mystery.     

Model pulsar magnetospheres: the perpendicular rotator

The simplest model illustrating the effect of the magnetospheric charge-current field on the structure of a pulsar magnetic field has the region within the light-cylinder filled with the GoldreichJulian charge density which corotates with the neutron star, but has no electric currents along the magnetic field lines. This model has previously been studied for the axisymmetric case, with the rotation and magnetic dipolar axes aligned. The analogous problem is now solved with the two axes mutually perpendicular, so that not only the material current arising from the rotating charges but also the displacement current contributes. Again, the constructed magnetic field B ₀ crosses the light-cylinder normally, and there is no energy flux to infinity. However, in a more realistic model there is a flow of current along B ₀, generating a field B ₁ which has a non-vanishing toroidal component at the light-cylinder, so yielding a finite integrated Poynting flux.     

The evolution of the core and surface magnetic fields in isolated neutron stars

We apply the model of flux expulsion from the superfluid and superconductive core of a neutron star, developed by Konenkov & Geppert, both to neutron star models based on different equations of state and to different initial magnetic field structures. Initially, when the core and the surface magnetic field are of the same order of magnitude, the rate of flux expulsion from the core is almost independent of the equation of state, and the evolution of the surface field decouples from the core field evolution with increasing stiffness. When the surface field is initially much stronger than the core field, the magnetic and rotational evolution resembles that of a neutron star with a purely crustal field configuration; the only difference is the occurrence of a residual field. In the case of an initially submerged field, significant differences from the standard evolution only occur during the early period of the life of a neutron star, until the field has been re-diffused to the surface. The reminder of the episode of submergence is a correlation of the residual field strength with the submergence depth of the initial field. We discuss the effect of the re-diffusion of the magnetic field on the difference between the real and the active age of young pulsars and on their braking indices. Finally, we estimate the shear stresses built up by the moving fluxoids at the crust–core interface and show that these stresses may cause crust cracking, preferentially in neutron stars with a soft equation of state.     

Type I and two-gap superconductivity in neutron star magnetism

Neutron star inner cores with several charged baryonic components are likely to be analogues of the two-gap superconductor which is of current interest in condensed-matter physics. Consequently, type I superconductivity is less probable than type II but may nevertheless be present in some intervals of matter density. The intermediate-state structure formed at finite magnetic flux densities after the superconducting transitions is subject to buoyancy, frictional and neutron vortex interaction forces. These are estimated and it is shown that the most important frictional force is that produced by the stable stratification of neutron star matter, the irreversible process being diffusion in the normal, finite magnetic flux density, parts of the structure. The length-scale of the structure, in directions perpendicular to the local magnetic field is of crucial importance. For small scales, the flux comoves with the neutron vortices, as do the proton vortices of a type II superconductor. But for much larger length-scales, flux movement tends to that expected for normal charged Fermi systems.     

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.     

Indirect imaging of the accretion stream in eclipsing polars – II. HU Aquarii

We apply our technique for indirect imaging of the accretion stream to the polar HU Aquarii, using eclipse profiles observed when the system was in a high accretion state. The accretion stream is relatively luminous, contributing as much as the accretion region on the white dwarf, or more, to the overall system brightness. We model the eclipse profiles using a model stream consisting of a ballistic trajectory from the L1 point followed by a magnetically channelled trajectory that follows a dipole field line out of the orbital plane. We perform model fits using two geometries: a stream that accretes on to both footpoints of the field line, and a stream that accretes only on to the footpoint of the field line above the orbital plane. The stream images indicate that the distribution of emission along the stream is not a simple function of the radial distance from the white dwarf. The stream is redirected by the magnetic field of the white dwarf at a distance 1.0–1.3×10¹⁰ cm from the white dwarf; this implies a mass transfer rate in the range 8–76×10¹⁶ g s⁻¹. The absorption dips in the light curve indicate that the magnetically entrained part of the stream moves from 42° to 48° from the line of centres over the three nights of observation. This is in close agreement with the results of the one-footpoint models, suggesting that this is the more appropriate geometry for these data. The stream images show that, in almost all sections of the stream, the flux peaks in B and is successively fainter in U , V and R .     

Magnetic field evolution in neutron stars

Neutron stars contain persistent, ordered magnetic fields that are the strongest known in the Universe. However, their magnetic fluxes are similar to those in magnetic A and B stars and white dwarfs, suggesting that flux conservation during gravitational collapse may play an important role in establishing the field, although it might also be modified substantially by early convection, differential rotation, and magnetic instabilities. The equilibrium field configuration, established within hours (at most) of the formation of the star, is likely to be roughly axisymmetric, involving both poloidal and toroidal components. The stable stratification of the neutron star matter (due to its radial composition gradient) probably plays a crucial role in holding this magnetic structure inside the star. The field can evolve on long time scales by processes that overcome the stable stratification, such as weak interactions changing the relative abundances and ambipolar diffusion of charged particles with respect to neutrons. These processes become more effective for stronger magnetic fields, thus naturally explaining the magnetic energy dissipation expected in magnetars, at the same time as the longer-lived, weaker fields in classical and millisecond pulsars. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The effect of asynchronism on wind-driven mass transfer rates in the polars

An asynchronous magnetic white dwarf affects the rate of orbital evolution in AM Herculis binaries. An over-synchronous star leads to a positive orbital magnetic torque which reduces the rate of shrinkage of the secondary star's Roche lobe, and hence reduces the mass transfer rate. An opposing effect occurs as a result of the orbital angular momentum loss via secondary mass transfer in the absence of an accretion disc. The modification of the magnetic braking-driven synchronous mass transfer rate is calculated for a range of degrees of asynchronism, and its effect is compared at different orbital periods.     

Studies of accretion flows around rotating black holes – I. Particle dynamics in a pseudo-Kerr potential

We study the formation of the absorption features, called the cyclotron–annihilation lines, in the γ-spectra of the neutron stars (pulsars), owing to the fundamental quantum-electrodynamic effect of the one–photon pair creation in magnetized vacuum. As a result, we substantiate a new method for the determination of the neutron star magnetic fields B based on measuring the interval between the main annihilation and the first cyclotron–annihilation absorption lines. It is found that these lines may be easily resolved, and, consequently, the method is surely applicable if the following conditions are satisfied. (i) A γ-source has to be compact enough and located near a star, but not close to its magnetic poles. For instance, it may be a disc in the plane of a star magnetic equator with latitudinal angular width less than     and radial extent up to 25 per cent of the star radius. (ii) The source is to produce detectable γ-radiation at large angles ≳60° to the local magnetic field. Being situated in a closed field line region and having a broad radiation pattern, such a source is not what is usually considered in the context of the polar cap and outer gap models of the pulsar γ-emission dealing with open field lines only. (iii) Magnetic field strength must lie in a certain narrow interval with the centre at  ∼(3–4) × 10¹²  G. Its width depends on the star orientation and disc radial extend and in the most favourable case is about 20–30 per cent of its lower boundary. Finally, the influence of the star rotation on this method employment is considered and new possibilities arising from forthcoming polarization observations are briefly discussed.     

Coronal Flux Rope Equilibria in Closed Magnetic Fields

Using a 2.5-dimensional ideal MHD model in Cartesian coordinates,we investigate the equilibrium properties of coronal magnetic flux ropes in background magnetic fields that are completely closed.The background fields are produced by a dipole,a quadrupole,and an octapole,respectively,located below the photosphere at the same depth.A magnetic flux rope is then launched from below the photo-sphere,and its magnetic properties,i.e,the annular magnetic fluxφp and the axial magnetic fluxφz,are controlled by a single emergence parameter.The whole sys-tem eventually evolves into equilibrium,and the resultant flux rope is characterized by three geometrical parameters:the height of the rope axis,the half-width of the rope,and the length of the vertical current sheet below the rope.It is found that the geometrical parameters increase monotonically and continuously with increasing φp and φz:no catastrophe occurs.Moreover,there exists a steep segment in the profiles of the geometrical parameters versus either φp or φz,and the faster the background field decays with height,the larger both the gradient and the growth amplitude within the steep segment will be.     

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.     

The effect of a magnetosphere on asynchronous magnetic torques in AM Herculis binaries

The interaction is investigated between a white dwarf magnetosphere and a red dwarf secondary star in an asynchronous AM Herculis binary. The poloidal magnetic field diffuses into the secondary and shearing motions, due to differential rotation between the star and the magnetosphere, generate azimuthal field. The effects of diffusion and field advection caused by a poloidal flow induced by magnetospheric motions are calculated. Outward radial motions reduce the amount of field penetration and limit the stellar magnetic torque at higher degrees of asynchronism. A resonance torque curve results, similar to the case of a precessing magnetic field with vacuum surroundings. Inward motions in the secondary increase field penetration, allowing the torque to reach higher values for larger degrees of asynchronism.     

The physics of strong magnetic fields in neutron stars

In this paper we present a new result, namely that the primal magnetic field of the collapsed core during a supernova explosion will, as a result of the conservation of magnetic flux, receive a massive boost to more than 90 times its original value by the Pauli paramagnetization of the highly degenerate relativistic electron gas just after the formation of the neutron star. Thus, the observed super-strong magnetic field of neutron stars may originate from the induced Pauli paramagnetization of the highly degenerate relativistic electron gas in the interior of the neutron star. We therefore have an apparently natural explanation for the surface magnetic field of a neutron star.     

Launching of conical winds and axial jets from the disc–magnetosphere boundary: axisymmetric and 3D simulations

We investigate the launching of outflows from the disc–magnetosphere boundary of slowly and rapidly rotating magnetized stars using axisymmetric and exploratory 3D magnetohydrodynamic simulations. We find long-lasting outflows in the following cases. (1) In the case of slowly rotating stars , a new type of outflow, a conical wind , is found and studied in simulations. The conical winds appear in cases where the magnetic flux of the star is bunched up by the disc into an X-type configuration. The winds have the shape of a thin conical shell with a half-opening angle  θ∼ 30°–40°  . About 10–30 per cent of the disc matter flows from the inner disc into the conical winds. The conical winds may be responsible for episodic as well as long-lasting outflows in different types of stars. There is also a low-density, higher velocity component (a jet) in the region inside the conical wind. (2) In the case of rapidly rotating stars (the 'propeller regime'), a two-component outflow is observed. One component is similar to the conical winds. A significant fraction of the disc matter may be ejected into the winds. The second component is a high-velocity, low-density magnetically dominated axial jet where matter flows along the opened polar field lines of the star. The jet has a mass flux of about 10 per cent of that of the conical wind, but its energy flux (dominantly magnetic) can be larger than the energy flux of the conical wind. The jet's angular momentum flux (also dominantly magnetic) causes the star to spin down rapidly. Propeller-driven outflows may be responsible for the jets in protostars and for their rapid spin-down. The jet is collimated by the magnetic force while the conical winds are only weakly collimated in the simulation region. Exploratory 3D simulations show that conical winds are axisymmetric about the rotational axis (of the star and the disc), even when the dipole field of the star is significantly misaligned.     

Correlation between the Directions of the Magnetic Fields and Major Axes of Extragalactic Radio Sources

The distribution of relative position angles between the integrated intrinsic polarization (perpendicular to the direction of the intrinsic magnetic field) and the major axis of an extragalactic radio source were studied for different types of radio sources. Data for 280 extragalactic radio sources were used and it was found that there are large differences in the relative orientation of different types of radio sources. The directions of the intrinsic integrated magnetic fields correlate with the major radio axes of more elongated radio sources (K > 2.5, where K is the ratio of lengths of the major and minor axes of the radio images) and for radio sources of type FR II, whereas for less elongated objects (K < 2.5) and for radio sources of type FR I the magnetic fields do not correlate at all with the radio axes. An alternative mechanism for the formation of a radio galaxy from relativistic plasma ejected from the central part of an optical galaxy and moving in its large-scale, dipole magnetic field may be a theoretical basis for classification with respect to the elongation parameter K of the radio image.     

Magnetic Energy of Force-Free Fields with Detached Field Lines

Using an axisymmetrical ideal MHD model in spherical coordinates, we present a numerical study of magnetic configurations characterized by a levitating flux rope embedded in a bipolar background field whose normal field at the solar surface is the same or very close to that of a central dipole. The characteristic plasma β (the ratio between gas pressure and magnetic pressure) is taken to be sosmall (β= 10^-4) that the magnetic field is close to being force-free. The system as a whole is then let evolve quasi-statically with a slow increase of either the annular magnetic flux or the axial magnetic flux of the rope, and the total magneticenergy of the system grows accordingly. It is found that there exists an energy threshold: the flux rope sticks to the solar surface in equilibrium if the magneticenergy of the system is below the threshold, whereas it loses equilibrium if the threshold is exceeded. The energy threshold is found to be larger than that of thecorresponding fully-open magnetic field by a factor of nearly 1.08 irrespective as towhether the background field is completely closed or partly open, or whether the magnetic energy is enhanced by an increase of annular or axial flux of the rope.This gives an example showing that a force-free magnetic field may have an energy larger than the corresponding open field energy if part of the field lines is allowed tobe detached from the solar surface. The implication of such a conclusion in coronal mass ejections is briefly discussed and some comments are made on the maximum energy of force-free magnetic fields.     

A new magnetic white dwarf: PG 2329+267

We have discovered that the white dwarf PG 2329+267 is magnetic, and, assuming a centred dipole structure, has a dipole magnetic field strength of approximately 2.3 MG. This makes it one of only approximately 4 per cent of isolated white dwarfs with a detectable magnetic field. Linear Zeeman splitting, as well as quadratic Zeeman shifts, is evident in the hydrogen Balmer sequence and circular spectropolarimetry reveals ∼10 per cent circular polarization in the two displaced σ components of Hα. We suggest from comparison with spectra of white dwarfs of known mass that PG 2329+267 is more massive than typical isolated white dwarfs, in agreement with the hypothesis that magnetic white dwarfs evolve from magnetic chemically peculiar Ap and Bp type main-sequence stars.