Chemical composition of the He-w stars HD 37058, 212454, and 224926

Our spectrophotometric analysis of the atmospheres of HD 37058, HD 212454, and HD 224926 shows these objects to be typical He-w stars with close-to-zero microturbulence velocities, very different magnetic fields, and wide scatter of chemical anomalies. However, one of the main manifestations of separation is that helium moves from the outer layers of the atmosphere into the star’s interior.Our analysis of the stars HD 212454 and 224926 with Be<100 G shows that despite their weak magnetic fields they have the same degree of chemical anomaly as highly magnetized stars. Chemical composition varies over a wide range for stars with the same magnitude of magnetic field. We find the conditions in the temperature interval 13000–16000 K to be the most favorable for the formation of He-w type stars. Helium underabundance is the strongest near the maximum of the distribution and it is observed in stars with weak as well as strong fields. Because of the scatter mentioned above the degree of chemical anomalies is not strictly related to the magnitude of the magnetic field, although the field has an appreciable effect on the formation of chemical inhomogeneities at the star’s surface. Its influence is minimal in stars with very weak magnetic fields and the presence of strong chemical anomalies indicates that microturbulence in these stars is sufficiently weak even without the effect of the magnetic field. It is plausible to assume that the anomalies arise due to slow rotation.The temperature dependences of rotation velocity vsini for stars with weak magnetic fields show no apparent trends associated with the magnitude of magnetic field. The rotation velocities vsini of almost all stars are lower than those of normal stars, except for HD 131120, 142096, 142990, and 143669, which rotate with the same velocity or even faster than normal stars. These objects do not obey the general rule and their example shows that stable atmospheres can also be found among fast rotators and that magnetic field takes no part in the spin-down of CP stars. We believe that CP stars inherited their slow rotation from protostellar clouds.     

The influence of magnetic field and rotation on the onset of convection in the envelopes of neutron stars

The influence of magnetic field and rotation on the occurrence of convective instabilities in the liquid layer of neutron star envelopes has been investigated. The critical wavelength _c , which denotes the boundary between stable and unstable behaviour of convective disturbances, is calculated for a neutron star model as a function of magnetic field and rotation. It is shown that the strength of the magnetic fields of neutron stars strongly suppresses the onset of convection, whereas the limiting effect of rotation acts only if the magnetic field vanishes.     

Some Comments on the Magnetic Braking of CP Stars

The low rotation velocities of magnetic CP stars are discussed. Arguments against the involvement of the magnetic field in the loss of angular momentum are given: (1) the fields are not strong enough in young stars in the stage of evolution prior to the main sequence; (2) there is no significant statistical correlation between the magnetic field strength and the rotation period of CP stars; (3) stars with short periods have the highest fields; (4) a substantial number of stars with very low magnetic fields (B _e < 500 G) have rotation speeds that are typical of other CP stars; (5) simulations of the magnetic fields by Leroy and the author show that the orientation of dipoles inside rotating stars, both slow and fast, is consistent with an arbitrary orientation of the dipoles; and, (6) slow rotators with P>25 days, which form 12% of the total, probably lie at the edge of the velocity distribution for low mass stars. All of these properties conflict with the hypothesis of magnetic braking of CP stars.     

The Relationship Between Kinematics and Spatial Structure of the Large-Scale Solar Magnetic Field

The rotation of large-scale solar magnetic fields has been investigated by analysing a 20-yr series of synoptic maps of the radial magnetic field. For this purpose, a specially adapted method of spectral analysis was used. We calculated rotation spectra of the magnetic field as functions of the rotation period, heliographic latitude, and longitudinal wave number, k. These spectra reveal the existence of a number of discrete, rigidly rotating components (modes) of the magnetic field, whose rotation periods lie in the wide range from 26.5 to 30.5 days. The significant spectral maxima lie in the (rotation period–latitude) plane close to the curve that represents the differential rotation of small-scale magnetic features. For the first harmonic of the magnetic field (k=1) the properties of the rotation spectra are consistent with those reported by Antonucci, Hoeksema, and Scherrer (1990). However, the distribution of the rigidly rotating modes over rotation period and their latitudinal structure change systematically with the harmonic number k. As k increases, the mean distance P in rotation period between the modes decreases, from 1.2 days for k=1 to 0.3–0.5 days for k=4. This decreasing period separation is accompanied by a decrease of the characteristic latitude separation between the mode maxima. The latitudinal and longitudinal discrete spatial scales of the non-axisymmetric magnetic field appear to be connected with each other, as well as with the temporal scale P.     

Magnetic fields of chemically peculiar stars. II: Magnetic fields and rotation of stars with strong and weak anomalies in the continuum energy distribution

We make a comparative analysis of magnetic fields and rotation parameters of magnetic CP stars with strong and weak anomalies in the spectral energy distribution. Stars with strong depressions in the continuum at 5200 Å are shown to have significantly stronger fields (the mean longitudinal component of the fields of these stars is 〈B _e〉 = 1341 ± 98 G) compared to objects with weaker depressions (〈B _e〉 = 645 ± 58 G). Stars with stronger depressions are also found to occur more commonly among slow rotators. Their rotation periods are, on the average, about 10 days long, three times longer than these of stars with weak depressions (about three days). This fact is indicative of a decrease of the degree of anomality of the magnetic stars continuum spectrum with increasing rotational velocity. Yet another proof has been obtained suggesting that slow rotation is one of the crucial factors contributing to the development of the phenomenon of magnetic chemically peculiar stars.Magnetic CP stars with weak depressions at 5200 Å are intermediate objects between stars with strong depressions and normal A- and B-type stars both in terms of field strength and rotational velocity.     

Sector Structure, Rotation, and Cyclic Evolution of Large-Scale Solar Magnetic Fields

Auto-correlation analysis was performed using digitized synoptic charts of photospheric magnetic fields for the past three solar activity cycles (1965–1994). The obtained correlograms were used to study the rotation and the zonal-sector structure of large-scale solar magnetic fields all over the observable region of heliolatitudes in various phases of solar activity. It is shown that the large-scale system of solar magnetic fields is rather complex and comprises at least three different systems. One is a global rigidly rotating system. It determines the cyclic variation of magnetic fields and is probably responsible for the behavior of magnetic fields in the polar zones. Another is a rigidly rotating 4-sector structure in the central (equatorial and mid-latitude) zone. The third is a differentially rotating system that determines the behavior of the LSSMF structure elements with a size of 30–60° and less. This one is the most noticeable in the central zone and absent in the polar zones. Various cyclic and rotation parameters of the three field structures are discussed.     

Simulations of jet formation from a magnetized accretion disk

Axisymmetric magnetohydrodynamic (MHD) simulations have been made of the formation of jets from a Keplerian disk threaded by a magnetic field. The disk is treated as a boundary condition, where matter with high specific entropy is ejected with a Keplerian azimuthal speed and a poloidal speed less than the slow magnetosonic velocity, and where boundary conditions on the magnetic fields correspond to a highly conducting disk. Initially, the space above the disk, the corona, is filled with high specific entropy plasma in the thermal equilibrium in the gravitational field of the central object. The initial magnetic field is poloidal and is represented by the superposition of the fields of monopoles located below the plane of the disk.The rotation of the disk twists the initial poloidal magnetic field lines, and this twist propagates into the corona pushing matter into jet-like outflow in a cylindrical region. After the first switch-on wave, which originates during the first rotation period of the inner radius of the disk, the matter outflowing from the disk starts to flow and accelerate in thez-direction owing to both the magnetic and pressure gradient forces. The flow accelerates through the slow magnetosonic and Alfvén surfaces and at larger distances through the fast magnetosonic surface. The flow velocity of the jet is approximately parallel to thez-axis, with the collimation mainly a result of the pinching force of the toroidal magnetic field. The energy flux of the flow increases with increasing magnetic field strength on the disk. Some of the cases studied have been run for long times, 60 rotation periods of the inner radius of the disk, and show indications of approaching a stationary state.     

Polar magnetic fields of the Sun: 1960–1971

Observations of the magnetic fields in the polar regions of the Sun are presented for the period 1960–1971. At the start of this interval the fields at the two poles were consistently of opposite sign and averaged around 1 G. Early in 1961 the field in the south decreased suddenly and the field in the north decreased in strength slowly over the next few years. By the mid-1960's the fields at both poles were quite weak and irregular. Throughout the period of these observations the fields at both poles often showed a remarkable tendency to vary in unison. About the middle of 1971 the north polar field became significantly positive, first at lower latitudes, then above 70 °. An autocorrelation analysis of the polar fields in the north shows a weak rotation peak, indicating significant features in these regions. A comparison of field strengths in the east and west quadrants in the north suggests that even at the extreme polar latitudes the following polarity fields are inclined slightly toward the rotation and the preceding polarity field lines are inclined slightly to trail the rotation.     

Complex structure of the magnetic field of the CP star HD32633

The method of “virtual magnetic charges” is used to analyze the structure of the magnetic field of the CP star HD32633. The phase relation of its magnetic field differs strongly from a sine wave. The structure of the star’s field can be described fairly well by two dipoles located in the opposite regions of the star near its rotation equator. Each of these dipoles produces two pairs of magnetic spots of opposite polarity similar to sunspots. The dipoles are located at a distance of Δa=0.6 R from the center, where R is the radius of the star. The field strength at the poles is equal to ±42 and ±19 kG.     

Structure and evolution of supermassive rotating magnetic polytropes

The structure of rotating magnetic polytropes is considered in Roche approximation. Investigation of the influence of poloidal as well as toroidal magnetic fields on the conditions of the beginning of matter outflow due to rotational instability is carried out. The influence of the turbulent convection and twisting of magnetic force lines on the time of smoothing of differential rotation is considered. The estimate of the magneto-turbulence energy generated by differential rotation is presented. Both maximum possible energy output and duration of the quasi-statical evolution phase up to the appearance of hydrodynamic instability due to the effects of General Relativity are calculated for supermassive magnetic polytropes of index three with uniform or differential rotation. The radiusmass relation is obtained for supermassive differentially-rotating magnetic polytropes referring to the longest part of the quasi-statistical evolution stage; some consequences are pointed out, including the period-luminosity relation.The evolution of the considered models of supermassive rotating magnetic polytropes with different character of rotation and different geometry of a magnetic field is discussed.The results obtained are summarized in the last section.Receipt delayed by postal strike in Great Britain.     

Rotation of the large-scale solar magnetic fields in the equatorial region

A study is made of the rotation of large-scale magnetic fields using the synoptic maps from the Kitt Peak National Observatory for the time interval 1976–1985. The auto-correlation method and the mass-centers method of magnetic structures was applied to infer mean differential rotation profiles and rotation profiles separately for each magnetic field polarity. It has been found that in both hemispheres the leading polarity rotates faster than the following polarity at all latitudes by about 0.04° day^–1. The maximum rotation rate of the leading polarity is reached at about 6° latitude. In the mean profile for both polarities, this brings about two angular velocity maxima at 6° latitudes in both hemispheres. Such a profile appears as to have a dimple on the equator.     

Propagation of spiral density waves in a magneto-active disk

The propagation of spiral density waves in a differentially rotating, self-gravitating, magnetoactive and highly flattened disk is investigated by using the asymptotic theory for tightly wound spirals developed by Lin and his collaborators. We adopt the continuum fluid model as the primary basis, and our treatment will be largely analytical. The disk plasma is studied in the frozen field approximation and inhomogenceous magnetic fields in the plane of the disk are considered in detail.In a differentially rotating disk with strong magnetic fields, the field lines will be considerably distorted and the mutual influence of magnetic fields and differential rotation is by no means obvious.In this paper we present a new asymptotic dispersion relation for tightly wound spiral density waves with magnetic fields along the spiral armsB (r). The effects of the magnetic fields lead to such terms likek ²(a ² +V _A ² ), wherek is the wave number,a represents the speed of sound,V _A = (B ²/4)^1/2 is the Alfvén speed,B denotes the field strength, and is the plasma density. These terms depict the well-known magnetoacoustic waves and could have been anticipated without a detailed computation. However the interaction of magnetic fields and differential rotation may give rise to other significant terms which are not so easy to foresee.We also present a more exact local dispersion relation by using the WKB approximation and study the effects of magnetic fields on the growth rate through the parametersQ andJ defined in the literature.Although the effects of the magnetic fields are rather insignificant for applications to Galactic dynamics, the effects of the magnetic fields are important for applications to star formation and problems related to the solar nebula.     

What we have learned about the Martian magnetic field

The evidence is presented for the existence of the magnetic field of the planet Mars and for the effectiveness of the dipolar part of the field as an obstacle to the solar wind at the most frequent parameters of the latter. The dipolar magnetic moment of Mars is (1.5–2.20 × 10²² G cm³. The dipole axis makes an angle i15 with the rotation axis of the panel. The magnetic north pole of Mars is located in its southern hemisphere.In terms of the precession dynamo model, the magnetic fields of the Earth and Mars are similar. This indicates that the Martian magnetic field is associated with the present-day dynamo-process in the Martian liquid core.     

A Rossby-wave dynamo for the Sun,II

To make the analysis more tractable, we simplify the equations of Part I to apply to two superposed layers of fluid, with horizontal variations in the motion and magnetic field represented by a small number of Fourier harmonics. The resulting set of eighteen ordinary nonlinear differential equations in time for the Fourier amplitudes is integrated numerically. We analyze in detail the dynamo action from a typical Rossby wave motion and compare it with the solar cycle.The field reversal process is similar in some respects to that put forth by Babcock. Toroidal fields are dragged up by vertical motions in the Rossby waves to form large-scale vertical fields, whose polarities alternate with longitude roughly like bipolar magnetic regions. Vertical fields of preferentially one polarity are carried toward the pole by the meridional motion in the wave to form an axisymmetric poloidal field. This poloidal field is then stretched out by the differential rotation into a new toroidal field of the opposite sign from the original. The poloidal field changes sign when the toroidal and bipolar region like fields are maximum, and vice versa.For the case studied, the reversal period is too short ( 2 years) and the poloidal fields too large ( 40 G) for the sun. Improvements for the model are discussed.Part I has been published in Solar Phys. 8, 316.     

Coronal Mass Ejections as Expanding Force-Free Structures

We model solar coronal mass ejections (CMEs) as expanding force-free magnetic structures and find the self-similar dynamics of configurations with spatially constant ??, where J=?? B, in spherical and cylindrical geometries, expanding spheromaks and Lundquist fields, respectively. The field structures remain force-free, under the conventional non-relativistic assumption that the dynamical effects of the inductive electric fields can be neglected. While keeping the internal magnetic field structure of the stationary solutions, expansion leads to complicated internal velocities and rotation, caused by inductive electric fields. The structure depends only on overall radius R(t) and rate of expansion $\dot{R}(t)$ measured at a given moment, and thus is applicable to arbitrary expansion laws. In case of cylindrical Lundquist fields, magnetic flux conservation requires that both axial and radial expansion proceed with equal rates. In accordance with observations, the model predicts that the maximum magnetic field is reached before the spacecraft reaches the geometric center of a CME.     

Magnetic Model of HD 2453

A model is constructed for the magnetic field of the star HD 2453, which has a very long rotation period (P=521^d). It is found that the structure of the field corresponds to the model of a dipole shifted by r=0.09R from the center. The angle of inclination of the axis of the dipole to the axis of rotation, =5°; that is, the star is viewed almost from its equator of rotation and magnetic equator. This explains the low amplitude of the phase dependence of the magnetic field, Be(P), and the low amplitude of the photometric variability. The field at the magnetic poles is equal to Bp=+4400 and -7660 G. The magnetic field parameters turn out to be close to those obtained by Landstreet and Mathys assuming a dipole-quadrupole-octupole model. A Mercator map of the magnetic field distribution of HD 2453 is produced.     

Fine structures of chromospheric magnetic field and material flow in a solar active region

In this paper, we analyze the relations between photospheric vector magnetic fields, chromospheric longitudinal magnetic fields and velocity fields in a solar active region. Agreements between the photospheric and chromospheric magnetograms can be found in large-scale structures or in the stronger magnetic structures, but differences also can be found in the fine structures or in other places, which reflect the variation of the magnetic force lines from the photosphere to the chromosphere. The chromospheric superpenumbral magnetic field, measured by the Hline, presents a spoke-like structure. It consists of thick magnetic fibrils which are different from photospheric penumbral magnetic fibrils. The outer superpenumbral magnetic field is almost horizontal. The direction of the chromospheric magnetic fibrils is generally parallel to the transverse components of the photospheric vector magnetic fields. The chromospheric material flow is coupled with the magnetic field structure. The structures of the H chromospheric magnetic fibrils in the network are similar to H dark fibrils, and the feet of the magnetic fibrils are located at the photospheric magnetic elements.     

Determination of the Coronal and Interplanetary Magnetic Field Strength and Radial Profiles from Large-Scale Photospheric Magnetic Fields

We propose a new model for the magnetic field at different distances from the Sun during different phases of the solar cycle. The model depends on the observed large-scale non-polar (\({\pm}\, 55^{\circ }\)) photospheric magnetic field and on the magnetic field measured at polar regions from \(55^{\circ }\) N to \(90^{\circ }\) N and from \(55^{\circ }\) S to \(90^{\circ }\) S, which are the visible manifestations of cyclic changes in the toroidal and poloidal components of the global magnetic field of the Sun. The modeled magnetic field is determined as the superposition of the non-polar and polar photospheric magnetic field and considers cycle variations. The agreement between the model predictions and magnetic fields derived from direct in situ measurements at different distances from the Sun, obtained with different methods and at different solar activity phases, is quite satisfactory. From a comparison of the magnetic fields as observed and calculated from the model at 1 AU, we conclude that the model magnetic field variations adequately explain the main features of the interplanetary magnetic field (IMF) radial, \(B_{\mathrm{x}}\), component cycle evolution at Earth’s orbit. The modeled magnetic field averaged over a Carrington rotation (CR) correlates with the IMF \(B_{\mathrm{x}}\) component also averaged over a CR at Earth’s orbit with a coefficient of 0.691, while for seven CR-averaged data, the correlation reaches 0.81. The radial profiles of the modeled magnetic field are compared with those of already existing models. In contrast to existing models, ours provides realistic magnetic-field radial distributions over a wide range of heliospheric distances at different cycle phases, taking into account the cycle variations of the solar toroidal and poloidal magnetic fields. The model is a good approximation of the cycle behavior of the magnetic field in the heliosphere. In addition, the decrease in the non-polar and polar photospheric magnetic fields is shown. Furthermore, the magnetic field during solar cycle maxima and minima decreased from Cycle 21 to Cycle 24. This implies that both the toroidal and poloidal components, and therefore the solar global magnetic field, decreased from Cycle 21 to Cycle 24.     

The appearance of polarization in radiation from hot stars due to the faraday rotation effect as a possible method of determining stellar magnetic fields

The effect of Faraday rotation is shown to lead to the appearance of linear polarization of stellar radiation scattered in an optically-thin circumstellar electron-magnetized shell, even in the case when the shell is spherical. The spectral dependence of the polarization degree is evaluated for scattering in (i) a spherically-symmetric magnetized shell with a power-law radial dependence of the electron density, and (ii) a non-spherical ellipsoidal uniform envelope. The position of maximum in the polarization spectrum permits us to determine the magnetic field magnitude on a star surface. If the rotational and magnetic axes do not coincide, the periodic variability of the polarization will be observed with the period of stellar rotation. Some Be-stars, such as Cas, 48 Lib, EW Lac, Aqr, HD 45677, X Per, are proposed as candidates to be investigated for magnetic fields, as well as some stars of the T Tau-type. This method may be also applied to supernovae shells.     

The solar dynamo

The solar dynamo continues to pose a challenge to observers and theoreticians. Observations of the solar surface reveal a magnetic field with a complex, hierarchical structure consisting of widely different scales. Systematic features such as the solar cycle, the butterfly diagram, and Hale's polarity laws point to the existence of a deep-rooted large-scale magnetic field. At the other end of the scale are magnetic elements and small-scale mixed-polarity magnetic fields. In order to explain these phenomena, dynamo theory provides all the necessary ingredients including the effect, magnetic field amplification by differential rotation, magnetic pumping, turbulent diffusion, magnetic buoyancy, flux storage, stochastic variations and nonlinear dynamics. Due to advances in helioseismology, observations of stellar magnetic fields and computer capabilities, significant progress has been made in our understanding of these and other aspects such as the role of the tachocline, convective plumes and magnetic helicity conservation. However, remaining uncertainties about the nature of the deep-seated toroidal magnetic field and the effect, and the forbidding range of length scales of the magnetic field and the flow have thus far prevented the formulation of a coherent model for the solar dynamo. A preliminary evaluation of the various dynamo models that have been proposed seems to favor a buoyancy-driven or distributed scenario. The viewpoint proposed here is that progress in understanding the solar dynamo and explaining the observations can be achieved only through a combination of approaches including local numerical experiments and global mean-field modeling.Received: 5 May 2003, Published online: 15 July 2003