Features of multi-dipole magnetic field structures in CP stars

Ten of the sixty investigated magnetic stars have two- or three-dipole structures. From the viewpoint of the relic hypothesis a wide variety of magnetic field structures and strengths allows to assume that in the initial phases of formation of magnetic stars, their fields were even more entangled and heterogeneous than now. This may be due to the complex structure of protostellar clouds, the consequence of non-stationary processes during the collapse, and, probably, the result of subsequent accretion interactions. The expected variation of the large-scale structure with age is lost at the background of a wide variety of structures, depending on the initial conditions. Complex structures occur both in the stars at ZAMS, and in the stars leaving the Main Sequence. As a result of quadratic dependence of the magnetic structure lifetime on their characteristic dimensions, large-scale configurations can exist for times comparable to the lifetime of stellar magnetic field, i.e. τ ≥ 10⁹ yrs. One of the common properties of multi-dipole stars is that the centers of the dipoles are predominantly located in the equatorial plane of rotation. In the majority of studied objects magnetic dipoles (i.e. the regions with the maximum field) are shifted from the center of the star by the distance greater than the radius of the convective core (approximately 0.1R*). This may indicate that the poloidal field is not compatible with the convective core and is not generated therein. Large distances between the monopoles, comparable to the radii of the stars are typical. This may be a sign indicating that inside the stars the field structure is slightly different from the dipole, what implies that the dipole is not a mathematical point, but rather some highly magnetized volume inside the star, comparable to a magnetized rod.     

Magnetic field structure and evolution features of selected stars. III.

We present the results of modeling for about a hundred magnetic stars. It is shown that the dipole representation of magnetic field structures describes the distribution of the magnetic field over stellar surfaces fairly well. We analyze some patterns which support the relic hypothesis of magnetic field formation.Arguments are given in favor of the assumption that themain properties ofmagnetic stars—slow rotation, predominant orientation of magnetic field lines along the plane of the rotation equator, complex internal structures of magnetic fields—are acquired in the process of gravitational collapse. There are no conditions for that in the non-stationary Hayashi phase and in the stage of a radiative young star.     

Magnetic fields of chemically peculiar stars. I. The catalog of magnetic CP stars

This is the first paper of the series dedicated to the analysis of the magnetism of chemically peculiar (CP) stars of the upper Main Sequence. We use our own measurements and published data to compile a catalog of magnetic CP stars containing a total of 326 objects with confidently detected magnetic fields and 29 stars which are very likely to possess magnetic field. We obtained the data on the magnetism of the overwhelming majority of the stars solely based on the analysis of longitudinal field component B _e . The surface magnetic field, B _s , has been measured for 49 objects. Our analysis shows that the number of magnetic CP stars decreases with increasing field strength in accordance with exponential law, and stars with B _e exceeding 5kG occur rarely (about 3% objects of our list).     

Main sequence for rotating stars of intermediate mass

We have investigated the evolutionary behaviour of intermediate mass (2, 3, 4, 5, and 7M ) Population I stars, assuming two different rates of rotation at the threshold of stability.In the first part of the study, stars are assumed to start with a critical rotation (fast rotation model) and to progress to the point of rotational instability. The stars evolve by losing mass and become rotationally unstable before they reach the zero-age Main Sequence. It is argued that multiple star systems might be formed through the evolution of rapidly rotating stars. An expression for the rotational mass loss rate is derived as a function of the physical parameters of stars.In the second part of the study, stars are assumed to rotate at a rate below the critical value (slow rotation model). The evolution of slowly rotating stars is followed as far as zero-age Main Sequence on the theoretical Hertzsprung-Russell diagram and compared with that of normal stars. The evolutionary paths are found to be more or less similar to those of normal stars; but their positions on the Main Sequence are characterized by effective temperatures and luminosities lower than those of normal stars. The zero-age Main-Sequence times of these stars are longer than those of normal stars. The rotational rates obtained for the zero-age Main Sequence are in good agreement with observed values.     

Accretion onto stars with octupole magnetic fields: Matter flow, hot spots and phase shifts

Recent measurements of the surface magnetic fields of classical T Tauri stars (CTTSs) and magnetic cataclysmic variables show that their magnetic fields have a complex structure. Investigation of accretion onto such stars requires global three-dimensional (3D) magnetohydrodynamic (MHD) simulations, where the complexity of simulations strongly increases with each higher-order multipole. Previously, we were able to model disc accretion onto stars with magnetic fields described by a superposition of dipole and quadrupole moments. However, in some stars, like CTTS V2129 Oph and BP Tau, the octupolar component is significant and it was necessary to include the next octupolar component. Here, we show results of global 3D MHD simulations of accretion onto stars with superposition of the dipole and octupole fields, where we vary the ratio between components. Simulations show that if octupolar field strongly dominates at the disc-magnetosphere boundary, then matter flows into the ring-like octupolar poles, forming ring-shape spots at the surface of the star above and below equator. The light-curves are complex and may have two peaks per period. In case where the dipole field dominates, matter accretes in two ordered funnel streams towards poles, however the polar spots are meridionally-elongated due to the action of the octupolar component. In the case when the fields are of similar strengths, both, polar and belt-like spots are present. In many cases the light-curves show the evidence of complex fields, excluding the cases of small inclinations angles, where sinusoidal light-curve is observed and ‘hides’ the information about the field complexity.We also propose new mechanisms of phase shift in stars with complex magnetic fields. We suggest that the phase shifts can be connected with: (1) temporal variation of the star’s intrinsic magnetic field and subsequent redistribution of main magnetic poles; (2) variation of the accretion rate, which causes the disc to interact with the magnetic fields associated with different magnetic moments. We use our model to demonstrate these phase shift mechanisms, and we discuss possible applications of these mechanisms to accreting millisecond pulsars and young stars.     

Magnetic field model for slowly rotating CP-stars. γEqu= HD201601

A magnetic field model is constructed for the extremely slow rotator γEqu based on measurements of its magnetic field over many years and using the “magnetic charge” method. An analysis of γEqu and of all the data accumulated up to the present on the magnetic field parameters of chemically peculiar stars leads to some interesting conclusions, of which the main ones are: the fact that the axis of rotation and the dipole axis are not parallel in γEqu and the other slowly rotating magnetic stars which we have studied previously is one of the signs that the braking of CP stars does not involve the participation of the magnetic field as they evolve “to the main sequence.” The axes of the magnetic field dipole in slow rotators are oriented arbitrarily with respect to their axes of rotation. The substantial photometric activity of these CP stars also argues against these axes being close. The well-known absence of sufficiently strong magnetic fields in the Ae/Be Herbig stars also presents difficulties for the hypothesis of “magnetic braking” in the “pre-main sequence” stages of evolution. The inverse relation between the average surface magnetic field Bs and the rotation period P is yet another fact in conflict with the idea that the magnetic field is involved in the braking of CP stars. We believe that angular momentum loss involving the magnetic field can hardly have taken place during evolution immediately prior “to the main sequence,” rather the slow rotation of CP stars most likely originates from protostellar clouds with low angular momentum. Some of the slowly rotating stars have a central dipole magnetic field configuration, while others have a displaced dipole configuration, where the displacement can be toward the positive or the negative magnetic pole. __________ Translated from Astrofizika, Vol. 49, No. 2, pp. 251–262 (May 2006).     

Magnetic fields of chemically peculiar and related stars. 2. Main results of 2015 and near-future prospects

We present an analytical survey of key publications concerned with the study of stellar magnetism published in 2015. We considered about 80 publications, the most significant from our point of view, presented brief reviews of them, and made generalizations. The paper considers: instruments, techniques of observations and analysis; large-scale magnetic fields of OBA stars on the Main Sequence (MS) (formation and evolution, field topology, search for new magnetic stars including the projects MiMeS, BOB, and BinaMIcS and observations with the Russian 6-m telescope, rotation and chemical abundance analysis of magnetic CP stars); magnetic fields, chemical abundance and variability of stars related to peculiar, primarily, active cool stars, solar-type stars and white dwarfs; multiple magnetic stars including interferometry data, exoplanets in a system of magnetic stars. We make a conclusion that the accuracy of magnetic field measurements has grown due to universal application of the multilinear method of observations especially with high-resolution spectropolarimeters. Usage of Zeeman-Doppler imaging technique (ZDI) when analyzing the obtained data allows us to confidently search and measure fields of complex topology of the order of 10 Gs. For the first time, a magnetic field has been detected for post-AGB stars and some other types of objects.     

Magnetic Models of HD 115708 and HD 119419

The magnetic fields of the chemically peculiar stars HD 115708 and HD 119419 were modeled using observed curves of variation of the magnetic field with the phase of the rotational period. It turned out that the field of HD 115708 is described, in a first approximation, by a central dipole, while the field of HD 119419 is described by an off-center dipole. The main parameters of the magnetic fields of both stars and maps of the surface field-strength distribution were obtained. The dipole axis of the first star lies in the equatorial plane while that of the second is almost parallel to the axis of rotation.     

Specificities of magnetic field structures in chemically peculiar stars

We continue our program of the study of large-scale structures of magnetic fields in chemically peculiar stars. In this paper we analyze eight stars, out of which three stars have the structure of a central dipole, three—the structure of a dipole shifted along the axis, and two—of a dipole shifted across the axis. High-precision measurements (with σ = 50 and 80 G) are available for two stars (HD62140 and HD71866, respectively). The model phase dependences agree with the measurements within the errors. This result shows that the hypothesis about the dipole structure of the magnetic fields of CP stars is well founded.     

Magnetic field structure of slow CP-rotators: HD 9996 and HD 188041

This is the final paper on a study of the magnetic field structure of CP stars with long rotation periods. It is first demonstrated that the orientation and strength of the magnetic field have no effect on their rotation velocity. The orientation of the dipole structures in slow magnetic rotators is shown to be random, as it is in fast rotators. The hypothesis that magnetic stars are slowed down under the influence of the magnetic field is called into question. The origin of CP stars is probably related to their initial slow rotation. __________ Translated from Astrofizika, Vol. 51, No. 2, pp. 295–303 (May 2008).     

Magnetic field models of CP stars HD18296, HD19832, HD22470, HD24712

We model the magnetic fields of four magnetic stars using published longitudinal (Be) field measurements. The structure of the magnetic field of each of the four stars is close to that of the central dipole. Unfortunately, the number of measurements for each star is insufficient for accurate finding of the field parameters, and therefore we find no dipole shift exceeding its error Δa ≈ 0.1, expressed as a fraction of the stellar radius. Our data support the opinion that the results of modeling depend most strongly on the adopted inclination of the star’s rotation axis i.     

Dynamo action in the presence of an imposed magnetic field

Dynamo action within the cores of Ap stars may offer intriguing possibilities for understanding the persistent magnetic fields observed on the surfaces of these stars. Deep within the cores of Ap stars, the coupling of convection with rotation likely yields magnetic dynamo action, generating strong magnetic fields. However, the surface fields of the magnetic Ap stars are generally thought to be of primordial origin. Recent numerical models suggest that a primordial field in the radiative envelope may possess a highly twisted toroidal shape. We have used detailed 3-D simulations to study the interaction of such a twisted magnetic field in the radiative envelope with the core-dynamo operating in the interior of a 2 solar mass A-type star. The resulting dynamo action is much more vigorous than in the absence of such a fossil field, yielding magnetic field strengths (of order 100 kG) much higher than their equipartition values relative to the convective velocities. We examine the generation of these fields, as well as the growth of large-scale magnetic structure that results from imposing a fossil magnetic field. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Are the magnetic fields of millisecond pulsars ∼108 G?

It is generally assumed that the magnetic fields of millisecond pulsars (MSPs) are ～10⁸ G. We argue that this may not be true and the fields may be appreciably greater. We present six evidences for this: (1) The ～10⁸G field estimate is based on magnetic dipole emission losses which is shown to be questionable; (2) The MSPs in low mass X-ray binaries (LMXBs) are claimed to have <10¹¹ G on the basis of a Rayleygh-Taylor instability accretion argument. We show that the accretion argument is questionable and the upper limit 10¹¹ G may be much higher; (3) Low magnetic field neutron stars have difficulty being produced in LMXBs; (4) MSPs may still be accreting indicating a much higher magnetic field; (5) The data that predict ～10⁸ G for MSPs also predict ages on the order of, and greater than, ten billion years, which is much greater than normal pulsars. If the predicted ages are wrong, most likely the predicted ～10⁸ G fields of MSPs are wrong; (6) When magnetic fields are measured directly with cyclotron lines in X-ray binaries, fields ?10⁸ G are indicated. Other scenarios should be investigated. One such scenario is the following. Over 85% of MSPs are confirmed members of a binary. It is possible that all MSPs are in large separation binaries having magnetic fields >10⁸ G with their magnetic dipole emission being balanced by low level accretion from their companions.     

Pre-Main-Sequence evolution of rotating low-mass stars

The evolutionary behaviour of rotating low-mass stars in the mass range 0.2 and 0.9M has been investigated during the pre-Main-Sequence phase. The angular momentum is conserved locally in radiative regions and totally in convective regions, according to a predetermined angular velocity distribution depending on the structure of the star. As the stars contract toward the zero-age Main Sequence, they spin up under the assumption that the angular momentum is conserved during the evolution of the stars. When the stars have differential rotations, their inner regions rotate faster than the outer regions. The effective temperatures and luminosities of rotating low-mass stars are obtained lower than those of non-rotating stars. They have lower central temperature and density values compared to those of non-rotating stars.     

Magnetic field models of nine CP stars from “accurate” measurements

The dipole models of magnetic fields in nine CP stars are constructed based on the measurements of metal lines taken from the literature, and performed by the LSD method with an accuracy of 10–80 G. The model parameters are compared with the parameters obtained for the same stars from the hydrogen line measurements. For six out of nine stars the same type of structure was obtained. Some parameters, such as the field strength at the poles B _p and the average surface magnetic field B _s differ considerably in some stars due to differences in the amplitudes of phase dependences B _e (Φ) and B _s (Φ), obtained by different authors. It is noted that a significant increase in the measurement accuracy has little effect on the modelling of the large-scale structures of the field. By contrast, it is more important to construct the shape of the phase dependence based on a fairly large number of field measurements, evenly distributed by the rotation period phases. It is concluded that the Zeeman component measurement methods have a strong effect on the shape of the phase dependence, and that the measurements of the magnetic field based on the lines of hydrogen are more preferable for modelling the large-scale structures of the field.     

中子星的热演化和磁衰减

本文研究了中子星的热演化、自转演化和磁场演化的相互影响．考虑了一个自洽模型：中子星因磁偶极辐射而自转减慢，在内部产生某些加热过程，中子星磁场通过壳层的欧姆耗散来衰减．结果表明，磁场衰减提高了加热过程的重要性；相反，加热效应减慢了磁衰减．因此可以得出，中子星的热、自转和磁场也许不是独立演化的．不仅如此，这些演化与初始条件有关，因此，人们也许可以从射电和Ｘ射线观测对脉冲星年龄、初始磁场和周期给出某些限制．     

Systematically Asymmetric Heliospheric Magnetic Field: Evidence for a Quadrupole Mode and Non-Axisymmetry with Polarity Flip-Flops

Recent studies of the heliospheric magnetic field (HMF) have detected interesting, systematic hemispherical and longitudinal asymmetries which have a profound significance for the understanding of solar magnetic fields. The in situ HMF measurements since the 1960s show that the heliospheric current sheet (HCS) is systematically shifted (coned) southward during solar minimum times, leading to the concept of a bashful ballerina. While temporary shifts can be considerably larger, the average HCS shift (coning) angle is a few degrees, less than the 7.2^∘ tilt of the solar rotation axis. Recent solar observations during the last two solar cycles verify these results and show that the magnetic areas in the northern solar hemisphere are larger and their intensity weaker than in the south during long intervals in the late declining to minimum phase. The multipole expansion reveals a strong quadrupole term which is oppositely directed to the dipole term. These results imply that the Sun has a symmetric quadrupole S0 dynamo mode that oscillates in phase with the dominant dipole A0 mode. Moreover, the heliospheric magnetic field has a strong tendency to produce solar tilts that are roughly opposite in longitudinal phase. This implies is a systematic longitudinal asymmetry and leads to a “flip-flop” type behaviour in the dominant HMF sector whose period is about 3.2 years. This agrees very well with the similar flip-flop period found recently in sunspots, as well as with the observed ratio of three between the activity cycle period and the flip-flop period of sun-like stars. Accordingly, these results require that the solar dynamo includes three modes, A0, S0 and a non-axisymmetric mode. Obviously, these results have a great impact on solar modelling.     

On the origin and structure of stellar magnetic fields

Newly formed stars have magnetic fields provided by the compression of the interstellar field, and contrary to a widely accepted idea these fields are not destroyed by convective motions. For the same reason, the fallacy of ‘turbulent diffusion’, turbulent dynamo action is not possible in any star. Thus all stellar magnetic fields have a common origin, and persist throughout the lifetime of each star, including degenerate phases. This common origin, and a general similarity in stellar evolutionary processes, suggest that the fields may develop similar structural characteristics and MHD effects. This would open new possibilities of coordinating the studies of different types of stars and relating them to solar physics which has tended to become isolated from general stellar physics. As an initial step we consider three features of solar magnetic fields and their MHD effects. First, the solar magnetic field comprises two separate components: a poloidal field and a toroidal field. The former is a dipole field, permeating the entire Sun and closely aligned with the rotational axis; at the surface it is always concealed by much stronger elements of the toroidal field. The latter is probably wound from the former by differential rotation at latitudes below about 35°, where sections emerge through the solar surface and are then carried polewards. The second feature of solar magnetic fields is that all flux is concentrated into flux tubes of strength some kG, isolated within a much larger volume of non-magnetic plasma. The third feature is that the flux tubes are helically twisted into flux ropes (up to ?10²²Mx) and smaller elements ranging down to flux fibres (? 10¹⁸Mx). Some implications of similar features in other stars are discussed.     

An equatorially symmetric rotator model for magnetic stars

Suggested by theoretical and empirical investigations, a very simple magnetic field distribution at the surface of magnetic stars is proposed. This model corresponds to the superposition of a dipole and a quadrupole, both lying in the equatorial plane with their axes in the same direction. The observed variations of the effective magnetic field strength of the sixteen stars investigated can be represented surprisingly well with this model. When the quadrupole contribution is large, the variation of the magnetic field vector over the surface of the star differs characteristically from that of the decentred dipole model; thus the difficulty with the latter, regarding the representation of both the effective magnetic field and the mean surface field with the same parameters may perhaps be avoided.     

On the radii of Ap and Am stars

The radii of several Ap and Am stars have been compared with those of the normal A stars of the Main Sequence. Though the brighter Ap stars have a little larger radii than the Main-Sequence stars, they may not be much different from those of the slightly evolved normal A stars. The Am stars have radii with which they appear to be merging with those of the cooler A stars of the Main Sequence. The Ap stars have radii predominantly in the range of 1.8 to 3.4R _⊙, while the Am stars are mainly concentrated between 1.8 and 2.2R _⊙.