Can late-type active stars be explained by a dipole magnetic trap?

In this paper we review four different types of X-ray and/or radio observations of active late-type stars. We then consider if a single magnetic source configuration – a toroidal dipole magnetic trap – can possibly explain these various different observations. We conclude that, indeed, dipole magnetic confinement (similar to the magnetic configurations of the Earth's radiation belts and the case of Jupiter and the Io torus) can explain all the diverse observational data. We take this to be very strong observational support for this type of magnetic confinement scheme. We also consider that this magnetic configuration is only likely to be established and maintained in the most active stars.     

Non-radial oscillations and stability of a polytropen=3 with a toroidal magnetic field

A perturbation method has been applied for the determination of the frequencies of the linear and adiabatic oscillations of a gaseous polytropic configuration pervaded by a purely toroidal magnetic field. The influence of a toroidal magnetic field on the frequencies of the different types of spheroidal oscillation modes is discussed.     

Large-scale magnetic field of the G8 dwarf ξ Bootis A

We investigate the magnetic geometry of the active G8 dwarf ξ Bootis A (ξ Boo A), from spectropolarimetric observations obtained in 2003 with the MuSiCoS échelle spectropolarimeter at the Télescope Bernard Lyot (Observatoire du Pic du Midi, France). We repeatedly detect a photospheric magnetic field, with periodic variations consistent with rotational modulation. Circularly polarized (Stokes V) line profiles present a systematic asymmetry, showing up as an excess in amplitude and area of the blue lobe of the profiles. Direct modelling of Stokes V profiles suggests that the global magnetic field is composed of two main components, with an inclined dipole and a large-scale toroidal field. We derive a dipole intensity of about 40 G, with an inclination of 35° of the dipole with respect to the rotation axis. The toroidal field strength is of the order of 120 G. A noticeable evolution of the field geometry is observed over the 40 nights of our observation window and results in an increase in field strength and dipole inclination.
This study is the first step of a long-term monitoring of ξ Boo A and other active solar-type stars, with the aim of investigating secular fluctuations of stellar magnetic geometries induced by activity cycles.     

Non-ideal evolution of non-axisymmetric, force-free magnetic fields in a magnetar

Recent numerical magnetohydrodynamic calculations by Braithwaite and collaborators support the 'fossil field' hypothesis regarding the origin of magnetic fields in compact stars and suggest that the resistive evolution of the fossil field can explain the reorganization and decay of magnetar magnetic fields. Here, these findings are modelled analytically by allowing the stellar magnetic field to relax through a quasi-static sequence of non-axisymmetric, force-free states, by analogy with spheromak relaxation experiments, starting from a random field. Under the hypothesis that the force-free modes approach energy equipartition in the absence of resistivity, the output of the numerical calculations is semiquantitatively recovered: the field settles down to a linked poloidal–toroidal configuration, which inflates and becomes more toroidal as time passes. A qualitatively similar (but not identical) end state is reached if the magnetic field evolves by exchanging helicity between small and large scales according to an α-dynamo-like, mean-field mechanism, arising from the fluctuating electromotive force produced by the initial random field. The impossibility of matching a force-free internal field to a potential exterior field is discussed in the magnetar context.     

Constraints on the magnetic field geometry of magnetars

We study the effect of the magnetic field geometry on the oscillation spectra of strongly magnetized stars. We construct a configuration of magnetic field where a toroidal component is added to the standard poloidal one. We consider a star with a type I superconductor core so that both components of the magnetic field are expelled from the core and confined in the crust. Our results show that the toroidal contribution does not influence significantly the torsional oscillations of the crust. On the contrary, the confinement of the magnetic field in the crust drastically affects the torsional oscillation spectrum. A comparison with estimations for the magnetic field strength, from observations, excludes the possibility that magnetars will have a magnetic field solely confined in the crust, that is, our results suggest that the magnetic field in whatever geometry has to permeate the whole star.     

The dynamics of a toroidal magnetic ring

Solving the nonlinear partial differential equations of magnetohydrodynamics numerically, we examine (1) the time development of a purely toroidal magnetic field (a magnetic ring) and (2) the interaction of a magnetic ring with a poloidal magnetic field. Axisymmetry and incompressibility are assumed. Parameters are chosen to correspond to photospheric conditions. In case (1), the magnetic ring contracts to the axis and then splits in two with one ring travelling up along the axis and the other down. In case (2), a large toroidal velocity field is generated which has opposite direction of flow above and below the magnetic ring. The magnetic and flow patterns of case (2) may persist with little change for a relatively long time. We conjecture that toroidal magnetic fields may be involved in the bright rings of sunspots or in the dynamics of spicules.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

The equilibrium and the stability of the Jeans spheroids with toroidal magnetic fields

We examine the effect of a toroidal magnetic field on the equilibrium and stability of homogeneous masses distorted by the tidal effects of a secondary (of massM at a distanceR). It is shown that if the toroidal magnetic field is assumed to be axisymmetric about the direction of the line joining the centres of mass of the primary and the secondary, then the equilibrium configuration is a prolate spheroid. Also determined are the characteristic frequencies of the various modes of oscillations belonging to the second harmonics. It is found that the magnetic field shifts these frequencies to higher values than the ones which prevail in the absence of a magnetic field.     

A model of the heliospheric magnetic field configuration

A three-dimensional model of the magnetic field configuration in the heliosphere is constructed by assuming that the interplanetary magnetic field consists of four components, (i) the solar dipole, (ii) a large number of small spherical dipoles located along an equatorial circle just inside the Sun (representing the magnetic field line arcade), (iii) the field of the poloidal current system generated by the solar unipolar induction and (iv) the field of an extensive current disc around the Sun lying in the ecliptic plane. The magnetic field intensity at a distance of 1 A.U. (about 20 R⊙ above the ecliptic plane) is normalized to fit the observed spiral configuration.     

Toroidal magnetic field of a superfluid neutron star in a postnewtonian approximation

The effect of proton superconductivity on the generation of a toroidal magnetic field inside a neutron star is examined. It is shown that including the entrainment of superconducting protons by superfluid neutrons does not change the previously obtained results. Proton superconductivity does influence the structure of the generated magnetic field since, over a time on the order of 10⁴–10⁵ years, the magnetic field increases linearly with time and can exceed the first critical field for proton superconductivity. The distribution of the stationary toroidal magnetic field inside a neutron star is also found.     

Equilibrium structure of stars with radiation pressure in the presence of a magnetic field

Equilibrium configuration of the upper Main-Sequence stars, with significant radiation pressure and having an interior magnetic field (matching with an external dipole field) has been cosidered. The structural parameters have been calculated for low and high magnetic fields by using a first-order perturbation method and a modified perturbation technique respectively. With the increase of radiation pressure, the star is seen to become more centrally condensed.     

Nonradial oscillations of low-mass stars in the presence of a magnetic field

Nonradial oscillations of a partially degenerate standard model, approximating a class of low-mass stars, have been studied in the presence of a weak poloidal magnetic field. The magnetic field in the interior of the configuration is taken to be continuous across the equilibrium surface and is matched with an external dipole field. Using a variational formulation, corrections to the oscillation frequencies of the Kelvin mode have been found for different values of the central degeneracy. It has been noted that the effect of the magnetic field is to increase the frequency of nonradial (l=2) mode of pulsation.     

Perturbation of the radial and non-radial oscillations of a star by a magnetic field

A generalization of the perturbation method is applied to the problem of the radial and the non-radial oscillations of a gaseous star which is distorted by a magnetic field. An expression is derived for the perturbation of the oscillation frequencies due to the presence of a weak magnetic field when the equilibrium configuration is a spheroid. The particular application to the homogeneous model with a purely poloidal field inside, due to a current distribution proportional to the distance from the axis of symmetry, and a dipole type field outside is considered in detail. The main result is that the magnetic field has a large and almost stabilizing effect on unstableg-modes, particularly on higher order modes. With the considered magnetic field the surface layers appear to have a large weight.     

The non-axisymmetrical configuration of a large-scale solar and stellar magnetic field

The non-axisymmetric and nonlinear solutions of the magnetostatic equations are given in three-dimensional space of spherical coordinates (r, θ, ?). These solutions are applied to the large-scale solar magnetic field. Their basic features are similar to a dipole field near the polar regions and the polarity reverses near the equator. These features agree with observations for the large-scale solar magnetic field. The solutions can also be applied to investigating the connection between the structure of the magnetic field and the density distribution of the corona. It is shown that the tops of the closed magnetic field associate with density enhancements. Similar results may apply to the large-scale configuration of the stellar field.     

Dynamical stability of a self-gravitating rotating cylinder in a helical magnetic field

The effect of a helical magnetic field on the oscillations and the stability of a homogeneous self-gravitating rotating cylinder is investigated. The axial field has a tendency to stabilise long wave numbers and to destabilise small wave numbers so that maximum instability occurs for a finite wave number. If the toroidal and the axial component of the field have the same sign, the instability associated with the toroidal field can be removed by the rotation or by the axial field. Rotational instability is reduced but cannot removed by the field. If the components of the field have the opposite sign, rotational instability is increased. The maximum growth rate of the magnetic instability is reduced by a small axial field and tends to a finite value for large axial fields.     

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.     

General properties of magnetic CP stars

We present the review of our previous studies related to observational evidence of the fossil field hypothesis of formation and evolution of magnetic and non-magnetic chemically peculiar stars. Analysis of the observed data shows that these stars acquire their main properties in the process of gravitational collapse. In the non-stationary Hayashi phase, a magnetic field becomes weakened and its configuration complicated, but the fossil field global orientation remains. After a non-stationary phase, relaxation of young star’s tangled field takes place and by the time of joining ZAMS (Zero Age Main Sequence) it is generally restored to a dipole structure. Stability of dipole structures allows them to remain unchanged up to the end of their life on the Main Sequence which is 10⁹ years at most.     

The structure and oscillations of low-mass stars in the presence of a magnetic field

The equilibrium structure and oscillations of a partially degenerate standard model in the presence of a poloidal magnetic field have been studied. The magnetic field in the interior has been matched with an outside dipole field. The effect of magnetic field on the various structural parameters, e.g., mass, central condensation, moment of inertia, and oblateness has been computed for different values of the central degeneracy of the model. We have also studied the effect of magnetic field on radial oscillations of the configuration. A variational formulation is used to compute the changes in the frequency of radial mode of oscillation. It has been shown that the changes in frequency computed for various models using a two-parameter eigenfunction are in fair agreement with the values obtained by using the exact eigenfunction.     

Relativistic expansion of magnetic loops at the self-similar stage

We obtained self-similar solutions of relativistically expanding magnetic loops taking into account the azimuthal magnetic fields. We neglect stellar rotation and assume axisymmetry and a purely radial flow. As the magnetic loops expand, the initial dipole magnetic field is stretched into the radial direction. When the expansion speed approaches the light speed, the displacement current reduces the toroidal current and modifies the distribution of the plasma lifted up from the central star. Since these self-similar solutions describe the free expansion of the magnetic loops, i.e.  d v /d t = 0  , the equations of motion are similar to those of the static relativistic magnetohydrodynamics. This allows us to estimate the total energy stored in the magnetic loops by applying the virial theorem. This energy is comparable to that of the giant flares observed in magnetars.     

Stability of the solar tachocline with magnetic fields

The stability of magnetic fields in the solar tachocline is investigated. We present stability limits for higher azimuthal wave numbers and results on the dependence of the stability on the location of toroidal magnetic fields in latitude. While the dependence of the wave number with the largest growth rate on the magnetic field strength and the magnetic Prandtl number is small, the dependence on the magnetic Reynolds number Rm indicates that lowest azimuthal modes are excited for very high Rm. Upon varying the latitudinal position of the magnetic field belts, we find slightly lower stability limits for high latitudes, and very large stability limits at latitudes below 10°, with little dependence on latitude in between. An increase of the maximum possible field was achieved by adding a poloidal field. The upper limit for the toroidal field which can be stored in the radiative tachocline is then 1000 G, compared to about 100 G for a purely toroidal field as was found in an earlier work. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermal generation of magnetic fields with radiation pressure in rotating stars

It has been suggested by Biermann that in rotating stars the electron partial pressure could generate a toroidal magnetic field of a considerable strength. However, Mestel and Roxburgh have shown recently that the generation of such a toroidal magnetic field could almost completely be suppressed when a weak primodial poloidal magnetic field exists in the star. In this paper it is shown that a toroidal magnetic field of a moderate strength could be generated even in the presence of a primodial poloidal magnetic field, if the effect of radiation pressure is taken into consideration. This considered mechanism is effective for moderately massive stars, and numerical estimate indicates that in A type stars a toroidal magnetic field of the order of a thousand gauss can be generated near the surface within the time scale of the evolution of the star.Visiting Scientist to the High Altitude Observatory on leave of absence from the Department of Astronomy, University of Tokyo, Japan.