The photospheric magnetic flux budget

The ensemble of bipolar regions and the magnetic network both contain a substantial and strongly variable part of the photospheric magnetic flux at any phase in the solar cycle. The time-dependent distribution of the magnetic flux over and within these components reflects the action of the dynamo operating in the solar interior. We perform a quantitative comparison of the flux emerging in the ensemble of magnetic bipoles with the observed flux content of the solar photosphere. We discuss the photospheric flux budget in terms of flux appearance and disappearance, and argue that a nonlinear dependence exists between the flux present in the photosphere and the rate of flux appearance and disappearance. In this context, we discuss the problem of making quantitative statements about dynamos in cool stars other than the Sun. This paper evolved out of a more comprehensive version which appeared in Harvey (1993).     

The emergence of magnetic flux

This paper first summarizes the morphology and dynamics of emerging flux regions and arch filament systems and then discusses detailed observations of a particular active region with emerging magnetic flux.The central part of the growing active region shows abnormal granulation and a weak magnetic field that, locally, is transverse. In the border zone, strong downward flows occur in the chromopshere and photosphere (small features with strong magnetic fields (faculae, pores) are formed here.) Near the leading and following edge, sunspots are formed by the coalescence of such small magnetic elements.The observational data are interpreted by means of a heuristic model of an emergent magnetic loop-shaped bundle consisting of many flux tubes. In this model we incorporate the theory of convective collapse and the buoyancy of flux tubes. The observed complexity in the structure and dynamics, including strong transverse fields and velocity shear, is attributed to the emergence of several flux regions within the active region at different orientations.     

Frequency response of magnetic flux sheaths

We suggest to identify the elementary flare bursts with the excitation of the small kernels that occur in flare loops that are observed in soft X-ray pictures of flares. We stress the need of simultaneous observations of spatial structure and time variations of hard X-ray bursts sources in various wavelength regions.     

The rise of twisted magnetic flux tubes

Sunspots are caused by the eruption of magnetic flux tubes through the solar photosphere: current theories of the internal magnetic field of the Sun suggest that such tubes must rise relatively unscathed from the base of the convection zone. In order to understand how the structure of the magnetic field within a buoyant flux tube affects its stability as it rises, we have considered the quasi-two-dimensional rise of isolated magnetic flux tubes through an adiabatically stratified atmosphere. The magnetic field is initially helical; we have investigated a range of initial field configurations, varying the distribution and strength of the twist of the field.     

Topological stability of finite-length magnetic flux tubes

It has been suggested that the activity of cosmical magnetic fields is a consequence of a general topological nonequilibrium in the neighbourhood of magnetostatic equilibria. Evidence for this suggestion can be obtained from the Kolmogorov-Arnold-Moser theorem of classical mechanics, applied to the magnetic field line flow as a Hamiltonian system. A finite-length magnetic flux tube, however, always possesses two independent sets of flux surfaces - or, equivalently, the corresponding Hamiltonian system two independent first integrals - and is topologically stable if in the volume occupied by the tube there are no singular (null) points of the magnetic field and the normal field component does not change its sign on the end faces of the tube. Therefore, the concept of nonequilibrium due to flux surface destruction is not applicable to solar atmospheric loops with each end situated in the interior of one polarity of the photospheric normal field component. Further, it seems unlikely that the tearing-mode mechanism can play a role in such loops.     

Thermodynamical properties of unresolved magnetic flux tubes

We propose a diagnostic method, based on the observation of circular polarization signals in line pairs, to derive the thermodynamical properties of unresolved magnetic elements in the solar atmosphere. The concept of response function for the ratio of circular polarization signals in two lines is introduced and its main properties are analyzed. Some detailed calculations for suitably selected line pairs are presented.     

The separation velocity of emerging magnetic flux

We measure the separation velocity of opposite poles from 24 new bipoles on the Sun. We find that the measured velocities range from about 0.2 to 1 km s^–1. The fluxes of the bipoles range over more than two orders of magnitude, and the mean field strength and the sizes range over one order of magnitude. The measured separation velocity is not correlated with the flux and the mean field strength of the bipole. The separation velocity predicted by the present theory of magnetic buoyancy is between 7.4Ba ^–1/4 cot and 13 cot km s^–1, where is the elevation angle of the flux tube at the photosphere (see Figure 9), B is the mean field strength, and a is the radius of the observed bipole. The rising velocity of the top of flux tubes predicted by the theory of magnetic buoyancy is between 3.7Ba ^–1/4 and 6.5 km s^–1. The predicted separation velocity is about one order of magnitude higher than those measured, or else the flux tubes are almost vertical at the photosphere. There is no correlation between the measured separation velocity and the theoretical value, 7.4Ba ^–1/4. The predicted rising velocity is also higher than the vertical velocity near the line of inversion in emerging flux regions observed by other authors.     

Radiative transfer across a magnetic flux tube

In the coming years, some solar telescopes will be able to yield the Stokes' parameters of polarized light with a resolution better than 1 arc sec (0.3 arc sec for THEMIS). We have simulated the Stokes' parameters of a solar magnetic flux tube as seen with such a resolution. We have shown that, observing with a line-of-sight not parallel to the axis of the flux tube (assumed vertical and axisymmetric), it is possible to see differences between different configurations of the magnetic field inside the flux tube (presence, and in what direction, of an azimuthal component of the field). Furthermore, along such a line-of-sight, the polarization profiles of any atomic line are strongly absorbed at the line center. We then suggest a strategy to infer the structure of the magnetic field from observations at high spatial resolution.     

Initiation of cmes by magnetic flux emergence

The initiation of solar Coronal Mass Ejections (CMEs) is studied in the framework of numerical magnetohydrodynamics (MHD). The initial CME model includes a magnetic flux rope in spherical, axi-symmetric geometry. The initial configuration consists of a magnetic flux rope embedded in a gravitationally stratified solar atmosphere with a background dipole magnetic field. The flux rope is in equilibrium due to an image current below the photosphere. An emerging flux triggering mechanism is used to make this equilibrium system unstable. When the magnetic flux emerges within the filament below the flux rope, this results in a catastrophic behavior similar to previous models. As a result, the flux rope rises and a current sheet forms below it. It is shown that the magnetic reconnection in the current sheet below the flux rope in combination with the outward curvature forces results in a fast ejection of the flux rope as observed for solar CMEs. We have done a parametric study of the emerging flux rate.     

The smallest observable elements of magnetic flux

We have followed disappearing elements of magnetic flux to determine the smallest elements detectable with the Big Bear videomagnetograph. All the elements followed were disappearing through interaction with elements of opposite polarity. The last remaining visible segment of magnectic field of such features can be used to infer the total magnetic flux of these and other small flux elements visible on the magnetograms.We used both photographic and digital videomagnetograms combining 4096 Zeeman frames made at Big Bear. Fifteen elements were measured near the vanishing point, in a 2–8 hr period. The minimum observable fluxes fall in the range of 1.0 × 10¹⁶ to 1.4 × 10¹⁷ Mx, and the apparent size of these elements is in the range of 1 to 9 square arc sec. The process of disappearance appears to be a smooth one. The smallest detectable elements of network field and ephemeral regions (ER) appear to be the same as the small intra-network (IN) field elements. The present limit is still instrumental; elements smaller than 1 × 10¹⁶ would not have been detected.Visiting Associates from Beijing Observatory, Academia Sinica, Beijing, China.     

Stability and equilibrium of emerged magnetic flux

We analyse stability and equilibrium of a unipolar large-scale magnetic field pervading a plane horizontal subphotospheric layer with the possible implications for sunspots in mind. Eddy diffusivity is applied to account for the effects of the small-scale convective turbulence. Diffusivity quenching by magnetic field results in a secondary large-scale instability. A linear stability analysis is performed to define the marginal stability boundary in parametric space and the unstable mode structure. The nonlinear dynamics of the unstable modes are followed numerically. The original state of a uniform vertical magnetic field is transformed via the instability into the nonlinear dynamical equilibrium with a highly intermittant distribution of the magnetic field. Magnetic flux is concentrated in a relatively small area surrounded by an almost field-free region. The role of the fluid motion in the hydromagnetic equilibrium is emphasized. Although the relevance of the instability to the process of sunspot formation is rather questionable, the resulting equilibrium structures are similar to mature spots in their thermal and magnetic properties. Also, the simulated flow structure agrees with helioseismic tomography results.     

Dissipation of magnetic flux and magnetic energy in partially ionized gases

Macroscopic equations of motion are used to derive several forms of the generalized Ohm's law for partially ionized ternary gases in magnetic fields, and a conductivity σ is defined that is independent of the magnetic field. A flux theorem is derived using a velocityu _H that can be defined to be the velocity of magnetic field lines;u _H is only slightly different from the velocity of the electron component of the gas. It is shown that σ is the conductivity relevant to the decay of magnetic flux through any surface moving everywhere with velocityu _H . The rate of increase of the thermal energy density of the gas arising through collisions between particles of different species can be resolved into Joule heating at the ratej ²/σ, wherej is the current density, and heating associated with ambipolar drift. The latter, contrary to what has been claimed by some authors, is not necessarily fully compensated by a decrease in the energy of the electromagnetic field. In many applications such compensation does occur, but it may not in interstellar clouds where large amounts of gravitational energy can be made available by collapse, and then both heating and an increase in electromagnetic field energy may occur.     

Catastrophe of coronal magnetic flux ropes in partially open magnetic fields

Using a 2.5-D, time-dependent ideal MHD model in Cartesian coordinates, a numerical study is carried out to find equilibrium solutions associated with a magnetic flux rope in the corona. The ambient magnetic field is partially open, consisting of a closed arcade in the center and an open field at the flank. The coronal magnetic flux rope is characterized by its magnetic properties, including the axial and annular magnetic fluxes and the magnetic helicity, and its geometrical features, including the height of the rope axis, the halfwidth of the rope and the length of the vertical current sheet below the rope. It is shown that for a given partially open ambient magnetic field, the dependence of the geometrical features on the magnetic properties displays a catastrophic behavior, namely, there exists a certain critical point, across which an infinitesimal enhancement of the magnetic parameters causes a finite jump of the geometrical parameters for the rope. The amplitude of the jump depends on the extent to which the ambient magnetic field in open, and approaches to zero when the ambient magnetic field becomes completely closed. The implication of such a catastrophe in solar active phenomena is briefly discussed.     

Transversal small-scale MHD perturbations in space plasma with magnetic surfaces

This paper analyzes transversal small-scale perturbations in arbitrary three-dimensional (3D) spatially nonuniform space plasma systems with magnetic surfaces and deduces a system of equations for these perturbations. It shows that a dipole magnetic field can have perturbations of two different polarizations. Within dipole geometry, it derives equations for MHD-eigenmodes and investigates stability of the perturbations.     

Stellar oscillations and magnetic field perturbations of the boundary conditions

The effect of a weak magnetic field on the adiabatic radial and non-radial oscillations of a stellar configuration is studied by means of a perturbation method. Special attention is devoted to the perturbation of the oscillation frequencies resulting from the change of the boundary conditions caused by the magnetic field. This change is related to the fact that the introduction of a magnetic field removes the singularity at the surface of the equilibrium configuration. The perturbation method is applied to Ferraro's model and the influence of a magnetic field on the frequencies of the different types of oscillation modes is discussed.     

Additional results for unstable stratified toroidal magnetic fields in stars

General conditions for adiabatic instability of weak axisymmetric toroidal magnetic fields are obtained. In particular all fields which haveH =0 and H ² />0 simultaneously are unstable. This includes all fields which exist near to the axis of symmetry and, indeed, any without an infinite current density anywhere. A detailed discussion is given of fields with an angular dependenceH ² |P (cos )|. These fields are dynamically unstable with respect to both axisymmetric and non-axisymmetric perturbations for all values of the azimuthal wave number |m|. The maximum growth rates are independent ofm and they are largest for the fields that are defined in the regions closest to the polar axis.     

A magnetic boundary signature within flux transfer events

We present high resolution AMPTE-UKS data for a FTE signature in the magnetosphere. When the observations are confronted with the canonical model for such events, we find that we can substantiate clearly the existence of the two field regions (draping vs twisting) predicted from the model. In addition to these regions there is a separate, distinct region close to the expected boundary between open and closed field lines which we estimate to be of order ten ion gyroradii thick. This region is distinguished by a distinctive field and particle signature. The magnetic signature has not been reported before, but the electron signature bears a close resemblance to the electron heat flow layer reported in the ISEE data by Scudder et al. [1984 in Magnetic Reconnection in Space and Laboratory Plasmas (Edited by Hones E.W., Jr.), p. 153. AGU, Washington]. Other observations we report are the occurrence of a large flow burst and, in the central region of the FTE signature, the presence of magnetic field oscillations of period ∼ 3 s.