Line formation in a magnetic field and the interpretation of magnetographic measurements

The strong temperature dependence of the line Fei 5250.2 has been studied by calculating line contours and magnetographic calibration curves for different spot models and the BCA. Line contours calculated for arbitrary depth dependence of the magnetic field vector show depolarization effects within the Zeeman components for transversal fields with variable direction and changes of the observed plane of polarization if anomalous dispersion is taken into account.The observed anomalous splitting of the -component may be interpreted best by suggesting discrete inhomogeneities of the magnetic field within sunspots.     

A New Method for Resolving the 180° Ambiguity in Solar Vector Magnetograms

We present a new method to resolve the 180° ambiguity for solar vector magnetogram measurements. The basic assumption is that the magnetic shear angle (), which is defined as the difference between the azimuth components of observed and potential fields, approximately follows a normal distribution. The new method is composed of three steps. First, we apply the potential field method to determine the azimuthal components of the observed magnetic fields. Second, we resolve the ambiguity with a new criterion: –90°+_mp lele90°+_mp, where _mp is the most probable value of magnetic shear angle from its number distribution. Finally, to remove some localized field discontinuities, we use the criterion B _tB _mt ge0, where B _t and B _mt are an observed transverse field and its mean value for a small surrounding region, respectively. For an illustration, we have applied the new ambiguity removal method (Uniform Shear Method) to a vector magnetogram which covers a highly sheared region near the polarity inversion line of NOAA AR 0039. As a result, we have found that the new ambiguity solution was successful and removed spatial discontinuities in the transverse vector fields produced in the magnetogram by the potential field method. It is also found that our solution to the ambiguity gives nearly the same results, for highly sheared vector magnetograms and vertical current density distributions, of NOAA AR 5747 and AR 6233 as those of other methods. The validity of the basic assumption for an approximate normal distribution is demonstrated by the number distributions of magnetic shear angle for the three active regions under consideration.     

Potential models of the unipolar sunspot magnetic field

The potential models of the unipolar sunspot magnetic field are calculated on the basis of magnetographic measurements of the magnetic field made in the three spectral lines of different intensities, H, Cai 6103 and Fei 4808. The computed distributions of the magnetic field vector are compared with actual distributions observed at these three levels. It is shown that the electric current density in the spot reaches values up to 10⁵ CGSE in the volume contained between formation depths of two pairs of lines, Fei 4808-Cai 6103 and Fei 4808 - H. Therefore, the magnetic field of the spot deviates strongly from a potential configuration. To the contrary, at higher levels, in the semi-infinite volume restricted at the bottom by the hydrogen H-line, the field appears to be quite close to a potential one.     

Vector magnetic fields in sunspots

Observations of a round, unipolar sunspot in the Zeeman triplet Fe i 6302.5 with the High Altitude Observatory Stokes Polarimeter are used to derive the vector magnetic field in the spot. The behavior of the magnitude, inclination, and azimuth of the field vector B across the spot is discussed. A linear relation is found between the continuum intensity I _c and the field magnitude B. Time series obtained in the umbra show significant power in the magnitude of the field at a period of t 180 s but the other components of the field vector do not display this behavior.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Topology of Magnetic Field and Coronal Heating in Solar Active Regions – II. The Role of Quasi-Separatrix Layers

The photospheric vector magnetic fields, H and soft X-ray images of AR 7321 were simultaneously observed with the Solar Flare Telescope at Mitaka and the Soft X-ray Telescope of Yohkoh on October 26, 1992, when there was no important activity in this region. Taking the observed photospheric vector magnetic fields as the boundary condition, 3D magnetic fields above the photosphere were computed with a new numerical technique. Then quasi-separatrix layers (QSLs), i.e., regions where 3D magnetic reconnection takes place, were determined in the computed 3D magnetic fields. Since Yohkoh data and Mitaka data were obtained in well-arranged time sequences during the day, the evolution of 3D fields, H features and soft X-ray features in this region can be studied in detail. Through a comparison among the 3D magnetic fields, H features and soft X-ray features, the following results have been obtained: (a) H plages are associated with the portions of QSLs in the chromosphere; (b) diffuse coronal features (DCFs) and bright coronal features (BCFs) are morphologically confined by the coronal linkage of the field lines related to the QSLs; (c) BCFs are associated with a part of the magnetic field lines related to the QSLs. These results suggest that as the likely places where energy release may occur by 3D magnetic reconnection, QSLs play an important role in the chromospheric and coronal heating in this active region.     

Coronal density and temperature gradients

Mean density models of the solar corona show evidence for two distinctive density regimes characterized by different density gradients. High density gradients are identified with regions of predominantly open magnetic lines of force and low density gradients are identified with regions of predominantly closed magnetic lines of force. Spectroscopic data yielding equivalent widths of forbidden lines of Fe x and Fe xiv strongly suggest that the coronal temperature for r > 2.5 R decreases considerably less rapidly in equatorial regions than r ^–2/7, which is the decrease predicted by conduction models with open field lines.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Photospheric electric current and transition region brightness within an active region

Distributions of vertical electric current density (J _z) calculated from vector measurements of the photospheric magnetic field are compared with ultraviolet spectroheliograms to investigate whether resistive heating is an important source of enhanced emission in the transition region. The photospheric magnetic fields in Active Region 2372 were measured on 6 and 7 April, 1980 with the MSFC vector magnetograph; ultraviolet wavelength spectroheliograms (L and Nv 1239 Å) were obtained with the UVSP experiment aboard the Solar Maximum Mission satellite. Spatial registration of the J _z (5 arc sec resolution) and UV (3 arc sec resolution) maps indicates that the maximum current density is cospatial with a minor but persistent UV enhancement, but there is little detected current associated with other nearby bright areas. We conclude that although resistive heating may be important in the transition region, the currents responsible for the heating are largely unresolved in our measurements and have no simple correlation with the residual current measured on 5 arc sec scales.National Research Council Resident Research Associate.National Oceanic and Atmospheric Administration Space Environment Laboratory; currently at MSFC/SSL.     

Electric currents and Hα emission in two active regions on the sun

We investigated the structure of magnetic field and vertical electric currents in two active regions through a comparison of the observed transverse field with the potential field, which was computed according to Neumann boundary-value problem for the Laplace equation using the observed H _z -value. Electric currents were calculated from the observations of the transverse magnetic field.There exist two systems of vertical electric currents in active regions: a system of local currents and a global one. The global current is about 2 × 10¹² A. In the leading part of the active regions it is directed upward, and in the tail downward.Flare activity is closely connected with the value and direction of both local and global currents: the flares tend to apear in places with upward currents. The luminosity of H flocculi is also connected with vertical electric currents; the brighter the flocculi, the more frequently they appear in places of upward electric currents.The sensitivity of H emission to the sign of the current suggests that charged particles accelerated in the upper parts of magnetic loops may be responsible for these formations. Joule heating might be important for flocculi, if plasma conductivity is about 5 × 10⁸ c.g.s.e.A model of a flare is suggested based on current redistribution in a system of emerging loops due to changes of loop inductance.     

Hβ Doppler-velocity fields within sites of flares in a solar active region

In this paper, we analyze the relationship between photospheric magnetic fields and chromospheric velocity fields in a solar active region, especially evolving features of the chromospheric velocity field at preflare sites. It seems that flares are related to unusually distributed velocity field structures, and initial bright kernels and ribbons of the flares appear in the red-shifted areas (i.e., downward flow areas) close to the inversion line of H Dopplergrams with steep gradients of the velocity fields, no matter whether the areas have simple magnetic structure or a weak magnetic field, or strong magnetic shear and complex structure of the magnetic fields. The data show that during several hours prior to the flares, while the velocity field evolves, the sites of the flare kernels (or ribbons) with red-shifted features come close to the inversion line of the velocity field. This result holds regardless of whether or not the flare sites are wholly located in blue-shifted areas (i.e., upward flow areas), or are far from the inversion line of the Doppler velocity field (V = 0 line), or are partly within red-shifted areas. There are two cases favourable for the occurrence of flares, one is that the gulf-like neutral lines of the magnetic field (B = 0 line) occur in the H red-shifted areas, the other is that the gulf-like inversion lines of the H Doppler velocity field (V = 0 line) occur in the unipolar magnetic areas. These observational facts indicate that the velocity field and magnetic field have the same effect on the process of flare energy accumulation and release.     

Complete determination of the magnetic field vector and of the electron density in 14 prominences from linear polarizaton measurements in the HeI D3 and Hα lines

The present paper is devoted to the interpretation of linear polarization data obtained in 14 quiescent prominences with the Pic-du-Midi coronagraph-polarimeter by J. L. Leroy, in the two lines Hei D₃ andH quasi-simultaneously. The linear polarization of the lines is due to scattering of the anisotropic photospheric radiation, modified by the Hanle effect due to the local magnetic field. The interpretation of the polarization data in the two lines is able to provide the 3 components of the magnetic field vector, and one extra parameter, namely the electron density, because the linear polarization of H is also sensitive to the depolarizing effect of collisions with the electrons and protons of the medium. Moreover, by using two lines with different optical thicknesses, namely Hei D₃, which is optically thin, and H, which is optically thick ( = 1), it is possible to solve the fundamental ambiguity, each line providing two field vector solutions that are symmetrical in direction with respect to the line of sight in the case of the optically thin line, and which have a different symmetry in the case of the optically thick line.It is then possible to determine without ambiguity the polarity of the prominence magnetic field with respect to that of the photospheric field: 12 prominences are found to be Inverse polarity prominences, whereas 2 prominences are found to be Normal polarity prominences. It must be noticed that in 12 of the 14 cases, the line-of-sight component of the magnetic field vector has a Normal polarity (to the extent that the notion of polarity of a vector component is meaningful; no polarity can be derived in the 2 remaining cases); this may explain the controversy between the results obtained with methods based on the Hanle effect with results obtained through the Zeeman effect. A dip of the magnetic field lines across the prominence has been assumed, to which the optically thick H line is sensitive, and the optically thin Hei D₃ line is insensitive.For the Inverse prominences, the average field strength is 7.5±1.2 G, the average angle,, between the field vector and the prominence long axis is 36° ± 15°, the average angle, , between the outgoing field lines and the solar surface at the prominence boundary is 29° ± 20°, and the average electron density is 2.1 × 10¹⁰ ± 0.7 × 10¹⁰ cm^–3. For the Normal prominences, the average field strength is 13.2±2.0 G, the average angle,, between the field vector and the prominence long axis is 53° ± 15°, the average angle, , between the outgoing field lines and the solar surface at the prominence boundary is 0° ± 20° (horizontal field), and the average electron density is 8.7 × 10⁹ ± 3.0 × 10⁹ cm^–3.     

Magnetic field and electric current structure in the chromosphere

Three dimensional vector magnetic field structure throughout the chromosphere above an active region is deduced by combining high resolution H filtergrams with a simultaneous digital magnetogram. An analog model of the field is made with 400 metal wires representing fieldlines which are assumed to outline the H structure. The height extent of the field is determined from vertical field gradient observations around sunspots, from observed fibril heights and from an assumption that the sources of the field should be largely local. After digitization the magnetic field H matrix is retrieved. Electric current densities j are computed from j=curl H. The currents (typically 10 mA m^–2) flow in patterns not similar to observed features and not parallel to magnetic fields. Lorentz forces are computed from {ie0323-01}. The force structures correspond to observed solar features and a series of observed dynamics may be expected: downward motion in bipolar areas in lower chromosphere, an outflow of the outer chromosphere into the corona with radially outward flow above bipolar plage regions (where coronal streamers are observed) and motions of arch filament systems. Observed current structure and magnitude agree well with previous vector magnetograph observations but disagree with theoretical current-free or force-free concepts. A dynamic chromosphere with electromagnetic forces in action is thus inferred from observations.     

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.     

The coronal and interplanetary magnetic fields at the time of the solar eclipse of 7 March, 1970

The magnetic field in the outer corona and in interplanetary space has been calculated from the photospheric magnetic fields measured around the time of the 7 March, 1970 eclipse. The field-line maps are compared with eclipse photographs showing coronal structures out to about 12 r . The projected field lines as well as the observed streamers appear straight. This is caused by the rapid expansion of the outer corona and is not an indication of corotation. The calculations show that the angular velocity of the coronal plasma decreases rapidly with distance.The relation between magnetic fields and density enhancements is discussed. The field strength in the photosphere seems to determine the amount of mechanical heating of the lower corona. The density structure higher up in the corona will, however, depend decisively on the topology of the field, particularly on whether we are on open or closed field lines, and not simply on field strength.The calculations show a sector structure of the interplanetary field, which agrees well with spacecraft observations. Also the magnitudes of the observed and calculated interplanetary field agree after the Mt. Wilson magnetograph data have been corrected to account for the temperature and saturation effects in the spectral line Fei 5250 Å.On leave from the Astronomical Observatory, Lund, Sweden.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Magnetic fields in quiescent prominences

We discuss the longitudinal component of the magnetic field, B , based on data from about 135 quiescent prominences observed at Climax during the period 1968–1969. The measurements are obtained with the magnetograph which records the Zeeman effect on hydrogen, helium and metal lines. Use of the following lines, H; Hei, D₃, Hei, 4471 Å; Nai, Di and D₂, leads to the same value for the observed magnetic field component in these prominences. For more than half of the prominences their mean field, B , satisfy the inequalities 3 G B 8 G, and the overall mean value for all the prominences is 7.3 G. As a rule, the magnetic field enters the prominence on one side and exits on the other, but in traversing the prominence material, the field tends to run along the long axis of the prominence.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Equilibrium of self-gravitating polytropic cylinders with a magnetic field

The effect of a prevalent magnetic field on static and uniformly rotating self-gravitating cylinders of infinite length is examined. The magnetic field is assumed to consist ofH andH _z components, which are taken to be functions of the radial coordinate alone. A variety of magnetic-field configurations are shown to be admissible solutions of equations of motion, from which some feasible cases are presented. A particular magnetic-field configuration having bothH andH _z components is studied in detail. The configuration is such that the assumption of a polytropic equation of state reduces the equation governing the density function to a non-homogeneous cylindrical analogue of the Lane-Emden equation for spherical polytropes. The homogeneous case is also studied and shows interesting magnetic-field patterns.     

Calculated profiles of H I lines of interest for solar plasma electric field measurements

We present calculated Stark-polarized line profiles for a number of H i lines observed in the visible and infrared emission spectrum of solar prominences and other limb activity. For use in measurements of possible electric fields in these structures, we also calculate curves giving the difference in line width between the 1/2 (I ± Q) profiles as a function of electric-field intensity. Our calculations take into account magnetic fields in these structures, and incorporate typical observed values of Doppler broadening. These calculations explicitly consider the H i fine structure neglected in previous work, and thus are more accurate in the range of low to intermediate electric-field intensity likely to be encountered in solar plasmas (E < 10³ V cm^–1). Our results enable us to compare behavior when E and B are parallel, or perpendicular. We draw particular attention to the high electric-field sensitivity of the transitions between high levels such as 12–8 and 15–9 in H i, observed in prominences at wavelengths around 11. Their sensitivity is roughly an order of magnitude larger than that of the high Paschen-series lines used in solar plasma electric field studies so far.     

Fe XXI emission line ratios as electron temperature diagnostics for the coronae of cool stars

A method for the reconstruction of the linear force-free magnetic field in a bounded domain (as a rectangular box, ) is presented here. The Dirichlet boundary-value problem for the Helmholtz equation is solved for the B _z component specified at the boundary. Chebyshev's iteration method with the optimal rearrangement of the iteration parameters sequence was used. The solution is obtained as for the positive-definite, and for the non-sign-definite difference analogue of the differential operator ² u + ² u. Specifying two scalar functions, B _x and B _y on the intersection of the lateral part of the boundary with one selected plane z = constant, and using B _z inside the , we have found B _x and B _y throughout .The algorithm was tested with the numerical procedure which gives the analytic solution B of the linear force-free field (LFFF) equations for the dipole in a half-space. The root-mean-square deviation of the analytic solution B from the calculated B does not exceed 1.0%. Boundary conditions for the B calculation were taken as given by the analytic LFFF solution B. Comparison of B with B, which was calculated by the potential non-photospheric boundary conditions, show that they differ significantly. Thus, the specification of boundary conditions at non-photospheric boundaries of the volume under consideration is of particular importance when modeling the LFFF in a bounded volume.The algorithm proposed here allows one to use the information about magnetic fields in the corona for the modeling of LFFF in a limited domain above an active region on the Sun.     

The behaviour of neutral lines in two-dimensional magnetohydrodynamic equilibria

Nonlinear equilibrium solutions for two-dimensional magnetic arcades (/z = 0) using a Grad-Shafranov equation in which the axial magnetic field and the pressure are specified as functions of the component of the vector potential in the z direction are re-examined.To compute nonlinear solutions one is restricted to seeking solutions on finite computational domains with specified boundary conditions. We consider two basic models which have appeared in the literature. In one model the field is laterally restricted by means of Dirichlet boundary conditions and free to extend vertically by means of a Neumann condition at the top of the domain. For such fields, bifurcating solutions only appear for a narrow range of values for the parameter (the ratio of a typical length scale of the field to the gravitational scale height). Nevertheless, we show that the presence of this parameter is essential for bifurcating solutions in such domains. For the second model with Neumann conditions on three sides of the domain representing the region above the photosphere we do not find bifurcating solutions. Instead high-energy solutions with detached field lines evolve smoothly from low-energy solutions which have all field lines attached to the photosphere. Again the presence or absence of detached flux is dependent on the magnitude of for those fields which are evolved quasi-statically via an increase in the plasma pressure.     

Singular points of the polarization tensor

The problem to compute the magnetic field above the chromosphere using data of the vector = B _t/Bt that gives the projected field direction can be solved with different approximations. The field of direction vectors is, however, not the only field accessible to observations. The Stokes parameters, which are components of the radiation tensor, can be measured at each point of the image plane. The directions of the eigenvectors of the radiation tensor define two mutually orthogonal systems of integral curves in the image plane. These families of curves have singular points, which are generally of different type than those of the vector field. When the morphology of H chromospheric fibrils are used to infer the topology of the magnetic field, a similar problem is met, suggesting that singular points should also be present there.