Computation of solar magnetic fields from photospheric observations

The observational difficulties of obtaining the magnetic field distribution in the chromosphere and corona of the Sun has led to methods of extending photospheric magnetic measurements into the solar atmosphere by mathematical procedures. A new approach to this problem presented here is that a constant alpha force-free field can be uniquely determined from the tangential components of the measured photospheric flux alone. The vector magnetographs now provide measurements of both the solar photospheric tangential and the longitudinal magnetic field. This paper presents derivations for the computation of the solar magnetic field from these type of measurements. The fields considered are assumed to be a constant alpha force-free fields or equivalent, producing vanishing Lorentz forces. Consequently, magnetic field lines and currents are related by a constant and hence show an identical distribution. The magnetic field above simple solar regions are described from the solution of the field equations.     

Force-free magnetic fields in the solar atmosphere

Reliable measurements of the solar magnetic field are restricted to the level of the photosphere. For about half a century attempts have been made to calculate the field in the layers above the photosphere, i.e. in the chromosphere and in the corona, from the measured photospheric field. The procedure is known as magnetic field extrapolation. In the superphotospheric parts of active regions the magnetic field is approximately force-free, i.e. electric currents are aligned with the magnetic field. The practical application to solar active regions has been largely confined to constant-α or linear force-free fields, with a spatially constant ratio, α, between the electric current and the magnetic field. We review results obtained from extrapolations with constant-α force-free fields, in particular on magnetic topologies favourable for flares and on magnetic and current helicities. Presently, different methods are being developed to calculate non-constant-α or nonlinear force-free fields from photospheric vector magnetograms. We also briefly discuss these methods and present a comparison of a linear and a nonlinear force-free magnetic field extrapolation applied to the same photospheric boundary data. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Microwave burst spectra and solar flare magnetic fields

Microwave burst spectra are compared with the position, within the active region, of their associated flares observed in H. The magnetic fields predicted by Takakura's burst model (1972) are found to be in reasonable agreement with the fields expected at the flare locations.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

Cells of solar photospheric background magnetic fields and coronal mass ejections

The cells of photospheric background magnetic fields during Carrington rotation 2009 in October–November 2003 are considered. The small number of large sunspots and the high activity on the Sun in this period allow the correspondence between the activity of background field cells (flares) and the appearance of coronal mass ejections (CMEs) observed with the LASCO coronagraphs to be established without statistical analyses. The sunspots of opposite polarities in one background field cell are shown to serve as the legs of the same CME. The separation between them is close to 30°.     

Semi-regularities in the photospheric magnetic fields

Using Stanford large-scale magnetic field synoptic charts of rotation 1676 to 1739 and by delineating LLUMR, i.e., long-lived unipolar magnetic regions of both polarities surviving at least for four solar rotations, the semi-regular nature of their photospheric magnetic field pattern and their rotational properties have been examined. The investigation demonstrates the existence of regularities in the background field patterns as shown from the regular patterns of LLUMR rows and streams. This confirms the results of Bumba and Howard concerning regularities in large-scale photospheric magnetic field patterns. LLUMR streams seem to be arranged in a wave pattern of alternating polarities. Coronal holes and associated sections of photospheric field patterns suffer differential rotation. The rotation rates of the background field patterns which are not associated with the coronal holes are different from those which are.     

On the nature of photospheric magnetic fields beneath large coronal holes

We consider proposed mechanisms for the formation of coronal holes, and identify as crucial the issue whether the holes are permeated by rigidly rotating fields. It is suggested that the interaction between such a field and the differentially rotating, diffusive solar envelope will produce a fore aft asymmetry in the distribution of fields which emerge to the photosphere. An initial study is carried out in the context of an illustrative example, and the results indicate that the asymmetry may be observed for a certain range of parameters involving the properties of the solar envelope and the characteristic size of the emerging field pattern.     

Variations of magnetic fields and electric currents associated with a solar flare

The high-resolution vector magnetograms obtained with the solar telescope magnetograph of the Beijing Astronomical Observatory of the active region AR 4862 on 7 October, 1987, close before and after a solar flare, were used to calculate the electric current densities in the region. Then the relations between the flare and the magnetic fields as well as the electric currents were studied. The results are: (i) the transverse magnetic fields, and hence the longitudinal electric currents in the region before and after the flare, are evidently different, while the longitudinal magnetic fields remain unchanged; (ii) this confirms the result obtained previously that the flare kernels coincide with the peaks of longitudinal electric density in active regions; (iii) the close relation between the flare kernels and the electric currents indicates that the variations of the transverse magnetic fields and the longitudinal electric currents arise not from the general global evolution of the active region, but from the flare. These results tend to the conclusion that the triggering of a solar flare might be related with the plasma instability caused by the surplus longitudinal electric currents at some local regions in the solar atmosphere.     

Ni I 6768 Å line profile variations during a solar flare and their effect on the SOHO/MDI magnetic field measurements

Observational data on the Ni I 6768 Å line profile variations during the impulsive and post-impulsive phases of the July 18, 2002 while light flare (WLF) in the kernel of WLF emission and in other flare kernels are presented. The line profiles at the sites of intense photospheric motions in active regions are also studied. The effect of the observed Ni I 6768 Å line profile variations on the SOHO/MDI magnetic field measurements is estimated. The following conclusions have been reached. (1) The thermodynamic structure of the photo-spheric layers changes significantly during the flare. As a result, the Ni I line profile changes, particularly at the site of WLF emission. At this time, the line depth decreases significantly, but the line does not show any emission reversal. Subsequently, a relatively slow return to the conditions of an undisturbed photosphere is observed. (2) The technique of SOHO/MDI magnetic field measurements is insensitive to such line variations. Therefore, the detected variations during the flare did not result in any noticeable errors in the MDI longitudinal magnetic field measurements. (3) The line profile is broadened, shifted as a whole, and asymmetric at the sites of active regions where intense photospheric motions appear. In the MDI measurements, such changes in the profile lead to an underestimation of the magnetic field by approximately 10% if the line-of-sight velocity of the photo-spheric ejection is about 1.6 km s^?1.     

Temporal changes of physical conditions in the photospheric layers of a solar flare

An M4.1/1B solar flare on November 5, 2004, is investigated. The Stokes I ± V profiles of nine photospheric Fe I, Fe II, Sc II, and Cr II lines are studied for three instants of this flare (11 ^h 35 ^m , 11 ^h 39 ^m , and 11 ^h 45 ^m UT). The magnetic fields in the flare were measured in two ways: using the center-of-gravity method and by comparing the observed profiles with the theoretical ones computed with Baranovsky’s code. Analysis of the profiles reveals that the magnetic field strength peaked in the upper photosphere (logτ₅₀₀ = ?2.7) at the flare maximum (11 ^h 35 ^m ); this peak was smeared and shifted into the deeper photospheric layers as the flare evolved. The semiempirical model of the flare has two layers with an enhanced temperature: in the upper and middle photosphere. These layers also shifted deep into the photosphere as the flare evolved. The turbulent velocities at the distribution maximum increased by almost a factor of 5 compared to those in the undisturbed photosphere, while the plasma density both increased and decreased by a factor of 3–6.     

Radial velocities of the photospheric matter in a solar flare with matter ejection

We present results of a study of photospheric horizontal motions at the initial and main phases of the solar flare which happened on September 4, 1990, near the solar limb. The flare was accompanied by matter ejection. Spectra of the flare were obtained using the AZU-26 horizontal solar telescope at the MAO NAS (Terskol observatory). We found variations of the matter motion velocity’s value and direction at different stages of the photosphere during the flare development. The velocity changed in a range from −4 to 2 km/s. Comparisons of the obtained data with variations of the chromospheric radial velocities showed that the horizontal matter motions in the photosphere and chromosphere are mostly directed toward the observer but at particular time moments their direction changed. At two different knots, the time shift of the photospheric velocities is different. The highest velocities were observed at the main phase of the flare. At the initial phase of the flare, in the matter ejection region, we note a velocity increase compared with its preflare value and at the flare knots.     

Scattering of fast flare electrons in solar atmosphere and their X-ray spectrum

The evolution of the energy distributions of fast flare electrons injected towards the chromosphere are computed by the Monte Carlo method for different depths. Using these distributions, power law bremsstrahlung spectra having spectral indices increasing with photon energies are obtained.     

Propagation of flare protons in the solar atmosphere

The velocity dispersion for a large number of solar proton events is analyzed in the energy regime of 10–60 MeV. It is found for all events that the time from the flare to particle maximum t _m is well represented by a sum of two components. The first component which is energy independent describes the propagation in the solar atmosphere, the second component describes the propagation in the interplanetary medium giving a velocity dispersion v × t _m = const. The additional study of time intensity profiles, onset times, and multispaceprobe observations reveals that the propagation in the solar atmosphere consists of three processes: (1) A rapid transport process in the initial ( 1 h) phase after the event fills up a fast propagation region (FPR), which may extend up to 60° from the flare site and which is tentatively identified with a large unipolar magnetic cell as seen on H synoptic charts, (2) a large-scale drift process which is energy independent with drift velocities v _D in the range 1° v _D 4°h^-1, and simultaneously (3) a diffusion process which yields the general broadening of the intensity time profiles for eastern hemisphere events, which is, however, of less importance than previously assumed.     

Structures of chromospheric magnetic fields in the solar flare producing active region 5747

In this paper, the formation and the measurement of the H line in chromospheric magnetic fields are discussed. The evolution of the chromospheric magnetic structures and the relation with the photospheric vector magnetic fields and chromospheric velocity fields in the flare producing active region AR 5747 are also demonstrated.The chromospheric magnetic gulfs and islands of opposite polarity relative to the photospheric field are found in the flare-producing region. This probably reflects the complication of the magnetic force lines above the photosphere in the active region. The evolution of the chromospheric magnetic structures in the active region is caused by the emergence of magnetic flux from the sub-atmosphere or the shear motion of photospheric magnetic fields. The filaments separate the opposite polarities of the chromospheric magnetic field, but only roughly those of the photospheric field. The filaments also mark the inversion lines of the chromospheric Doppler velocity field which are caused by the relative motion of the main magnetic poles of opposite polarities in the active region under discussion.     

Lower atmosphere in the main phase of a two-ribbon solar flare

This paper investigates the physical state of the photosphere in the main phase of the two-ribbon solar flare on June 3, 1979. The derived models show that the photosphere was in a disturbed state for a long time during the main phase of the flare. In the models, the temperature in the upper photospheric layers is higher and that in the lower layers is lower than in the quiet-sun model atmosphere. During the flare, the heating extends to the lower photospheric layers, and the upper layers cool down. A comparison of the obtained models to those for the two-ribbon solar flare on October 7, 1979, shows that the height distributions of the temperature in the main phase of the flares are strongly different.     

A note on the magnetic network of photospheric magnetic fields

It is suggested that the magnetic network in the unipolar region of the photosphere can be interpreted as the field of loop currents along the boundary of the supergranulation cells. The currents are generated by the dynamo process associated with the supergranulation.     

Electric fields in the solar atmosphere

The gross-structure of the force-free currents in the solar atmosphere and their possible dynamics have been discussed as caused by quasi short-circuited electric fields, generated by the motion of the solar magnetic features.     

Velocity fields in the solar atmosphere

Observations of velocity fields in the solar atmosphere made with the Mount Wilson solar magnetograph are analyzed. These observations, which were made with very high velocity sensitivity, cover nearly 250 hours and were made with apertures of several sizes and at various parts of the solar disk, and in strong and weak magnetic fields. The amplitudes of the 300-sec oscillations are about 25% weaker in regions where the magnetic field is greater than 80 gauss than where the field is less than 10 gauss. No difference in the frequencies of the oscillations could be found between strong-field and field-free regions. It is suggested that the oscillations occur only where the field is absent and the lower amplitude in a strong field represents the fraction of the magnetograph aperture occupied by a magnetic field. The element sizes for the 300-sec oscillations are probably at least 5–10 arc seconds.Observations made simultaneously with two lines formed at different depths in the solar atmosphere showed small phase differences in the 5-min oscillations. The upper level showed shorter period oscillations when the lower level oscillations underwent phase changes.A short period oscillation is found superposed on the 300-sec oscillation. These SPOs come in bursts that last for a minute or two and have average amplitudes that fall in the range 0.05–0.10 km/sec peak to peak. All attempts to explain them as instrumental or seeing effects have failed. Their periods fall in the range 1–5 seconds. The horizontal scale of these oscillations is smaller than that of the 300-sec oscillations, and the SPOs are more nearly isotropic oscillations than are these around 300 seconds. They do not represent a high-frequency tail of the latter. These observations did not have a digitizing interval short enough to analyze the SPOs for power spectra, but it is clear from the tracings that they are not a nearly monochromatic oscillation as are the longer waves. The amplitudes of the SPOs in the solar atmosphere must be very large and they contribute greatly to the non-radiative energy flux. It is suggested that they represent a large microturbulence line-broadening effect.     

The generation of magnetic fields in photospheric layers

Recent observations concerning the growth and decay of photospheric magnetic flux present a challenge to the conventional picture of the photosphere as a passive medium through which flux tubes emerge inertly. Rather, they suggest the possibility that interactions between the magnetic flux and the photospheric velocity fields may give rise to changes in the observed surface flux.In this paper the physics of flux changes are reviewed and the various terms in the hydromagnetic equation which give rise to the growth and decay of magnetic flux are examined. Several kinematic models for field changes are examined and it is shown that new flux loops may be generated by suitable oscillatory velocity fields near the boundaries of existing magnetic structures, thus increasing the gross flux through the photosphere. It is suggested that this mechanism may account for the appearance of moving magnetic features (knots of opposite polarities) at the boundaries of decaying sunspots.Other models are discussed and a tentative explanation of the apparently unbalanced growth of opposite polarities is given in terms of a current-sheet model.     

An X-ray observation in the atmosphere during the August 7, 1972 solar flare

An observation carried out with a balloon-borne detector of an additional flux of secondary X-rays (E 30 keV) at large depths in the atmosphere is described. This excess is attributed to the emission of very hard X-rays during the solar flare of August 7, 1972. The propagation in the atmosphere of the secondary photons resulting from their electromagnetic interactions in the air is computed by utilizing the Monte Carlo method. The computations agree with the observed flux when a very hard solar X-ray spectrum is assumed.     

The Hanle effect and the diagnostics of turbulent magnetic fields in the solar atmosphere

The theory of the Hanle effect is used to interpret the linear polarization measured in a number of spectral lines on the solar disk near the heliographic north and south poles, in search for a turbulent magnetic field in the solar atmosphere. The Hanle depolarization is separated from a number of other effects, including collisional depolarization and scattering geometry. Although the main aim of the paper is to elucidate the physics of the Hanle effect as applied to the Sun, our results indicate the existence of hidden or turbulent magnetic flux near the temperature minimum of the solar atmosphere, with a field strength between 10 and 100 G. This field is hidden in the sense that it is not seen in measurements of the longitudinal Zeeman effect (solar magnetograms). It carries more total magnetic flux than the kG network fields.