On magnetic field gradients in sunspots

This paper is devoted mainly to a method of determining the gradient of magnetic fields. Utilizing the numerical solution of the equations of transfer of the Stokes parameters, we have calculated quantities characterizing the asymmetry and the amount of rotation of the wings of the “o” and “e” profiles of the magnetically sensitive line Fe Iλ 6302.499 as functions of the magnetic field gradient. The results of calculations have been verified with our own spectrophotometric observations of a large sunspot. The range of validity of the method is discussed, and the possible influence of the presence of magnetic field gradients on the observational data of magnetographs is investigated.     

Temporal fluctuations of the magnetic field in sunspots

The magnetic field strength in sunspots was derived from time series of two-dimensional spectra taken with the Göttingen 2D-spectrometer at the Vacuum Tower Telescope on Tenerife in August 1997. For the present measurements the magnetically sensitive line Fe?i 684.3 nm was selected. The main spot of the investigated sunspot group has a maximum magnetic field strength of 2270 G. Enhanced power of the magnetic field variations was found at the boundary between umbra and penumbra for all frequency ranges. These fluctuations are not well correlated with those of intensity variations or line shifts. Other spatial power peaks occur in a dark patch inside the centreside penumbra and at the centres of some accompanying small spots. Since no clear peaks at certain frequencies are found, the variations are not harmonic oscillations. A possible relation to Hα flares is investigated. There are several cases of published observations of magnetic field variations where flares occurred soon after the measurements, but very little before. Therefore it is not very probable that flares act as exciters of magnetic field variations.

     

A possible diagnostic method for magnetic field and velocity gradients in sunspots

We present a diagnostic method for detecting magnetic field gradients and velocity gradients in sunspots through the analysis of Stokes parameters profiles in magnetoactive lines. On one hand, the method is based on the concept of response functions for the Stokes profiles introduced by Landi Degl'Innocenti and Landi Degl'Innocenti (1977); on the other hand, it takes advantage of the diagnostic content of the residuals between observed Stokes profiles and best-fit Unno-profiles. The analysis of synthesis profiles obtained for the line 6302.502 FeI forming in the Sunspot Sunspot Model (Avrett, 1981) suggests that the method could actually be promising, at least if the dependence of the magnetic field vector on optical depth is sufficiently simple.     

Temporal variations of the magnetic field in sunspots

We obtained simultaneous spectra with a spatial resolution of 1/2 and a temporal resolution of 15 s in H, Ca ii-K, Caii 8542 Å, and three Fei lines of the sunspot group responsible for the large flares of August, 1972 (McMath No. 11976). A time series taken 1972, August 3 in the Fei 6173 Å Zeeman sensitive line was analyzed for oscillations of field strength and the angle between the field and the line of sight, and for changes of the field associated with the Ca ii-K umbral flashes discovered by Beckers and Tallant (1969). The power spectra show no significant peaks, conflicting with the results of Mogilevskii et al. (1972) who reported oscillations in the longitudinal component of the field strength with periods of 56, 90, and 150 s. Changes in the field were not observed to be correlated with the occurrence of umbral flashes. These results place restrictions on magnetic modes of energy transport between the photospheric layers and the chromospheric layers where the umbral flashes are observed.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Mangeto-optical effects in sunspots and their vector magnetic field

The system of transfer equations of the four Stokes parameters I, Q, U, V under the action of the magneto-optical effect (i.e. the Unno-Beckers equations) are numerically solved in this paper for the magneto-sensitive lines FeI λλ 6302.499 and 5324.191 using an appropriate sunspot model. The errors in the expressions for the coefficients _r and _W in Beckers' paper [2] have been corrected for. From the results of calculations, features of the profiles of the Stokes parameters dependent on the magnetic vector have been isolated. Our computations also show that the magneto-optical effect should be taken into consideration in the measurement of the vector magnetic fields.

In the fourth section of this paper we have established a simple and convenient method for obtaining-information on the magnetic vector (including the field strength B, its inclination to the line of sight γ and its azimuth χ) from the profiles of the Stokes parameters. It consists of three steps: (1) The value of B is determined from the distance of the highest point in the V-profile from the central line. (2) γ is then found from V_max, i.e maximum value of V. (3) Lastly, the angle χ is found from Q₀, i.e. the value of Q at line centre.     

The east-west inclination of magnetic field lines in sunspots

Digitized Mount Wilson sunspot data covering the interval from 1917 to 1985 are analyzed to examine the average areas of individual sunspot umbrae over small zones of central meridian distance. Assuming that systematic, east-west differences in these quantities are due to the inclination of the magnetic fields of the spots, one can calculate average east-west inclination angles for all spots and for subsets of the full data set. It is found from such an analysis that on average spot fields are inclined such as to trail the rotation by a few deg. Leading and following spots may show a tendency to be inclined slightly away from each other, in contrast to the results of an earlier study of plage magnetic fields. Growing spots tend to be inclined much more to the east than decaying spots. This is in the opposite sense to the analogous result derived from plage magnetic fields.Operated by the Association of Universities for Research in Astronomy, Inc., under Cooperative Agreement with the National Science Foundation.     

The topology of force-free magnetic field near bipolar sunspots

The topological character of a new type of solution representing a force-free magnetic field near bipolar sunspots is examined. It is shown that some of the observed topological features of chromospheric fibrils and filaments in H can be interpreted in terms of the configuration of the magnetic lines of force of the present solution. In particular, by the examples considered the observed twisted S-shape topology of lower lying fibrils and the orientation of prominences (higher filaments) associated with sunspots are successfully reproduced.Visiting scientist at the High Altitude Observatory.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

A diagnostic method for probing the possible twist of magnetic field lines in sunspots

In order to study the three-dimensional structure of sunspot magnetic fields it is necessary to determine whether the field lines are twisted, i.e., if the azimuthal angle of transverse field changes with depth. For this purpose we propose the following method. At a fixed point in a spot, and in a certain wavelength interval of a magnetic-sensitive spectral line, one may measure the two Stokes parameters Q and U and then calculate the azimuthal angle of the polarization plane. If the wavelength interval of observation is moved successively from the line center to a wing, one may draw the azimuth diagram by the method proposed by Makita (1986) and refined by us (Ye Shi-hui and Jin Jie-hai, 1987). According to our theoretical calculations, described in this paper, if sunspot field lines are sufficiently strongly twisted, the curve on this diagram contains loop structures. If the twist is rather weak, the curve is approximately semi-circular. From the direction in which the curve winds (clockwise or counterclockwise) one may infer whether the magnetic field is twisting in one direction or in the opposite. In the case of no twist at all, the curve is comparatively simple and similar to a parabola.When the sensitivity of observational data is high enough, our method can also be applied to regions of weak magnetic fields outside sunspots.This work has been supported by the National Natural Science Foundation of China under grant No. 9187006-01.     

The relationship between the longitudinal magnetic field and the line-of-sight velocity at different angular positions of sunspots

Using observational data on 14 sunspots from the Sayan Observatory vector magnetograph, a study was made of the relationship between the sunspot magnetic field and the Evershed motions. It is shown that the central area of the solar disk is dominated by an anti-correlation of the longitudinal magnetic field B and the line-of-sight velocity V when a maximum of V corresponds to the neutral line of the longitudinal field. Near the limb there usually is a coincidence of the field and velocity neutral lines. There is evidence for the possible asymmetric character of the effect with respect to the central meridian.     

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.     

Small-scale magnetic field diagnostics outside sunspots: Comparison of different methods

We analyse different observational data related to the problem of intrinsic magnetic field strength in small-scale fluxtubes outside sunspots. We conclude that the kG range of fluxtube fields follows from not only classical line ratio method, but also from other old and new techniques. For the quiet regions on the Sun, the most probable mode of such fields has a magnetic field strength of 1.2–1.5 kG assuming the rectangular field profile. To best interpret the observations, a weak background field between fluxtubes should be assumed, and its magnetic field strength is expected to increase with the filling factor of fluxtubes. The alternative point of view about subkilogauss fluxtube fields is critically examined, and possible sources of different conclusions are presented.     

On the continuum intensity-magnetic field relation along the decay phase of sunspots

We present continuum intensity-magnetic field distributions for a decaying sunspot. It is shown that a very simple model accounts for the observed correlation. The Wilson depression is determined.Based on observations made with the Vacuum Gregory Telescope (V.G.T.) and the Vacuum Newton Telescope (V.N.T.) operated on the island of Tenerife by the Universitäts-Sternwarte Göttingen and the Kiepenheuer-Institut at the Observatorio del Teide of the Instituto de Astrofisica de Canarias.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

On fine structure of the magnetic field and brightness in the penumbrae of sunspots

From investigating spectrograms of penumbrae of some sunspots it is concluded that the maximum magnetic field strength occurs in dark filaments and amounts to 1800–1900 G; the intensity of the magnetic field in dark filaments is 100–400 G larger than in the neighbouring bright filaments; the bright filaments seen in the space between the dark features cannot be attributed to the ordinary undisturbed photosphere.     

The relation between the intensities of umbra and penumbra of large sunspots

Based on pinhole photometer observations in 4–6 wavelength regions we have searched for a connection between the intensities of the umbra and the penumbra of sunspots. For the 1.67 μm wavelength region it is apparent that spots with dark umbrae also have dark penumbrae. In the other wavelength regions similar relations are found. The darkness of the spot is probably connected with the degree of complexity of the spot.     

Relation between the toroidal field in the solar convective layer and the BI-polar field of sunspots

In the solar convective layer, there is a strong toroidal field and a vertical gradient in the turbulent magnetic diffusivity. As a fluid blob rises through magnetic buoyancy, a steep gradient in the turbulent magnetic diffusivity across the surface of the blob is generated. This will perturb the toroidal field, resulting in the formation of a magnetic ring around the blob. An attempt is made to account for the concentration of the bipolar sunspot field in terms of this ring.     

Time delay effect between long quasi-periodic oscillations of 37 GHz radio sources and the magnetic field of the nearest sunspots

Measurements and the interpretation of the time delay effect between long quasi-periodic oscillations of sunspot magnetic fields and nearby millimeter radio sources observed at 37 GHz were the main goals of this work. Ground-based radio telescope operated by Metsähovi Radio Observatory, Aalto University, Finland was used to obtain time series variations of radio intensity at 37 GHz frequency, as well as, the Helioseismic and Magnetic Imager instrument on-board the Solar Dynamics Observatory spacecraft was used to obtain the magnetic field time series variations. Lags (time delays) in the interval of 15–35 minutes were obtained by cross-correlation analysis of time series and by direct geometrical measurements of distances between the radio sources and nearby sunspots. These distances were in the interval of 11–24 Mm. Corresponding time delays were defined as the relation of these distances to the sound speed. Time delays obtained by two different independent methods turned to be very close. This fact confirms the interpretation of the phenomenon under the study as a process of propagation of disturbances from the slowly oscillating sunspot to the radio source with the sound speed.     

A study of the relation between intensity oscillations and magnetic field parameters in a sunspot: Hinode observations

We present properties of intensity oscillations of a sunspot in the photosphere and chromosphere using G band and Ca II H filtergrams from Hinode. Intensity power maps as function of magnetic field strength and frequency reveal reduction of power in the G band with an increase in photospheric magnetic field strength at all frequencies. In Ca II H, however, stronger fields exhibit more power at high frequencies, particularly in the 4.5–8.0 mHz band. Power distributions in different locations of the active region show that the oscillations in Ca II H exhibit more power compared to that of the G band. We also relate the power in intensity oscillations with different components of the photospheric vector magnetic field using near simultaneous spectro-polarimetric observations of the sunspot from the Hinode spectropolarimeter. The photospheric umbral power is strongly anti-correlated with the magnetic field strength and its line-of-sight component but there is a good correlation with the transverse component. A reversal of this trend is observed in the chromosphere except at low frequencies(ν≤ 1.5 mHz). The power in sunspot penumbrae is anti-correlated with the magnetic field parameters at all frequencies(1.0 ≤ν≤ 8.0 mHz) in both the photosphere and chromosphere, except that the chromospheric power shows a strong correlation in the frequency range 3–3.5 mHz.     

Two-dimensional observations of the velocity field in and around sunspots

Doppler spectroheliograms of sunspots and their surroundings have been obtained with a spatial resolution approaching one second of arc and a time resolution of 20 s per frame. Observations of 5 sunspots, located 18°, 45°, 56°, 60° and 72° from the disk center respectively, showed considerable long-lived fine structure and, in particular, indicated the following:

1. The Evershed outflow terminated in spoke-like structures that constitute the ragged outer boundary of the penumbra. Some of these spokes extended more than 8000 km beyond the average outer boundary.
2. Although there was considerable long-lived fine structure of both Doppler polarities in the extra-penumbral photosphere, the spatially-averaged horizontal flow was outward for roughly 10000 km beyond the outer boundary of the penumbra. This extra-penumbral velocity field was distinct from the Evershed flow, and, in particular, did not represent its extension beyond the end of the penumbral spokes.

Although these results are based on observations of relatively few sunspots, they do suggest that if magnetic fields are carried outward from sunspots by material motions, then these motions are more like the supergranulation than an extension of the Evershed velocity.