Monochromatic images of sunspots in linearly polarized radiation and the structure of their magnetic fields

When unipolar sunspots are observed in the linearly polarized radiation represented by the Stokes parametersQ andU of magneto-sensitive spectral lines, their images display a complicated and interesting configuration. This is caused by the magneto-optical effect and also is connected with the 3-D structure of spot magnetic fields. In the process of numerical simulation it is possible to infer the regularity of variation of the angle of inclination of magnetic lines of force with distance from the spot center.     

On the diagnostic of magnetic fields in sunspots through the interpretation of stokes parameters profiles

The inversion routine proposed by Aueret al. (1977), for the determination of vector magnetic fields from Stokes profiles, has been generalized to include magneto-optical and damping effects. Synthetic profiles have then been generated from a sunspot model atmosphere accounting for the depth variation of the relevant physical parameters such as the magnetic field amplitude, inclination angle, etc...., each variation being considered one at a time. Alfvén waves and magnetic inhomogeneities over the field of view have also been considered. These synthetic profiles have been presented to the inversion routine. The results of the fits show that the magnetic field amplitude and direction are always recovered with good accuracy when these quantities are constant in the model atmosphere, and, in those cases where te magnetic field vector is supposed to vary monotonically with optical depth, the values recovered are always intermediate between the values corresponding to the top and bottom of the atmosphere. Moreover, we found that the differences between synthetic and best-fit profiles are able to characterize, in many cases, the particular physical situation considered.     

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.     

Measurements of magnetic fields and the analysis of stokes profiles

Recent advances in polarimetry allowing the recording of polarized line profiles with high spectral resolution and signal-to-noise ratio over large portions of the solar spectrum offer rich new diagnostic possibilities. Thus we can now in a systematic way build models of the height variation of the magnetic field, temperature, density, and mass motions in the spatially unresolved subarcsecond magnetic structures. The analysis of the Stokes spectra also allows us to build a foundation for proper diagnostics of vector magnetic fields, a goal that cannot be achieved before the intrinsic properties of the spatially unresolved magnetic fields have been determined. Another new diagnostic tool is the Hanle effect. A recent exploratory survey of coherence effects through the recording of the linear polarization with high spectral resolution throughout the whole visible solar spectrum aims at establishing a foundation for the exploitation of the Hanle effect on the solar disk.This review describes these developments, most of which have taken place in the 1980s, and summarizes the results obtained so far.     

On the magnetic fields and motions in sunspots at different atmospheric levels

The distribution of the magnetic field and radial velocities in the sunspot group were investigated simultaneously at two atmospheric levels (H and 6302.499 Å) of the Sun inside the area of 35 × 80 photographically (Abdussamatov, 1970) using the method of escalation. The outward motion of matter in the spot umbra was detected.Distributions of the magnetic field at both levels are well correlated. The magnetic field motions are observed in the sunspot. The vertical gradient H decreases slightly in the direction of increasing H. The minimum of brightness I in sunspots corresponds to the maximum of H.     

The determination of vector magnetic fields from stokes profiles

The application of Unno's (1956) solution of the transfer equation for polarized radiation to the determination of thevector magnetic field is investigated. An analysis procedure utilizing non-linear least squares techniques is developed that allows one to automate the reduction of measured spectral profiles of the Stokes parameters to determine the field angles, strength as well as other parameters. The method is applied to synthetic spectra generated using a model solar atmosphere and yields results of remarkably high accuracy. The influence of additional factors upon determination of the vector field are also considered. These factors include effects of asymmetric profiles, magneto-optical effects, magnetic field gradients, unresolved field elements, scattered light, and instrumental noise.The National Center for Atmospheric Research is sponsored by the National Science Foundation.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

The profiles of the stokes parameters and the magnetic field vector

On the basis of our numerical solution of the equations of transfer of Stokes parameters, we have established in this paper a method for the determination of the magnetic field strength H and the angle between the field line and the line of sight γ, using observed profile of parameter Q.     

Magneto-optical effects and the determination of vector magnetic fields from stokes profiles

The analysis procedure proposed by Auer et al. (1977) for deducing magnetic field vectors from Stokes profiles has been tested to investigate the influence of magneto-optical effects on the deduced field parameters. The quality of the fit between synthetic profiles generated with the inclusion of magneto-optical effects and the profiles returned by the inversion routine is also investigated. The results show that magneto-optical effects should be included in the inversion routine especially to increase the accuracy of the deduced, azimuth of the magnetic field.     

The measurement of magnetic fields in the solar atmosphere above sunspots using gyroresonance emission

An analysis of the local sources (LS) structure of the S-component of solar radio emission confirms the presence of a core component which is characterized by strong circular polarization and a steep growing spectrum at shorter centimeter wavelengths. These details coincide in position with the sunspots' umbra and their height above the photosphere does not generally exceed about 2000 km. Gyroresonance emission of thermal electrons of the corona is generally accepted as being responsible for this type of emission. The spectral and polarization observations of LS made with RATAN-600 using high resolution in the wavelength range 2.0–4.0 cm, allow us to measure the maximum magnetic fields of the corresponding sunspots at the height of the chromosphere-corona transition region (CCTR). This method is based on determining the short wavelength limit of gyroresonance emission of the LS and relating it to the third harmonic of gyrofrequency.An analysis of a large number of sunspots and their LS (core component) has shown a good correlation between radio magnetic fields near the CCTR and optical photospheric ones. The magnetic field in CCTR above a sunspot is found only 10 to 20% lower than in the photosphere. The resulting gradient of the field strength is not less than 0.25 G km^–1. This result seems to contradict the lower values of magnetic fields generally found above sunspots using the chromospheric H line. Some possible ways of overcoming this difficulty are proposed.     

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.     

Magnetic fields in small and young sunspots

Preliminary results of magnetic field measurements in small sunspots from spectrograms obtained with the aid of the McMath Solar Telescope at the Kitt Peak National Observatory are presented. The measured intensities are greater than or equal to about 1200 Gauss. Furthermore, a broadening of the Fei line 6302.508 Å was found in some places of intergranular space. The importance of intergranular space as a possible potential earliest stage of sunspot development is mentioned.Kitt Peak National Observatory, Contribution No. 222.Visiting Astronomer, 1964, Kitt Peak National Observatory.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the Nat. Science Foundation.     

On the use of seares' formulae in the determination of the direction of magnetic fields in sunspots

In this paper our numerical solution of the transfer equations of the Stokes parameters in the presence of magnetic fields is used to calculate the intensity ratios of the components of Zeeman triplets and their relations with the intensity and direction of magnetic fields. From this we have shown that the application of Seares' formulae to the determination of the direction of the magnetic fields in sunspots may give rise to very large errors. A suggestion for the improvement of this method is made.     

On the height scale of magnetic fields above sunspots derived from RATAN-600 observations

Model calculations of the S-component are compared with observations of the RATAN-600 telescope at five discrete microwave frequencies referring to active region McMath No. 15974 on May 1, 1979. The spectral variations of source diameter, flux density, and degree of polarization are used to derive the height scale of the magnetic field in accordance with a magnetic dipole distribution under the assumption of advanced temperature and electron density distributions according to most recent EUV observations.     

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.

     

On the internal structure and magnetic fields of

First, a sequence of four-zone models for the interior of Venus is constructed under the assumption of hydrostatic equilibrium. While the equation of state for each zone is taken to be the Bullen's relation with its coefficients consistent with the PREM Earth model (Dziewonski and Anderson, 1981), the position of core-mantle boundary is determined by matching solutions of the Emden's equation in different regions. The results of hydrostatic models indicate the presence of a reasonably large molten iron core in Venus, broadly similar to the Earth. It is also found that the position of the core-mantle interface is nearly model-independent. Second, we focus on the question why Venus does not possess a significant global magnetic field and on what we can learn from this fact. Solutions of magnetohydrodynamic equations appropriate for the molten core of Venus are discussed. It is argued that, because the Elsasser number measuring the relative importance of Coriolis and Lorentz forces satisfies 1, equations for the problem of thermal convection in the Venusian fluid core must be nearly uncoupled with the dynamo equation. The existence of a global magnetic field, though small, then suggests that the size of the magnetic Reynolds numberR _m must beR _m =O(10), sustaining a dynamo action near its marginal state but not an active dynamo in the Venusian molten core. On the basis of asymptotic relations for finite amplitude convection, a useful constraint on important physical parameters for the liquid core of Venus is derived and discussed.     

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.     

Development of structure in pores and sunspots: flows around axisymmetric magnetic flux tubes

Flux elements, pores and sunspots form a family of magnetic features observed at the solar surface. As a first step towards developing a fully non-linear model of the structure of these features and of the dynamics of their interaction with solar convection, we conduct numerical experiments on idealized axisymmetric flux tubes in a compressible convecting atmosphere in cylindrical boxes of radius up to 8 times their depth. We find that the magnetic field strength of the flux tubes is roughly independent of both distance from the centre and the total flux content of the flux tube, but that the angle of inclination from the vertical of the field at the edge of the tube increases with flux content. In all our calculations, fluid motion converges on the flux tube at the surface. The results compare favourably with observations of pores; in contrast, large sunspots lie at the centre of an out-flowing moat cell. We conjecture that there is an inflow hidden beneath the penumbrae of large spots, and that this inflow is responsible for the remarkable longevity of such features.     

The structure of sunspots

As a first step in constructing three-dimensional decaying sunspot models we select the relevant observational data. From these we conclude:

1. sunspots, except the smallest, obey a radial and evolutionary similarity;
2. sunspots may be considered as isolated, fairly well defined flux tubes, wrapped in thin current sheets;
3. a substantial number among stable regular spots show a phase of slowest decay whose rate is independent of the spot's area.

Arguments are given that the slowest rate of decay is ultimately determined by Ohmic dissipation in the inner part of the current sheet. Preliminary asymptotic models for the deep layers (deeper than 2000 km below the photosphere) are given which satisfy the above three constraints. To meet the observed rate of slowest decay the current sheet has to be very thin, about 10^?5 to 10^?4 times the umbral radius. Radial large-scale fluid motions are required in the current sheet to maintain the similarity of the structure. The radial motions are linked with the vertical motions which may be connected with the Evershed flow. Finally we discuss details which are less relevant in the large-scale structure of stable sunspots, such as fine structures, twists, the break-down of the similarity and the relation between sunspots and smaller magnetic structures, and the intrinsic scatter in some observed quantities.