Monochromatic images in stokes parameters and the structure of magnetic fields in sunspots

Taking into account magneto-optical effects, we have obtained numerical solutions of the transfer equations for the Stokes parameters, calculated the linearly polarized intensity (U) and constructed its monochromatic images of unipolar sunspots. By comparison with the observational material of the vector magnetograph of the Marshall Space Flight Center, Huntsville (Alabama), we have found that the model of radial magnetic fields may give rise to U monochromatic images close to those observed. The same conclusion has been obtained previously by Landi Degl'Innocenti (1979), although his analysis was performed with the Milne-Eddington approximation instead of a detailed sunspot model. Moreover, we have shown that the model of spiral magnetic fields leads to results in contrast with observations.     

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.     

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.     

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.     

Distribution of sunspots according to their magnetic fluxes

The occurrence frequency distribution of sunspots in different magnetic flux values has been examined. The number of sunspots decreases as ^-1.9 for sunspots with magnetic flux greater than 3 × 10²¹ Maxwell, where is the said flux of a sunspot.     

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 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.     

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 polarization of continuum radiation in sunspots

Expressions are derived for the Stokes parameters of light scattered by a layer of free electrons and hydrogen atoms in a sunspot. A physically reasonable sunspot model was found so that the direction of the calculated linear polarization agrees reasonably with observations. The magnitude of the calculated values of the linear polarization agrees generally with values observed in the continuum at 5830 Å. Circular polarization in the continuum also accompanies electron scattering in spot regions; however for commonly accepted values of the longitudinal magnetic field, the predicted circular polarization is much smaller than observed.