On the structure of sunspot penumbra

The structure of sunspot penumbrae is discussed in terms of bright filaments on a dark background, as opposed to dark filaments above a bright granular background.     

On the temperature structure of sunspot umbrae

From a high-resolution spectrum of a sunspot umbra (1.1 < < 2.3 m) we derive models of the temperature stratification in the deep layers of the umbra. The observed spectrum is corrected for straylight using the Hi Paschen line at gl = 1.282 m. A method is described for the iterative fitting of empirical temperature models to spectral information, and the method is applied to the present data. We find that the observed profiles of 3 high-excitation lines of Sii and the observed continuum contrast between umbra and photosphere cannot be reproduced with a single one-component model of the umbral atmosphere: the Si i lines require a model that is 460 K hotter at gt _0.5 = 3 than the continuum model. This indicates that hot and cool components coexist within the umbra. A temperature model derived from the relative intensity in the wings of 3 low-excitation lines of Mgi, Ali, and Sii is not significantly different from the continuum model.Based on observations obtained at Kitt Peak National Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc. (AURA), under contract with the National Science Foundation.     

On the inhomogeneous structure of the chromosphere-corona transition region above sunspot umbrae

Multiple wavelength observations of sunspot umbrae can only be expalined by an inhomogeneous, two-component model for the structure of the umbral transition region and lower corona. The ‘Wroclaw-Ondrejov sunspot model’ was a first step in this direction. This working model has now been improved using analytic expressions for the atmospheric structure in each component and fitting the free parameters to recent sunspot observations, particularly in EUV lines. The main component has a shallow transition region and a deep-set corona. The second, ‘active’ component has a vast transition region in relatively cool fine structure elements embedded in the coronal main component. The spatial filling factor of this active component amounts to 5–10% in sunspots with bright EUV plumes, but is is more than ten times smaller in sunspot without such plumes. Observations with high spatial and temporal resolutions are necessary to understand in more detail the basic physical processes.     

On the sunspot transition region

The EUV line emission and relative line-of-sight velocity in the transition region between the chromosphere and corona of 36 sunspot regions are investigated, based on observations with the Coronal Diagnostic Spectrometer – CDS and the Solar Ultraviolet Measurements of Emitted Radiation – SUMER on the Solar and Heliospheric Observatory – SOHO. The most prominent features in the transition-region intensity maps are the sunspot plumes. In the temperature range between log T=5.2 and log T=5.6 we find that 29 of the 36 sunspots contain one or two sunspot plumes. The relative line-of-sight velocity in sunspot plumes is high and directed into the Sun in the transition region, for 19 of the sunspots the maximum velocity exceeds 25 km s^?1. The velocity increases with increasing temperature, reaches a maximum close to log T=5.5 and then decreases abruptly.

Attention is given to the properties of oscillations with a period of 3 min in the sunspot transition region, based on observations of six sunspots. Comparing loci with the same phase we find that the 3-min oscillations affect the entire umbral transition region and part of the penumbral transition region. Above the umbra the observed relation between the oscillations in peak line intensity and line-of-sight velocity is compatible with the hypothesis that the oscillations are caused by upward-propagating acoustic waves. Information about intensity oscillations in the low corona is obtained from observations of one sunspot in the 171 Å channel with the Transition Region And Coronal Explorer – TRACE. We conclude that we observe the 3-min sunspot oscillations in the chromosphere, the transition region and the low corona. The oscillations are observable over a wider temperature range than the sunspot plumes, and show a different spatial distribution than that of the plumes.

     

The structure of a sunspot

Typical intensity profiles across a sunspot at several heliocentric angles are selected from recent observations of the Wilson Effect. In addition, the profile of the mean intensity at the surface of the spot is inferred from these observed profiles.With these data, the transfer equation is solved for the two-dimensional source function distribution within the sunspot for several models of the opacity distribution. For an opacity model in which unit optical depth in the umbra occurs at least 700 km below unit optical depth in the mean photosphere, it is possible to reproduce qualitatively all the features of the observed profiles.Although no assumption is made about the extent of the umbra below the surface, these solutions clearly show that, at a depth of 700 km below unit optical depth in the photosphere, the diameter of the umbral region, which is 10800 km at the surface, has increased to about 12000 km. Thus the shape of the umbral region below the surface is part of an inverted cone of semi-vertical angle approximately 45°. The run of gas pressure and density in the umbra is computed for the model and compared with the corresponding photospheric values.Of the National Bureau of Standards and University of Colorado.     

On forecasting the sunspot numbers

We have applied a technique recently proposed basing on learning nonlinear dynamics locally to describe the annual sunspot relative numbers. It is proved that the number of past points for prediction should be greater than 4 but less than 10. This rather simple approach yields in average relatively good results for short-term forecasts (< 11 yr). Particularly, it predicts that the current cycle no. 22 will reach a very high maximum. However, this approach must be modified in the vicinity of a grand minimum.     

The structure of a sunspot

A new model for the structure of a sunspot is put forward. The features of the model are (i) the deep inhibition of convection by magnetic fields, (ii) the formation of a cool cone above the region of inhibition of convective transfer by the energy diverted around this region, and (iii) the development of the penumbra by the interaction of strong magnetic field with thermal forces in a region where the opacity prevents the transport of energy by radiation alone. A clear distinction is made between a pore, which results from the inhibition of deep convection across an area considerably greater than that of the pore, and isolated penumbral filaments, which result from strong local fields in the surface regions.It is shown that this new model provides a simple account of the birth and development of a sunspot, and this is contrasted with the difficulties faced by alternative models.On leave from the University of Sydney.     

The structure of a sunspot

White-light photographs of a fairly regular sunspot have been obtained for all but one day of its passage across the disk. From microphotometer tracings across these photographs, intensity profiles across the spot have been obtained at several heliocentric angles, θ. Apparent sunspot, umbral and penumbral widths, have been obtained from these profiles, and an examination of these reveals that the well-known Wilson effect (Wilson, 1774) is a rather complex phenomenon comprising four main features:

1. The intensity profiles become increasingly asymmetric at large θ. The penumbra remote from the limb is poorly defined while the penumbral intensity plateau nearer the limb is well defined and sometimes enhanced by an intensity maximum near the umbra-penumbra boundary.
2. A gradual decrease in the apparent width of the disk-side penumbra may occur but this effect is barely significant compared with the rms errors of the observations.
3. The apparent width of the limb-side penumbra is independent of θ for θ < 60° but at larger heliocentric angles it increases sharply and by a significant amount.
4. The apparent umbral diameter also shows no θ-dependence for θ < 60° but beyond this it decreases in an almost complementary manner.

A general model for the structure of a sunspot is put forward which readily explains these results in a qualitative manner but it is emphasised that an adequate analysis of sunspot structure based on these observations requires solutions of the three-dimensional equation of radiative transfer.     

On the dissolution of sunspot groups

The behavior of magnetic fluxes from active regions is investigated for times near sunspot disappearance. It is found that the magnetic fluxes decrease on or near the date the spot vanishes. We investigate this effect, and conclude that it is actually due to changes in the field, rather than through dissipation of the active region fields. This is important in considerations of the large-scale behavior of solar magnetic fields.     

On the electron density in sunspot plumes

Skylab observations of EUV line intensities in sunspot plumes, reported by Noyes et al. (1985), have been used to determine electron densities from theoretical curves of MgVI and MgVIII density-sensitive line ratios.     

On the rotation rates of sunspot groups

The analysis of Greenwich sunspot data for cycle No. 18 shows: (1) higher rotation rates for the southern sunspot belt than for the northern belt, (2) lower rotation rates and a tendency to a more rigid rotation for greater sunspot groups, (3) lower rotation rates and a tendency to a more rigid rotation for older sunspot groups, (4) no dependence of rotation rates on the life-time of sunspot groups, (5) a tendency to a more rigid rotation at the activity minimum. Results Nos. 2, 3, and 5 could be interpreted in terms of the evolution and interplay of the active regions, as the regions age. If we assume that the sunspot group life-time is a function of their depth in the solar atmosphere, result No. 4 shows that rotation rates do not depend on the depth.     

On long-term periodicities in the sunspot cycle

Occurrences of interplanetary shock waves near the Earth after the powerful isolated flares of 1957–1978 are investigated. The close connection between the occurrences of shock waves and the positions of magnetic axes of bipolar groups of sunspots is suggested on the basis of a statistical study. The shock waves are principally observed when the Earth finds itself near the planes that are projected through the flares in parallel to the appropriate magnetic axes of the nearest bipolar groups. This regularity is interpreted as an indirect argument for a three-dimensional geometry for the interplanetary shock waves which, when projected on these flattened to corresponding planes, are traces of large circular arcs. The typical angular scales of isolated interplanetary shock waves are estimated as 150° and 30° parallel and perpendicular, respectively, to the magnetic axes correspondingly.     

On the center-to-limb variation of sunspot brightness

A preliminary analysis of recent measurements of the brightness ratio spot-photosphere of various authors leads to the result, that the limb-darkening of the umbra is considerably less than that of the photosphere. The small value of the center-to-limb variation implies a very small temperature gradient, which is, for optical depths >0.2, about one order of magnitude smaller than previously thought (Figure 3). This result would seem to rule out radiative equilibrium in the deeper layers (\S>0.2) of sunspot umbrae.Mitteilung aus dem Fraunhofer Institut Nr. 83.     

On the average rate of growth in sunspot number and the size of the sunspot cycle

The average rate of growth during the ascending portion of the sunspot cycle, defined here as the difference in smoothed sunspot number values between elapsed time (in months) t and sunspot minimum divided by t, is shown to correlate (r 0.78) with the size of the sunspot cycle, especially for t 18 months. Also, the maximum value of the average rate of growth is shown to highly correlate (r = 0.98) with the size of the cycle. Based on the first 18 months of the cycle, cycle 22 is projected to have an R(M) = 186.0 ± 27.2 (at the ± 1 level), and based on the first 24 months of the cycle, it is projected to have an R(M) = 201.0 ± 20.1 (at the ± 1 level). Presently, the average rate of growth is continuing to rise, having a value of about 4.5 at 24 months into the cycle, a value second only to that of cycle 19 (4.8 at t = 24 and a maximum value of 5.26 at t = 27). Using 4.5 as the maximum value of the average rate of growth for cycle 22, a lower limit can be estimated for R(M); namely R(M) for cycle 22 is estimated to be 164.0 (at the 97.5% level of confidence). Thus, these findings are consistent with the previous single variate predictions that project R(M) for cycle 22 to be one of the greatest on record, probably larger than cycle 21 (164.5) and near that of cycle 19 (201.3).     

Fine structure and evershed motions in the sunspot penumbra

The observed inhomogeneity of the intensity and Evershed motions means any model of the penumbra must be essentially inhomogeneous. A simple model is put forward in which the interaction of convection rolls with an initially homogeneous magnetohydrostatic sunspot field causes a concentration of flux in the dark filaments. This process drives Evershed motions outwards in these regions; the motions are superficial and shear the lines of force, so that the field appears stronger and more horizontal in the dark filaments. This situation must be time-dependent to avoid rapid destruc tion of the whole spot.     

On the outer boundary of the sunspot penumbra

Comparison of photographic observations and vector-magnetograph measurements demonstrate that the outer boundary of the sunspot penumbra – even in complex sunspot groups – closely follows the 0.075 T iso-gauss line of the total value of the magnetic field, corresponding approximately to the equipartition value in the photosphere. Radio observations also show this feature. The thick penumbra model with interchange convection (Jahn and Schmidt, 1994) gives the best explanation of the penumbral structure. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1020985530075     

On the maximum rate of change in sunspot number growth and the size of the sunspot cycle

Statistically significant correlations exist between the size (maximum amplitude) of the sunspot cycle and, especially, the maximum value of the rate of rise during the ascending portion of the sunspot cycle, where the rate of rise is computed either as the difference in the month-to-month smoothed sunspot number values or as the average rate of growth in smoothed sunspot number from sunspot minimum. Based on the observed values of these quantities (equal to 10.6 and 4.63, respectively) as of early 1989, one infers that cycle 22's maximum amplitude will be about 175 ± 30 or 185 ± 10, respectively, where the error bars represent approximately twice the average error found during cycles 10–21 from the two fits.