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.     

The intensity,velocity and magnetic structure of a sunspot region

A time sequence of high-resolution sunspot photographs, exposed almost simultaneously in two continuum wavelengths (4680 Å and 6400 Å), was used to study some properties of umbral fine structures (umbral dots). The lifetime of the umbral dots is found to be 1500 sec. Photometry of some bright dots leads to an observed intensity excess of 0.129 I _phot and 0.134 I _phot in the blue and red respectively. The observed mean diameter of the dots is found to be 420 km. These values still include the action of image blurring. From the color index the true intensity and diameter of the dots are estimated. It appears that the umbral dots are in reality of photospheric brightness having true diameters of 150–200 km. The spatial distribution of the dots in sunspot umbrae is discussed. Some peculiarities in recent sunspot magnetic-field observations may be explained by magnetic inhomogeneities associated with umbral dots.Presently guest investigator at the Göttingen Observatory.Previously member of the High Altitude Observatory solar project at Sacramento Peak (Contract Nr. AF (628) - 4078).     

The temperature variation across the boundary of dark spots on the solar surface

We suppose the transport of energy in a sunspot (or pore) is described by a diffusion process. The thermal conductivities in the spot and its surroundings are assumed to be constant and isotropic, but with a reduced conductivity in the spot. The sunspot and the ambient medium are represented by semi-infinite strips of variable depth, with one common boundary. This interface is a plane inclined at an arbitrary angle with respect to the vertical in order to simulate the inclined magnetic field at the umbral/penumbral, penumbral/photospheric or pore/photospheric boundary.We show that the region with high conductivity below the interface produces a thermal disturbance in the surface layers of the umbra which manifests itself as a temperature enhancement at the umbral surface in a region near the boundary, resulting in a decreased temperature contrast across the surface. The thermal disturbance in the neighboring medium is confined to a very small region.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Photospheric and chromospheric umbral dots in a decaying sunspot

Time-sequenced H filtergrams and narrow-band blue filtergrams (₀ = 4308 Å, = 10 Å) of umbral dots in a decaying sunspot were studied. The results are: (a) Photospheric umbral dots have lifetimes of about 40 min. (b) Two types of proper motion were found for photospheric umbral dots. Umbral dots born in the umbra or in the light bridge show virtually no proper motion. On the other hand, umbral dots of penumbral origin move inward to the umbra with speeds of about 0.4 km s ^–1. (c) Chromospheric umbral dots, which have dimensions of 0.6 × 1.2 in the mean, were more numerously found than photospheric umbral dots. (d) Photospheric umbral dots were observed to be associated with chromospheric umbral dots. Thus umbral dots are not phenomena confined to photospheric levels but also extend to chromospheric levels. (e) Some of the chromospheric umbral dots are unrelated to the photospheric umbral dots. They may be excited by the infalling matter from the umbral corona.Contribution from the Kwasan and Hida Observatories, University of Kyoto, No. 266.     

The fine structure of light-bridges in sunspots

High resolution photographs obtained at the Pic du Midi Observatory show that there are three types of sunspot light bridges according to their morphological structures: the photospheric ones, the penumbral ones and the umbral ones. Consequently there are no specific structures in light bridges; it results that they should not be due to specific physical properties. Properties of the fine structure of a penumbral light bridge are described.     

The intensity,velocity and magnetic structure of a sunspot region

High resolution sunspot photographs in the blue, red and infrared continuum exposed on various days were used to derive the center-to-limb variation of the intensity ratio = I _sp / I _ph. Special care was taken to correct for image blurring, scattered light and the influence of line absorption.The observed increase of specific umbral intensities _u towards the limb leads to an extremely small temperature gradient in the umbra. From geometrical changes of the profiles (Wilson effect), we derived an umbral depression of about 650 km and a density scale height of about 450 km when H ^- is assumed to be the predominant source of absorption. The penumbral depression was found to be 50 km or less. The density scale height of the umbra as computed from the observed temperature distribution is 80 km in the case of hydrostatic equilibrium. We conclude that either magnetic pressure components produce deviations from hydrostatic equilibrium or that another source of absorption, dominating in the outer layers, has to be taken into account.     

On the generation of umbral flashes and running penumbral waves

From a review of the observed properties of umbral flashes and running penumbral waves it is proposed that the source of these periodic phenomena is the oscillatory convection which Danielson and Savage (1968) and Savage (1969) ave shown is likely to occur in the superadiabatic subphotospheric layers of sunspot umbras. Periods and growth rates are computed for oscillatory modes arising in a simple two-layer model umbra. The results suggest that umbral flashes result from disturbances produced by oscillatory convection occurring in the upper subphotospheric layer of the umbra where the superadiabatic temperature gradient is much enhanced over that in lower layers, while running penumbral waves are due to oscillations in a layer just below this upper layer.     

The Relationships of Sunspot Magnetic Field Strength with Sunspot Area, Umbral Area and Penumbra-Umbra Radius Ratio

Stokes profile inversion is very important to get the information on the vector magnetic field. Because the magnetic fields cannot be directly observed, adopting Stokes spectrum analysis to obtain vector magnetic field has become the major technique recently. Therefore, by Stokes profile inversion, we obtained vector magnetic fields of two layers based on the numerical solution (DELO solution, ReEs et al., 1989) to the polarized radiative transfer equation. We analyze the relationships of sunspot magnetic field strength with sunspot area, umbral area and penumbra-umbra radius ratio. By statistical research, it is found that the field strengths of the upper layer and the lower one decrease with the increasing penumbra-umbra radius ratio, and that the logarithmic expression is able to fit well the relationship between the maximum field strength of the upper layer and the sunspot area. Furthermore, we verify the result obtained by Ringnes and Jensen (1961) about the relationship between the maximum magnetic field strength and the umbral area, and the result obtained by Antalová (1991) of the relationship between the field strength and the penumbra-umbra radius ratio.     

Multilevel Analysis of Oscillation Motions in Active Regions of the Sun

The nature of the three-minute and five-minute oscillations observed in sunspots is considered to be an effect of propagation of magnetohydrodynamic (MHD) waves from the photosphere to the solar corona. However, the real modes of these waves and the nature of the filters that result in rather narrow frequency bands of these modes are still far from being generally accepted, in spite of a large amount of observational material obtained in a wide range of wave bands. The significance of this field of research is based on the hope that local seismology can be used to find the structure of the solar atmosphere in magnetic tubes of sunspots. We expect that substantial progress can be achieved by simultaneous observations of the sunspot oscillations in different layers of the solar atmosphere in order to gain information on propagating waves. In this study we used a new method that combines the results of an oscillation study made in optical and radio observations. The optical spectral measurements in photospheric and chromospheric lines of the line-of-sight velocity were carried out at the Sayan Solar Observatory. The radio maps of the Sun were obtained with the Nobeyama Radioheliograph at 1.76 cm. Radio sources associated with the sunspots were analyzed to study the oscillation processes in the chromosphere – corona transition region in the layer with magnetic field B=2000 G. A high level of instability of the oscillations in the optical and radio data was found. We used a wavelet analysis for the spectra. The best similarities of the spectra of oscillations obtained by the two methods were detected in the three-minute oscillations inside the sunspot umbra for the dates when the active regions were situated near the center of the solar disk. A comparison of the wavelet spectra for optical and radio observations showed a time delay of about 50 seconds of the radio results with respect to the optical ones. This implies an MHD wave traveling upward inside the umbral magnetic tube of the sunspot. For the five-minute oscillations the similarity in spectral details could be found only for optical oscillations at the chromospheric level in the umbral region or very close to it. The time delays seem to be similar. Besides three-minute and five-minute ones, oscillations with longer periods (8 and 15 minutes) were detected in optical and radio records. Their nature still requires further observational and theoretical study for even a preliminary discussion.     

The molecular spectrum of sunspots

The sunspot spectrum shows many molecular lines, of which some have been identified. These lines are formed farther out in the sunspot atmosphere than the atomic lines or the continuum, and are thus useful for probing the outer layers. Photographic spectrograms were obtained for three different sunspots under carefully selected seeing conditions, showing molecular absorption lines due to MgH, CaH, and TiO. Analysis led to estimates of the effective rotational temperatures of each; in the case of CaH, no definite conclusions could be drawn. Predicted rotational temperatures and observational f-values were calculated on the basis of model umbral atmospheres due to several authors. A new model was derived from the molecular lines measured here, and shown to differ widely from previous models. The usefulness of photographic spectra for this purpose is seriously questioned, and suggestions are made for new observations.     

OBSERVATIONS OF SUNSPOT UMBRAL OSCILLATIONS

The solar vacuum telescopes VTT and GCT at Tenerife have been used to obtain high-resolution two-dimensional spectro-polarimetric observations of oscillations in the photospheric layers of sunspots. At the GCT the area of the sunspot has been scanned by shifting the spectrograph slit; at the VTT a Fabry–Pérot interferometer has been applied to get narrow-band filtergrams directly and to scan through the line profile.The spectra of velocity oscillations show the known features of closely packed power peaks in bands of periods around 3 min (strengthened) and 5 min (weakened with respect to the quiet Sun). In the same frequency bands the more reliable VTT data show significant oscillations of the magnetic field strength as well, which could not be attributed to disturbing influences. Maximum power of both velocity and magnetic oscillations and a strong correlation between them, in the 3-min band in particular, is found to occur in those parts of the umbra where the magnetic lines of force are parallel to the line of sight. The oscillations are characterized by a marked spatial fine structure and a non-stationary behaviour.     

On the possibility of investigation of the magnetic field structure in subphotospheric layers of the Sun according to observations of sunspot torsional oscillations

A method of investigation of the magnetic field structure in subphotospheric layers of the Sun has been developed. The method is based on observations of the torisonal oscillations of single sunspots. Characteristics of the torsional oscillations have been obtained from observations of the longitudinal magnetic field and radial velocities of seven single sunspots in the photospheric line Fe I λ5253 Å. The parameters of the torsional oscillations and magnetic tubes in the deep layers have been determined. The radius of the cross section of a magnetic flux tube forming a sunspot is greatest near the Sun’s surface and is approximately equal to the radius of a sunspot umbra. Down to the deeper layers, it decreases quite quickly. The longitudinal electric current appearing in the magnetic tube changes direction. The typical time of the current changes is determined by the period of the torsional oscillations. The intensity of the longitudinal magnetic field in the tube increases with depth. The Alfven wave velocity averaged over the length of a magnetic tube is tens or hundreds of times less than this velocity in a sunspot umbra. It decreases with an increase in the period of oscillations. A decrease in the Alfven wave velocity leads to an increase in the twisting angle of magnetic field lines.     

Analysis and results of cooperative magnetographic measurements III. Vertical gradients of the magnetic field in the sunspot photosphere

We compare vertical gradients of sunspot magnetic fields which were derived for the first time from nearly simultaneous vector magnetograms. The measurements were obtained in the photospheric lines Fe I 5250 and Fe I 5253 by the vector magnetographs of the Sayan-Observatory (Irkutsk) and the Solar Observatory “Einsteinturm”. The gradients derived from the different measurements show a good correspondence with respect to the numerical values as well as to the morphological structure of the distributions in the magnetograph's field of view. In the umbral region of the spot the vertical gradients amount to about 0.32 Gkm^-1 indicating that the umbral field can extend with strong field strengths into chromosphere and corona. A circle-like area with opposite sign to the umbral gradient was found on the boundary between penumbra and surrounding photosphere. The physical significance of this area should be the goal of further observations and interpretations. Wir vergleichen Vertikalgradienten des Magnetfeldes von Sonnenflecken, die erstmals aus fast simultan aufgenommenen Vektormagnetogrammen abgeleitet wurden. Die Messungen erfolgten unter Verwendung der photosphärischen Linien Fe I 5250 Å und Fe I 5253 Å mit den Vektormagnetografen des Sayan-Observatoriums (Irkutsk) und des Sonnenobservatoriums “Einsteinturm”. Die aus den verschiedenen Messungen ermittelten Gradienten zeigen sowohl hinsichtlich der numerischen Werte als auch bezüglich der morphologischen Struktur ihrer Verteilung im Bildfeld der Magnetografen eine gute Übereinstimmung. Im Kern des Flecks erreicht der Vertikalgradient 0,32 g kin^-1. Das weist darauf hin, daß sich das umbrale Feld mit hoher Feldstärke bis in die Chromosphäre und Korona erstrecken kann. Ein kreisförmiges Gebiet mit entgegengesetztem Vorzeichen zum umbralen Gradienten ist an der Grenze zwischen Penumbra und umgebender Photosphäre zu finden. Die physikalische Bedeutung dieses Gebietes soll durch weitere Beobachtungen und Auswertungen geklärt werden.     

Vector magnetogram and dopplergram observation of magnetic flux emergence and its explanation

During 23–28 August 1988, at the Huairou Solar Observation Station of Beijing Observatory, the full development process of the region HR 88059 was observed. It emerged near the center of the solar disk and formed a medium active region. A complete series of vector magnetograms and photospheric and chromospheric Dopplergrams was obtained. From an analysis of these data, combined with some numerical simulations, the following conclusions can be drawn. (1) The emergence of new magnetic flux from enhanced networks followed by sunspot formation is an interesting physical process which can be simply described by MHD numerical simulation. The phenomena accompanying it occur according to a definite law summarized by Zwaan (1985). The condition for gas cooling and sunspot formation seems to be transverse field strength > 50 G together with longitudinal field strength > 700 G. For a period of 4 to 5 hours, the orientation of the transverse field shows little change. The configuration of field lines may be derived from vector magnetograms. The arch filament system can be recognized as an MHD shock. (2) New opposite bipolar features emerge within the former bipolar field with an identical strength which will develop a sunspot group complex. Also, arch filament systems appear there located in the position of flux emergence. The neutral line is often pushed aside and curved, leading to faculae heating and the formation of a current sheet. In spite of complicated Dopplergrams, the same phenomena occur at the site of flux emergence as usual: upward flow appears at the location of the emerging and rapidly varying flux near the magnetic neutral line, and downdraft occurs over large parts of the legs of the emerging flux tubes. The age of magnetic emerging flux (or a sunspot) can be estimated in terms of transverse field strengths: when 50 G < transverse field < 200 G, the longitudinal magnetogram and Dopplergram change rapidly, which indicates a rigourously emerging magnetic flux. When the transverse field is between 200 and 400 G, the area concerned is in middle age, and some of the new flux is still emerging there. When the transverse field > 400 G, the variation of the longitudinal magnetogram slows down and the emerging arch becomes relatively stable and a photospheric Evershed flow forms at the penumbra of the sunspot.     

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.     

Microwave emission from a sunspot

From the gyroresonance brightness temperature spectrum of a sunspot, one can determine the magnetic field strength by using the property that microwave brightness is limited above a frequency given by an integer-multiple of the gyrofrequency. In this paper, we use this idea to find the radial distribution of magnetic field at the coronal base of a sunspot in the active region, NOAA 4741. The gyroresonance brightness temperature spectra of this sunspot are obtained from multi-frequency interferometric observations made at the Owens Valley Radio Observatory at 24 frequencies in the range of 4.0–12.4 GHz with spatial resolution 2.2″–6.8″. The main results of present study are summarized as follows: first, by comparison of the coronal magnetic flux deduced from our microwave observation with the photospheric magnetic flux measured by KPNO magnetograms, we show that theo-mode emission must arise predominantly from the second harmonic of the gyrofrequency, while thex-mode arises from the third harmonic. Second, the radial distribution of magnetic fieldsB(r) at the coronal base of this spot (say, 2000–4000 km above the photosphere) can be adequately fitted by $$B(r) = 1420(1 \pm 0.080)\exp \left[ { - \left( {\frac{r}{{11.05''(1 \pm 0.014)}}} \right)^2 } \right]G,$$ wherer is the radial distance from the spot center at coronal base. Third, it is found that coronal magnetic fields originate mostly from the photospheric umbral region. Fourth, although the derived vertical variation of magnetic fields can be approximated roughly by a dipole model with dipole moment 1.6 × 10³⁰ erg G^?1 buried at 11000 km below the photosphere, the radial field distribution at coronal heights is found to be more confined than predicted by the dipole model.     

On some characteristics of umbral fine structure

Photographic spectra of the umbra of a sunspot (1971, August 24, Rome No. 6205) around 6150 Å show fine bright threads which were identified as the spectra of a lightbridge, of the bright end of a penumbral filament and of umbral dots, respectively. It was found, in agreement with the results of other authors, that the magnetic field in bright structures is considerably weaker than in dark umbral material. Analysis of line profiles of Fe ii 6149.2 Å in umbral dots indicates (a) a fieldstrength reduced by a factor 2 compared to the surroundings, (b) an outflow with v3.0 km s^–1 relative to the penumbra and (c) possibly photospheric temperatures in umbral dots.Mitteilungen aus dem Fraunhofer Institut Nr. 115.     

On the origin of strong downdrafts associated with the birth of sunspots

During the emerging phase of sunspot pores strong downdrafts are observed in photospheric lines, whereas the upward flow is not detected within the observational accuracy. For the study of the origin of these downdrafts, we present the numerical solutions of non-steady hydrodynamic equations in one dimension along the rising magnetic flux tubes. In these solutions, it is assumed that the solar gas inside the tube is initially in the hydrostatic HSRA and then the tube rises with a given velocity and configuration. The results reproduce well the observed radial velocity distributions, hence it is concluded that the observed strong downdrafts originate from the sliding matter along the rising magnetic flux tubes.     

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.     

About the Influence of a Magnetic Field on the Model Atmosphere of a Magnetic Star

A quasi-static magnetic field similar to that of a large single sunspot is assumed to be embedded in a photospheric model of an Ao star. The differences of the model atmosphere within the magnetic spot relative to the photosphere are calculated by means of the equations of hydromagnetics. The differences are small for τ ≧ I but increase towards smaller τ. The spot model is more transparent in its high layers. In equal geometrical depth the thermodynamic parameters are reduced by the magnetic field. While a small spot is darker than its photospheric surroundings, a large spot appears brighter; the wavelength dependence of its excess in brightness coincides with observations. Compared with the photosphere, the Balmer lines show narrower and deeper cores in the large spot, these differences increase towards larger quantum numbers. Also these features are qualitatively confirmed by observations. An outline is given how to extend and generalize the present model calculations.