Umbral boundaries,convection, and the depth of sunspots

The boundary between the umbra and penumbra of a sunspot is consistently observed to be very sharp, on the order of 500 km. Approximating the sunspot as a static region in a homogeneous medium with a radiative surface, temperature distributions resulting from a variety of convective motions exterior to the sunspot are calculated. The calculations suggest that, for the exterior convection to produce the observed boundary, the maximum depth of the region of inhibited convection below a sunspot umbra is on the order of 10³ km.     

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.     

The structure of sunspots

Magnetic field strengths in small umbrae and pores are measured using the line Ti i 6064.6 Å, which is formed purely in umbrae. We find field strengths between 1900 and 2600 G in the darkest parts of small umbrae and of well established pores; the spread is partly intrinsic. The field strength in diffuse transient protopores amounts to 1500 ± 250 G.We demonstrate that usage ofthe well-known magnetic line 6173.3 Å and other Fe i lines yield systematically smaller magnetic field strengths than Ti i 6064.6 Å. This is due to blending ofthe components with the central component due to photospheric stray light and the component. Routine measurements are therefore unreliable for small spots 251-01Based on observations at Sacramento Peak Observatory, Sunspot, New Mexico, U.S.A.     

The Faraday rotation of sunspots

In this paper the numerical solutions of the Unno-Beckers's equations for the magneto-sensitive line Fei 5250.216 are used to demonstrate the importance and role of Faraday rotation in sunspot magnetic fields and to study the influence of this effect on the measurements of the azimuth of the transverse field. We propose a method to determine the intrinsic direction of the transverse field with the observed azimuthal angle of the plane of linear polarization.     

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.     

The filamentary structure in sunspots

I use the method given in Ref. [l] to solve the nonaxisymmetric magnetostatic equation, to explain the filamentary structure in sunpots. I shall show that the dark filaments in the penumbral region of sunspots are associated with stronger magnetic fields.     

The Evershed motion in sunspots

The Evershed motion is postulated as a steady, laminar flow of material along a limiting field line which separates the umbral magnetic field from the penumbral. Assuming that the Evershed flow starts from the spot-base with a velocity which is adequate to carry the convective flux at that level, the velocity at the surface comes out to be of the order of 1 km/sec, in good agreement with the observed Evershed velocity.Supported in part by the National Science Foundation [GP-5391] and the Office of Naval Research [Nonr-220 (47)].     

Naked sunspots

Naked sunspots are spots seen in Hα to be devoid of associated plage. In magnetograms and K-line little if any opposite polarity field is found, and in soft X-ray images a blank appears in the region of the spot. In almost all cases studied in which naked spots resulted the spot groups had emerged in unipolar regions of the same polarity as the naked spot. At least half of the naked spots are associated with coronal holes. The naked spots are long-lived and show rotation rates close to the Newton-Nunn curve. Most of the naked spots had bright rims in Hα, and the one spot observed to disappear left no trace in the background magnetic field. These spots may be a means by which separation of p from f magnetic polarity occurs.     

The distribution of sunspots over the Sun

The distribution of the sunspots for the period 1967–1987 (solar cycles 20 and 21) is presented here. We find that the ±11–20° latitude belt is most prolific for the occurrence of various spot types irrespective of magnetic-field ranges. Furthermore, longitudinally sunspots occur most prolifically at six or more places on the Sun. Spatially 7–9 zones are present in each hemisphere (north or south) of the Sun where about 50% sunspots occur and occupy only about 4% area of the Sun. During the above cycles at least 5 flare zones were regularly present in each hemisphere. The existing models cannot explain these active zones on the Sun. Thus, the present analysis emphasizes the need for a new magnetic models of the Sun.     

The effects of sunspots on solar irradiance

Sunspots have an obvious direct effect upon the visible radiant energy falling upon the Earth. We show how to estimate this effect and compare it quantitatively with recent observations of the solar total irradiance (Willson et al., 1981). The sunspots explain about half of the total observed variance of one-day averages. Since the sunspot effect on irradiance produces an asymmetry of the solar radiation, rather than (necessarily) a variation of the total luminosity, we have also estimated the sunspot population on the invisible hemisphere. This extrapolation allows us to estimate the true luminosity deficit produced by sunspots, in a manner that tends toward the correct long-term average value. We find no evidence for instantaneous global re-emission to compensate for the sunspot flux deficit.     

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.     

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.     

Structure of sunspots

The sunspot models published so far do not reproduce the observed run of the umbral continuum intensities over the entire spectral range 0.5 < < 4 m. Moreover, in several previous models is the temperature gradient smaller than both the adiabatic and the radiative equilibrium gradient.Agreement between intensities computed from acceptable models and measured intensities can be obtained by introducing an additional opacity for 0.8 m, which is probably caused by the crowding of atomic and molecular lines. We present a new umbral model atmosphere with a wavelength dependent opacity enhancement factor which explains the continuum intensities and also reproduces plausible center-to-limb variations and line profiles. This model is in radiative equilibrium down to _0.5 = 1.5, with an effective temperature of 4000 ± 100K. For the deeper superadiabatic layers a small but probably significant departure from radiative equilibrium is indicated by the intensities in the range 1.5 < < 2.4 m.The uncertainties in the present model and the effect of the additional opacity on line profiles are briefly discussed.     

The intensity of the penumbra of large sunspots

Simultaneous photoelectric observations of sunspot penumbrae at 5790, 6690, 8760 and 16700Å are presented. No change in penumbral intensity from spot to spot is found in a sample of 11 large sunspots.     

Vortical distribution of sunspots

A remarkable vortical distribution of sunspots, photographed at National Solar Observatory, Tucson, may be an important indication that a vortex flow is essential in the formation of sunspots. It is argued that the concept of vortex flow around a spot is not a heresy, since a generation mechanism of non-trivial force-free fields requires the presence of time varying vorticity in the photosphere.     

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 velocity field associated with the birth of sunspots

A velocity field is found to occur prior to the birth of sunspots or during the rapidly developing phase of new spots. Fraunhofer lines are always shifted redwards in the observed active regions which are situated at various distances from the disk center. The velocity amplitude derived from Na i D1-line, 5895.940, amounts to, at maximum, 1.5 km s^–1 which is always a little larger than that derived from the weaker line, NI i 5892.883. The velocity field disappears when the spot ceases to grow. The lifetime of the velocity is, at least, 1 hr. The velocity field is interpreted in terms of the continuous downward flow in the process of formation of sunspots.Bray and Loughhead (1964) regard the disturbance in the granulation pattern accompanying the birth and growth of sunspot pores as an evidence of the existence of rising loops of magnetic flux. In view of the similarity of the phase of development of active regions and the lifetime in the observations by Bray and Loughhead and by us, we suggest that the velocity field may be a spectroscopic feature accompanying the rising magnetic loops in the photosphere and the chromosphere. We briefly discuss the observed mode of penetration of the magnetic flux to the solar surface before and after the appearance of AFS's.     

The latitudinal motion of sunspots and solar meridional circulations

A fundamental distinction can be made between those theories of the solar general circulation which require a mean north-south circulation in the photosphere and those which do not. Regardless of the theoretical merits of either group, they must either explain the data, or a theoretical set of data which falls within the observed limits. A detailed analysis of the Greenwich sunspot data supports a mean meridional circulation in either direction with a velocity less than one meter per second. The sunspot data therefore cannot be used to establish the existence of a mean north-south circulation, but may be used as an argument against any theoretical requirement for such a circulation much in excess of 1 m s^–1.     

Material flow in sunspots

Observations nowadays reveal more and more details about the small‐scale structure of the penumbra and umbra. Recent measurements of the motions in the penumbra indicate that (i) the Evershed flow is confined to a thin photospheric layer and (ii) the material rises from and sinks to subphotospheric layers within the penumbra. This flow pattern solves the question of the mass budget of the Evershed flow in a natural way. The nature of umbral dots and their role for the spot's energy budget remains unclear, since they are obviously unresolved even in the best existing measurements.