P. R. Wilson

A new model for flux emergence and the evolution of sunspots and the large-scale fields

Existing models for the evolution of sunspots and sunspot groups, describing the subsurface structure of the magnetic fields and their interactions with the convective motions, are briefly reviewed. It is shown that they are generally unable to account for the most recent data concerning the relationship between the large-scale solar magnetic field structures and the magnetic fields of active regions. In particular, it is shown that the former do not arise directly from the decay of the latter, as required by the Babcock model and all other models based on it. Other observations which are not adequately explained by current models are also cited.A new model is put forward based on the expulsion of toroidal magnetic flux by the dominant (i.e. giant) cells of the convection zone. The flux expelled above these cells forms the large-scale field and thus the configuration of this field provides a clue to the structure of the giant cell patterns. The flux expelled below the cells becomes twisted into a rope as in the Babcock model but a loop or stitch forms only in the region of upflow of the giant cells. The interaction of this loop with intermediate-sized cells as it rises to the surface determines the configuration and extent of the active region which appears at the surface. The compatibility of the model with other observations is discussed and its implications for theories of the solar cycle are noted.

Coronal Holes and the Polar Field Reversals

A description of the reversal of the solar north polar magnetic field during cycle 22 is provided using polar projections which combine the large-scale magnetic fields as inferred from Hα synoptic charts and coronal holes mapped from Hei λ1083 nm spectroheliograms. These plots are supported by polar plots of the magnetic fields derived from synoptic magnetic field data from the Mount Wilson Observatory. The coronal holes showed some unexpected evolutionary patterns in relation to the polarity reversals, and these patterns appear to be coordinated with changes in the global patterns of coronal holes and the heliospheric current sheet, suggesting that the polar reversal originates from global processes rather than from local magnetic flux annihilation. Similar patterns have been observed in the reversal of the southern polar magnetic field in cycle 22 and in both hemispheres in cycle 21. The consequences of these findings for the solar dynamo process are discussed.

FACULAR MODELS AND THE SUNSPOT ENERGY DEFICIT.

The problem of the energy deficit in a sunspot is shown to be critically related to the depth of a given sunspot model. Recent facular models are discussed and a new model is derived from recent data using a two-dimensional radiative transfer analysis. The excess non-radiative energy required by this and other models is evaluated and it is shown that in some models this may account for a considerable fraction of the sunspot energy deficit. For these models the Alfvén energy travelling along the closed flux loops from the sunspot is insufficient to supply the requirements of the faculae and it is suggested that excess energy flux from below the faculae is also required. These results provide further support for ‘deep’ as opposed to ‘shallow’ sunspot models.

Hydromagnetic waves in structured magnetic fields

Although the inhomogeneous nature of solar magnetic fields is now well established, most theoretical analyses of hydromagnetic wave propagation assume infinite homogeneous fields. Here we reformulate the hydromagnetic wave problem for magnetic fields which vary in one direction perpendicular to the field. The permitted modes of small amplitude hydromagnetic oscillations are considered, first in the case of a single interface between semi-infinite magnetic and non-magnetic compressible regions, and secondly for a magnetic flux sheath of given thickness imbedded in a nonmagnetic region. It is shown that, for small values of R (the ratio of the Alfvén to the sound speed), an acoustic or p-mode wave front passes through the flux sheath with only minor deformation. However, for large R, the transmitted acoustic wave is attenuated and, depending upon the thickness of the flux sheath and the angle of incidence, a hydromagnetic wave may be effectively trapped and guided along the flux sheath.It is also shown that, for the symmetric vibration of the flux sheath in the absence of incident acoustic waves, only slow mode type waves are permitted. Thus, in compressible regions for which R > 1 the Alfvénic-type fast mode is not a permitted mode of free vibration of a flux sheath.

CENTER LIMB OBSERVATIONS OF INHOMOGENEITIES IN THE SOLAR ATMOSPHERE. III. TIME DEPENDENT FINE STRUCTURE OF THE Ca II EMISSION.

High resolution Ca II K-line spectra obtained at Kitt Peak National Observatory in September 1970 at a dispersion of 20 mm/Å and a spatial resolution approaching 1 arc sec are described.We first investigate the claim made by Zirin, Pasachoff and others that, at high spatial resolution, the K2 emission occurs either in the red wing or the blue but not both. In fact, it is shown that although some spectra exhibit predominantly singly-peaked emission features, other spectra, at equally high spatial resolution, show mainly doubly-peaked structures. We suggest that both types of spectra may be regarded as ‘normal’.Secondly, time series studies reveal at least two cases in which features exhibiting single emission peaks in either the red or the blue wings evolve into doubly-peaked structures in a time scale of 15sec.Finally, two features on the slit are observed to separate in a manner which implies velocities of order 50 km/sec. Other alternative explanations of the phenomena are discussed but are found to be even more implausible than velocities of this magnitude. Nevertheless, we urge the need for independent confirmation of this result.The implications of these observations for inhomogeneous models for the formation of the Caii K-line are discussed.

The Rotational Structure of the Region below the Solar Convection Zone

Frequency splittings derived from the first 4 month string of GONG data in the form of the Clebsch-Gordon coefficients are analyzed with particular emphasis on the region near the base of and just below the convection zone. It is found that the greatest changes in angular velocity occur across the region 0.60 < r = R/R☉ < 0.72. At equatorial latitudes, the angular velocity increases (outward) from 416 nHz at r = 0.645 to 455 nHz at r = 0.71, with a maximum angular velocity gradient dω(λ)/dr of order 2.2 × 10-3 (in units of nHz km-1) at r = 0.68 ± 0.01. At latitude 30°, there are some fluctuations in the angular velocity between r = 0.70 and r = 0.75, but below r = 0.70 the angular velocity is relatively uniform. At latitude 45°, the angular velocity decreases from 449 nHz at r = 0.645 to 415 nHz at r = 0.71, with a maximum (negative) gradient of magnitude 1.9 × 10-3 again at r = 0.68 ± 0.01; while at latitude 60° the angular velocity decreases from 440 nHz at r = 0.67 to 383 nHz at r = 0.775, with a maximum negative gradient of order 2.4 × 10-3 at r = 0.70 ± 0.01. Models exhibiting a discontinuous shear between the convection zone and a uniformly rotating radiative region are not strongly supported by these data. A model with a uniformly rotating core below r = 0.58 and with some latitudinal structure in the range 0.58 < r < 0.70 is found to be consistent with the data.

The generation of magnetic fields in photospheric layers

Recent observations concerning the growth and decay of photospheric magnetic flux present a challenge to the conventional picture of the photosphere as a passive medium through which flux tubes emerge inertly. Rather, they suggest the possibility that interactions between the magnetic flux and the photospheric velocity fields may give rise to changes in the observed surface flux.In this paper the physics of flux changes are reviewed and the various terms in the hydromagnetic equation which give rise to the growth and decay of magnetic flux are examined. Several kinematic models for field changes are examined and it is shown that new flux loops may be generated by suitable oscillatory velocity fields near the boundaries of existing magnetic structures, thus increasing the gross flux through the photosphere. It is suggested that this mechanism may account for the appearance of moving magnetic features (knots of opposite polarities) at the boundaries of decaying sunspots.Other models are discussed and a tentative explanation of the apparently unbalanced growth of opposite polarities is given in terms of a current-sheet model.

Alfvén waves in umbral flux tubes

Savage has suggested that an energy flux of 2 × 1010 erg cm−2 s−1 passes through the umbra of a sunspot in the form of hydromagnetic waves. In this paper some of the consequences of this flux are considered. It is first shown that it is not inconsistent with the energy requirements for the heating of umbral dots and for solar wind storms, assuming in the latter case that the flux tubes emerging from about one tenth of the area of a large spot are open-ended.However, the hypothesis also requires that Alfvén waves travel along the closed flux tubes linking the umbra either with the umbra of another spot or with the surrounding faculae and passing through regions of variable field strength and density. It is shown that, for a very simplified model, standing waves are possible in a symmetrical field configuration. For velocities of 3 km/s in the umbra, the maximum particle velocity in the loop is of order 80 km/s which strains the perturbation assumption severely. However, it is pointed out that periodic velocities of this order are observed in the chromosphere near sunspots.It is further shown that mechanical dissipation of these waves in local regions of the flux tube may contribute to the heating of faculae.

A three-component model for the formation of the chromospheric Caii K line

A recent two-component model for the formation of the Caii K line in the solar chromosphere put forward by Beebe and Johnson is discussed. Although this model is a great advance on existing one-component models, it is pointed out that observations require a minimum of three components in order to understand the formation of the K2 peaks.In order to make some progress in the study of multicomponent models an adaptation of the empirical (or analytic) approach is suggested. This relates the line source function directly to observations and places a secondary importance (at this stage) on the synthetic approach to the problem. A model is obtained which is in adequate agreement with observed mean profiles and its features are briefly discussed.

On the properties of umbral dots

On the basis of a three-dimensional radiative transfer analysis of several models it is shown that bright structures in sunspot umbrae which have horizontal diameters of 300 km or less cannot extend more than 300 km down into the umbra. Thus, such models are inconsistent with the hypothesis that the bright features are due to convection from the deep regions of the umbra. No such restrictions can be applied if the surface diameter is of order 500 km, but a model of this type is shown to be inconsistent with the available data. Thus a convective explanation of these bright features appears to be ruled out.A model having a diameter of 200 km is shown to be consistent with the available observations but these are not sufficiently precise to warrant any strong claim for the validity of this model. The features of this model are described and it is shown that near the limb the apparent brightness of these features compared to the umbral background should increase. However, order-of-magnitude calculations show that there is some doubt whether joule heating can account for the non-radiative energy requirements of this model.