Sunspot Decay Research Articles

Fractal model for sunspot evolution

This paper analyzes the model for the evolution of sunspots considered as fractal clusters of magnetic flux tubes. Formation of sunspots is regarded as a result of magnetic tubes aggregation to the cluster. It is proved that magnetic field dissipation in the tubes results in effective sunspot decay. Sunspot formation and decay times deduced by the model as well as the rate of magnetic flux loss are in a good agreement with the observational data. The diffusion of magnetic flux tubes in sunspot penumbra is considered as a random walk on a fractal geometry. Disappearance of umbra in decaying sunspots is interpreted as a phase transition.

Decay rates of sunspot groups from 1874 to 1976

The global behaviour and fine structure of the distribution of sunspot decay rates from activity cycle 13 to 20 are presented. It is shown that the distribution of this parameter is lognormal. Statistically significantly lower values of decay rates are found in cycles 13, 14, and 18 for isolated spots. The complex groups had no appreciable changes.

VII. Active Regions: Structure and Evolution

The corona above active regions is now recognized as an assemblage of magnetically confined loops of plasma. This advance in understanding the active upper atmosphere is documented in the monograph resulting from the Third Skylab Workshop (Solar Active Regions, 1981, ed., F.Q. Orrall). International collaborative programs during the Solar Maximum Year (SMY) have further stimulated the study of active regions with emphasis on the search for the underlying causes of solar flares. Scores of analyses of individual regions, combining space- and ground-based observations, have been published. We have as a result an improved picture of interactions between active regions: from creation of shear in the magnetic topology to inter-region connections via the corona. A revived interest in the phenomena of recurrent active regions and sunspot decay has highlighted a basic problem for solar magnetism: the removal of magnetic flux from the solar surface. The interpretation of temporary dips in the solar irradiance caused by active regions continues to generate lively debate.

Differences in the temporal variations of solar UV flux, 10.7‐cm solar radio flux, sunspot number, and Ca‐K plage data caused by solar rotation and active region evolution

Two types of temporal variations in the solar UV spectral irradiance, caused by solar rotation and active region evolution, are presented and discussed. These particular UV variations differ markedly from the concurrent variations in the 10.7‐cm radio flux and sunspot number. The temporal variations of the modeled UV flux based on Ca‐K plage data are similar to the observed UV flux. The first type of dissimilar temporal behavior occurs when concentrations of solar active regions evolve at solar longitudes nearly 180° apart. Both the UV observations and modeled UV fluxes based on Ca‐K plage data then show strong 13‐day periodicity, while the 10.7‐cm solar radio flux and sunspot number exhibit quite dissimilar temporal variations. This type of dissimilarity is related to the modeled UV flux, having a dependence on the solar central meridian distance that is narrower than that for the 10.7‐cm radio flux or for sunspot numbers. A second case of marked dissimilarity occurs when major new solar active regions arise and dominate the full‐disk fluxes for several rotations. The strongest peaks in 10.7 cm and sunspot numbers tend to occur on their first rotation, for example, during major dips in the total solar irradiance, while the Ca‐K plages and UV enhancements peak on the next rotation and then decay more slowly on subsequent rotations. This type of dissimilarity is related to major active regions having a more rapid growth, peak and decay of sunspots, their strong magnetic fields and related coronal radio emission at centimeter wavelengths than for the Ca‐K plages and their related UV enhancements.

The flux-rope-fibre theory of solar magnetic fields

The flux-rope theory of solar magnetic fields is reviewed briefly and, together with the dynamo theory, compared with various observational results. Dynamo and related theories are based on fields controlled by the plasma, and it is shown that such fields cannot account for the strong surface fields or even emerge without becoming tangled. Observations which appear uniquely explicable in terms of powerful (⪝4000 G), helically twisted flux ropes and their many twisted flux fibres (≈3×1018 Mx) are listed as follows. (i) Emerging magnetic flux is seen first as pairs of small, closely spaced flux concentrations whose motions suggest magnetic control to provide bipolar regions of extent⪞105 km. The associated system of arch filaments rotates on the disk as would a series of emerging flux fibres twisted into a rope. (ii) Sunspots form by the accretion of pores and magnetic knots of like polarity, sometimes moving along curved paths between stationary elements of opposite polarity. (iii) Fluxes of⪞1022 Mx in large sunspots must have been concentrated to strengths of⪞4000 G before emerging, and also strongly helically twisted to avoid the flute instability. (iv) The trumpet-shaped flux-rope-fibre sunspot model (Figure 6) accounts readily for the phenomena of the moat convection, the sunspot energy deficit, the complex Evershed flow, penumbral filaments (flux ≈3×1018 Mx) and temporary light bridges. (v) Asymmetries in sunspot groups (in spot size, lifetime and proper motion) show that the spot fields are extensions of two submerged magnetic structures comprising strong fields. (vi) Sunspots decay by the loss of magnetic knots with strong fields and flux ≈5×1018 Mx. These must be isolated flux tubes, twisted to account for their stability. (vii) Flux fibres leaving a spot are prone to the kink instability, thus accounting for their sudden appearance in pairs, the transport of total flux several times that of the spot and net flux equal to that of the spot. (viii) Ephemeral active regions and X-ray bright points are explained similarly without invoking improbably huge quantities of new flux. (ix) Atmospheric structures show a high prevalence of helical twists (force-free fields) and rotary motions on all scales from spicules to large prominences. It is difficult to account for these twists unless they are present in emerging flux. (x) In and above the photosphere the flux fibres (≈3×1018 Mx) fray into loose associations of flux threads (≈3×1017 Mx) to provide a simple, selfconsistent model of the solar filigree and the chromospheric rosette (bush) with its group of mottles (spicules). (xi) Global patterns of surface and coronal magnetic fields reveal puzzling features such as the migration of large unipolar regions and the freedom from differential rotation of some structures. Submerged flux ropes ‘peeling’ out of the Sun provide a starting point for explaining these effects. These results provide a strong case for the flux-rope theory against the entrenched dynamo theory, and suggest that more observations should be made of the above ten phenomena. Where possible, simultaneous observations should be made of Zeeman effects and of plasma distributions and velocity field seen in white light and spectral lines.

The elementary theory of a twisted flux tube. II - Stability

Using models for magnetic flux tubes developed in Paper I, we calculate the total potential energy of a tube embedded in an isothermal horizontally stratified compressible atmosphere. By comparing this with the total energy of a system of n flux tubes having the same total flux as the original tube a necessary condition is obtained that the system is consistent with the adiabatic subdivision of a single untwisted flux tube.It is shown that under nonadiabatic conditions such as exist in the solar photosphere, the subdivision process must be endothermic (i.e., external energy is required) if the temperature within the original tube is significantly less than its surroundings but exothermic if the temperatures are comparable. Thus it is conjectured that magnetic structures are less susceptible to subdivision if they are significantly cooler than their surroundings.While a twisted flux tube cannot subdivide simply like an untwisted tube, it may fray into several spiral filaments; and it is shown that the cooling required to prevent this is actually greater than for an equivalent untwisted tube.It is shown that several features of the growth and decay of sunspots may be explained in terms of this conjecture.

A Discussion on the physics of the solar atmosphere - Optical and magnetic measurements of the photosphere and low chromosphere

Sequences of photographs at a resolution of 1'" achieved during the past ten years have had a very significant impact upon our understanding of the development, mature structure and decay of active regions. Cinematic studies, especially, have allowed the emergence of new fields and their motions within the active centre to be studied in detail. Cinematic magnetic observations show how sunspots decay through the outward flight of tiny knots of magnetic flux. The newest advances are being made with arrays of photosensitive diodes at the focal planes of high dispersion spectrographs. The diode array at the Sacramento Peak Observatory produces simultaneous photometric observations at many different wavelengths throughout the visible and near infrared spectrum. Quantitative studies of magnetic fields and chromospheric structure are discussed. In particular, the moving magnetic features apparently produce surges in the superpenumbra around large sunspots.

The Growth and Decay of Sunspots

The evolution of a sunspot is related to supergranular convection. Magnetic flux is concentrated by converging supergranular flow to form the sunspot. Equilibrium requires a magnetic field strong enough to inhibit convection in the photosphere but small scale convection is still possible at depths greater than 2000 km below the spot. The region surrounding this flux rope is imperfectly cooled. As a result the direction of flow in adjacent super-granules may be reversed. If the flux rope is inclined or split it may be broken up and the spot will decay rapidly; if it is predominantly vertical the reversed flow forms an annular cell (corresponding to the moat) about the spot, which is preserved through a phase of slow decay. The strong field prevents large scale convection in this cell from penetrating into the flux rope beneath the spot but small flux tubes diffuse outwards at a rate which is determined by the modified small scale convection. They are then torn away from the penumbra and carried across the moat, appearing as moving magnetic features in the photosphere. A simple model of this decay process explains the observed linear decay of flux with time and is supported by some numerical experiments.

Streaming of solar particles between Sun and Earth

It has long been known that the physical state of the Earth’s upper atmosphere is closely related to solar activity-the growth and decay of sunspots, the corona, uprushing prominences and bright chromospheric flares. In particular, transient radiative and corpuscular emissions associated with solar flares produce the most outstanding electromagnetic disturbances in the environment of the Earth. It is generally believed that geomagnetic storms are caused by the impact of solar plasma clouds with the geomagnetic field(l). Associated aurora1 and ionospheric effects are the direct consequence of disturbances induced in the upper atmosphere. The evidence of continual agitation of the geomagnetic field in the polar regions suggests a constant stream of incoming particles even during geomagnetically quiet periods. This accords with certain observations of the motion of comet tailP, for which the name solar wind or streaming plasma has been proposed in contrast to the storm-producing plasma cloud(3). The accumulated evidence of recent years indicates that the Sun emits not only lowenergy plasmas but also, on occasions, very-high-energy particles, known as solar cosmic raysc4). Since 1942, eight events showing an unusual increase in cosmic ray intensity have been found in ground-based observations. They were associated with intense solar flares, and the particles arrived at the Earth within very short time-delay, indicating that the energy exceeded the relativistic range. Several small but distinct solar cosmic ray events have also been identified since the International Geophysical Year (1957-8) strengthened considerably the precise world network of neutron monitors. An arrival of sub-relativistic-energy particles is not detectable at ground level, but this information is now available from recently developed rocket and balloon measurements and indirectly by ionospheric observations. These particles emitted from a solar flare impinge onto the ionosphere in the polar-cap regions, thereby producing enhanced ionization and a particular type of aurora1 glow. Thus, the events are known as polar-cap blackouts(5-7), polar-cap absorptionPlO) and polar-glow auroraeol). Direct measurements by balloon(12) and by satellites (13) .have revealed that the energy spectrum of these solar particles is considerably broad, ranging from 1 to 1000 MeV. Statistical studies have shown that such events are much more numerous than was ever suspectedo4), and also that they are closely related to the particular type of solar flares associated with strong radio outbursts of continuum radiationul in particular, comprehensive measurements by recent space probes and satellites. Thus, it is now evident that an enormous number of particles with a considerable wide-energy spectrum is streaming out from the Sun. Since solar particles detected in the environment of