Three-minute oscillations in sunspots: Seismology of sunspot atmospheres

We show that no eigenmodes of sunspot oscillations with periods of ～ 3 min or shorter exist. A complex spectrum of the 3-min oscillations arises, because the sunspot atmosphere is a multiband filter for slow MHD waves. To ascertain why the filter transmission bands appear, we have investigated the propagation of waves through a sunspot atmosphere using both multilayered isothermal model atmospheres and various empirical model atmospheres. It turns out that there are several different mechanisms responsible for the appearance of transmission bands in the atmospheric filter for slow waves. The filter lowest-frequency transmission band arises from the effect of a Fabry-Perot interference filter at the resonance frequency of the temperature plateau. The frequency of this band is always lower than the cutoff frequency of the temperature minimum. The next (in frequency) transmission band appears at the cutoff frequency. The higher-frequency transmission bands result from the antireflection of the atmosphere, an effect well-known in optics and acoustics. The nonlinearity of the 3-min oscillations observed in the upper chromosphere and transition region has only an indirect effect on the properties of the filter, increasing its transmission in most bands due to a decrease in the amplitude of the wave reflected from the upper atmosphere caused by nonlinear wave absorption. Knowledge of the formation mechanisms for the 3-min oscillation spectrum has allowed us to suggest a technique for estimating the parameters of sunspot atmospheres from the 3-min oscillation spectrum, i.e., to lay the foundations for the seismology of sunspot atmospheres.     

Relationship between sunspot numbers during years of sunspot maximum and sunspot minimum

A correlation analysis shows that the sunspot numbers at the peaks of the last eight solar cycles are well-correlated with the sunspot numbers in heliolatitudes 20°–40° (specially in the southern hemisphere) occurring in the solar minimum years immediately preceding the solar maximum years.On leave from Physical Research Laboratory, Ahmedabad, India.     

Global Coronal Seismology

Following the observation and analysis of large-scale coronal-wave-like disturbances, we discuss the theoretical progress made in the field of global coronal seismology. Using simple mathematical techniques we determine average values for the magnetic field together with a magnetic map of the quiet Sun. The interaction between global coronal waves and coronal loops allows us to study loop oscillations in a much wider context, i.e. we connect global and local coronal oscillations.     

Relationship between group sunspot numbers and Wolf sunspot numbers

Continuous wavelet transform and cross‐wavelet transform have been used to investigate the phase periodicity and synchrony of the monthly mean Wolf (R_z) and group (R_g) sunspot numbers during the period of June 1795 to December 1995. The Schwabe cycle is the only one common period in R_g and R_z, but it is not well‐defined in case of cycles 5–7 of R_g and in case of cycles 5 and 6 of R_z. In fact, the Schwabe period is slightly different in R_g and R_z before cycle 12, but from cycle 12 onwards it is almost the same for the two time series. Asynchrony of the two time series is more obviously seen in cycles 5 and 6 than in the following cycles, and usually more obviously seen around the maximum time of a cycle than during the rest of the cycle. R_g is found to fit R_z better in both amplitudes and peak epoch during the minimum time time of a solar cycle than during the maximum time of the cycle, which should be caused by their different definition, and around the maximum time of a cycle, R_g is usually less than R_z. Asynchrony of R_g and R_z should somewhat agree with different sunspot cycle characteristics exhibited by themselves (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Seismology of a Sunspot Atmosphere

Two competing theories of sunspot oscillations are discussed. It is pointed out that the normal mode (eigenoscillations) theory is in contradiction with a number of observations. The reasons for this are discussed. The revised filter theory of the three-minute sunspot oscillations is outlined. It is shown that the reason for the occurrence of the multipassband filter for the slow waves is the interference that appears from the multilayer structure of the sunspot atmosphere. In contrast with Zhugzhda and Locans (Sov. Astron. Lett. 7, 25?–?27, 1981) it is shown that along with the Fabry?–?Perot chromospheric passband the cutoff frequency passband and a number of the high-frequency passbands occur. The effect of the nonlinearity of the sunspot oscillations in the upper chromosphere and the transition region is taken into account. The spectra of the distinct empirical models of the sunspot atmosphere are explored. An example of the interpretation of the sunspot oscillations based on the revised filter theory is presented. Only the filter theory can explain the complicated behavior of the oscillations across the sunspot. The observations provide evidence of the nonuniformity of the sunspot atmosphere.     

Seismology of the solar atmosphere

We describe a new instrument for seismically probing the properties of the Sun's lower atmosphere, and present some first results from an observational campaign carried out at the geographic South Pole during the austral summer of 2002/2003. A preliminary analysis of the data (simultaneous, high-cadence observations of the velocity signals from the photosphere and low chromosphere) shows that the well-known suppression of acoustic power in regions of strong magnetic field, and enhancement of high-frequency power around active regions (acoustic halos), are both consistent with a spreading out of the magnetic field lines with increasing height in the atmosphere. The data have also revealed some unexpected wave behavior. First, evanescent-like waves are found at frequencies substantially above the acoustic cut-off frequency in regions of intermediate magnetic field. Second, upward- and downward-propagating waves are detected in areas of strong magnetic field such as sunspots and plage: even at frequencies below the acoustic cut-off frequency. Third, the wave behavior in regions of strong magnetic field can change over periods of a few hours from propagating to evanescent. While we have no concrete explanation for the first two results, the latter result opens up the question of whether sound waves are involved in short-term events such as flares or CME's.     

Structure of a sunspot

From enlargements of patrol photographs of the disk passage of the sunspot of July 20 – August 2, 1966, intensity profiles across the spot are obtained at several positions near the disk-center and at each limb. It is found that these profiles show asymmetric features near each limb (increasingly sharp limb-side penumbra and poorly resolved disk-side penumbra) which are similar to those reported in Paper III of this series. It is suggested that these profile asymmetries are the essential feature of the center-limb variations in the appearance of a sunspot which have become known as the Wilson effect.Conventionally the Wilson effect is described as the extreme foreshortening and eventual disappearance of the disk-side penumbra and, recently, Suzuki has referred to this as the occultation of the penumbra by the photosphere. We find no evidence at all for the disappearance of the disk-side penumbra at the limb in this spot. Defining half-height points on the profile curves as the umbral and penumbral boundaries, we find that, near the west limb where the spot is stable and regular, the limb-side penumbra increases by about 10% at the expense of the umbra. This result qualitatively supports the results reported in Paper III although it is smaller in magnitude.Other observations of sunspots which appear to exhibit the conventional Wilson effect are discussed and it is concluded that in no case yet published is the resolution and seeing of sufficient quality to demonstrate unambiguously the disappearance of the disk-side penumbra.     

On the sunspot structure

The fine structure of a sunspot is studied on a series of photographs obtained during the third flight of the Soviet Stratospheric Solar Station. The main results are as follows:

1. The micro-photometer tracings on the frames show extremely high Rayleigh resolution of small elements, the smallest distances being near to the theoretical limit. The half-widths of the brighter elements are given in Tables III and VI. The corrected brightness of umbral dots has large dispersion.
2. The dimensions of the smallest dots are equal to the diffraction image of bright points. So the real radii of these objects are smaller than 150km, which is consistent with opaque models of sunspot umbra.
3. The penumbra and umbra structure (dark and bright objects) is in good agreement with the picture of magnetic field splitting in a system of magnetic ropes giving rise to the magnetic arcs in the chromosphere and corona. Only in the umbra do we meet the large scale continuities.

     

The lifetimes of sunspot moats

In the standard model of the solar convective zone, turbulent eddies transport entropy rather than temperature. We consider the turbulent mean field equations for the convective zone, including entropy transport, and show that the zone can be unstable to larger scale motion which we identify with the supergranulation and giant cells.     

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 cooling of a sunspot

The coordinates of the cooling cycle described in Paper I are re-defined in order to provide an account in which the part played by the cycle in cooling the sunspot is separated from the role of the supergranule cells in transporting energy away from it.More recent observations of velocity fields and magnetic outflow near sunspots are discussed. A model suggested by Harvey and Harvey to explain the observed magnetic flux transported across the moat region is refined and extended using the cooling cycle model.     

Rhythm of physical sunspot cycles

The time series of the relative sunspot number is interpreted as a sequence of physical cycles of sunspot activity overlapping in the minimum. The cycle periodicity, i.e., the time interval between neighboring cycles, can be considered as a quantitative characteristic of the sequence. Estimates of this interval have been obtained for 11 and 22-year cycles. In the growth phase and in the century cycle maximum, the 22-year cycles follow one another with an interval of 21 ± 0.4 years, and in the decline phase, 23 ± 0.3 years. This division of intervals into two groups depending on the century cycle phase should be taken into consideration when developing a theory of solar activity cycles.     

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.     

Diagnostic features of sunspot regions

Five-minutes p-mode oscillations are heavily attenuated in the active sunspot region. A comparative study of wave modes and luminosity variations outside and inside the sunspot region is found to depict certain diagnostic features of sunspot regions.     

The cooling of a sunspot

A mechanism is proposed to explain the cooling of a sunspot in terms of the detailed interactions between the magnetic field and the convective motions. The mechanism provides that an axially symmetric concentration of magnetic field deforms the normal supergranule cell pattern below the sunspot into a radial outflow of plasma over a region of diameter 60 Mm.The flow occurs at depths where the magnetic and kinetic energy densities are approximately equal ( 5 Mm) and is described in terms of a Carnot refrigeration cycle. Application of the hydromagnetic equations to a very simple model shows that, because the magnetic field concentration causes the outflow, the field will itself decay in a time short compared with the lifetime of a spot. However, a slightly more sophisticated model does suggest conditions under which this decay is considerably reduced.Observations of the outward drift of magnetic knots around sunspots and of supergranule-type surface motions extending radially outwards from the penumbra of a spot to the nearest faculae are discussed in relation to the mechanism.     

Seismology of the solar convection zone

An attempt is made to infer the structure of the solar convection zone from observedp-mode frequencies of solar oscillations. The differential asymptotic inversion technique is used to find the sound speed in the solar envelope. It is found that envelope models which use the Canuto-Mazzitelli (CM) formulation for calculating the convective flux give significantly better agreement with observations than models constructed using the mixing length formalism. This inference can be drawn from both the scaled frequency differences and the sound speed difference. The sound speed in the CM envelope model is within 0.2% of that in the Sun except in the region withr > 0.99R _⊙. The envelope models are extended below the convection zone, to find some evidence for the gravitational settling of helium beneath the base of the convection zone. It turns out that for models with a steep composition gradient below the convection zone, the convection zone depth has to be increased by about 6 Mm in order to get agreement with helioseismic observations.     

Magneto-convection in sunspot penumbrae

Finite amplitude convection in the presence of a horizontal magnetic field has been investigated in a region where thermal diffusivity (κ) is less than magnetic diffusivity (η) and whenκ/η > 1,Q ≤Q _c, where $$Q_c = \frac{{(1 + \sigma _1 )(\pi ^2 + q_c^2 )^2 }}{{q_c^2 (\sigma _2 - \sigma _1 )}}$$ ,Q is the Chandrasekhar number,σ ₁ the Prandtl number,σ ₂ the magnetic Prandtl number, andq _c the critical wave number at the onset of stationary convection. We have derived a nonlinear time-dependent Landau—Ginzburg equation near the onset of supercritical stationary convection and a nonlinear, second-order equation at the Takens—Bogdanov bifurcation. We have obtained steady-state solutions of these equations, which describe the nonlinear behaviour near the onset of stationary convection.