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.     

Can oscillations grow in a sunspot umbra?

Umbral flashes and running penumbral waves have been attributed by Moore (1972) to overstable oscillations in the umbra. His numerical results were derived by inserting physical conditions at two particular depths beneath the umbral surface. Seven variables must be specified at each point. We have extended Moore's analysis to examine the depth-dependence of overstable oscillations in a recently computed umbral model. Electrical conductivity is evaluated taking full account of partial ionization and magnetic fields. In the surface layers, within 250 km of the top of the umbral convection zone, the conductivity is so low that Joule dissipation is more rapid than the growth rate of oscillations. In these layers, Moore's results are therefore not applicable. At greater depths, oscillations can grow and we agree with Moore that both umbral flashes and penumbral waves may be due to overstable oscillations. However, we suggest that both phenomena can arise at the same depth in the spot, and not in two layers, as Moore suggests.The umbral model we used is based on Öpik's cellular convection model. The interaction between the vertical magnetic field and convection is included by varying the diameter of the cell, and not its height. The diameter is assumed to be proportional to the distance that gas diffuses relative to the field during its upward convection.Work supported by NASA Contract NGR-39-005-066.     

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 nature of the sunspot phenomenon

The properties of Alfvén waves in a vertical column of field are pointed out as a guide in treating the complicated problem of overstability. There are internal Alfvén waves of arbitrary form propagating along the magnetic field, without disturbing the fluid outside the column. There are also surface waves which involve the fluid both inside and outside the column of field. The surface waves propagate at a speed less than the Alfvén speed.Convective forces couple the internal and external fluid motions. If the forces are not too strong, the identity of the modes, as internal waves or surface waves, is maintained. The surface waves are unstable and, we suggest, may contribute to some of the activity of a sunspot. We suggest that the internal Alfvén wave modes are of more central interest for producing the basic sunspot phenomena. They represent the degenerate case, and their form is worked out in some detail. The overstable Alfvén wave modes peak sharply near the outer edge of the field, and do not strongly disturb the fluid outside. We suggest that this effect contributes to the sharp edge of the sunspot umbra.Recent observations by Giovanelli show intense wave activity originating inside the edge of the umbra. We tentatively identify the activity with the peak in the overstable modes within the umbra.This work was supported in part by the National Aeronautics and Space Administration under Grant NGL 14-001-001.     

Electrical conductivity gradients in sunspots

Recently E. H. Schroeter showed that the electrical conductivity of the sunspot umbra, at least in the upper photospheric layers, is about ten-thousand times less than the value used by Cowling. This result implies that electrical conductivity gradients near sunspots may be relatively large. Upon taking such gradients into consideration, we find that the photosphere is current free and that current rings might encircle the sunspot, under suitable conditions, both in the lower photosphere and in the chromosphere. Plasma motions are neglected in the calculation.     

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.     

Numerical MHD Simulations of Solar Magnetoconvection and Oscillations in Inclined Magnetic Field Regions

The sunspot penumbra is a transition zone between the strong vertical magnetic field area (sunspot umbra) and the quiet Sun. The penumbra has a fine filamentary structure that is characterized by magnetic field lines inclined toward the surface. Numerical simulations of solar convection in inclined magnetic field regions have provided an explanation of the filamentary structure and the Evershed outflow in the penumbra. In this article, we use radiative MHD simulations to investigate the influence of the magnetic field inclination on the power spectrum of vertical velocity oscillations. The results reveal a strong shift of the resonance mode peaks to higher frequencies in the case of a highly inclined magnetic field. The frequency shift for the inclined field is significantly greater than that in vertical-field regions of similar strength. This is consistent with the behavior of fast MHD waves.     

Correction of solar observations for stray light by numerical integration,with application to Mercury's drop

A numerical method for correction of stray light in solar observations has been developed. In particular a regular sunspot, where the circular contours of penumbra and umbra are projected as ellipses, has been studied. When a specified set of values for the stray light parameters is given, and also tentative values for the relative intensities of penumbra and umbra, the integration of stray light can be performed in any point. The result will be the observable intensity if the conditions were as given by these initial values.By means of limb observations the stray light parameters may be improved, and finally a variation of the penumbra- and umbra intensities in the computation, enables a determination of these quantities by comparison with observations.The method is tested on observations of the transit of Mercury, May 9, 1970. Calculation of isophotes with Mercury close to the limb shows the black drop phenomenon; which thus may be explained as an effect of stray light only.It is also shown that the Wilson effect on a sunspot cannot be produced by stray light alone.     

H and K lines in the sunspot umbra: A source function and Doppler width

An inversion of line profiles H and K Ca ii in the umbra of two sunspots is performed. By means of a numerical experiment, a tentative study of possible application of the method of intercomparison of lines in the multiplet (Goldberg's method) is made in cases when the condition of source function equality in multiplet is not fulfilled. It is found that the source functions of H and K lines in the sunspot umbra vary in a monotonous way. Their ratio in the layers for which measured values of Δλ_D are available differs from unity. In the region of the lower chromosphere under consideration, the Doppler width is decreasing with height.     

Enhanced emission of Alfvén waves from sunspots during proton flares

Thomas (1978) has shown that, if Alfvén waves exist in a sunspot umbra, they are normally reflected so strongly by the temperature minimum as to be essentially undetectable in the upper solar atmosphere. However, it is known that in many proton flares, chromospheric emission overlies the umbra of a sunspot, indicating that the transition region (TR) between chromosphere and corona in the umbral flux tube has moved down to lower altitudes. As a result of this lowering, umbral Alfvén waves have readier access to the corona: the coronal leakage depends exponentially on the altitude of the TR. We find that the Alfvén wave flux which leaks out of the umbra into the corona can exceed 10⁷ ergs cm^-2 s^-1. A flux of this magnitude is expected to dissipate rapidly in the corona, thereby contributing to a positive feedback loop which ensures prolonged (1 hr) leakage of the umbral Alfvén waves into the corona. We propose that these Alfvén waves may contribute significantly to prolonged energization of proton flares in which umbral coverage occurs.     

Turbulent effects of sunspot magnetic field reconstruction

We study the effects of two-dimensional turbulence generated in sunspot umbra due to strong magnetic fields and Alfven oscillations excited in sunspots due to relatively weak magnetic fields on the evolution of sunspots. Two phases of sunspot magnetic field decaying are shown to exist. The initial rapid phase of magnetic field dissipation is due to two-dimensional turbulence. The subsequent slow phase of magnetic field decaying is associated with Alfven oscillations. Our results correspond to observed data that provide evidence for two types of sunspot evolution. The effect of macroscopic diamagnetic expulsion of magnetic field from the convective zone or photosphere toward sunspots is essential in supporting the long-term stability and equilibrium of vertical magnetic flux tubes in sunspots.     

A Flare and Umbral Flashes in a Sunspot

We studied the evolution and dynamic processes in the chromosphere above a sunspot umbra. A relatively rarely occurring phenomenon of bright long-lasting emission observed in the umbra of a unipolar sunspot of the AR 9570 group on August 11, 2001 was investigated. It was found that during the course of the observation, emission was spreading, gradually occupying nearly the entire sunspot umbra. Based on the analysis of the observations from other observatories, we arrived at the conclusion that the bright emission was a sympathetic flare that occurred in the sunspot umbra. It was assumed that there occurred an interaction with a neighboring, rapidly evolving group that exhibited subflares on the day of observation. In the same umbra, there was taking place an oscillatory process of the type of umbral flash (observations from August 11 and 12, 2001). The characteristics of the oscillatory process in the presence of the flare were studied. As the bright emission propagated in the sunspot umbra, brightness fluctuations ceased to be seen in the umbral flashes against the background of this brighter emission. The character of velocity variations did not change substantially, although the oscillation amplitude did decrease.     

Spatial distributions of sunspot oscillation modes at different temperatures

Three-and five-minute sunspot oscillations have different spatial distributions in the solar atmospheric layers. The spatial distributions are crucial for revealing the physical origin of sunspot oscillations and to investigate their propagation. In this study, six sunspots observed by Solar Dynamics Observatory/Atmospheric Imaging Assembly were used to obtain the spatial distributions of three-and five-minute oscillations. The fast Fourier transform method is applied to represent the power spectra of oscillation modes. We find that, from the temperature minimum to the lower corona, the powers of the fiveminute oscillation exhibit a circle-shape distribution around its umbra, and the shapes gradually expand with temperature increase. However, the circle-shape disappears and the powers of the oscillations appear to be very disordered in the higher corona. This indicates that the five-minute oscillation can be suppressed in the high-temperature region. For the three-minute oscillations, from the temperature minimum to the high corona, their powers mostly distribute within an umbra, and part of them are located at the coronal fan loop structures. Moreover, those relative higher powers are mostly concentrated in the position of coronal loop footpoints.     

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.     

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.     

Broad-band circular polarimetry of sunspots, 0.4–1.7 microns: Spatial scans with a 3.4 arc sec diameter aperture

Spatial scans with a resolution of 3.4 arc sec of the broad-band circular polarization of several sunspots have been made in five filter bands over the wavelength range 0.4–1.7µ with a sensitivity of 1 × 10^–6 fractional polarization. The scans, across a spot through the penumbra and umbra center, revealed two important features: (1) The broad-band circularly polarized fluxV reverses in sign, or diminishes to near zero, at the center of the umbral region relative to the outer penumbra. This effect was wavelength dependent and was most clearly detected as a definite reversal in a band at 1.2µ, although a reversal was also detected in a very broad band extending from 0.8 to 1.6µ. (2) There is a marked asymmetry: in all cases the limbward penumbral region exhibited strongerV values than did the disk-center (inward) side of the spot, at all observed wavelengths. Such previously unreported structure in the magnetic circular polarization of sunspots provides new clues for understanding the anomalous large broad-band polarization at short wavelengths and at the same time imposes new constraints on sunspot models. For example, the polarization reversal in the umbra relative to the penumbra can be naively explained by return-flux sunspot models; but this is not the only interpretation. Alternatively, it can relate to reversals in mass-flow velocities and/or vertical velocity gradients, as between the umbra and penumbra.     

Development of a Code to Analyze the Solar White-Light Images from the Kodaikanal Observatory: Detection of Sunspots,Computation of Heliographic Coordinates and Area

Sunspots are the most conspicuous aspects of the Sun. They have a lower temperature, as compared to the surrounding photosphere; hence, sunspots appear as dark regions on a brighter background. Sunspots cyclically appear and disappear with a 11-year periodicity and are associated with a strong magnetic field ( ～10³ G) structure. Sunspots consist of a dark umbra, surrounded by a lighter penumbra. Study of umbra–penumbra area ratio can be used to give a rough idea as to how the convective energy of the Sun is transported from the interior, as the sunspot’s thermal structure is related to this convective medium.An algorithm to extract sunspots from the white-light solar images obtained from the Kodaikanal Observatory is proposed. This algorithm computes the radius and center of the solar disk uniquely and removes the limb darkening from the image. It also separates the umbra and computes the position as well as the area of the sunspots. The estimated results are compared with the Debrecen photoheliographic results. It is shown that both area and position measurements are in quite good agreement.     

Basic properties of sunspots: equilibrium,stability and long-term eigen oscillations

A number of fundamental questions as regards the physical nature of sunspots are formulated. In order to answer these questions, we apply the model of a round-shaped unipolar sunspot with a lower boundary consisting of cool plasma and with strong magnetic field at the depth of about 4 Mm beneath the photosphere, in accordance with the data of local helioseismology and with certain physically sound arguments (the shallow sunspot model). The magnetic configuration of a sunspot is assumed to be close to the observed one and similar to the magnetic field of a round solenoid of the appropriate size. The transverse (horizontal) and longitudinal (vertical) equilibria of a sunspot were calculated based on the thermodynamic approach and taking into account the magnetic, gravitational, and thermal energy of the spot and the pressure of the environment. The dependence of the magnetic field strength in the sunspot center, B ₀, on the radius of the sunspot umbra a is derived theoretically for the first time in the history of sunspot studies. It shows that the magnetic field strength in small spots is about 700 Gauss (G) and then increases monotonically with a, tending asymptotically to a limit value of about 4000 G. This dependence, B ₀(a) includes, as parameters, the gravity acceleration on the solar surface, the density of gas in the photosphere, and the ratio of the radius of the spot (including penumbra), a _p, to the radius of its umbra a. It is shown that large-scale subsurface flows of gas in the sunspot vicinity, being the consequence but not the cause of sunspot formation, are too weak to contribute significantly to the pressure balance of the sunspot. Stability of the sunspot is provided by cooling of the sunspot plasma and decreasing of its gravitational energy due to the vertical redistribution of the gas density when the geometric Wilson depression of the sunspot is formed. The depth of a depression grows linearly with B ₀, in contrast to the quadratic law for the magnetic energy. Therefore, the range of stable equilibria turns out to be limited: large spots, with radius a larger than some limit value (about 12–18 Mm, depending on the magnetic field configuration), are unstable. It explains the absence of very large spots on the Sun and the appearance of light bridges in big spots that divide the spot into a few parts. The sunspots with B ₀≈2.6÷2.7 kilogauss (kG) and a≈5 Mm are most stable. For these spots, taken as a single magnetic structure, the period of their vertical eigen oscillations is minimal and amounts, according to the model, to 10–12 hours. It corresponds well to the period derived from the study of long-term oscillations of sunspots using SOHO/MDI data.     

Arch filaments associated with the formation of sunspots by umbral merging

The formation of a sunspot during the emergence of a new group is described. The spot forms from a cluster of small umbrae that do not converge. Rather, the individual umbrae enlarge and merge into a spot covering the same area. The formation of each umbra is accompanied by an intensification of the arch filament anchored in it. The formation of the sunspot produces no apparent change in the total field.     

The influence of faculae on sunspot heat blocking

We study the influence of faculae on sunspot heat blockage using a thermal model based on eddy heat diffusion through the convection zone. The facula is represented as a localized area of excess emission surrounding the sunspot, which is represented as a thermal plug. Our computations using a range of reasonable combinations of spot and facular depths show no significant influence of the facula on the long storage times of heat blocked by sunspots. However, the local cooling of surface layers produced by excess facular emission in this model propagates globally within the convection zone in a similar way to the heating produced by a spot. The net effect of spots and faculae on L over time scales longer than an active region lifetime should thus be determined by the global sum of sunspot flux deficits and facular excesses.