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.     

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.     

Magnetoactive lines in the medium with the velocity gradient

The magnetic splitting peculiarities of the absorption lines in the sunspot spectrum are considered. The most common and typical of them is breaking of all Stokes parameter symmetry in regard to the line center. The possible reason of this effect is the macroscopic gas motion with inhomogeneous velocity. Computed contours are given for the line Fe i λ5250 Å with various combinations of magnetic and velocity fields. Magneto-optical effects within the line which are connected with the magnetic and velocity field inhomogeneity are discussed. The observation results are discussed for longitudinal magnetic field zero lines. These observations were carried out for the sunspot and photosphere in two spectral lines Fe i λλ 5250 and 5233 Å. In the sunspot the regular displacement of one zero line with respect to the other zero line takes place whereas in the photosphere the displacements are random. The possible reason of the regular displacement is the change of the magnetic field direction in the different optical layers wherein corresponding spectral lines are formed effectively. The connection between the zero line displacement of a longitudinal magnetic field and the crossover effect is discussed. The computation results are given which agree with observations and illustrate the above-mentioned relationship. The influence of the Stokes parameter asymmetry on the measured magnetic field signals is considered.     

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.     

A Detailed Comparison of Cosmic Ray Gaps with solar Gnevyshev Gaps

After increasing almost monotonically from sunspot minimum, sunspot activity near maximum falters and remains in a narrow grove for several tens of months. During the 2–3 years of turmoil near sunspot maximum, sunspots depict several peaks (Gnevyshev peaks). The spaces between successive peaks are termed as Gnevyshev Gaps (GG). An examination showed that the depths of the troughs varied considerably from one GG to the next in the same cycle, with magnitudes varying in a wide range (<1% to ∼20%). In any cycle, the sunspot patterns were dissimilar to those of other solar parameters, qualitatively as well as quantitatively, indicating a general turbulence, affecting different solar parameters differently. The solar polar magnetic field reversal does not occur at the beginning of the general turmoil; it occurs much later. For cosmic ray (CR) modulation which occurs deep in the heliosphere, one would have thought that the solar open magnetic field flux would play a crucial role, but observations show that the sunspot GGs are not reflected well in the solar open magnetic flux, where sometimes only one peak occurred (hence no GG at all), not matching with any sunspot peak and with different peaks in the northern and southern hemispheres (north – south asymmetry). Gaps are seen in interplanetary parameters but these do not match exactly with sunspot GGs. For CR data available only for five cycles (19 – 23), there are CR gaps in some cycles, but the CR gaps do not match perfectly with gaps in the solar open magnetic field flux or in interplanetary parameters or with sunspot GGs. Durations are different and/or there are variable delays, and magnitudes of the sunspot GGs and CR gaps are not proportional. Solar polar magnetic field reversal intervals do not coincide with either sunspot GGs or CR gaps, and some CR gaps start before magnetic field reversals, which should not happen if the magnetic field reversals are the cause of the CR gaps.     

Search for magnetic field oscillations in a sunspot umbra

In order to search for oscillations in velocity and magnetic field strength within a sunspot umbra, a time series of spectra has been obtained through a circular analyzer and the Gregory-Coudé telescope at the Observatorio del Teide, Tenerife. The velocity oscillations clearly show peaks of power at periods between 2 and 7 minutes, with a maximum at 5 minutes. The apparent variations of the magnetic field strength, however, don't exhibit significant oscillations; these fluctuations are rather produced by the influence of parasitic stray light from the surrouding quiet sun which are also visible in the measured time variations of the umbral contrast of continuum intensity.     

Local solar magnetic and velocity field development and related photospheric and chromospheric activity

We have compiled the results of our long-term studies of the local magnetic field and its activity development, derived from investigating sunspot group evolution, photoelectrically measured longitudinal magnetic and velocity fields, and measurements of sunspot proper motions. We estimate certain regularities according to which the magnetic and velocity fields, and photospheric, as well as chromospheric activities develop. We speculate about the physical background of such processes.Dedicated to Cornelis de Jager     

On the relationship between magnetic fields and supergranule velocity fields

We studied the size, correlation lifetime and horizontal velocity amplitude of supergranules in regions with different magnetic activity. We found that the supergranule velocity cells have similar scale, correlation lifetime and horizontal velocity amplitude in the unipolar enhanced magnetic network regions and in the mixed-polarity quiet Sun. However, the correlation lifetime of magnetic structure is much longer in the enhanced network. We investigated the velocity pattern of moving magnetic features (MMF) surrounding a decaying sunspot. The velocity of MMFs is consistent with the outflow surrounding the sunspot as measured by Dopplergrams. The velocity cell surrounding the sunspot has a much larger velocity amplitude and a longer lifetime than regular supergranule cells. We found that ephemeral regions (ER) have a slight tendency to emerge at or near boundaries of supergranules. Almost all the magnetic flux disappears at the supergranule boundaries. In most cases, two poles of cancelling features with opposite magnetic polarities approach along the boundaries of supergranules.     

Equilibrium and decay of sunspots

We suggest a quantitative sunspot model developed in terms of mean-field magnetohydrodynamics (MHD). The model consistently describes the distributions of magnetic field, fluid velocity, and thermodynamic parameters in a sunspot and the surrounding matter. Two versions of the model allow the MHD equilibrium in sunspots and their slow decay to be analyzed. The baroclinic flow converging to the sunspot plays an important role in the equilibrium. Several calculated characteristics—almost uniform distributions of brightness and magnetic field inside sunspots, their abrupt changes at the boundary, and nearly linear decreases in the area and magnetic flux of decaying sunspots with time—qualitatively agree with the observations.     

Sunspots and large-scale magnetic fields at various heights

Height variation of the magnetic field structure over groups of sunspots for heights ranging from the photosphere to the source surface (R = 2.5 Ro, where Ro is the radius of the Sun) is examined. For all heights, starting from the photospheric level, groups of sunspot are shown as being independent of long-lived boundaries of large-scale structures rotating with a period shorter than the Carrington period. At heights of 1–1.5 Ro, there is a clear relation between sunspot groups and boundaries separating the head and tail sunspots in the groups (the Hale boundaries). The rotation periods of these structures are close to the Carrington period, their lifespan being less than three to five rotations. The maximal intensity of the solar magnetic field drops by two orders when height increases from H = 1 to H = 1.1 Ro. Further decrease in intensity proceeds gradually (dropping by one order from H = 1.1 to 2.5 Ro). The results obtained can be considered as evidence that large-scale magnetic field structures and long-lived boundries between them (the lines dividing polarities of the magnetic field or zero lines) all exist irrespective of sunspot fields being generated by other sources than sunspots. At the photospheric level, active regions fields are superimposed on these structures.     

An interpretation of the broad-band circular polarization of sunspots

The broad-band circular polarization of sunspots is discussed on the basis of the observations made in the Okayama Astrophysical Observatory. The observation with the spectrograph proves that it is the integrated polarization of spectral lines in the observed spectral range. A velocity gradient in the line-of-sight can produce this integrated polarization due to the differential saturation between Zeeman components of magnetically sensitive lines. The observed degree of polarization and its spatial distribution in sunspots is explained when we introduce a differentially twisted magnetic field in addition to the velocity gradient. The differential twist has the azimuth rotation of the magnetic field along the line-of-sight and generates the circular polarization from the linear polarization due to the magneto-optical effect. The required azimuth rotation is reasonable and amounts at most to 30°. The required velocity gradient is compatible with the line asymmetry and its spatial distribution observed in sunspots. The observed polarity rule leads to the conclusion that the sunspot magnetic field has the differential twist with the right-handed azimuth rotation relative to the direction of the main magnetic field, without regard to the magnetic polarity and to the solar cycle. The twist itself is left-handed under the photosphere, when the sunspot is assumed to be a unwinding emerging magnetic field.     

Long term evolution of solar sector structure

The large-scale structure of the solar magnetic field during the past five sunspot cycles (representing by implication a much longer interval of time) has been investigated using the polarity (toward or away from the Sun) of the interplanetary magnetic field as inferred from polar geomagnetic observations. The polarity of the interplanetary magnetic field has previously been shown to be closely related to the polarity (into or out of the Sun) of the large-scale solar magnetic field. It appears that a solar structure with four sectors per rotation persisted through the past five sunspot cycles with a synodic rotation period near 27.0 days, and a small relative westward drift during the first half of each sunspot cycle and a relative eastward drift during the second half of each cycle. Superposed on this four-sector structure there is another structure with inward field polarity, a width in solar longitude of about 100° and a synodic rotation period of about 28 to 29 days. This 28.5 day structure is usually most prominent during a few years near sunspot maximum. Some preliminary comparisons of these observed solar structures with theoretical considerations are given.     

Analysis of the Helioseismic Power-Spectrum Diagram of a Sunspot

The continuous high spatial resolution Doppler observation of the Sun by the Solar Dynamics Observatory/Helioseismic and Magnetic Imager allows us to compute a helioseismic k–ω power-spectrum diagram using only oscillations inside a sunspot. Individual modal ridges can be clearly seen with reduced power in the k–ω diagram that is constructed from a 40-hour observation of a stable and round sunspot. Comparing this with the k–ω diagram obtained from a quiet-Sun region, one sees that inside the sunspot the f-mode ridge is more reduced in power than the p-mode ridges, especially at high wavenumbers. The p-mode ridges all shift toward lower wavenumber (or higher frequency) for a given frequency (or wavenumber), implying an increase of phase velocity beneath the sunspot. This is probably because the acoustic waves travel across the inclined magnetic field of the sunspot penumbra. Line-profile asymmetries exhibited in the p-mode ridges are more significant in the sunspot than in the quiet Sun. Convection inside the sunspot is also highly suppressed, and its characteristic spatial scale is substantially larger than the typical convection scale of the quiet Sun. These observational facts demand a better understanding of magnetoconvection and interactions of helioseismic waves with magnetic field.     

Large-Scale Structure of the Sunspot Activity and the Background Magnetic Field Formation

Large-scale distribution of the sunspot activity of the Sun has been analyzed by using a technique worked out previously (Erofeev, 1997) to study long-lived, non-axisymmetric magnetic structures with different periods of rotation. Results of the analysis have been compared with those obtained by analyzing both the solar large-scale magnetic field and large-scale magnetic field simulated by means of the well-known flux transport equation using the sunspot groups as a sole source of new magnetic flux in the photosphere. A 21-year period (1964–1985) has been examined.The rotation spectra calculated for the total time interval of two 11-year cycles indicate that sunspot activity consists of a series of discrete components (modes) with different periods of rotation. The largest-scale component of the sunspot activity reveals modes with 27-day and 28-day periods of rotation situated, correspondingly, in the northern and southern hemispheres of the Sun, and two modes with rotation periods of about 29.7 days situated in both hemispheres. Such a modal structure of the sunspot activity agrees well with that of the large-scale solar magnetic field. Moreover, the magnetic field distribution simulated with the flux transport equation also reveals the same modal structure. However, such an agreement between the large-scale solar magnetic field and both the sunspot activity and simulated magnetic field is unstable in time; so, it is absent in the northern hemisphere of the Sun during solar cycle No. 20. Thus the sources of magnetic flux responsible for formation of the large-scale, rigidly rotating magnetic patterns appear to be closely connected, but are not identical with the discrete modes of the sunspot activity.     

Radiation transfer through a model sunspot

We present a cylindrically symmetric model for a sunspot atmosphere using the similarity principle of Schlüter and Temesvary for the magnetic field configuration. The equations of magnetostatic equilibrium are used, augmented by a radial Evershed flow. The LTE radiative transfer equations for the Stokes vector were solved under a variety of conditions for a ray emerging from a typical penumbral point. The contribution from isolated lines to the broadband circular polarization in sunspot penumbrae is evaluated using a more realistic model sunspot atmosphere than has hitherto been considered. Results indicate that the inclusion of a velocity field along B is unable to give a net circular polarization of sufficient magnitude, although the variation with the angle between the line-of-sight and B is in qualitative agreement with observations. The corresponding results for the net linear polarization are satisfactory.     

The Observed Long- and Short-Term Phase Relation between the Toroidal and Poloidal Magnetic Fields in Cycle 23

The observed phase relations between the weak background solar magnetic (poloidal) field and strong magnetic field associated with sunspots (toroidal field) measured at different latitudes are presented. For measurements of the solar magnetic field (SMF) the low-resolution images obtained from Wilcox Solar Observatory are used and the sunspot magnetic field was taken from the Solar Feature Catalogues utilizing the SOHO/MDI full-disk magnetograms. The quasi-3D latitudinal distributions of sunspot areas and magnetic fields obtained for 30 latitudinal bands (15 in the northern hemisphere and 15 in the southern hemisphere) within fixed longitudinal strips are correlated with those of the background SMF. The sunspot areas in all latitudinal zones (averaged with a sliding one-year filter) reveal a strong positive correlation with the absolute SMF in the same zone appearing first with a zero time lag and repeating with a two- to three-year lag through the whole period of observations. The residuals of the sunspot areas averaged over one year and those over four years are also shown to have a well defined periodic structure visible in every two – three years close to one-quarter cycle with the maxima occurring at − 40° and + 40° and drifts during this period either toward the equator or the poles depending on the latitude of sunspot occurrence. This phase relation between poloidal and toroidal field throughout the whole cycle is discussed in association with both the symmetric and asymmetric components of the background SMF and relevant predictions by the solar dynamo models.     

Exact static equilibrium of vertically oriented magnetic flux tubes

A method is prescribed for generating exact solutions of magnetostatic equilibrium describing a cylindrically symmetric magnetic flux tube oriented vertically in a stratified medium. Given the geometric shape of the field lines, compact formulae are presented for the direct calculation of all the possible distributions of pressure, density, temperature and magnetic field strength compatible with these field lines under the condition of static equlibrium. The plasma satisfies the ideal gas law and gravity is uniform in space. A particular solution is obtained by this method for a medium sized sunspot whose magnetic field obeys the similarity law of Schlüter and Temesváry (1958). With this solution, it is possible for the first time to illustrate explicitly the confinement of the magnetic field of the cool sunspot by the hotter external plasma in an exact relationship involving both magnetic pressure and field tension as well as the support of the weight of the plasma by pressure gradients. It is found that the cool region of the sunspot is not likely to extend much more than a few density scale heights below the photosphere. The sunspot field approaches being potential in the neighbourhood of the photosphere so that the Lorentz force exerting on the photosphere is less than what the magnetic pressure would suggest. This accounts for how the sunspot field can be confined in the photosphere where its magnetic pressure is often observed to even exceed the normal photospheric pressure. The energy mechanism operating in the sunspot and the question of mechanical stability are not treated in this paper.Normally at Lau Kuei Huat (Singapore) Private Limited, 55 Shipyard Road, Singapore 22, Singapore.     

Double maxima of 11-year solar cycles

We propose a scenario to explain the observed phenomenon of double maxima of sunspot cycles, including the generation of a magnetic field near the bottom of the solar convection zone (SCZ) and the subsequent rise of the field from the deep layers to the surface in the royal zone. Five processes are involved in the restructuring of the magnetic field: the Ω-effect, magnetic buoyancy, macroscopic turbulent diamagnetism, rotary ?ρ-effect, and meridional circulation. It is found that the restructuring of magnetism develops differently in high-latitude and equatorial domains of the SCZ. A key role in the proposed mechanism of the double maxima is played by two waves of toroidal fields from the lower base of the SCZ to the solar surface in the equatorial domain. The deep toroidal fields are excited by the Ω-effect near the tachocline at the beginning of the cycle. Then these fields are transported to the surface due to the combined effect of magnetic buoyancy, macroscopic turbulent diamagnetism, and the rotary magnetic ?ρ-flux in the equatorial domain. After a while, these magnetic fragments can be observed as bipolar sunspot groups at the middle latitudes in the royal zone. This first, upward-directed wave of toroidal fields produces the main maximum of sunspot activity. However, the underlying toroidal fields in the high-latitude polar domains are blocked at the beginning of the cycle near the SCZ bottom by two antibuoyancy effects — the downward turbulent diamagnetic transfer and the magnetic ?ρ-pumping. In approximately 1 or 2 years, a deep equatorward meridional flow transfers these fields to low-latitude parts of the equatorial domain (where there are favorable conditions for magnetic buoyancy), and the belated magnetic fields (the second wave of toroidal fields) rise to the surface. When this second batch of toroidal fields comes to the solar surface at low latitudes, it leads to the second sunspot maximum.     

Evolution of magnetic fields and mass flow in a decaying active region

Five days of coordinated observation were carried out from 24–29 September, 1987 at Big Bear and Huairou Solar Observatories. Longitudinal magnetic fields of an p sunspot active region were observed almost continuously by the two observatories. In addition, vector magnetic fields, photospheric and chromospheric Doppler velocity fields of the active region were also observed at Huairou Solar Observatory. We studied the evolution of magnetic fields and mass motions of the active region and obtained the following results: (1) There are two kinds of Moving Magnetic Features (MMFs). (a) MMFs with the same magnetic polarity as the center sunspot. These MMFs carry net flux from the spot, move through the moat, and accumulate at the moat's outer boundary. (b) MMFs in pairs of mixed polarity. These MMFs are not responsible for the decay of the spot since they do not carry away the net flux. MMFs in category (b) move faster than those of (a). (2) The speed of the mixed polarity MMFs is larger than the outflow measured by photospheric Dopplergrams. The uni-polar MMFs are moving at about the same speed as the Doppler outflow. (3) The chromospheric velocity is in approximately the opposite direction from the photospheric velocity. The photospheric Doppler flow is outward; chromospheric flow is inward. We also found evidence that downward flow appears in the photospheric umbra; in the chromosphere there is an upflow.     

What do the solar activity indices represent?

Sunspot number, sunspot area, and radio flux at 10.7 cm are the indices which are most frequently used to describe the long‐term solar activity. The data of the daily solar full‐disk magnetograms measured at Mount Wilson Observatory from 19 January 1970 to 31 December 2012 are utilized together with the daily observations of the three indices to probe the relationship of the full‐disk magnetic activity respectively with the indices. Cross correlation analyses of the daily magnetic field measurements at Mount Wilson observatory are taken with the daily observations of the three indices, and the statistical significance of the difference of the obtained correlation coefficients is investigated. The following results are obtained: (1) The sunspot number should be preferred to represent/reflect the full‐disk magnetic activity of the Sun to which the weak magnetic fields (outside of sunspots) mainly contribute, the sunspot area should be recommended to represent the strong magnetic activity of the Sun (in sunspots), and the 10.7 cm radio flux should be preferred to represent the full‐disk magnetic activity of the Sun (both the weak and strong magnetic fields) to which the weak magnetic fields mainly contribute. (2) On the other hand, the most recommendable index that could be used to represent/reflect the weak magnetic activity is the 10.7 cm radio flux, the most recommendable index that could be used to represent the strong magnetic activity is the sunspot area, and the most recommendable index that could be used to represent the full‐disk magnetic activity of the Sun is the 10.7cm radio flux. Additionally, the cycle characteristics of the magnetic field strengths on the solar disk are given. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)