Phase-sensitive Holography of Solar Activity

Phase-correlation statistics comparing acoustic radiation coming out of a particular point on the solar photosphere with acoustic radiation going into it show considerably reduced sound travel times through the subphotospheres of active regions. We have now applied techniques in phase-sensitive seismic holography to data from the Solar Oscillations Investigation – Michelson Doppler Imager (SOI-MDI) on the Solar and Heliospheric Observatory (SOHO) spacecraft to obtain high resolution phase-correlation maps of a large, complex active region and the `acoustic moat' which surrounds it. We report the following new results: First, the reduced sound travel-time perturbations in sunspots, acoustic moats, and isolated plages increase approximately in proportion to the logarithm of the surface magnetic flux density, for flux densities above 10 G. This is consistent with an interpretation of the travel-time anomalies, observed with holographic and other local-helioseismic procedures, as caused by acoustic Wilson-like depressions in photospheres of magnetic regions. Second, we find that, compared with isolated plages, the acoustic moats have an additional sound travel-time reduction on the order of 3–5 s which may be explained by a thermal excess due to the blockage of convective transport by the sunspot photosphere. Third, the combined effect of the Wilson depression in plages, acoustic moats, and sunspots may explain the observed variation of global p-mode frequencies with the solar cycle. Fourth, we find that active regions, including sunspots, acoustic moats, and plages, significantly reflect p modes above the acoustic cut-off frequency, where the surface of the quiet Sun acts as a nearly perfect absorber of incident acoustic radiation.     

The rotation of active regions with differing magnetic polarity separations

The separation of the leading and following portions of plages and (multi-spot) sunspot groups is examined as a parameter in the analysis of plage and spot group rotation. The magnetic complexity of plages affects their average properties in such a study because it tends to make the polarity separations of the plages less than they really are (by the definition of polarity separation used here). Correcting for this effect, one finds a clear and very significant dependence of the total magnetic flux of a region on its polarity separation. Extrapolating this relationship to zero total flux leads to an X intercept of about 25 Mm in polarity separation. The average residual rotation rates of regions depend upon the polarity separation in the sense that larger separations correspond to slower rotation rates (except for small values of separation, which are affected by region complexity). In the case of sunspots, the result that smaller individual spots rotate faster than larger spots is confirmed and quantified. It is shown also that smaller spot groups rotate faster than larger groups, but this is a much weaker effect than that for individual spots. It is suggested that the principal effect is for spots, and that this individual spot effect is responsible for much or all of the group effect, including that attributed in the past to group age. Although larger spot groups have larger polarity separations, it is shown that the rotation rate-polarity separation effect is the opposite in groups than one finds in plages: groups with larger polarity separations rotate faster than those with smaller separations. This anomalous effect may be related to the evolution of plages and spot groups, or it may be related to connections with subsurface toroidal flux tubes. It is suggested that the polarity separation is a parameter of solar active regions that may shed some light on their origin and evolution.Operated by the Association of Universities for Research in Astronomy, Inc., under Cooperative Agreement with the National Science Foundation.     

Axial tilt angles of active regions

Separate Mount Wilson plage and sunspot group data sets are analyzed in this review to illustrate several interesting aspects of active region axial tilt angles. (1) The distribution of tilt angles differs between plages and sunspot groups in the sense that plages have slightly higher tilt angles, on average, than do spot groups. (2) The distributions of average plage total magnetic flux, or sunspot group area, with tilt angle show a consistent effect: those groups with tilt angles nearest the average values are larger (or have a greater total flux) on average than those farther from the average values. Moreover, the average tilt angles on which these size or flux distributions are centered differ for the two types of objects, and represent closely the actual different average tilt angles for these two features. (3) The polarity separation distances of plages and sunspot groups show a clear relationship to average tilt angles. In the case of each feature, smaller polarity separations are correlated with smaller tilt angles. (4) The dynamics of regions also show a clear relationship with region tilt angles. The spot groups with tilt angles nearest the average value (or perhaps 0-deg tilt angle) have on average a faster rotation rate than those groups with extreme tilt angles.All of these tilt-angle characteristics may be assumed to be related to the physical forces that affect the magnetic flux loop that forms the region. These aspects are discussed in this brief review within the context of our current view of the formation of active region magnetic flux at the solar surface.Dedicated to Cornelis de JagerOperated by the Association of Universities for Research in Astronomy, Inc., under Cooperative Agreement with the National Science Foundation.     

The XUV structure of solar active regions

XUV spectroheliograms of 2 active regions are studied. The images are due to lines emitted at temperatures between 8 x 10⁴ K and 2 x 10⁶ K and thus are indicative of transition region and coronal structures. The hot coronal lines are formed solely in loop structures which connect regions of opposite photospheric magnetic polarity but are not observed over sunspots. Transition region lines are emitted in plages overlying regions of intense photospheric magnetic field and in loops or loop-segments connecting such regions. The hot coronal loops are supported hydrostatically while only some of the transition zone loops are. The coronal and transition zone loops are distinctly separated and are not coaxial. A comparison of direct measurements of electron densities using density sensitive line ratios with indirect measurements using emission measures and path lengths shows the existence of fine structures of less than a second of arc in transition region loops. From a similar analysis, hot coronal loops do not have any fine structure below about 2 seconds of arc.     

Kinematics and evolution of local features of the large-scale magnetic field – II. Relation to Active Regions

Relationships have been studied between the background magnetic field and the distribution of active regions over the solar surface and time. A series of magnetic-field synoptic maps covering a 20-year period has been cross-correlated with spatio-temporal distributions of three types of active formations (sunspots, calcium plages, and solar flares) used as indicators of the active regions. To make the data analysis more effective, we expanded both the magnetic-field and the active-region distributions in terms of Fourier series in longitude, and then cross-correlated the latitude-dependent Fourier harmonics. Cross-correlation functions calculated from the lower-order Fourier harmonics exhibit prolonged maxima of the amplitude. For the first-order harmonic, the maxima can be tracked throughout a long time interval of at least 13 Carrington rotations, but the time of cross-correlation decreases down to 2 rotations, as the harmonic order increases up to 8. The maxima of the cross-correlation functions indicate moreover a poleward directed drift of the magnetic features that occurred with a velocity of 10–15 m s^–1. The cross-correlation functions calculated separately by using the three types of active formations as indicators of the active regions are similar to each other, although they differ in some details of minor significance. The results of the data analysis make it possible to conclude that the cross-correlation between the magnetic-field and the active-region distributions displays long-term evolution of the magnetic features emerged in the photosphere in the form of the active regions, and that the evolution occurs in accordance with Leighton's (1964) concept known at present as the flux transport model. In order to verify this conclusion, we applied the cross-correlation technique to analyze a magnetic field distribution simulated by means of the flux transport equation by using an ensemble of local-scale magnetic bipoles as a source of magnetic flux. Results of the simulated magnetic field analysis exhibit a substantial qualitative agreement with those obtained by examining the observational data.     

Green coronal intensity enhancements and their relation to the underlying photospheric/chromospheric activity

Analysis of the photospheric and chromospheric activity at the sites of enhanced 5303 Å coronal intensity revealed some important aspects of their association. We have examined the daily maps of 5303 Å coronal line intensity of Lomnický tít for the low sunspot activity years 1985 and 1986 in association with the cotemporal daily maps of sunspots, plages and Stanford magnetograms and identified strong field gradients at the sites of enhanced intensity regions. We found that the peak intensity does not depend on the strength of the underlying magnetic field though the coronal intensity-enhanced feature is almost sure to occur at the locations of sunspots with strong magnetic fields and at the locations of plages having larger areas.     

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.     

The magnetic fields of active regions

The Mount Wilson coarse array data set is used to define active regions in the interval 1967 to August, 1988. From the positions of these active regions on consecutive days, rotation rates are derived. The differential rotation of the active regions is calculated and compared with previous magnetic field and plage rates. The agreement is good except for the variation with time. The active region rates are slower by a few percent than the magnetic field or facular rates. The differential rotation rate of active regions with reversed magnetic polarity orientations is calculated. These regions show little or no evidence for differential rotation, although uncertainties in this determination are large. A correlation is found between rotation rate and region size in the sense that larger regions rotate more slowly. A correlation between rotation rate and cycle phase is suggested which is in agreement with earlier sunspot results. Leading and following portions of active regions, unlike leading and following spots, show little or no difference in their rotation rates. The regions with polarity orientations nearest the normal configuration tend to show rotation rates that are nearest the average values. Most of these results generally support the conclusion that old, weaker magnetic fields have evolved different subsurface connections from the time they were a part of sunspots or plages. It seems possible that they are connected at a shallower layer than are sunspot or plage fields.Operated by the Association of Universities for Research in Astronomy, Inc., under Contract with the National Science Foundation.     

The effect of an interaction of magnetic flux and supergranulation on the decay of magnetic plages

This paper studies how the properties of large-scale convection affect the decay of plages. The plage decay, caused by the random-walk dispersion of flux tubes, is suggested to be severely affected by differences between the mean size of cellular openings within and around plages. The smaller cell size within a plage largely explains the smaller diffusion coefficient within plages as compared to that of the surrounding regions. Moreover, the exchange of flux tubes between the inner regions of the plage and the surrounding network is suggested to be modified by this difference in cell size, and the concept of a partially transmitting plage periphery is introduced: this periphery preferentially turns back flux parcels that are moving out of the plage and preferentially lets through flux parcels that are moving into the plage, thus confining the flux tubes to within the plage. This semi-permeability of the plage periphery, together with the dependence of the diffusion coefficient on the flux-tube density, can explain the observed slow decay of plages (predicting a typical life time of about a month for a medium-sized plage), the existence of a well-defined plage periphery, and the observed characteristic mean magnetic flux density of about 100 G. One effect of the slowed decay of the plage by the semi-permeability of the plage periphery is the increase of the fraction of the magnetic flux that can cancel with flux of the opposite polarity along the neutral line to as much as 80%, as compared to at most 50% in the case of non-uniform diffusion. This may explain why only a small fraction of the magnetic flux is observed to escape from the plage into the surrounding network.     

On Absorption and Scattering of P Modes by Small-Scale Magnetic Elements

The solar surface is characterised everywhere by the presence of small-scale magnetic structures. Their collective behaviour in the form of active regions is known to have strong influence on p-mode power. For example, sunspots and plages are strong absorbers of acoustic waves. This paper studies the effects of individual small-scale magnetic elements to understand the details of absorption of p-mode power. For this, we consider a thin magnetic flux tube and calculate the phase shifts and the absorption coefficients by numerically solving the linearised MHD equations. The phase shifts calculated from the Born Approximation are then compared for the same range of degrees. The results are discussed with a view to understanding the physical mechanism.     

Kinematics of solar prominences

Two sequences of OSO-4 spectroheliograms in Mg x and Si xii obtained during October–November 1967 and covering the intervals of 83 and 22 hr, respectively, have been analyzed to reveal quasi-periodic oscillations of EUV flux from solar sources with a periodicity of 5–14 hr. The oscillation periods of the emission flux from local sources over sunspots and magnetic field enhancements in plages without spots have been investigated in correlation with characteristics of the respective AR and plages. The greatest periods (> 8 hr) are shown to be peculiar of small sunspots or sunspot groups at the initial or final stage of their development, whereas the smallest periods ( 5–6 hr) are observed in the case of large well-developed groups at the maximum stage of development. In quiet regions on the Sun and plages without spots, the oscillation periods are 6–8 hr. The surface areas in which the oscillations are synchronous and coincide in phase have typical dimensions of 1 in quiet and 1 to 5 in active regions. These areas form a spatial structure similar to the chromospheric network and supergranules. The characteristic lifetime of the structure elements is 1.5–2 days.     

Sunspot velocity correlations: Are they due to Reynolds stresses or to the Coriolis force on rising flux tubes?

Observations have consistently pointed out that the longitudinal and latitudinal motions of sunspots are correlated. The magnitude of the covariance was found to increase with latitude, and its sign was found to be positive in the N-hemisphere and negative in the S-hemisphere. This correlation was believed to be due to the underlying turbulence where the sunspot flux tubes are anchored, and the covariance had the right sign and magnitude needed to explain the transfer of angular momentum toward the equator through Reynolds stresses.Here we present an alternate explanation for these sunspot velocity correlations: It is believed that the dynamo operates in a thin overshoot layer beneath the base of the convection zone, and the flux tubes generated there produce sunspots at the photosphere. By studying the dynamics of flux tubes emerging from the base of the convection zone to the photosphere, we show that these velocity correlations of sunspots could be merely a consequence of the effect of Coriolis force on rising flux tubes. The effect of the Coriolis force, as demonstrated by even a back-of-the-envelope calculation, is to push the faster rotating spots equatorward and the slower rotating spots poleward, giving rise to a correlation in their longitudinal and latitudinal velocities, which is positive in the N-hemisphere and negative in the S-hemisphere. The increase in the correlation with latitude is due to the increase in magnitude of the Coriolis force. Hence we show that these velocity correlations might have nothing to do with the Reynolds stresses of the underlying turbulence.We present analyses of observations, and show that the covariances of plages are an order of magnitude higher than the sunspot covariances. If plages and sunspots share the same origin, and if their horizontal velocity correlations are wholly due to the effect of Coriolis force on rising flux tubes, then the study of their dynamics suggests that the flux tubes that form plages should have diameters of a couple of thousand km at the base of the convection zone and remain intact until they reach the photosphere, whereas sunspots should be formed by a collection of small flux tubes (each measuring about a hundred km in diameter), that rise through the convection zone as individual elements and coalesce when they emerge through the photosphere.Operated by the Association of Universities for Research in Astronomy, Inc., under Cooperative Agreement with the National Science Foundation.     

The Big Bear Solar Observatory Ca II K‐line index for solar cycle 23

We present an analysis of 2634 Ca II K‐line full‐disk filtergrams obtained with the 15‐cm aperture photometric full‐disk telescope at Big Bear Solar Observatory during the period from 1996 January 1 to 2005 October 24. Using limb darkening corrected and contrast enhanced filtergrams, solar activity indices were derived, which are sensitive to the 11‐year solar activity cycle and 27‐day rotational period of plages around active regions and the bright chromospheric network. The present work extends an earlier study (solar cycle 22), which was based on video data. The current digital data are of much improved quality with higher spatial resolution and a narrower passband ameliorating photometric accuracy. The time series of chromospheric activity indices cover most of solar cycle 23. One of the most conspicuous features of the Ca II K indices is the secondary maximum in late 2001/early 2002 after an initial decline of chromospheric activity during the first half of 2001. We conclude that a secular trend exists in the Ca II K indices, which has its origin in the bright chromospheric network and brightenings related to decaying active regions. Superposed on this secular trend are the signatures of recurring, long‐lived active regions, which are clusters of persistent and continuously emerging magnetic flux. Such features are less visible, when the activity belts on both side of the equator are devoid of the brightenings related to decaying active regions as was the case in October/November 2003 at a time when a superactivity complex including several naked‐eye sunspots emerged (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The emergence of magnetic flux

This paper first summarizes the morphology and dynamics of emerging flux regions and arch filament systems and then discusses detailed observations of a particular active region with emerging magnetic flux.The central part of the growing active region shows abnormal granulation and a weak magnetic field that, locally, is transverse. In the border zone, strong downward flows occur in the chromopshere and photosphere (small features with strong magnetic fields (faculae, pores) are formed here.) Near the leading and following edge, sunspots are formed by the coalescence of such small magnetic elements.The observational data are interpreted by means of a heuristic model of an emergent magnetic loop-shaped bundle consisting of many flux tubes. In this model we incorporate the theory of convective collapse and the buoyancy of flux tubes. The observed complexity in the structure and dynamics, including strong transverse fields and velocity shear, is attributed to the emergence of several flux regions within the active region at different orientations.     

Sunspot and Auroral Activity During Maunder Minimum

The extremely low sunspot activity during the period of the Maunder minimum 1645–1715 was confirmed by group sunspot numbers, a new sunspot index constructed by Hoyt and Schatten (1998a,b). Neither sunspots nor auroral data time behavior indicate the presence of 11-year solar cycles as stated by Eddy (1976). The evidence for solar cycles was found in the butterfly diagram, constructed from observations made at Observatoire de Paris. After Clivier, Boriakoff, and Bounar (1998) the solar cycles were reflected also in geomagnetic activity. Results are supported by the variation of cosmogenic isotopes ¹⁰Be and ¹⁴C. The majority of the observed 14 naked-eye sunspots occurred on days when telescopic observations were not available. A part of them appeared in the years when no spot was allegedly observed. Two-ribbon flares appear in plages with only very small or no sunspots. Some of these flares are geoactive. Most aurorae (90%), which were observed during the Maunder minimum, appeared in years when no spot was observed. Auroral events as a consequence of proton flares indicate that regions with enhanced magnetic field can occur on the Sun when these regions do not produce any sunspots.     

Are short-time variations of the solar S-component emission identical with microwave bursts?

Extended time series (time resolution about 2–3 min) of spatially resolved observations (≫ 17 arcsec) in one dimension of solar S-component sources obtained at the Siberian Solar Radio Telescope (SSRT) at 5.2 cm wavelength allow the detection of evolutional features of the growth and decay of active regions in the solar corona. Characteristic slow flux variations with timescales of about 1–2 hours occurring during the decay phase of the radio emission in the low corona above plages and sunspots are compared with recently detected step-like flux increases on timescales of about 10–20 min followed by quasi-constant periods appearing in the initial phase of the development of active regions. Superimposed on this basic behaviour, also fluctuations at shorter timescales (or even periodic oscillations) have been observed. As it is well known from emission-model calculations, the variations of the S-component radiation can be due to variations of the magnetic field and/or changes of the energy of the radiating particles, which is basically the same emission mechanism as for microwave bursts. Since the “S-component” is originally defined by its long timescale behaviour derived from whole-Sun flux density measurements, the presently detected small-timescale features in S-component sources require either a revised definition of S-component emission or must be considered as “burst-like”.     

From Sunspot Area to Solar Variability: A Linear Transformation

The relationship between sunspot area and other observable solar parameters, such as spectral solar irradiance or total magnetic flux, is frequently sought by examining scatterplots of daily data, which generally show a non-linear distribution of points. We show that the scatterplots are consistent with our published result that these observable solar parameters are related to sunspot area by a transformation that is both linear and time invariant, namely by convolution with a finite impulse response function. Most solar parameters are affected by extended active regions, not just by sunspots. The fact that a complex active region evolves much more slowly than its associated sunspots provides a simple physical explanation of the observed non-linearities in scatterplots.     

prior to surface appearance of sunspot flux tubes and magneto-thermal pulsation of the Sun

We found an evidence that the luminosity of the Sun systematically decreased about 20 days before sunspot surface appearance by analysing time-lag correlation of time derivatives of running mean time profiles of the data of the Active Cavity Radiometer Irradiance Monitor (ACRIM) I experiment on board of Solar Maximum Mission (SMM) and of the data of the daily sunspot number. This indicates that sunspot flux tube cooling and heat transport blocking by the flux tubes start to take place in the interior of the solar convection zone well before the sunspot surface appearance. From this finding and our previous finding that the luminosity of the Sun systematically increased and the blocked heat appeared on the surface about 50 days after the sunspot surface appearance, a new view of sunspot formation and dynamics and a new view of the luminosity modulation emerged. (i) Sunspots of a solar cycle are formed from clusters of flux tubes which can be seen in the running mean time profile of the sunspot number as a peak with duration on the order of 100 to 200 days. (ii) Heat flow is blocked by the cluster of sunspot flux tubes inside the convection zone to decrease the luminosity about 20 days before the surface emergence of the sunspot cluster. (iii) The blocked heat appears on the surface about 50 days after the surface emergence of the cluster of sunspot flux tubes to heat up the surface. This appears as a thermal pulse in the running mean time profile of the ACRIM dat in between the peaks of the sunspot running mean time profile. This process of heating the surface makes the temperature gradient less steep and weakens the buoyancy of sunspot flux tubes below the surface. (vi) The radiative cooling of the surface layer by the excess heat release steepens the temperature gradient so that the buoyancy of the sub-surface magnetic flux tubes becomes stronger to cause the next surge of emergence of a cluster of sunspots and other magnetic activities, which creates a peak in the time profile of the sunspot number. We call this peak a magnetic pulse of the Sun and the coupled process of alternating pulsed appearance of heat and sunspots the magneto-thermal pulsation of the Sun.     

The rotation of sunspots in the solar active region NOAA 10930

The rotation of sunspots in the solar active region NOAA 10930 was investigated on the basis of the data on the longitudinal magnetic field and the Doppler velocities using magnetograms and dopplergrams taken with the Solar Optical Telescope installed aboard the HINODE mission. Under the assumption of axial symmetry, areally-mean vertical, radial, and azimuthal components of the magnetic field and velocity vectors were calculated in both sunspots. The plasma in the sunspots rotated in opposite directions: in the leading sunspot, clockwise, and in the following sunspot, counterclockwise. The magnetic flux tubes that formed sunspots of the active region on the solar surface were twisted in one direction, clockwise. Electric currents generated as a result of the rotation and twisting of magnetic flux tubes were also flowing in one direction. Azimuthal components of magnetic and velocity fields of both sunspot umbrae reached their maximum on December 11, 2006. By the start of the X3.4 flare (December 13, 2006), their values became practically equal to zero.     

The line-ratio method applied to vectormagnetographic measurements

Since solar magnetic fields are inhomogeneous, the averaging of Stokes parameter I within the entrance slit of the magnetograph is different from averaging Stokes Q₀ and V, because the former contains also light from non-magnetic, while the latter only contain light from magnetic regions. If the magnetographic calibration functions are calculated for homogeneous magnetic fields, errors arise, when they are used to reduce measurements of inhomogeneous fields. Therefore, we propose to use the line-ratio method to transform magnetographic measurements into the parameters of the magnetic vector field. The Q ratios and the V ratios of two carefully selected lines are free from errors of this kind. This is also the case for the Q ratios in line core and line wings in single-line magnetographs. An iterative method is presented to calculate the magnetic field parameters using the corresponding new calibration functions. An important advantage is, that the influence of scattered light in sunspots is also eliminated in a good approximation and the filling factor in plages can be estimated. This method is now used to determine magnetic vector fields in plages and sunspots of active regions with a new double-vector magnetograph.