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.     

Characteristics of active-region sources of solar wind near solar maximum

Previous studies of the source regions of solar wind sampled by ACE and Ulysses showed that some solar wind originates from open magnetic flux rooted in active regions. These solar wind sources were labeled active-region sources when the open flux was from a strong field region with no corresponding coronal hole in the NSO He 10830 Å synoptic coronal-hole maps. Here, we present a detailed investigation of several of these active-region sources using ACE and Ulysses solar wind data, potential field models of the corona, and solar imaging data. We find that the solar wind from these active-region sources has distinct signatures, e.g., it generally has a higher oxygen charge state than wind associated with helium-10830 Å coronal-hole sources, indicating a hotter source region, consistent with the active region source interpretation. We compare the magnetic topology of the open field lines of these active-region sources with images of the hot corona to search for corresponding features in EUV and soft X-ray images. In most, but not all, cases, a dark area is seen in the EUV and soft X-ray image as for familiar coronal-hole sources. However, in one case no dark area was evident in the soft X-ray images: the magnetic model showed a double dipole coronal structure consistent with the images, both indicating that the footpoints of the open field lines, rooted deep within the active region, lay near the separatrix between loops connecting to two different opposite polarity regions.     

Characteristics of active-region sources of solar wind near solar maximum

Previous studies of the source regions of solar wind sampled by ACE and Ulysses showed that some solar wind originates from open magnetic flux rooted in active regions. These solar wind sources were labeled active-region sources when the open flux was from a strong field region with no corresponding coronal hole in the NSO He 10830 Å synoptic coronal-hole maps. Here, we present a detailed investigation of several of these active-region sources using ACE and Ulysses solar wind data, potential field models of the corona, and solar imaging data. We find that the solar wind from these active-region sources has distinct signatures, e.g., it generally has a higher oxygen charge state than wind associated with helium-10830 Å coronal-hole sources, indicating a hotter source region, consistent with the active region source interpretation. We compare the magnetic topology of the open field lines of these active-region sources with images of the hot corona to search for corresponding features in EUV and soft X-ray images. In most, but not all, cases, a dark area is seen in the EUV and soft X-ray image as for familiar coronal-hole sources. However, in one case no dark area was evident in the soft X-ray images: the magnetic model showed a double dipole coronal structure consistent with the images, both indicating that the footpoints of the open field lines, rooted deep within the active region, lay near the separatrix between loops connecting to two different opposite polarity regions.     

The reversal of the solar polar magnetic fields

Observations of the first major active regions and large-scale magnetic field patterns of Cycle 22 are presented. These show that, following the emergence of a trans-equatorial pattern, or cell, of positive flux related to old cycle activity, the first new cycle active regions of the longitude range emerged across the neutral lines of this cell, which continued to grow and expand across the equator for several rotations. The development of a parallel trans-equatorial band of flux of opposite (negative) polarity and the emergence of both new and old cycle active regions across a neutral line of this cell are also described.Simulations using the flux transport equation, and based on synoptic magnetic data provided by the Mount Wilson Observatory, show that, while the growth of the positive region could, in part, be explained by the decay of flux from these new regions, there were significant differences between synoptic contour charts based on the simulations and those constructed from the observed fields. They also show that the development of the negative region cannot reasonably be explained by the decay of the observed active regions.A further example of the counter rotation of decaying active region fields is reported. Here the initial tilt of the negative-positive magnetic axes of two adjacent regions is normal, and simulations based on these data show their combined follower flux moving preferentially polewards. However, the observations show that, after three rotations, the decaying leader flux is entirely poleward of the follower flux.On leave from the School of Mathematics, University of Sydney.     

Multiresolution Analysis of Active Region Magnetic Structure and its Correlation with the Mount Wilson Classification and Flaring Activity

Two different multiresolution analyses are used to decompose the structure of active-region magnetic flux into concentrations of different size scales. Lines separating these opposite polarity regions of flux at each size scale are found. These lines are used as a mask on a map of the magnetic field gradient to sample the local gradient between opposite polarity regions of given scale sizes. It is shown that the maximum, average, and standard deviation of the magnetic flux gradient for α,β,β γ, and β γ δ active-regions increase in the order listed, and that the order is maintained over all length scales. Since magnetic flux gradient is strongly linked to active-region activity, such as flares, this study demonstrates that, on average, the Mt. Wilson classification encodes the notion of activity over all length scales in the active-region, and not just those length scales at which the strongest flux gradients are found. Further, it is also shown that the average gradients in the field, and the average length-scale at which they occur, also increase in the same order. Finally, there are significant differences in the gradient distribution, between flaring and non-flaring active regions, which are maintained over all length scales. It is also shown that the average gradient content of active-regions that have large flares (GOES class “M” and above) is larger than that for active regions containing flares of all flare sizes; this difference is also maintained at all length scales. All of the reported results are independent of the multiresolution transform used. The implications for the Mt. Wilson classification of active-regions in relation to the multiresolution gradient content and flaring activity are discussed.     

Some factors affecting the growth and decay of plages

The Mount Wilson coarse array magnetograph data set is analyzed to examine the dependence of growth and decay rates on the tilt angles of the magnetic axes of the regions. It is found that there is a relationship between these quantities which is similar to that found earlier for sunspot groups. Regions near the average tilt angle show larger average (absolute) growth and decay rates. Thepercentage growth and decay rates show minima (in absolute values) at the average tilt angles because the average areas of regions are largest near this angle. This result is similar to that derived earlier for sunspot groups. As in the case of spot groups, this suggests that, for decay, the effect results from the fact that the average tilt angle may represent the simplest subsurface configuration of the flux loop or loops that make up the region. In the case of region growth, it was suggested that the more complicated loop configuration should result in increased magnetic tension in the flux loop, and thus in a slower ascent of the loop to the surface, and thus a slower growth rate. In order to examine this further, the growth and decay rates of plage regions were examined as functions of the magnetic complexity of the regions. In the case of decay, the result was as expected from the model suggested above - that is, the more complex regions decayed more slowly. But for growing regions the effect is the opposite to that expected (more complex regions grow faster, even in terms of percentage growth), so the explanation of the tilt angle effect for growing regions proposed earlier may not be valid.Operated by the Association of Universities for Research in Astronomy, Inc., under Cooperative Agreement with the National Science Foundation.     

The Relationship Between Plasma Flow Doppler Velocities and Magnetic Field Parameters During the Emergence of Active Regions at the Solar Photospheric Level

A statistical study has been carried out of the relationship between plasma flow Doppler velocities and magnetic field parameters during the emergence of active regions at the solar photospheric level with data acquired by the Michelson Doppler Imager (MDI) onboard the Solar and Heliospheric Observatory (SOHO). We have investigated 224 emerging active regions with different spatial scales and positions on the solar disc. The following relationships for the first hours of the emergence of active regions have been analysed: i) of peak negative Doppler velocities with the position of the emerging active regions on the solar disc; ii) of peak plasma upflow and downflow Doppler velocities with the magnetic flux growth rate and magnetic field strength for the active regions emerging near the solar disc centre (the vertical component of plasma flows); iii) of peak positive and negative Doppler velocities with the magnetic flux growth rate and magnetic field strength for the active regions emerging near the limb (the horizontal component of plasma flows); iv) of the magnetic flux growth rate with the density of emerging magnetic flux; v) of the Doppler velocities and magnetic field parameters for the first hours of the appearance of active regions with the total unsigned magnetic flux at the maximum of their development.     

Subsurface Zonal Flows

We study the zonal flow in solar subsurface layers, analyzing about six years of GONG++ high-resolution Doppler data with ring-diagram analysis. We focus on the variation of zonal flow with magnetic activity over a range of depths from the surface to about 16 Mm. There is a positive correlation between unsigned magnetic flux and zonal flow at most depths. We calculate the average zonal flow for a quiet- and an active-region subset defined as dense-pack locations with an unsigned magnetic flux less than 3.4 G and locations with greater than 65.0 G, respectively. The average zonal flow of active regions is about 4 m s⁻¹ larger than the average flow of quiet regions. This difference increases slightly with increasing depth, which might be explained by a nonradial inclination of the flux tubes or a different extent in depth of different magnetic features. The difference shows no apparent pattern in time and latitude, which makes it unlikely that it is simply a manifestation of the torsional-oscillation pattern. As a byproduct, we find that the size of the North – South asymmetry of the rotation rate decreases during the same epoch.     

The reversal of the solar polar magnetic fields

Observations of the first large-scale patterns of magnetic fields near the sunspot minimum of 1986 (the start of cycle 22) are presented using synoptic magnetic data provided by the National Solar Observatory and contour maps constructed from data provided by the Mount Wilson Solar Observatory. The latter are compared with simulated contour maps derived from numerical solutions of the flux transport equation using data from particular Carrington rotations as initial conditions.The simulated evolutions of the large-scale magnetic fields are qualitatively consistent with observed evolutions, but differ in several significant respects. Some of the differences can be removed by varying the diffusivity and the parameters of the large-scale velocity fields. The remaining differences include: (i) the complexity of fine structure, (ii) the response to differential rotation, (iii) the evolution of decaying active regions, and (iv) the emergence of new elements in the weak, large-scale fields independent of the evolution of the observed active regions.It is concluded that the patterns of weak magnetic fields which comprise the large-scale features cannot be formed entirely by the diffusive decay of active regions. There must be a significant contribution to these patterns by non-random flux eruptions within the network structure, independent of active regions.     

Subsurface Velocity of Emerging and Decaying Active Regions

We study the temporal variation of subsurface flows of 828 active regions and 977 quiet regions. The horizontal flows cover a range of depths from the surface to about 16 Mm and are determined by analyzing Global Oscillation Network Group high-resolution Doppler data with ring-diagram analyses. The vertical velocity component is derived from the divergence of the measured horizontal flows using mass conservation. For comparison, we analyze Michelson Doppler Imager (MDI) Dynamics Run data covering 68 active regions common to both data sets. We determine the change in unsigned magnetic flux during the disk passage of each active region using MDI magnetograms binned to the ring-diagram grid. We then sort the data by their flux change from decaying to emerging flux and divide the data into five subsets of equal size. We find that emerging flux has a faster rotation than the ambient fluid and pushes it up, as indicated by enhanced vertical velocity and faster-than-average zonal flow. After active regions are formed, downflows are established within two days of emergence in shallow layers between about 4 and 10 Mm. Emerging flux in existing active regions shows a similar scenario, where the upflows at depths greater than about 10 Mm are enhanced and the already established downflows at shallower depths are weakened. When active regions decay, the corresponding flow pattern disappears as well; the zonal flow slows down to values comparable to that of quiet regions and the upflows become weaker at deeper layers. The residual meridional velocity is mainly poleward and shows no obvious variation. The magnitude of the residual velocity, defined as the sum of the squares of the residual velocity components, increases with increasing magnetic flux and decreases with decreasing flux.     

The Evolution of Sunspot Magnetic Fields Associated with a Solar Flare

Solar flares occur due to the sudden release of energy stored in active-region magnetic fields. To date, the precursors to flaring are still not fully understood, although there is evidence that flaring is related to changes in the topology or complexity of an active-region’s magnetic field. Here, the evolution of the magnetic field in active region NOAA 10953 was examined using Hinode/SOT-SP data over a period of 12 hours leading up to and after a GOES B1.0 flare. A number of magnetic-field properties and low-order aspects of magnetic-field topology were extracted from two flux regions that exhibited increased Ca ii H emission during the flare. Pre-flare increases in vertical field strength, vertical current density, and inclination angle of ≈ 8° toward the vertical were observed in flux elements surrounding the primary sunspot. The vertical field strength and current density subsequently decreased in the post-flare state, with the inclination becoming more horizontal by ≈ 7°. This behavior of the field vector may provide a physical basis for future flare-forecasting efforts.     

Empirical Modeling of Radiative <Emphasis Type="Italic">versus</Emphasis> Magnetic Flux for the Sun-as-a-Star

We study the relationship between full-disk solar radiative flux at different wavelengths and average solar photospheric magnetic-flux density, using daily measurements from the Kitt Peak magnetograph and other instruments extending over one or more solar cycles. We use two different statistical methods to determine the underlying nature of these flux – flux relationships. First, we use statistical correlation and regression analysis and show that the relationships are not monotonic for total solar irradiance and for continuum radiation from the photosphere, but are approximately linear for chromospheric and coronal radiation. Second, we use signal theory to examine the flux – flux relationships for a temporal component. We find that a well-defined temporal component exists and accounts for some of the variance in the data. This temporal component arises because active regions with high magnetic-field strength evolve, breaking up into small-scale magnetic elements with low field strength, and radiative and magnetic fluxes are sensitive to different active-region components. We generate empirical models that relate radiative flux to magnetic flux, allowing us to predict spectral-irradiance variations from observations of disk-averaged magnetic-flux density. In most cases, the model reconstructions can account for 85 – 90% of the variability of the radiative flux from the chromosphere and corona. Our results are important for understanding the relationship between magnetic and radiative measures of solar and stellar variability.     

Vorticity of Subsurface Flows of Emerging and Decaying Active Regions

We study the temporal variation of the vorticity of subsurface flows of 828 active regions and 977 quiet regions. The vorticity of these flows is derived from measured subsurface velocities. The horizontal flows are determined by analyzing high-resolution Global Oscillation Network Group Doppler data with ring-diagram analysis covering a range of depths from the surface to about 16 Mm. The vertical velocity component is derived from the divergence of the measured horizontal flows using mass conservation. We determine the change in unsigned magnetic flux density during the disk passage of each active region using Michelson Doppler Imager (MDI) magnetograms binned to the ring-diagram grid with centers spaced by 7.5° ranging ± 52.5° in latitude and central meridian distance with an effective diameter of 15° after apodization. We then sort the data by their flux change from decaying to emerging flux and divide the data into five subsets of equal size. We find that the vorticity of subsurface flows increases during flux emergence and decreases when active regions decay. For flux emergence, the absolute values of the zonal and meridional vorticity components show the most coherent variation with activity, while for flux decrease the strongest signature is in the absolute values of the meridional and vertical vorticity components. The temporal variation of the enstrophy (residual vorticity squared) is thus a good indicator for either flux increase or decrease. There are some indications that the increase in vorticity during flux emergence happens about a day later at depths below about 8 Mm compared to layers shallower than about 4 Mm. This timing difference might imply that the vorticity signal analyzed here is caused by the interaction between magnetic flux and turbulent flows near the solar surface. There are also hints that the vorticity decrease during flux decay begins about a day earlier at layers deeper than about 8 Mm compared to shallower ones. However, the timing difference between the change at different depths is comparable to the time step of the analysis.     

How growth and decay of sunspot groups depend on axial tilt angles

Digitized Mount Wilson sunspot data covering the interval from 1917 to 1985 are analyzed to examine the average growth and decay rates of sunspot groups as a function of the tilt angles of the magnetic axes of the groups. It is found that in absolute terms, both growth and decay rates of groups peak at the average tilt angle of the groups (about +5°). In percentage terms these rates are a minimum near these tilt angles because average group areas are largest at the average tilt angle. The clear peaks at the average tilt angle (rather than at 0°) may be related to the structure or geometry of the subsurface flux loops that form the regions. One suggestion to explain this effect is that this is the angle that represents no twist of these subsurface flux loops. This implies, however, that these loops do not get twisted, on average, during their ascent to the surface by Coriolis forces, as has been suggested in the past. The average percentage growth rates for groups with negative tilt angles show high average values and large dispersions for certain tilt angle intervals, suggesting slower growth rates, for some unknown reason, for many small spot groups in certain tilt angle ranges.     

Formation of a Switchback During the Rising Phase of Solar Cycle 21

The customary notion that high-latitude filaments arise from magnetic flux originating in the active-region belts finds its modern expression in numerical models that generate filament channels from flux patterns migrating from active latitudes to the polar caps. Polarity inversions underlying high-latitude filament channels are swept into distinct patterns called `switchbacks' under the joint influence of differential rotation, supergranular diffusion, and meridional flow. The numerical model of Mackay and van Ballegooijen (2001) predicts a heretofore unsuspected solar-cycle dependence to the hemispheric pattern of filament magnetic fields. Observations presented here of a switchback formed early in cycle 21 confirm some key aspects of their model. In this remarkable example the flux diffusing out of the source region migrates to the opposite side of the Sun before it encounters another active region with which to create the quadrupolar field configuration wherein a return arm forms to complete the switchback.     

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”.     

Comparing Simulations of Rising Flux Tubes Through the Solar Convection Zone with Observations of Solar Active Regions: Constraining the Dynamo Field Strength

We study how active-region-scale flux tubes rise buoyantly from the base of the convection zone to near the solar surface by embedding a thin flux tube model in a rotating spherical shell of solar-like turbulent convection. These toroidal flux tubes that we simulate range in magnetic field strength from 15 kG to 100 kG at initial latitudes of 1^° to 40^° in both hemispheres. This article expands upon Weber, Fan, and Miesch (Astrophys. J. 741, 11, 2011) (Article 1) with the inclusion of tubes with magnetic flux of 10²⁰ Mx and 10²¹ Mx, and more simulations of the previously investigated case of 10²² Mx, sampling more convective flows than the previous article, greatly improving statistics. Observed properties of active regions are compared to properties of the simulated emerging flux tubes, including: the tilt of active regions in accordance with Joy’s Law as in Article 1, and in addition the scatter of tilt angles about the Joy’s Law trend, the most commonly occurring tilt angle, the rotation rate of the emerging loops with respect to the surrounding plasma, and the nature of the magnetic field at the flux tube apex. We discuss how these diagnostic properties constrain the initial field strength of the active-region flux tubes at the bottom of the solar convection zone, and suggest that flux tubes of initial magnetic field strengths of ≥?40 kG are good candidates for the progenitors of large (10²¹ Mx to 10²² Mx) solar active regions, which agrees with the results from Article 1 for flux tubes of 10²² Mx. With the addition of more magnetic flux values and more simulations, we find that for all magnetic field strengths, the emerging tubes show a positive Joy’s Law trend, and that this trend does not show a statistically significant dependence on the magnetic flux.     

Some characteristics of the development and decay of active region magnetic flux

Mount Wilson synoptic data of both plages and sunspots are examined in an effort to determine in some detail the manner of the appearance and disappearance of the magnetic flux of active regions at the solar surface. Separating regions into leading and following portions by magnetic polarity in the case of the plages and by position in the case of sunspots (for which there is no magnetic information available in this data set), various characteristics of these features are studied, namely their rotation, their relative longitudinal motions, and the east-west inclinations of their magnetic fields. The evidence, taken together, suggests that the magnetic flux loops which comprise a region rise to the surface at the time of its formation, and (at least some of them) sink back below the surface at the time of the decay of the region. It is likely that not all the magnetic flux that arises sinks again below the surface.Operated by the Association of Universities for Research in Astronomy, Inc., under Cooperative Agreement with the National Science Foundation.     

Evidence for a poleward meridional flow on the sun

We define for observational study two subsets of all polar zone filaments, which we call polemost filaments and polar filament bands. The behavior of the mean latitude of both the polemost filaments and the polar filament bands is examined and compared with the evolution of the polar magnetic field over an activity cycle as recently distilled by Howard and LaBonte (1981) from the past 13 years of Mt. Wilson full-disk magnetograms. The magnetic data reveal that the polar magnetic fields are built up and maintained by the episodic arrival of discrete f-polarity regions that originate in active region latitudes and subsequently drift to the poles. After leaving the active-region latitudes, these unipolar f-polarity regions do not spread equatorward even though there is less net flux equatorward; this indicates that the f-polarity regions are carried poleward by a meridional flow, rather than by diffusion. The polar zone filaments are an independent tracer which confirms both the episodic polar field formation and the meridional flow. We find:

1. The mean latitude of the polemost filaments tracks the boundary of the polar field cap and undergoes an equatorward dip during each arrival of additional polar field.
2. Polar filament bands track the boundary latitudes of the unipolar regions, drifting poleward with the regions at about 10 m s^-1.
3. The Mt. Wilson magnetic data, combined with a simple model calculation, show that the filament drift expected from diffusion alone would be slower than observed, and in some cases would be equatorward rather than poleward.
4. The observation that filaments drift poleward along with the magnetic regions shows that fields of both polarities are carried by the meridional flow, as would be expected, rather than only the f-polarity flux which dominates the strength. This leads to the prediction that in the mid-latitudes during intervals between the passage of f-polarity regions, both polarities are present in nearly equal amounts. This prediction is confirmed by the magnetic data.