Differential rotation and sector structure of solar magnetic fields

The differential rotation and sector structure of solar magnetic fields has been studied using digitized data on photospheric magnetic fields recorded at the Mount Wilson Observatory during the period August 1959–May 1970. The power spectra show considerable power in high-frequency peaks, corresponding to harmonic components with wavelengths less than 1/10 solar rotation. Calculations for a series of shorter time intervals show how the distribution of power over the various harmonic components in the sector pattern varies strongly with the solar cycle. The equatorial rotation rate of solar magnetic fields is about 0.1 km s^-1 faster than that of the photospheric plasma determined from Doppler shifts. It is shown that the Doppler measurements mainly refer to the non-network regions. The differential flow of 0.1 km s^-1 forms streamlines around the magnetic fine structures. The different rotation rates of various solar features can be explained in terms of the rotation rates of magnetic and non-magnetic regions. The rotation rates of the magnetic fields in active and quiet regions agree at the equator. At higher latitudes, however, the background fields deviate less from solid-body rotation, indicating that their source is below the deepest layers to which the sunspot magnetic fields penetrate. This suggests that turbulent diffusion of the field in old active regions may not be the main source for the background magnetic field, but that the source is located close to a rigidly rotating solar core with a synodic rotation period of 26.87 days.     

The mean coronal magnetic field determined from HELIOS Faraday rotation measurements

Coronal Faraday rotation of the linearly polarized carrier signals of the HELIOS spacecraft was recorded during the regularly occurring solar occultations over almost a complete solar cycle from 1975 to 1984. These measurements are used to determine the average strength and radial variation of the coronal magnetic field at solar minimum at solar distances from 3–10 solar radii, i.e., the range over which the complex fields at the coronal base are transformed into the interplanetary spiral. The mean coronal magnetic field in 1975–1976 was found to decrease with radial distance according to r ^?α, where α = 2.7 ± 0.2. The mean field magnitude was 1.0 ± 0.5 × 10 ^?5 tesla at a nominal solar distance of 5 solar radii. Possibly higher magnetic field strengths were indicated at solar maximum, but a lack of data prevented a statistical determination of the mean coronal field during this epoch.     

Differential rotation and the structure and energy content of coronal magnetic fields

It is argued that differential rotation of the photospheric magnetic fields will induce currents in the corona. The work done against surface magnetic stresses will increase the energy content of the coronal magnetic field. The electrical conductivities are high and the foot points of field lines move with the differential rotation. The force-free field equations are solved with this constraint to obtain a minimum estimate of the energy increase for a quadrupole field. During a solar rotation the magnetic energy increases by 25%. Local release of this energy in the corona would have a significant effect. The expansion of field lines as a result of the differential rotation should increase the amount of flux and the field strength in the solar wind region.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

On the solar rotation and activity

The interaction between differential rotation and magnetic fields in the solar convection zone was recently modelled by Brun (2004). One consequence of that model is that the Maxwell stresses can oppose the Reynolds stresses, and thus contribute to the transport of the angular momentum towards the solar poles, leading to a reduced differential rotation. So, when magnetic fields are weaker, a more pronounced differential rotation can be expected, yielding a higher rotation velocity at low latitudes taken on the average. This hypothesis is consistent with the behaviour of the solar rotation during the Maunder minimum. In this work we search for similar signatures of the relationship between the solar activity and rotation determined tracing sunspot groups and coronal bright points. We use the extended Greenwich data set (1878–1981) and a series of full-disc solar images taken at 28.4 nm with the EIT instrument on the SOHO spacecraft (1998–2000). We investigate the dependence of the solar rotation on the solar activity (described by the relative sunspot number) and the interplanetary magnetic field (calculated from the interdiurnal variability index). Possible rotational signatures of two weak solar activity cycles at the beginning of the 20th century (Gleissberg minimum) are discussed. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Radial variation of differential rotation in the solar electron corona

Long-lived brightness structures in the solar electron corona persist over many solar rotation periods and permit an observational determination of coronal magnetic tracer rotation as a function of latitude and height in the solar atmosphere. For observations over 1964–1976 spanning solar cycle 20, we compare the latitude dependence of rotation at two heights in the corona. Comparison of rotation rates from East and West limbs and from independent computational procedures is used to estimate uncertainty. Time-averaged rotation rates based on three methods of analysis demonstrate that, on average, coronal differential rotation decreases with height from 1.125 to 1.5 R _S. The observed radial variation of differential rotation implies a scale height of approximately 0.7 R _S for coronal differential rotation.Model calculations for a simple MHD loop show that magnetic connections between high and low latitudes may produce the observed radial variations of magnetic tracer rotation. If the observed tracer rotation represents the rotation of open magnetic field lines as well as that of closed loops, the small scale height for differential rotation suggests that the rotation of solar magnetic fields at the base of the solar wind may be only weakly latitude dependent. If, instead, closed loops account completely for the radial gradients of rotation, outward extrapolation of electron coronal rotation may not describe magnetic field rotation at the solar wind source. Inward extrapolations of observed rotation rates suggest that magnetic field and plasma are coupled a few hundredths of a solar radius beneath the photosphere.     

Changes of solar magnetic asymmetry

The results of an analysis of the north–south asymmetry in solar activity and solar magnetic fields are reported. The analysis is based on solar mean magnetic field and solar polar magnetic field time series, 1975–2015 (http://wso.stanford.edu), and the Greenwich sunspot data, 1875–2015 (http://solarscience.msfc.nasa.gov/greenwch.shtml). A long-term cycle (small-scale magnetic fields, toroidal component) of ~140 years is identified in the north–south asymmetry in solar activity by analyzing the cumulative sum of the time series for the north–south asymmetry in the area of sunspots. A comparative analysis of the variations in the cumulative sums of the time series composed of the daily values of the sun’s global magnetic field and in the asymmetry of the daily sunspot data over the time interval 1975–2015 shows that the photospheric large-scale magnetic fields may also have a similar long-term cycle. The variations in the asymmetry of large-scale and small-scale solar magnetic fields (sunspot area) are in sync until 2005.5 and in antiphase since then.     

Distribution of Helical Properties of Solar Magnetic Fields

We summarize studies of helical properties of solar magnetic fields such as current helicity and twist of magnetic fields in solar active regions (ARs), that are observational tracers of the alpha-effect in the solar convective zone (SCZ). Information on their spatial distribution is obtained by analysis of systematic mag-netographic observations of active regions taken at Huairou Solar Observing Station of National Astronomical Observatories of Chinese Academy of Sciences. The main property is that the tracers of the alpha-effect are antisymmetric about the solar equator. Identifying longitudinal migration of active regions with their individual rotation rates and taking into account the internal differential rotation law within the SCZ known from helioseismology, we deduce the distribution of the effect over depth. We have found evidence that the alpha-effect changes its value and sign near the bottom of the SCZ, and this is in accord with the theoretical studies and numerical simulations. We discuss     

Case studies of EUV cyclones and their associated magnetic fields

EUV cyclones are rotating structures in the solar corona, and they are usually rooted in the underlying rotating network magnetic fields in the photosphere.However, their connection with the surrounding magnetic fields remains unknown.Here we report an observational study of four typical cyclones which are rooted in different kinds of magnetic fields. We use Solar Dynamics Observatory/Atmospheric Imaging Assembly data to investigate the rotation of EUV features in cyclones and Helioseismic and Magnetic Imager data to study the associated magnetic fields. The results show that,(1) an EUV cyclone rooted in a sunspot rotates with the photospheric magnetic field;(2) two EUV cyclones in two faculae of an active region are connected to the same sunspot of the active region but rotate oppositely;(3) an EUV cyclone is rooted in a coronal hole with weak open magnetic fields;(4) a pair of conjugated cyclones is rooted in magnetic fields that have opposite polarity with opposite directions of rotation. The differences in the spatial extent of a cyclone, characteristics of its rotation and underlying fields indicate that cyclones are ubiquitous over the solar atmosphere and that the magnetic structures relevant to the cyclones are more complicated than expected.     

Photospheric and heliospheric magnetic fields

The magnetic field in the heliosphere evolves in response to the photospheric field at its base. This evolution, together with the rotation of the Sun, drives space weather through the continually changing conditions of the solar wind and the magnetic field embedded within it. We combine observations and simulations to investigate the sources of the heliospheric field from 1996 to 2001. Our algorithms assimilate SOHO/MDI magnetograms into a flux-dispersal model, showing the evolving field on the full sphere with an unprecedented duration of 5.5 yr and temporal resolution of 6 hr. We demonstrate that acoustic far-side imaging can be successfully used to estimate the location and magnitude of large active regions well before they become visible on the solar disk. The results from our assimilation model, complemented with a potential-field source-surface model for the coronal and inner-heliospheric magnetic fields, match Yohkoh/SXT and KPNO/He?10830 Å coronal hole boundaries quite well. Even subject to the simplification of a uniform, steady solar wind from the source surface outward, our model matches the polarity of the interplanetary magnetic field (IMF) at Earth ～3% of the time during the period 1997–2001 (independent of whether far-side acoustic data are incorporated into the simulation). We find that around cycle maximum, the IMF originates typically in a dozen disjoint regions. Whereas active regions are often ignored as a source for the IMF, the fraction of the IMF that connects to magnetic plage with absolute flux densities exceeding 50 Mx cm^?2 increases from ?10% at cycle minimum up to 30–50% at cycle maximum, with even direct connections between sunspots and the heliosphere. For the overall heliospheric field, these fractions are ?1% to 20–30%, respectively. Two case studies based on high-resolution TRACE observations support the direct connection of the IMF to magnetic plage, and even to sunspots. Parallel to the data assimilation, we run a pure simulation in which active regions are injected based on random selection from parent distribution functions derived from solar data. The global properties inferred for the photospheric and heliospheric fields for these two models are in remarkable agreement, confirming earlier studies that no subtle flux-emergence patterns or field-dispersal properties are required of the solar dynamo beyond those that are included in the model in order to understand the large-scale solar and heliospheric fields.

     

Solar cycle general magnetic fields of 1959–1974 and dynamical structure of the convection zone

The concept of the solar general magnetic field is extended from that of the polar fields to the concept of any axisymmetric fields of the whole Sun. The poloidal and toroidal general magnetic fields are defined and diagrams of their evolutionary patterns are drawn using the Mount Wilson magnetic synoptic chart data of Carrington rotation numbers from 1417 to 1620 covering approximately half of cycle 19 and cycle 20. After averaging over many rotations long-term regularities appear in the patterns. The diagrams of the patterns are compared with the Butterfly Diagram of sunspots of the same period. The diagram of the poloidal field shows that the Sun behaves like a magnetic quadrupole, each hemisphere having two branches of opposite polarities with mirror images on the other hemisphere. This was predicted by a solar cycle model driven by the dynamo action of the global convection by Yoshimura and could serve as a verification of the model. The diagram of the toriodal field is similar to the Butterfly Diagram of sunspots. The slight differences which do exist between the two diagrams seems to show that the fields responsible for the two may originate from different zones of the Sun. Common or different characteristics of the three diagrams are examined in terms of dynamical structure of the convection zone referring to the theoretical model of the solar cycle driven by the dynamo action of the global convection.     

Magnetic field and differential rotation in the radiative zone of the Sun

The problem of the interaction between magnetic fields and differential rotation in the radiative zone of the Sun is investigated. It is demonstrated that effects of magnetic buoyancy can be neglected in the analysis of this interaction. It is shown that hydromagnetic torsional waves propagating from the solar core cannot be responsible for the 22-year solar cycle. A possible geometry of the magnetic field that conforms with stationary differential rotation is considered. A verifying method for hypotheses on the structure of the magnetic field and torsional oscillations in the radiative zone of the Sun is proposed based on helioseismic data.     

High-Resolution Studies of the Solar Polar Magnetic Fields

We present high-resolution studies of the solar polar magnetic fields near sunspot maximum in 1989 and towards sunspot minimum in 1995. We show that, in 1989, the polar latitudes were covered by several unipolar regions of both polarities. In 1995, however, after the polar field reversal was complete, each pole exhibited only one dominant polarity region.Each unipolar region contains magnetic knots of both polarities but the number count of the knots of the dominant polarity exceeds that of the opposite polarity by a ratio of order 4:1, and it is rare to find opposite polarity pairs, i.e., magnetic bipoles.These knots have lifetimes greater than 7 hours but less than 24 hours. We interpret the longitudinal displacement of the knots over a 7-hour period as a measure of the local rotation rate. This rotation rate is found to be generally consistent with Snodgrass' (1983) magnetic rotation law.In an attempt to obtain some insight into the operation of the solar dynamo, sketches of postulated subsurface field configurations corresponding to the observed surface fields at these two epochs of the solar cycle are presented.     

Regularities in the growth of background magnetic fields

The cyclicity in the latitudinal distribution of the growth and decay rates of the total magnetic fluxes for weak magnetic fields is investigated. The synoptic maps of the line-of-sight solar magnetic field strength obtained at the Kitt Peak Observatory (USA) from January 1, 1977, to September 30, 2003, are used as the observational material. The latitudinal distributions of the growth rates of total magnetic fluxes with various strengths constructed from them and their evolution during three solar cycles have been compared with the analogous distribution of the total powers of rotation with various periods as well as the relative sunspot numbers and areas. The results obtained allow a unified picture of the development of solar cycles for weak and strong magnetic fields to be formulated. A new cycle begins with the growth of weak magnetic fields with a strength of 0–200 G at latitudes 20°–25° in both hemispheres. This occurs one year before the activity minimum determined from sunspots. Two years later, the growth rate of the total magnetic flux, which begins to propagate equatorward and poleward, reaches a maximum. This process coincides with the onset of the growth of strong sunspot magnetic fields at the corresponding latitudes and the formation of zones with a stable rotation. Subsequently, a fall-off in growth rate and then a flux decay for weak magnetic fields correspond to the growth of the sunspot areas. In light of the dynamo theory, the results obtained suggest that strong and weak magnetic fields are generated near the bottom of the convection zone, while the observed differences in their behavior are determined by the interaction of emerging magnetic flux tubes of various strengths with turbulent plasma motions inside the Sun.     

Background magnetic fields during last three cycles of solar activity

This paper describes our studies of evolution of the solar magnetic field with different sign and field strength in the range from –100 G to 100 G. The structure and evolution of large‐scale magnetic fields on the Sun during the last 3 cycles of solar activity is investigated using magnetograph data from the Kitt Peak Solar Observatory. This analysis reveals two groups of the large‐scale magnetic fields evolving differently during the cycles. The first group is represented by relatively weak background fields, and is best observed in the range of 3–10 Gauss. The second group is represented by stronger fields of 75–100 Gauss. The spatial and temporal properties of these groups are described and compared with the total magnetic flux. It is shown that the anomalous behaviour of the total flux during the last cycle can be found only in the second group. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The mean coronal magnetic field determined from HELIOS Faraday rotation measurements

Coronal Faraday rotation of the linearly polarized carrier signals of the HELIOS spacecraft was recorded during the regularly occurring solar occultations over almost a complete solar cycle from 1975 to 1984. These measurements are used to determine the average strength and radial variation of the coronal magnetic field at solar minimum at solar distances from 3–10 solar radii, i.e., the range over which the complex fields at the coronal base are transformed into the interplanetary spiral. The mean coronal magnetic field in 1975–1976 was found to decrease with radial distance according to r ^–, where = 2.7 ± 0.2. The mean field magnitude was 1.0 ± 0.5 × 10 ^–5 tesla at a nominal solar distance of 5 solar radii. Possibly higher magnetic field strengths were indicated at solar maximum, but a lack of data prevented a statistical determination of the mean coronal field during this epoch.     

The Topology of Background Magnetic Fields and Solar Flare Activity

We investigate the topological properties and evolution of background magnetic fields on synoptic maps from Wilcox Solar Observatory using mathematical morphology methods in terms of the Minkowski functionals. The total length of the neutral line, the total areas occupied by positive and negative polarities, and the Euler characteristics of background magnetic fields vary over an eleven-year cycle. Changes in the length of the neutral line that separates the polarities of the background magnetic field correlate well with flare activity. A time–longitude analysis of solar flare activity revealed a complicated organization and rotation of the entire flare ensemble. On the time–longitude diagram, flare activity is organized into the patterns which follow the rearrangements in background magnetic field and exhibit coexisting and alternating modes of rigid rotation. The character of rotation of the entire flare ensemble is similar to the rotation of background magnetic fields. The emergence of background magnetic fields and changes in their topology and rotation are often accompanied by enhancements in flare activity. A comparative analysis of the topological changes in background magnetic fields and flare activity reveals their causal relation.     

Dynamo action in simulations of penetrative solar convection with an imposed tachocline

We summarize new and continuing three-dimensional spherical shell simulations of dynamo action by convection allowed to penetrate downward into a tachocline of rotational shear. The inclusion of an imposed tachocline allows us to examine several processes believed to be essential in the operation of the global solar dynamo, including differential rotation, magnetic pumping, and the stretching and organization of fields within the tachocline. In the stably stratified core, our simulations reveal that strong axisymmetric magnetic fields (of ∼ 3000 G strength) can be built, and that those fields generally exhibit a striking antisymmetric parity, with fields in the northern hemisphere largely of opposite polarity to those in the southern hemisphere. In the convection zone above, fluctuating fields dominate over weaker mean fields. New calculations indicate that the tendency toward toroidal fields of antisymmetric parity is relatively insensitive to initial magnetic field configurations; they also reveal that on decade-long timescales, the magnetic fields can briefly enter (and subsequently emerge from) states of symmetric parity.We have not yet observed any overall reversals of the field polarity, nor systematic latitudinal propagation. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Observation of solar differential rotation with the aid of magnetic tracers

We tried to search for the manifestation of differential rotation in the distribution of weak remnants of magnetic fields measured with a very low resolution. We found that, during the periods of low solar activity and in parts of the solar photosphere with smaller density of new magnetic flux sources, it was possible to observe the distribution of magnetic tracers in the form of differential rotation parabolas which increase their curvature from one rotation to the next. The obtained differential rotation rates are not far from those given by highly averaged sunspot data or by the daily magnetic fields. The characteristic differential rotation parabolas as well as specific cellular-like features disturbing their smooth patterns are always formed from fields of one main polarity, the sign of which depends on the phase of the activity cycle.Solar Cycle Workshop Paper.     

Cyclic and Long-Term Variation of Sunspot Magnetic Fields

Measurements from the Mount Wilson Observatory (MWO) were used to study the long-term variations of sunspot field strengths from 1920 to 1958. Following a modified approach similar to that presented in Pevtsov et al. (Astrophys. J. Lett. 742, L36, 2011), we selected the sunspot with the strongest measured field strength for each observing week and computed monthly averages of these weekly maximum field strengths. The data show the solar cycle variation of the peak field strengths with an amplitude of about 500?–?700 gauss (G), but no statistically significant long-term trends. Next, we used the sunspot observations from the Royal Greenwich Observatory (RGO) to establish a relationship between the sunspot areas and the sunspot field strengths for cycles 15?–?19. This relationship was used to create a proxy of the peak magnetic field strength based on sunspot areas from the RGO and the USAF/NOAA network for the period from 1874 to early 2012. Over this interval, the magnetic field proxy shows a clear solar cycle variation with an amplitude of 500?–?700 G and a weaker long-term trend. From 1874 to around 1920, the mean value of magnetic field proxy increases by about 300?–?350 G, and, following a broad maximum in 1920?–?1960, it decreases by about 300 G. Using the proxy for the magnetic field strength as the reference, we scaled the MWO field measurements to the measurements of the magnetic fields in Pevtsov et al. (2011) to construct a combined data set of maximum sunspot field strengths extending from 1920 to early 2012. This combined data set shows strong solar cycle variations and no significant long-term trend (the linear fit to the data yields a slope of ??0.2±0.8 G?year^?1). On the other hand, the peak sunspot field strengths observed at the minimum of the solar cycle show a gradual decline over the last three minima (corresponding to cycles 21?–?23) with a mean downward trend of ≈?15 G?year^?1.     

Fractal properties of solar magnetic fields

We study the spatial properties of solar magnetic fields using data from the Solar Vector Magnetograph of the Marshall Space Flight Center (MSFC) (FeI 5250.2 Å) and SOHO/MDI longitudinal magnetic field measurements (Ni 6767.8 Å) (96-min full-disk maps). Our study is focused on two objects: the fractal properties of sunspots and the fractal properties of the spatial magnetic field distribution of active and quiet regions considered as global structures. To study the spatial structure of sunspots, we use a well-known method of determining the fractal dimension based on an analysis of the perimeter—area relation. To analyze the fractal properties of the spatial magnetic field distribution over the solar surface, we use a technique developed by Higuchi. We have revealed the existence of three families of self-similar contours corresponding to the sunspot umbra, penumbra, and adjacent photosphere. The fractal coefficient has maxima near the umbra—penumbra and penumbra—photosphere boundaries. The fractal dependences of the longitudinal and transverse magnetic field distributions are similar, but the fractal numbers themselves for the transverse fields are larger than those for the longitudinal fields approximately by a factor of 1.5. The fractal numbers decrease with increasing mean magnetic field strength, implying that the magnetic field distribution is more regular in active regions.