The decay of the mean solar magnetic field

We have analyzed the effects that differential rotation and a hypothetical meridional flow would have on the evolution of the Sun's mean line-of-sight magnetic field as seen from Earth. By winding the large-scale field into strips of alternating positive and negative polarity, differential rotation causes the mean-field amplitude to decay and the mean-field rotation period to acquire the value corresponding to the latitude of the surviving unwound magnetic flux. For a latitudinally broad two-sector initial field such as a horizontal dipole, the decay is rapid for about 5 rotations and slow with a t ^–1/2 dependence thereafter. If a poleward meridional flow is present, it will accelerate the decay by carrying the residual flux to high latitudes where the line-of-sight components are small. The resulting decay is exponential with an e-folding time of 0.75 yr (10 rotations) for an assumed 15 m s^–1 peak meridional flow speed.E.O. Hulburt Center for Space Research.Laboratory for Computational Physics.     

The Sun’s Large-Scale Magnetic Field and Its Long-Term Evolution

The Sun’s large-scale external field is formed through the emergence of magnetic flux in active regions and its subsequent dispersal over the solar surface by differential rotation, supergranular convection, and meridional flow. The observed evolution of the polar fields and open flux (or interplanetary field) during recent solar cycles can be reproduced by assuming a supergranular diffusion rate of 500 – 600 km² s⁻¹ and a poleward flow speed of 10 –20 m s⁻¹. The nonaxisymmetric component of the large-scale field decays on the flow timescale of ∼1 yr and must be continually regenerated by new sunspot activity. Stochastic fluctuations in the longitudinal distribution of active regions can produce large peaks in the Sun’s equatorial dipole moment and in the interplanetary field strength during the declining phase of the cycle; by the same token, they can lead to sudden weakenings of the large-scale field near sunspot maximum (Gnevyshev gaps). Flux transport simulations over many solar cycles suggest that the meridional flow speed is correlated with cycle amplitude, with the flow being slower during less active cycles.     

Properties of the large- and small-scale flow patterns in and around AR 19824

We trace the photospheric motions of 170 concentrations of magnetic flux tubes in and around the decaying active region No. 19824 (CMP 23 October 1986), using a series of magnetograms obtained at the Big Bear Solar Observatory. The magnetograms span an interval of just over five days and cover an area of about 4 × 5 arc min centered on the active region. We find a persistent large-scale flow pattern that is superposed on the small-scale random motions of both polarities. Correction for differential rotation unveils the systematic, large-scale flow surrounding the core region of the magnetic plage. The flow (with a mean velocity of 30 m s^–1) is faster and more pronounced around the southern side of the core region than around the northern side, and it accelerates towards the western side of the active region. The northern and southern branches of the large-scale flow converge westward of the core region, dragging along the westernmost sunspot and some of the magnetic flux near it. The overall pattern of the large-scale flow resembles the flow of a river around a sand bar. The long-term evolution of the active region suggests that the flow persists for several months. We discuss the possible association of the large-scale flow with the torsional oscillation.We correct the observed motions of concentrations of flux tubes for the large-scale flow in order to study their random motions. The small-scale random motions (with a mean speed of 150 m s^–1) can be characterized by a diffusion coefficient of 250 km² s^–1 for the area surrounding the core region of the magnetic plage. The diffusion coefficient characterizing the small-scale motions within the core region (mostly observed near its periphery and in areas of relatively low flux density) is only 110 km² s^–1. The lower diffusion coefficient in the core region appears to be caused mainly by a smaller step length rather than by a distinct difference in velocities.Visitor at the Lockheed Palo Alto Research Laboratories.     

Simulations of the sun's polar magnetic fields during sunspot cycle 21

Regarding new bipolar magnetic regions as sources of flux, we have simulated the evolution of the radial component of the solar photospheric magnetic field during 1976–1984 and derived the corresponding evolution of the line-of-sight polar fields as seen from Earth. The observed timing and strength of the polar-field reversal during cycle 21 can be accounted for by supergranular diffusion alone, for a diffusion coefficient of 800 km² s^-1. For an assumed 300 km² s^-1 rate of diffusion, on the other hand, a poleward meridional flow with a moderately broad profile and a peak speed of 10 m s^-1 reached at about 5° latitude is required to obtain agreement between the simulated and observed fields. Such a flow accelerates the transport of following-polarity flux to the polar caps, but also inhibits the diffusion of leading-polarity flux across the equator. For flows faster than about 10 m s^-1 the latter effect dominates, and the simulated polar fields reverse increasingly later and more weakly than the observed fields.Laboratory for Computational Physics and Fluid Dynamics.E. O. Hulburt Center for Space Research.     

The Mechanism involved in the Reversals of the Sun's Polar Magnetic Fields

Models of the polarity reversals of the Sun's polar magnetic fields based on the surface transport of flux are discussed and are tested using observations of the polar fields during Cycle 23 obtained by the National Solar Observatory at Kitt Peak. We have extended earlier measurements of the net radial flux polewards of ±60° and confirm that, despite fluctuations of 20%, there is a steady decline in the old polarity polar flux which begins shortly after sunspot minimum (although not at the same time in each hemisphere), crosses the zero level near sunspot maximum, and increases, with reversed polarity during the remainder of the cycle. We have also measured the net transport of the radial field by both meridional flow and diffusion across several latitude zones at various phases of the Cycle. We can confirm that there was a net transport of leader flux across the solar equator during Cycle 23 and have used statistical tests to show that it began during the rising phase of this cycle rather than after sunspot maximum. This may explain the early decrease of the mean polar flux after sunspot minimum. We also found an outward flow of net flux across latitudes ±60° which is consistent with the onset of the decline of the old polarity flux. Thus the polar polarity reversals during Cycle 23 are not inconsistent with the surface flux-transport models but the large empirical values required for the magnetic diffusivity require further investigation.     

An Evolving Synoptic Magnetic Flux map and Implications for the Distribution of Photospheric Magnetic Flux

We describe a procedure intended to produce accurate daily estimates of the magnetic flux distribution on the entire solar surface. Models of differential rotation, meridional flow, supergranulation, and the random emergence of background flux elements are used to regularly update unobserved or poorly observed portions of an initial traditional magnetic synoptic map that acts as a seed. Fresh observations replace model estimates when available. Application of these surface magnetic transport models gives us new insight into the distribution and evolution of magnetic flux on the Sun, especially at the poles where canopy effects, limited spatial resolution, and foreshortening result in poor measurements. We find that meridional circulation has a considerable effect on the distribution of polar magnetic fields. We present a modeled polar field distribution as well as time series of the difference between the northern and southern polar magnetic flux; this flux imbalance is related to the heliospheric current sheet tilt. We also estimate that the amount of new background magnetic flux needed to sustain the `quiet-Sun' magnetic field is about 1.1×10²³ Mx d^–1 (equivalent to several large active regions) at the spatial resolution and epoch of our maps. We comment on the diffusive properties of supergranules, ephemeral regions, and intranetwork flux. The maps are available on the NSO World Wide Web page.     

Rigidly rotating modes of the solar magnetic field

Discrete rigidly rotating components (modes) of the large-scale solar magnetic field have been investigated. We have used a specially calculated basic set of functions to resolve the observed magnetic field into discrete components. This adaptive set of functions, as well as the expansion coefficients, have been found by processing a series of digitized synoptic maps of the background magnetic field over a 20-year period. As a result, dependences have been obtained which describe the spatial structure and the temporal evolution of the 27-day and 28-day rigidly rotating modes of the Sun's magnetic field.The spatial structure of the modes has been compared with simulations based on the known flux-transport equation. In the simulations, the rigidly rotating modes were regarded as stationary states of the magnetic field whose rigid rotation and stability were maintained by a balance between the emergence of magnetic flux from stationary sources located at low latitudes and the horizontal transport of flux by turbulent diffusion and poleward directed meridional flow. Under these assumptions, the structure of the modes is determined solely by the horizontal velocity field of the plasma, except for the low-latitude zone where sources of magnetic flux concentrate. We have found a detailed agreement between the simulations and the results of the data analysis, provided that the amplitude of the meridional flow velocity and the diffusion constant are equal to 9.5 m s^–1 and 600 km² s^–1, respectively.The analysis of the expansion coefficients has shown that the rigidly rotating modes undergo rapid step-like variations which occur quasi-periodically with a period of about two years. These variations are caused by separate surges of magnetic flux in the photosphere, so that each new surge gives rise to a rapid replacement of old large-scale magnetic structures by newly arisen ones.     

The Global Solar Magnetic Field Through a Full Sunspot Cycle: Observations and Model Results

Based on 11 years of SOHO/MDI observations from the cycle minimum in 1997 to the next minimum around 2008, we compare observed and modeled axial dipole moments to better understand the large-scale transport properties of magnetic flux in the solar photosphere. The absolute value of the axial dipole moment in 2008 is less than half that in the corresponding cycle-minimum phase in early 1997, both as measured from synoptic maps and as computed from an assimilation model based only on magnetogram data equatorward of 60° in latitude. This is incompatible with the statistical fluctuations expected from flux-dispersal modeling developed in earlier work at the level of 7 – 10 σ. We show how this decreased axial dipole moment can result from an increased strength of the diverging meridional flow near the Equator, which more effectively separates the two hemispheres for dispersing magnetic flux. Based on the combination of this work with earlier long-term simulations of the solar surface field, we conclude that the flux-transport properties across the solar surface have changed from preceding cycles to the most recent one. A plausible candidate for such a change is an increase of the gradient of the meridional-flow pattern near the Equator so that the two hemispheres are more effectively separated. The required profile as a function of latitude is consistent with helioseismic and cross-correlation measurements made over the past decade.     

Surface magnetic fields during the solar activity cycle

We examine magnetic field measurements from Mount Wilson that cover the solar surface over a 13 1/2 year interval, from 1967 to mid-1980. Seen in long-term averages, the sunspot latitudes are characterized by fields of preceding polarity, while the polar fields are built up by a few discrete flows of following polarity fields. These drift speeds average about 10 m s^-1 in latitude - slower early in the cycle and faster later in the cycle - and result from a large-scale poleward displacement of field lines, not diffusion. Weak field plots show essentially the same pattern as the stronger fields, and both data indicate that the large-scale field patterns result only from fields emerging at active region latitudes. The total magnetic flux over the solar surface varies only by a factor of about 3 from minimum to a very strong maximum (1979). Magnetic flux is highly concentrated toward the solar equator; only about 1% of the flux is at the poles. Magnetic flux appears at the solar surface at a rate which is sufficient to create all the flux that is seen at the solar surface within a period of only 10 days. Flux can spread relatively rapidly over the solar surface from outbreaks of activity. This is presumably caused by diffusion. In general, magnetic field lines at the photospheric level are nearly radial.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.     

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.     

Photospheric Plasma Flows Around a Solar Spot

We study photospheric plasma flows in an active region NOAA 8375, by using uninterrupted high-resolution SOHO/MDI observations (137 intensity images, 44 hours of observations). The active region consists of a stable large spot and many small spots and pores. Analyzing horizontal flow maps, obtained with local correlation tracking technique, we found a system of stable persistent plasma flows existing in the active region. The flows start on either side of the sunspot and extend over 100′′ to the east. Our measurements show that the speed of small sunspots and pores, averaged over 44 hours, was about 100 m s⁻¹, which corresponds to root-mean-square longitudinal drifts of sunspots of 0.67°–0.76° day⁻¹. We conclude that these large-scale flows are due to faster proper motion of the large sunspot relative to the ambient photospheric plasma. We suggest that the flows may be a good carrier to transport magnetic flux from eroding sunspots into the outer part of an active region.     

Transterminator ion flow in the Martian ionosphere

The upper ionospheres of Mars and Venus are permeated by the magnetic fields induced by the solar wind. It is a long-standing question whether these fields can put the dense ionospheric plasma into motion. If so, the transterminator flow of the upper ionosphere could explain a significant part of the ion escape from the planets atmospheres. But it has been technically very challenging to measure the ion flow at energies below 20 eV. The only such measurements have been made by the ORPA instrument of the Pioneer Venus Orbiter reporting speeds of 1-5 km/s for O⁺ ions at Venus above 300 km altitude at the terminator ( [Knudsen et al., 1980] and [Knudsen et al., 1982]). At Venus the transterminator flow is sufficient to sustain a permanent nightside ionosphere, at Mars a nightside ionosphere is observed only sporadically. We here report on new measurements of the transterminator ion flow at Mars by the ASPERA-3 experiment on board Mars Express with support from the MARSIS radar experiment for some orbits with fortunate observation geometry. We observe a transterminator flow of O⁺ and O₂⁺ ions with a super-sonic velocity of around 5 km/s and fluxes of 0.8×10⁹/cm² s. If we assume a symmetric flux around the terminator this corresponds to an ion flow of 3.1±0.5×10²⁵/s half of which is expected to escape from the planet. This escape flux is significantly higher than previously observed on the tailside of Mars. A possible mechanism to generate this flux can be the ionospheric pressure gradient between dayside and nightside or momentum transfer from the solar wind via the induced magnetic field since the flow velocity is in the Alfvénic regime. We discuss the implication of these new observations for ion escape and possible extensions of the analysis to dayside observations which may allow us to infer the flow structure imposed by the induced magnetic field.     

Evolution of latitude zonal structure of the large-scale magnetic field in solar cycles

Properties of a latitude zonal component of the large-scale solar magnetic field are analyzed on the basis of H charts for 1905–1982. Poleward migration of prominences is used to determine the time of reversal of the polar magnetic field for 1870–1905. It is shown that in each hemisphere the polar, middle latitude and equatorial zones of the predominant polarity of large-scale magnetic field can be detected by calculating the average latitude of prominence samples referred to one boundary of the large-scale magnetic field. The cases of a single and three-fold polar magnetic field reversal are investigated. It is shown that prominence samples referred to one boundary of the large-scale magnetic field do not have any regular equatorward drift. They manifest a poleward migration with a variable velocity up to 30 m s^-1 depending on the phase of the cycle. The direction of migration is the same for both low-latitude and high-latitude zones. Two different time intervals of poleward migration are found. One lasts from the beginning of the cycle to the time of polar magnetic field reversal and the other lasts from the time of reversal to the time of minimum activity. The velocity of poleward migration of prominences during the first period is from 5 m s^-1 to 30 m s^-1 and the second period is devoid of regular latitude drift.     

Large-scale flow and transport of magnetic flux in the solar convection zone

Horizontal large-scale velocity field describes horizontal displacement of the photospheric magnetic flux in zonal and meridian directions. The flow systems of solar plasma, constructed according to the velocity field, create the large-scale cellular-like patterns with up-flow in the center and the down-flow on the boundaries. Distribution of the largescale horizontal eddies (with characteristic scale length from 350 to 490 Mm) was found in the broad equatorial zone, limited by 60‡ latitude circles on both hemispheres. The zonal averages of the zonal and meridian velocities, and the total horizontal velocity for each Carrington rotation during the activity cycles no. 21 and 22 varies during the 11-yr activity cycle. Plot of RMS values of total horizontal velocity is shifted about 1.6 years before the similarly shaped variation of the magnetic flux.     

Three-Dimensional Geometry of Planar Magnetic Structure in the Corona

The coronal magnetic field (CMF) during Carrington rotation 1870 is inferred by using the so-called 'potential model' with the photospheric magnetic field observed at Kitt Peak. Magnetic field lines starting at areas restricted (90deg; ± 30deg; in longitude and 0deg; ± 20deg; in latitude) in both the photosphere and the source surface of 2.5 solar radii are traced to examine fine geometrical structures of the CMF. We found a well-ordered planar magnetic structure (PMS) near 90° Carrington longitude in the corona. The PMS consists of magnetic flux of negative polarity emanating from several small areas in the photosphere. The magnetic flux expands into a wide longitudinal angle in the source surface making a planar magnetic structure.     

Multiwavelength Observations of a Failed Flux Rope in the Eruption and Associated M-Class Flare from NOAA AR 11045

We present the multiwavelength observations of a flux rope that was trying to erupt from NOAA AR 11045 and the associated M-class solar flare on 12 February 2010 using space-based and ground-based observations from TRACE, STEREO, SOHO/MDI, Hinode/XRT, and BBSO. While the flux rope was rising from the active region, an M1.1/2F class flare was triggered near one of its footpoints. We suggest that the flare triggering was due to the reconnection of a rising flux rope with the surrounding low-lying magnetic loops. The flux rope reached a projected height of ≈0.15R _⊙ with a speed of ≈90 km s⁻¹ while the soft X-ray flux enhanced gradually during its rise. The flux rope was suppressed by an overlying field, and the filled plasma moved towards the negative polarity field to the west of its activation site. We found the first observational evidence of the initial suppression of a flux rope due to a remnant filament visible both at chromospheric and coronal temperatures that evolved a couple of days earlier at the same location in the active region. SOHO/MDI magnetograms show the emergence of a bipole ≈12 h prior to the flare initiation. The emerged negative polarity moved towards the flux rope activation site, and flare triggering near the photospheric polarity inversion line (PIL) took place. The motion of the negative polarity region towards the PIL helped in the build-up of magnetic energy at the flare and flux rope activation site. This study provides unique observational evidence of a rising flux rope that failed to erupt due to a remnant filament and overlying magnetic field, as well as associated triggering of an M-class flare.     

Observations of the reappearance of polar coronal holes and the reversal of the polar magnetic field

We examine observations relating to the evolution of the polar magnetic field around sunspot maximum, when the net polar flux reverses polarity and coronal holes redevelop around the poles. Coronal hole observations during the last two solar maxima are examined in detail. Long-term averages of the latitudinal dependence of the photospheric magnetic field and the evolutionary pattern of the polar crown filaments are used to trace the poleward motion of the reversal of the large-scale surface field, and are compared to the redevelopment of the polar holes. The polar holes evolve from small, mid-latitude holes of new-cycle polarity which expand poleward until they join and cover the pole. We find that the appearance of these mid-latitude holes, the peak of flux emergence at low latitudes, and the polar polarity reversal all occur within a few solar rotations. Lagging 6 months to 1 1/2 yr after this time, the polar crown disappears and the polar holes redevelop.These results are examined in the context of phenomenological models of the solar cycle. We believe the following results in particular must be accounted for in successful models of the solar cycle: (1) The process of polarity reversal and redevelopment of the polar holes is discontinuous, occurring in 2 or 3 longitude bands, with surges of flux of old-cycle polarity interrupting the poleward migration of new-cycle flux. There is a persistent asymmetry in these processes between the two hemispheres; the polarity reversal in the two hemispheres is offset by 6 months to 1 1/2 yr. (2) Contrary to the Babcock hypothesis, the polar crown disappears months after the magnetic polar reversal. We suggest one possible scenario to explain this effect. (3) Our observations support suggestions of a poleward meridional flow around solar maximum that cannot be accounted for by Leighton-type diffusion.     

The heliographic latitude dependence and sector structure of the interplanetary magnetic field 1969–1974: Results from the HEOS satellites

Data from the two HEOS satellites obtained during the period December 1968 to August 1974 are used to investigate the large-scale properties of the interplanetary magnetic field.The sector structure has been deduced from the observed times of sector boundary crossings which are tabulated. A two-sector pattern existed throughout most of the period with occasional intervals of 2–3 months duration in which four sectors appeared. The variation of the dominant sector polarity with heliographic latitude showed a reversal in sense during 1971 at the time of the reported reversal in the Sun's polar field. A statistical analysis of the change in polarity distribution with latitude suggests that at Earth's orbit the sector boundaries are inclined to the solar equator on average at an angle of 12 deg.No evidence was found in the HEOS measurements of the north-south field component to confirm the systematic latitude-dependent deviation of the plasma flow away from the solar equatorial plane suggested by several analyses of data from previous spacecraft. The mean field magnitude and the average amplitude of the directional fluctuations appeared to be independent of heliographic latitude within the ±7.3° range explored.     

Characteristic size and diffusion of quiet sun magnetic patterns

We have previously studied large-scale motions using high-resolution magnetograms taken from 1978 to 1990 with the NSO Vacuum Telescope on Kitt Peak. Latitudinal and longitudinal motions were determined by a two-dimensional crosscorrelation analysis of pairs of consecutive daily observations using small magnetic features as tracers. Here we examine the shape and amplitude of the crosscorrelation functions. We find a characteristic length scale as indicated by the FWHM of the crosscorrelation functions of 16.6 ± 0.2 Mm. The length scale is constant within ±45° latitude and decreases by about 5% at 52.5° latitude; i.e., the characteristic size is almost latitude independent. The characteristic scale is within 3% of the average value during most times of the solar cycle, but it increases during cycle maximum at latitudes where active regions are present. For the time period 1978–1981 (solar cycle maximum), the length scale increases up to 1.7 Mm or 10% at 30° latitude. In addition, we derive the average amplitude of the crosscorrelation functions, which reflects the diffusion of magnetic elements and their evolutionary changes (including formation and decay). We find an average value of 0.091 ± 0.003 for the crosscorrelation amplitude at a time lag of one day, which we interpret as being caused by the combined effect of the lifetime of magnetic features and a diffusion process. Assuming a lifetime of one day, we find a value of 120 km² s^–1 for the diffusion constant, while a lifetime of two days leads to 230 km² s^–1.Operated by the Association of Universities for Research in Astronomy, Inc. under cooperative agreement with the National Science Foundation.     

Meridional flow of small photospheric magnetic features

We study the meridional flow of small magnetic features, using high-resolution magnetograms taken from 1978 to 1990 with the NSO Vacuum Telescope on Kitt Peak. Latitudinal motions are determined by a two-dimensional crosscorrelation analysis of 514 pairs of consecutive daily observations from which active regions are excluded. We find a meridional flow of the order of 10 m s^–1, which is poleward in each hemisphere, increases in amplitude from 0 at the equator, reaches a maximum at mid-latitude, and slowly decreases poleward. The average observed meridional flow is fit adequately by an expansion of the formM () = 12.9(±0.6) sin(2) + 1.4(±0.6) sin(4), in m s^–1 where is the latitude and which reaches a maximum of 13.2 m s^–1 at 39°. We also find a solar-cycle dependence of the meridional flow. The flow remains poleward during the cycle, but the amplitude changes from smaller-than-average during cycle maximum to larger-than-average during cycle minimum for latitudes between about 15° and 45°. The difference in amplitude between the flows at cycle minimum and maximum depends on latitude and is about 25% of the grand average value. The change of the flow amplitude from cycle maximum to minimum occurs rapidly, in about one year, for the 15–45° latitude range. At the highest latitude range analyzed, centered at 52.5°, the flow is more poleward-than-average during minimumand maximum, and less at other times. These data show no equatorward migration of the meridional flow pattern during the solar cycle and no significant hemispheric asymmetry. Our results agree with the meridional flow and its temporal variation derived from Doppler data. They also agree on average with the meridional flow derived from the poleward migration of the weak large-scale magnetic field patterns but differ in the solar-cycle dependence. Our results, however, disagree with the meridional flow derived from sunspots or plages.Operated by the Association of Universities for Research in Astronomy, Inc. under cooperative agreement with the National Science Foundation.