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.     

The direction of propagation of the solar dynamo wave

We propose a solution to one of the oldest problems in the solar-dynamo theory: explaining the equatorward drift of magnetic activity in the solar cycle. The well-known suggestion that the dynamo waves propagate along the surfaces of constant angular velocity is shown to be restricted to an isotropic medium. Allowance for the rotation-induced anisotropy in turbulent diffusion leads to an equatorward deviation of the wave phase velocity from the isorotational surface. Estimates for the dynamo waves are illustrated with two-dimensional numerical models in a spherical geometry. The model with anisotropic diffusion also shows an equatorward drift of the toroidal magnetic field when the rotation is radially uniform.     

Meridional drift in the large-scale solar magnetic field pattern

A method of two-dimensional correlation functions has been applied to a sequence of synoptic maps of the large-scale magnetic field to obtain the meridional drift pattern of field structures. The meridional drift profile obtained is antisymmetric about the equator. The meridional drift is directed from the equator to the poles at latitudes below 45°. A maximum drift velocity of 11–13 m s^–1 is attained in the latitude range 30°. A picture of the space-time distribution of meridional drift is also obtained, which may be interpreted as resulting from the effect of azimuthal convective rolls (3 rolls per hemisphere) on the large-scale magnetic field. Rolls originate at high latitudes following the cycle maximum, and migrate equatorwards until the minimum of the next cycle. The picture in the equatorial region can correspond to convective rolls with lifetimes of about two years, or to the process of interaction of rolls from two hemispheres.     

Meridional motions of magnetic features in the solar photosphere

We cross-correlate pairs of Mt. Wilson magnetograms spaced at intervals of 24–38 days to investigate the meridional motions of small magnetic features in the photosphere. Our study spans the 26-yr period July 1967–August 1993, and the correlations determine longitude averages of these motions, as functions of latitude and time. The time-average of our results over the entire 26-yr period is, as expected, antisymmetric about the equator. It is poleward between 10° and 60°, with a maximum rate of 13 m s^–1, but for latitudes below ±10° it is markedly equatorward, and it is weakly equatorward for latitudes above 60°. A running 1-yr average shows that this complex latitude dependence of the long-term time average comes from a pattern of motions that changes dramatically during the course of the activity cycle. At low latitudes the motion is equatorward during the active phase of the cycle. It tends to increase as the zones of activity move toward the equator, but it reverses briefly to become poleward at solar minimum. On the poleward sides of the activity zones the motion is most strongly poleward when the activity is greatest. At high latitudes, where the results are more uncertain, the motion seems to be equatorward except around the times of polar field reversal. The difference-from-average meridional motions pattern is remarkably similar to the pattern of the magnetic rotation torsional oscillations. The correspondence is such that the zones in which the difference-from-average motion is poleward are the zones where the magnetic rotation is slower than average, and the zones in which it is equatorward are the zones where the rotation is faster.Our results suggest the following characterization: there is a constant and generally prevailing motion which is perhaps everywhere poleward and varies smoothly with latitude. On this is superimposed a cycle-dependent pattern of similar amplitude in which the meridional motions of the small magnetic features are directed away from regions of magnetic flux concentration. This is suggestive of simple diffusion, and of the models of Leighton (1964) and Sheeley, Nash, and Wang (1987). The correspondence between the meridional motions pattern and the torsional oscillations pattern in the magnetic rotation suggests that the latter may be an artifact of the combination of meridional motion and differential rotation.     

The relationship between meridional drift and rotation of the large-scale solar magnetic field

The pattern of torsional oscillations was detected in the rotation of the large-scale magnetic field using the method of two-dimensional correlation functions. The position of areas of fast and slow rotation agrees with the Doppler picture obtained by Ulrich et al. (1988). The torsional wave amplitude is 20–40 ms^–1 and increases with latitude. A strong correlation of the pattern of residual E-W rate with the meridional drift pattern, obtained from the same data, was determined. The sign of correlation is consistent with the results reported by Ward (1965).     

The concentration of the large-scale solar magnetic field by a meridional surface flow

We calculate analytical and numerical solutions to the magnetic flux transport equation in the absence of new bipolar sources of flux, for several meridional flow profiles and a range of peak flow speeds. We find that a poleward flow with a broad profile and a nominal 10 m s^–1 maximum speed concentrates the large-scale field into very small caps of less than 15° half-angle, with average field strengths of several tens of gauss, contrary to observations. A flow which reaches its peak speed at a relatively low latitude and then decreases rapidly to zero at higher latitudes leads to a large-scale field pattern which is consistent with observations. For such a flow, only lower latitude sunspot groups can contribute to interhemispheric flux annihilation and the resulting decay and reversal of the polar magnetic fields.     

Large-Scale Magnetic Field of the Sun and Evolution of Sunspot Activity

The evolution of the large-scale magnetic field of the Sun has been studied using an algorithm of tomographic inversion. By analyzing line-of-sight magnetograms, we mapped the radial and toroidal components of the Sun??s large-scale magnetic field. The evolution of the radial and toroidal magnetic field components in the 11-year solar cycle has been studied in a time?Clatitude aspect. It is shown that the toroidal magnetic field of the Sun is causally related to sunspot activity; i.e., the sunspot formation zones drift in latitude and follow the toroidal magnetic fields. The results of our analysis support the idea that the high-latitude toroidal magnetic fields can serve as precursors of sunspot activity. The toroidal fields in the current cycle are anomalously weak and also show a barely noticeable equatorward drift. This behavior of the toroidal magnetic field suggests low activity levels in the current cycle and in the foreseeable future.     

Rotation of the large-scale solar magnetic fields in the equatorial region

A study is made of the rotation of large-scale magnetic fields using the synoptic maps from the Kitt Peak National Observatory for the time interval 1976–1985. The auto-correlation method and the mass-centers method of magnetic structures was applied to infer mean differential rotation profiles and rotation profiles separately for each magnetic field polarity. It has been found that in both hemispheres the leading polarity rotates faster than the following polarity at all latitudes by about 0.04° day^–1. The maximum rotation rate of the leading polarity is reached at about 6° latitude. In the mean profile for both polarities, this brings about two angular velocity maxima at 6° latitudes in both hemispheres. Such a profile appears as to have a dimple on the equator.     

Studies of solar magnetic fields

Magnetic flux data from the Mount Wilson magnetograph are examined over the interval 1967–1973. The total flux in the north is greater than that in the south by about 7% over this interval, reflecting a higher level of activity in the northern hemisphere. Close to 95% of the total flux is confined to latitudes equatorward of 40°, which means that close to 95% of the flux cancels with flux of opposite polarity before it can migrate poleward of 40°. It is pointed out that a consequence of this flux distribution is that ephemeral regions must make a negligible contribution to the long-term largescale magnetic flux distribution. A broad peak in the total flux may be seen centered about one year after activity maximum in the north below 40°. In the south there is a very sharp increase in flux about the same time. In the north, several poleward migrations of flux may be seen. Two of these may correspond with the two poleward prominence migrations seen by Waldmeier. In both the north and the south there is a poleward migration of negative flux about the time of activity maximum. Poleward flux drift rates are about 20 m s^?1.     

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.

     

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.     

Propagation of flare protons in the solar atmosphere

The velocity dispersion for a large number of solar proton events is analyzed in the energy regime of 10–60 MeV. It is found for all events that the time from the flare to particle maximum t _m is well represented by a sum of two components. The first component which is energy independent describes the propagation in the solar atmosphere, the second component describes the propagation in the interplanetary medium giving a velocity dispersion v × t _m = const. The additional study of time intensity profiles, onset times, and multispaceprobe observations reveals that the propagation in the solar atmosphere consists of three processes: (1) A rapid transport process in the initial ( 1 h) phase after the event fills up a fast propagation region (FPR), which may extend up to 60° from the flare site and which is tentatively identified with a large unipolar magnetic cell as seen on H synoptic charts, (2) a large-scale drift process which is energy independent with drift velocities v _D in the range 1° v _D 4°h^-1, and simultaneously (3) a diffusion process which yields the general broadening of the intensity time profiles for eastern hemisphere events, which is, however, of less importance than previously assumed.     

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 Alpha Effect and the Observed Twist and Current Helicity of Solar Magnetic Fields

We present a straightforward comparison of model calculations for the α-effect, helicities, and magnetic field line twist in the solar convection zone with magnetic field observations at atmospheric levels. The model calculations are carried out in a mixing-length approximation for the turbulence with a profile of the solar internal rotation rate obtained from helioseismic inversions. The magnetic field data consist of photospheric vector magnetograms of 422 active regions for which spatially-averaged values of the force-free twist parameter and of the current helicity density are calculated, which are then used to determine latitudinal profiles of these quantities. The comparison of the model calculations with the observations suggests that the observed twist and helicity are generated in the bulk of the convection zone, rather than in a layer close to the bottom. This supports two-layer dynamo models where the large-scale toroidal field is generated by differential rotation in a thin layer at the bottom while the α-effect is operating in the bulk of the convection zone. Our previous observational finding was that the moduli of the twist factor and of the current helicity density increase rather steeply from zero at the equator towards higher latitudes and attain a certain saturation at about 12 – 15^∘. In our dynamo model with algebraic nonlinearity, the increase continues, however, to higher latitudes and is more gradual. This could be due to the neglect of the coupling between small-scale and large-scale current and magnetic helicities and of the latitudinal drift of the activity belts in the model.     

Long term evolution of solar sector structure

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

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.     

Motion of solar cosmic rays in the coronal magnetic field

Trajectories of solar cosmic rays have been calculated in a static ninth-order coronal magnetic field. It is found that as a result of field curvature and gradients, protons drift across the field lines at a rate of up to 200 ² deg hr^–1. These drift rates are of the same order as, but somewhat smaller than, empirically derived rates. Localized enhancements of magnetic field have been inserted into the ninth-order field in order to model (in a highly idealized manner) the effects of the small-scale magnetic features which give rise to X-ray bright points. The motions of the particles in the presence of these scattering centers can be parameterized approximately by a cross-field diffusion coefficient. Our estimates of this coefficient, although crude, overlap with empirical values which have been deduced over a wide range of energies.We propose that coronal propagation of solar cosmic rays has two components. One is independent of particle velocity, and is associated with dynamic field phenomena (such as an expanding magnetic bottle): this is the only component which is important in flares which occur close to the foot-point of the Sun-Earth field line. The second component is velocity dependent, but is independent of mass, and is associated with scattering off (relatively static) magnetic inhomogeneities with scale sizes of at least 500 km: the second component contributes to coronal propagation if the flare occurs more than about 50–60 deg away from the Sun-Earth field line.     

Cyclical Behavior of Coronal Mass Ejections

With the use of coronal mass ejections (CMEs) observed by the Large Angle and Spectrometric Coronagraph (LASCO) onboard the Solar and Heliospheric Observatory (SOHO) from January 1996 through December 2005, it is found that, for the cyclical activity of CMEs, there is surprisingly no equatorward drift at low latitudes (thus, no “butterfly diagram”) and no poleward drift at high latitudes, and no antiphase relationship between CME activity at low and high latitudes. The cyclical behaviors of CMEs differ in a significant way from that of the small-scale solar photospherical and chromospherical phenomena. Thus, our analysis leads to results that are inconsistent with a close, physical relationship with small-scale aspects of solar activity, and it is suggested that there is possibly a single so-called large-scale activity cycle in CMEs.     

Butterfly diagrams of strongly spotted late type stars

At present, long-term (over 30 years) multicolor photometric observations give the possibility to determine general properties of spotted areas on late-type stars. Star-spot modeling from broadband photometric data has been carried out by Alekseev and Gershberg since 1996 under the assumption that spots are situated in two latitudinal zones. Here we propose a new analysis of their results for several G and K dwarf stars with high irregular activity. On these stars, EK Dra, VY Ari, V775 Her, and V833 Tau, two spot belts exist separately and do not merge into a single equatorial active region, as occurs on cooler red-dwarf stars. The zonal spottedness models allow us to fit simultaneously both rotational modulation and long-term variability of stellar brightness. These models give evidence for an equatorward drift of the lower latitude boundary of the spotted region, φ₀, during the rising phase of activity, beyond any possible errors concerned with our methodology. In order to evaluate the drift rate we introduce the concept of `effective' spot belt, whose width is independent of longitude. This permits us to construct butterfly diagrams for stellar spots. The equatorward drift rates of the lower boundary of the spotted region D=dφ_low/dt are (− 1)–(− 2) deg year⁻¹ in the years of increasing spottedness. These values are less than the analogous solar one D≈−4 deg year⁻¹ for the rising phase of the cycle. Thus, cyclic activity can be revealed from butterfly diagrams and derived drifts of starspots prior to a possible detection from the spectral analysis of photometric variability. Finally, we briefly discuss a possible explanation of high-latitude activity and surface drifts of starspots in the framework of the current state of dynamo theory.     

Latitude-time distribution of 3 types of magnetic field activity in the global solar cycle

Large-scale solar activity is considered as a manifestation of 3 types of magnetic field activity which is demonstrated in the 22-year cycle (a) of small-scale flux emergence (polar faculae at latitudes > 40°), (b) of somewhat larger scale flux emergence (sunspots at latitudes < 40°), and (c) of the global magnetic neutral lines at all latitudes. The migration (poleward or equatorward) of the place of birth and/or of the phenomena themselves of these three types of manifestation of magnetic field is discussed. The poleward migration of the global field is explained in a phenomenological way.