The large-scale solar magnetic field

The large-scale photospheric magnetic field, measured by the Mt. Wilson magnetograph, has been analyzed in terms of surface harmonics (P _n ^m )()cosm and P _n ^m ()sinm) for the years 1959 through 1972. Our results are as follows. The single harmonic which most often characterized the general solar magnetic field throughout the period of observation corresponds to a dipole lying in the plane of the equator (2 sectors, n = m = 1). This 2-sector harmonic was particularly dominant during the active years of solar cycles 19 and 20. The north-south dipole harmonic (n = 1, m = 0) was prominent only during quiet years and was relatively insignificant during the active years. (The derived north-south dipole includes magnetic fields from the entire solar surface and does not necessarily correlate with either the dipole-like appearance of the polar regions of the Sun or with the weak polar magnetic fields.) The 4-sector structure (n = m = 2) was prominent, and often dominant, at various times throughout the cycle. A 6-sector structure (n = m = 3) occasionally became dominant for very brief periods during the active years. Contributions to the general solar magnetic field from harmonics of principal index 4 n 9 were generally relatively small throughout this entire solar cycle with one outstanding exception. For a period of several months prior to the large August 1972 flares, the global photospheric field was dominated by an n = 5 harmonic; this harmonic returned to a low value shortly after the August 1972 flare events. Rapid changes in the global harmonics, in particular, relative and absolute changes in the contributions of harmonics of different principal index n to the global field, imply that the global solar field is not very deep or that very strong fluid flows connect the photosphere with deeper layers.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

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.     

A large-scale pattern in the solar magnetic field

A clearly evident large-scale pattern in the interplanetary magnetic field during 1964 is used to search for a similar large-scale pattern in the solar magnetic field. It is found that such a pattern did exist in the photospheric field observations on both sides of the equator over a range of at least 40°N to 35°S. The pattern is basically similar at all these latitudes, and differs from that to be expected from solar differential rotation in three important respects. It is found that the solar magnetic pattern changed at all latitudes investigated within an interval of a few solar rotations.     

The structure of the white-light corona and the large-scale solar magnetic field

The large-scale density structure of the white-light solar corona has been compared to the organization of the solar magnetic field as identified by the appearance of neutral lines in the photosphere in order to examine whether any consistent relationship exists between the two. Data from the High Altitude Observatory's Mk-III K-coronameter have been used to describe the coronal density structure, and observations from several sources, beginning with observations from the University of Hawaii Stokes Polarimeter have been used to establish the magnetic field distribution. Stanford magnetograms as well as the neutral line inferred from potential field models have also been examined. During the period covering Carrington rotations 1717 to 1736 brightness enhancements in the low corona tend to lie over the global neutral sheet identified in the photospheric magnetic field. The brightest of these enhancements, however, are associated with neutral lines through active regions. These associations are not 1-1, but do hold both in stable and evolving conditions of the corona. We find a significant number of long-lived neutral lines, including filaments seen in H, for which there are not coronal enhancements.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

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.     

The non-axisymmetrical configuration of a large-scale solar and stellar magnetic field

The non-axisymmetric and nonlinear solutions of the magnetostatic equations are given in three-dimensional space of spherical coordinates (r, θ, ?). These solutions are applied to the large-scale solar magnetic field. Their basic features are similar to a dipole field near the polar regions and the polarity reverses near the equator. These features agree with observations for the large-scale solar magnetic field. The solutions can also be applied to investigating the connection between the structure of the magnetic field and the density distribution of the corona. It is shown that the tops of the closed magnetic field associate with density enhancements. Similar results may apply to the large-scale configuration of the stellar field.     

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.     

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 large-scale build-up of solar magnetic cycles

The purpose of the present article is to analyze the solar cycles from the point of view of the large-scale surface magnetic field (LSMF) polarity distributions. Using synoptic charts of the LSMF for the 1870–1991 time interval at maxima and minima and the spherical harmonic analysis of the polarity distributions, a connection between magnetic cycles has been found. The weight of the large-scale sectoral mode (m = 1) in the common LSMF polarity distribution at minima of the sunspot cycle is the source of sunspot activity at maxima after 16–18 years. The connections found suggest that surface LSMFs have a dual nature - the main source below the convective zone and a secondary source (sunspot production). The sunspot production has no visible influence on the LSMF cycles.     

Spatial distribution of large-scale solar magnetic fields and their relation to the interplanetary magnetic field

The spatial organization of the observed photospheric magnetic field, as well as its relation to the polarity of the interplanetary field, have been studied using high resolution magnetograms from Kitt Peak National Observatory. Systematic patterns in the large scale field have been found to be due to contributions from both concentrated flux and more diffuse flux. It is not necessary to assume, as has often been done in previous studies, that there is a weak background solar magnetic field causing the large-scale patterns in the photosphere, although the existence of such a field cannot be excluded. The largest scale structures in the photosphere correspond to the expected pattern at the base of a warped heliomagnetic equator.The polarity of the photospheric field, determined on various spatial scales, correlates with the polarity of the interplanetary field, with the most significant correlation due to mid-latitude fields. However, because the interplanetary field is likely to be rooted in concentrated photospheric regions, rather than across an entire polarity region, both the strength and polarity of the field are important in determining the interplanetary field. Thus studies of the interplanetary field which are based on either instrumental or numerical averaging of fields in the solar photosphere are subject to serious inherent limitations.Analyses based on several spatial scales in the photosphere suggest that new flux in the interplanetary medium is often due to relatively small photospheric features which appear in the photosphere up to one month before they are manifest at the Earth. The evolution of the over-all photospheric pattern may be due to individual sub-patterns which have slightly different rotation properties and which alternate in their relative dominance of the interplanetary medium.     

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 magnetic field in the solar atmosphere

This publication provides an overview of magnetic fields in the solar atmosphere with the focus lying on the corona. The solar magnetic field couples the solar interior with the visible surface of the Sun and with its atmosphere. It is also responsible for all solar activity in its numerous manifestations. Thus, dynamic phenomena such as coronal mass ejections and flares are magnetically driven. In addition, the field also plays a crucial role in heating the solar chromosphere and corona as well as in accelerating the solar wind. Our main emphasis is the magnetic field in the upper solar atmosphere so that photospheric and chromospheric magnetic structures are mainly discussed where relevant for higher solar layers. Also, the discussion of the solar atmosphere and activity is limited to those topics of direct relevance to the magnetic field. After giving a brief overview about the solar magnetic field in general and its global structure, we discuss in more detail the magnetic field in active regions, the quiet Sun and coronal holes.     

The dipole-quadrupole cycle of the background solar magnetic field

The evolution of the background magnetic field with the solar cycle has been studied using the dipole-quadrupole magnetic energy behaviour in a cycle. The combined energy of the axisymmetric dipole, non-axisymmetric quadrupole, and equatorial dipole is relatively lowly variable over the solar cycle. The dipole field changed sign when the quadrupole field was near a maximum, andvice versa. A conceptual picture involving four meridional magnetic polarity sectors proposed to explain these features may be in agreement with equatorial coronal hole observations. The rate of sector rotation is estimated to be 8 heliographic degrees per year faster than the Carrington rotation (P = 27.23^d synodic). Polarity boundaries of sectors located 180° apart show meridional migrations in one direction, while the boundaries of the other two sectors move in the opposite direction. A simple model of how the magnetic field energy varies, subject to specifying reasonable initial photospheric magnetic and velocity field patterns, follows the observed evolution of the dipole and quadrupole field energies quite nicely.     

The structure of the solar flare stream magnetic field

The structure of the interplanetary magnetic field within the flare streams as well as associated variations of the geomagnetic disturbancy are considered. It is shown that in the main body of the flare stream the magnetic field is determined by the configuration of the large scale magnetic field on the Sun at the flare region. Within the head part of the flare stream the magnetic field represents by itself the compressed field of the background solar wind and hence is determined by the distribution of the super large scale solar magnetic field outside the flare region.A certain asymmetry in the parameters of the magnetic field within the streams associated with geoeffective and non-effective flares is shown to exist.     

Meridional component of the large-scale magnetic field at minimum and characteristics of the subsequent solar activity cycle

The polar magnetic field near the cycle minimum is known to correlate with the height of the next sunspot maximum. There is reason to believe that the hemispheric coupling can play an important role in forming the next cycle. The meridional component of the large-scale magnetic field can be one of the hemispheric coupling indices. For our analysis we have used the reconstructed data on the large-scale magnetic field over 1915–1986. We show that in several cycles not only the height but also the general course of the cycle can be described in this way about 6 years in advance. This coupling has been confirmed by the currently available data from 1976 to 2016, but the ratio of the meridional field to the total absolute value of the field vector has turned out to be a more promising parameter. In this paper it was calculated at a height of ～70 Mm above the photosphere. The date of the forthcoming minimum is estimated using this parameter to be mid-2018; using the global field as a forecast parameter gives a later date of the minimum, early 2020.     

The magnetic field transfer in the solar convective zone

The large-scale azimuth magnetic field is pumping to the bottom of the solar convective zone due to the diamagnetic action of turbulent conductive fluids. When the field at the bottom is of about 10³ G, an equilibrium is established between diamagnetic pumping and buoyancy.If, in addition to the density gradient, an additional anisotropy exists (for instance, due to rotation), another mechanism of the magnetic field transfer appears, the efficiency of which greatly depends on the magnitude of the anistropy parameter.     

On the large-scale diffuse magnetic field of the sun

Although the sunspots migrate towards the equator, the large-scale weak diffuse magnetic fields of the Sun migrate poleward with the solar cycle, the polar field reversing at the time of the sunspot maxima. We apply the vector model of Dikpati and Choudhuri (1994, Paper I) to fit these observations. The dynamo layer at the base of the convection zone is taken to be the source of the diffuse field, which is then evolved in the convection zone subject to meridional circulation and turbulent diffusion. We find that the longitudinally averaged observational data can be fitted reasonably well both for positive and negative values of the-effect by adjusting the subsurface meridional flow suitably. The model will be extended in a future paper to include the decay of active regions as an extra source of the diffuse field, which may be necessary to explain the probable phase lag betweenB _r andB at lower latitudes.     

Meridional drift of the large-scale solar magnetic fields in different phases of solar activity

An analysis is made of mean latitudinal profiles of the meridional drift of the large-scale solar magnetic fields. The previously detected equatorward migration of the drift pattern in the course of a cycle is confirmed. Evidence for the existence of a near-equatorial narrow zone ±7° with an equatorward drift with a rate of about 1 m s^-1 is obtained. The study revealed a significant difference in shapes and variations of average drift profiles for the large-scale magnetic field and small magnetic features (Komm, Howard, and Harvey, 1993).