The relationship between coronal and interplanetary magnetic fields

Adv. Space Res. VoL 13, No.9,

Printed in Great Britain.

pp. (9)31—(9)42, 1993

0273—1177/93 $24.00 1993 COSPAR

THE RELATIONSHIP BETWEEN CORONAL AND INTERPLANETARY MAGNETIC FIELDS Steven T. Suess NASA Marshall Space Flight Center, Space Science Laboratory/ES52, Huntsville, AL 35812, U.S.A.

ABSTRACT The morphology of the interplanetary magnetic field (IMF) is being used increasingly often to diagnose the state and solar origin of interplanetary plasma. For example, the heliospheric current sheet has been used to locate the magnetic equator and relate it to the coronal streamer belt. More often, recently, has been use of variance analysis of the IMF to infer the topology of apparent magnetic loops, magnetic draping, and relationships between the IMF and photospheric fields. These time-dependent IMF variations open new horizons for relating the IMF to the coronal field. Here, I review applications of coronal magnetic field models to predicting the quasi-steady IMF morphology and review recent applications of IMF variance analysis to diagnose origins and history of solar wind plasma. INTRODUCTION The two components of this review, the coronal and the interplanetary magnetic fields, comprise very different types of data. The later has benefitted from a lengthy, continuing, and even expanding in silu observation program while the former (above Ca. i. 1R 0) is presently accessible only through models using photospheric data or through proxy observations of streamers, coronal holes, rays, plumes, and coronal transients. This situation determines the types of relationships studied between the two data sets. There are recent reviews of coronal models and interplanetary data separately /1,2/, so emphasis here can be on their relationships, with only a summary of the state of knowledge of the two data types. The types of relationships cover a broad range of phenomena, extending from simple averages, the steady structure, and rotation of sector boundaries and the heliospheric current sheet (HCS) at one extreme, through formation of magnetic clouds and flux transport from the Sun, to investigations of the character of fluctuations in the interplanetary magnetic field (IMF) and whether or how these relate to magnetic field fluctuations in the corona at the other extreme. These studies are motivated by new missions like Ulysses and SOHO, by ongoing analysis of data from Pioneers, Voyagers, IMP, ICE, Helios, and other spacecraft, by ever-improving ground based observations of the Sun, and by a recent surge in theoretical understanding of magnetohydrodynamic (MHD) waves and turbulence in the solar wind and corona. Early obstacles to understanding - differences in instruments between spacecraft, uncertainty about the nature of IMF fluctuations, sparsity of coronal observations, and a complete lack of global IMF coverage - are giving way to improved theory and analysis techniques, new missions, new ideas, and finally to the luxury of a long, continuous run of data. The next section summarizes our present understanding of the steady-state corona as a source of the spiral IMP and the heliospheric current sheet. The following section will address attempts to relate transient phenomena to coronal structure, reflecting current interest in coronal mass ejections (CMEs), magnetic draping, the source of southward IMF, and advection of magnetic flux away from the Sun. Finally, a short section will summarize research on Alfvén waves and Alfvénic turbulence. It will be apparent that much of the research on time-dependent phenomena reflects the necessity of using plasma data in analysis of the IMP: research on the modification of the IMP between Sun and the observer, the modeling of this process, the use of these models to extrapolate the IMF back to the Sun, and the eternal problem of separating spatial and temporal structures all require consideration of the state of the plasma. QUASI-STEADY STRUCTURE The Potential Magnetic Field Model and IMF Polarity Observations of the IMF began in the early 1960s, with measurements proving two theoretical predictions: JASR 13:9-D

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that the solar magnetic field would be drawn into an Archimedean spiral and that the field near the heliographic equator would have a pattern of alternating polarity corotating magnetic sectors /3,4,5,6/. These predictions were based on measurements ofthe photospheric magnetic field strength, on the shape ofthe visible corona suggesting a dipolar field, and the knowledge that the Sun rotates. Today, a continuing program compares the polarity and other parameters of the IMF with those expected from the coronal field. The majority of this research is based on the potential field model (PPM) of the coronal magnetic field between the photosphere and a ‘source surface,’ usually placed at 2.5R~,where the field is assumed to be radial. This model is viable because the corona is a low-fl plasma. The PFM field is calculated in terms ofspherical harmonics, using the observed photospheric field for the inner boundary condition. The bottom panel of Figure 1 shows an example of the photospheric line-of-sight (LOS) magnetic field measured at the Wilcox Solar Observatory over slightly more than one Carrington Rotation in September 1986. Using this field as the lower boundary condition for the PFM, the resulting magnetic field at the source surface of 2.51?e is that shown in the top panel of Figure 1 /1/. The magnetic field on the source caninto then the be mappedsurface outward interplanetary medium. This mapping is done in the same way the original Archimedean spiral magnetic field pattern was predicted, by assuming the magnetic field is passively embedded in a spherically symmetric solar wind /7/, with fleldlines rooted in the Sun (or the source surface). This model predicts a spiral angle of ca. 45°at 1 AU and a field strength of several microgauss for a solar wind speed of 425 km/s. The most easily identified feature of this magnetic field is the boundary across which it changes sign - the sector boundary. This boundary is the outward mapping of the neutral line on the source surface, the heavy line dividing regions of opposite magnetic polarity and extending to latitudes between 10°Sand 15°Nin Figure 1 (top). The sur-

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1779 Fig. 1: These two panels show synoptic charts from the Wilcox Solar Observatory of the photospheric (bottom) and computed coronal (upper) field in September 1986. The heavy solid line shows the neutral line dividing inward and outward polarity regions. The dashed contours and heavy shading show negative (inward) field regions. Solid contours and ligh shading show positive areas. Thading begins at ±lOOpTin the photosphere and at ±pT at the source surface located at 2.5R 0. Near minimum the surface field was not very strong and the coronal field looked much like a dipole with a flat neutral line near the equator /1,11/.

face defined by this boundary, the HCS, is modeled from the shape of the neutral line at the source surface and the theory for the Archimedean spiral IMF. For example, if it is assumed the neutral line is a sine-curve, with a tilt of 15°,and that there is everywhere a constant solar wind speed of 300 km/s, the resulting HCS surface out to 5 AU is that shown in Figure 2(a). The ‘tilt’ of the HCS is defined as the latitude enveloped by the surface (15°in this case), not the slope of the surface at an arbitrary location. Sector boundaries naturally tend to reoccur on successivesolar rotations. Besides the average field strength, they are the only information from the source surface magnetic field that is not lost beyond a few tens of solar radii through solar wind dynamical interactions. Considering again Figure 1, a spacecraft would detect two magnetic sectors between latitudes of 1O°Sand 15°N,and no sectors above “~‘ 20°. The tilt is thus 10° in the southern hemisphere and 15°in the northern hemisphere. This simple geometry is common near solar minimum, when the neutral line is approximately a sine-curve. At other times during the solar cycle, the neutral line has a more contorted shape and there are often four (or even more) sectors per solar rotation. The latitudinal reach of the neutral line can be up to 90°. There are even occasional periods when there is more than one neutral line on the source surface, corresponding to more than one isolated current sheet in the interplanetary medium /1,2,8,9/. The HCS correspondingly evolves over the solar cycle in response to the eruption of new magnetic flux and the consequent changing geometry of the neutral line on the source surface /10/. The basic pattern is the same as for the large-scale solar magnetic field in each cycle, and the corona acts as a kind offilter that is most sensitive to the large-scale field pattern. Consequently the coronal pattern and, by extension the heliospheric pattern, is similar from cycle to cycle.

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Fig. 2: An idealized heliospheric current sheet surface that divides regions of positive and ,negative magnetic polarities in the interplanetary medium. The assumptions are a solar rotation period of 27 days and a neutral line at the source surface (see Figure 1) that is a sine-curve tilted at 15 to the heliographic equator. (a) The solar wind speed here is assumed to be spherically symmetric and equal to 300 km/s. The plot extends to 5 AU and shows the warped spiral of the heliospheric current sheet in this simplest east. (b) The solar wind speed here is assumed to increase linearly from 300 km/s at the heliographic equator to 400 km/s at the maximum latitudinal extent of the current sheet. The plot again extends to 5 AU. Here, the higher flow speeds at higher latitude are seen t? carry the high latitude portions of the current sheet outward with respect to the equator, resulting in an extremely different picture than seen in the classical plot shown in (a). The PFM has been applied to photospheric magnetic field data for every Carrington rotation since 1976. Extensive analysis has been made of sector widths, how often four and more sectors occur per solar rotation, the rotation rates of sectors, the stability ofsectors, the correlation with other solar and interplanetary data, and the tilt of the HCS /1,8,11,12,13,14/. This research has the double goals of exploring the utility of the PFM/HCS concept and defining its limitations. The formal uncertainty of the coronal model has been established to be ±5°to 10°in latitude and longitude, and only O[20%J of the 12-hour average IMP directions are oriented more than 60°away from the nominal Archimedean spiral direction. These fluctuations originate near or at the Sun, from stream interaction, and from transient structures and transient-associated interactions. Because of this type of fluctuation and those due to ‘flapping’ motions that cause multiple HCS crossing by spacecraft /15/, the IMP polarity must be smoothed for intercomparison of large-scale patterns. With this smoothing, the PFM/HCS relationship becomes very strong. Only during rotations irs which the field is undergoing rapid evolution does the model fail badly. However, sector boundaries become more disturbed (less well defined) with increasing heliocentric distance /8/. Conversely, the tilt of the HCS seems to remain well defined in the outer solar system /2/. The inference is that although there is radial and longitudinal ‘mixing’ of HCS boundaries, there is relatively little systematic meridional motion; the envelope in latitude defined by the tilt of the HCS is not changing by a large amount beyond a few AU. The reasons why this might be the case have to do with how the HCS undergoes secular distortions. Figures 3 and 4 are graphic illustrations of the systematic nature of the HCS evolution in time. Figure 3 shows a comparison of equatorial PFM polarity patterns and those observed by Pioneer Venus Orbiter during the period 19791984, demonstrating the obviously good correlation that exists between the two patterns and the gradual and consistent evolution of the sectors in response to the changes in the large-scale solar magnetic field /8/. Figure 4 is a plot of the HCS tilts in the northern and southern hemispheres and their average (‘Alpha’) /10/ (the appearance of a plateau at ±70°in this figure is an artifact of the lack of observational resolution at high heliographic latitudes). The data in Figure 4 show that tilt behavior is statistically indistinguishable from one solar cycle to the next, permitting a tilt prediction to be made for the coming solar cycle that will be testable by the Ulysses mission - which provides the first opportunity to directly test the tilt of the HCS at high latitudes. The PFM/HCS concept is particularly useful for analyzing rotation rates. Sector boundaries specifically provide a timing mark that can be related back to coronal and photospheric rotation rates. This type of study has been long undertaken and continues today. In cycle 21, coronal and photospheric large-scale longlived patterns rotated every 26.9 days in the northern hemisphere; the southern field rotated every 28 days. Similar periods were present in the IMP /1,11/. The coronal rates reflect a smaller gradient in latitude

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S.T. Suess

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than exists in photospheric differential rotation /16,17/ and this is reflected in the IMP to the limited degree it can be tested

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teresting new problem, for which an answer sphere. Thisbeen is providing least one the inhas not yet produced.at Although structure of the corona does not have an O[1] effect on the spiral angle, it has been found that there is a north/south asym metry that cannot be explained either in terms of the solar wind speed or solar rotation /18/. If this is ofsolar origin, it would have to be caused by a north/south difference in coronal field strength and struc ture. MilD coronal models with this much detail do not yet exist. Alternatively, the asymmetry could be due to the influence of an interstellar wind or magnetic field /19/, which is also beyond the reach of existing models. A systematic attack using the PFM/HCS model together with all of the accumulating data seems necessary to understand the source of this north-south asymmetry. Acceptance of the PFM/HCS concept means it has become a paradigm for visualizing the structure ofthe quasi-steady IMP as imposed by coronal magnetic structure. This paradigm has some interesting characteristics. For example, the pattern of the neutral line at the source surface (Figure 1) is the same at any larger heliocentric distance - only being displaced in longitude - in the presence of a spherically symmetnc solar wind. Sector widths are therefore independent of radius, the tilt is an invariant, and the ‘inclination’ is an invariant.

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~orth solartilt. Here, the HCS wind inclination For surface, speed sector on means which different widths the is independent tosector local change, slope boundthe of ~o ~, ~ 30 I South 1 ~ ~pha ~. uN aries would have to differ, which implies ~ 0 i”~1(~ solar wind stream interaction that in turn c . limits the amount the sector width could < -30 A’ . It I fl change. For this reason, sector widths de~ , Mt . . ( pend only weakly, or not at all, on distance ~~60 from the Sun /8,20/, in spite of the solar wind speed varying strongly with lon -________________________________________ gitude. HCS tilts have also been observed ~9~975 •19~5 1990 1995 to vary only weakly with heliocentric distance. The reason for this is that there is no strong forcing of meridional motions in Decimal Year (ticks at beginning of rach year) the solar wind beyond a few solar radii displacements of more than 10°— 15° over many AU are unlikely. Fig. 4: Heliospheric current sheet tilts from mid-1976 to the present, computed using the PPM and Wilcox Solar The PFM/HCS paradigm is, however, sufObservatory data. Tilts are shown for the northern and ficiently flexible to use in analyzing more southern hemispheres, separately, and for the average magcomplex situations than simple spherically nitude (‘Alpha’). There is one data point per Carrington symmetric solar wind flow. For example, Rotation. The appearance of a plateau at 70°latitude in a detailed investigation of the paradigm both hemispheres is an artifact ofthe lack of observational was carried out using Helios data /20,21/, resolution at high heliographic latitudes /10/. wherein the solar projected latitudes and

Coronal-Interplanetary Magnetic Fields

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longitudes of individual sector boundary crossings were compared with a sine-curve on the source-surface. The result suggests the existence of small local distortions of the HCS as shown in Figure 5 in a threedimensional view of one possible configuration of the inferred distorted boundary that gives a four-sector pattern at some latitudes and scatter about a sine-curve at all latitudes. The tilt of the HCS at this time closely matched the PFM/HCS prediction, while the detailed longitudinal structure illustrated by the distortion in Figure 5 differs strongly from the PFM expectation. The authors emphasize that this is only one possible interpretation. However, this type of distortion has been shown to result from typical solar wind speed variations measured on the HCS /13/. Small latitudinal gradients in the solar wind speed on the HCS, such as those producing the results in Figure 5, can dramatically alter the HCS. This is illustrated by a simple exercise, the results of which are shown in Figure 2(b). Typical meridional gradients on the HCS are 5-10 km/s. If the model + + ÷ in Figure 2(a) is red one assuming the speed increases from 300 -~f’~\ + ± km/s at the equator to 400 km/s It: at 15°, the result is the HCS configuration shown in Figure 2(b). The consequence is that the high-latitude HCS has been carried forward in radius with re spect to the equatorial portions (see also /22,23/). This type of gradient can persist because it does not invoke any dynamic stream interaction or meridional transport. It shows the secular increase in distortion that results. Such gradients, on a small scale, ai’e certainly responsible for a portion of the inferred distortion in Figure 5, and these effects continue to grow with heliocentric distance. Figure 6 shows this by taking solar wind speed fluctuations measured along a nearly east-west portion of the HCS and applying them to a hypothetical northsouth HCS. This has important implications for the HCS in the outer heliosphere. Given the probable existence of speed fluetuations, the HCS will become sheared on small scales. Any small time-dependent meridional motions will then more easily tend to mix the boundary and increase the uncertainty ofits location with increasing heliocentric distance. This is precisely what is observed /2,8/, and this loss of definition of the HCS location with increasing distance is probably a natural consequence of kinematic distortion and the existence of any small turbulent or wave-like fluctuations. The ultimate state in the distant

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heliosphere, under this process, is a current sheet that has a large ‘filling factor’, in the sense that the distance in the meridional direction between successive layers of the current sheet is relatively small, up to the latitudinal extent of the HCS. This picture has already been, in some sense, implicitly incorporated into cosmic ray propagation models that involve the HCS /24/, in which the

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three-dimensional spiral, warped current sheet is approximated by a two-dimensional effect inside the volume enclosed by the tilt angle.- Therefore, in the outer solar system the relationship between the coronal and interplanetary magnetic fields is reduced to mainly being a definition ofthe tilt ofthe HCS, with the structure of the tICS within that boundary being only weakly related to the coronal field. It is even possible that this ultimate state can detected during the Ulysses mission during its rapid north-south excursion between polar passages. What would be expected is a larger number of individual field reversals at a sector boundary during a north-south passage than during a radial passage. The configuration of the HCS will be much better known after 1995, when Ulysses has passed from the southern to the northern polar regions ofthe heliosphere. Between polar passages, Ulysses will rapidly pass through the HCS when it is inclined moderately (at a phase of the solar cycle equivalent to the inclinations in Ca. 1984 in Figure 4). The Maximum Brightness Contour and IMP Polarity The other common method of identifying the neutral line and current sheet near the Sun is to identify it with the ‘maximum brightness contour’ (MBC) in the K-corona /12,25,26,27/. Streamers, which are located around the Sun in a belt, are bipolar magnetic features containing closed magnetic loops in their interiors and open fieldlines on their flanks. Simple arguments make the case that the IMF across a streamer will reverse direction and hence the streamer belt marks the base of the HCS. These two approaches to coronal magnetic field structure are best viewed as complimentary. The PFM provides magnetic field geometries (spreading factors) in coronal holes and field amplitudes on the source surface. The MBC provides an unambiguous measure of streamer locations and the latitudinal extent ofthe HCS, thereby also providing a calibration for the PFM. However, the MBC is apparently of lower spatial and temporal resolution than the PPM: MBC measurements are necessarily made only on the limb. The MBC also provides essentially no information on the interior of coronal holes. I

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Results from MBC studies have recently led to a marked improvement in ~ the PFM. This has come about because ~ o 2 the MBC has been found to lie system- ~ . ~. atically equatorward of the PFM neu- ~ tral line for high tilt angles /25,28,29/. CO .. These differences have been ascribed ~ o.i~ to poor determination of polar mag- ~ : netic fields by existing magnetometers Co /25/. To compensate, the polar field a. : had been strengthened by a varying ° 0.1 . amount through the solar cycle /1,2/. ~ ~ However, a recent calculation appears ~ . • !‘ to resolve the question of why the MBC neutral line lies systematically equator- ~ 0.05 . ward of the PPM neutral line in a more physical way /25/. In the new calcula- ~tion, the usual line-of-sight (LOS) data in the PPM was replaced by the de0 I I I I I rived radial field component under the 76 78 80 82 84 86 88 90 92 assumption that the field is radial at YEAR the level the LOS component is measured. In this case a detailed comparison was made both with the observed K-corona and with the equiv- Fig. 7: Fraction, s~,of the solar surface covered by open magalent LOS derived PFM. This proce- netic regions during 1976-1991 (Carrington Rotations 1645-1844), dure yields much stronger polar fields as inferred using the radial (solid curve) and line-of-sight (dofled that the LOS method, resulting in re- curve) methods /25/. The source surface is at 2.51?~.The curves duced neutral line latitudes, reduced represent 3 month running averages of t~. HCS tilts, and an increased fraction of the solar surface covered by open magnetic regions as shown in Figure 7. This last result is due to the larger size of the polar coronal holes. The underlying assumption is that the solar field is nonpotential at the observing level and the results seem to justify the approach and the assumption. Another important result is that computed coronal hole areas more nearly reproduce observed areas (20%, as opposed to much less using the LOS method). Successors to the Potential Field Model Potential field models (PFMs) of the coronal magnetic field are the only models presently used to quantitatively relate field observations at the photosphere to observations of the interplanetary magnetic field. However, because of the weaknesses of the PFM, this situation will not last forever. The weakest assumption is the approximation of collapsing onto a spherical shell the volume currents associated with solar wind flow forcing fieldlines to be open to the interplanetary medium. In other words, the source surface may not

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be well approximated by a thin sphere. One alternative is to use a nonspherical source surface; although technically feasible, this is a tedious numerical calculation /30/. Another alternative would be to construct a numerical MilD solution that uses observed photospheric parameters, but this is beyond present capabilities. There is evolving a class of semi-analytic magnetostatic models that assume distributed currents in the corona /31 32/ - as opposed to confining these currents to the ‘source-surface’ as done in the PFM. These models have been applied only to two-dimensional problems, but their mathematical and physical simplicity admits application to three-dimensional problems. Conversely, combining (necessarily numerical) MHD models of coronal structure with photospheric observations is not possible with the existing two-dimensional models /33,34/. Even without this limitation, numerical models remain restricted in spatial resolution and technically difficult to construct. Nevertheless, numerical MHD, as well as magnetostatic, models are being developed in support of the Solar-Heliospheric Observatory (SOHO), to be launched in 1995. They at least offer the potential of leading to more realistic coronal magnetic field models in the future. In particular, they will probably be the first to be able to establish quantitative relationships between the IMP average magnitude /35/ and the solar mean magnetic field - a relationship which has so far escaped detailed analysis because of the influence of coronal energetics on the amount of flux opening to the interplanetary medium and on a poor understanding of how new magnetic flux is carried away from the Sun. CORONAL MASS EJECTIONS, MAGNETIC CLOUDS, FLUX TRANSPORT, AND RELATED TRANSIENT PHENOMENA Transient phenomena encompass a wide variety oftopics. Included here are discussions of attempts to predict occurrences of southward IMP and of studies measuring the magnetic flux being carried away from the Sun. The later, in turn, depend on attempts to detect magnetic reconnection and disconnection events using proxy data (white light coronagraphs) and on the perennial problem of whether CMEs are magnetically connected to, or disconnected from, the Sun. Application of the PFM to Predicting Southward IMF One of the more urgent requirements in solar-terrestrial relations is prediction of southward IMF (B 0) intervals, because it is these intervals which are most likely to produce major geomagnetic storms /36,37/. IMP fluctuations often appear to be quasi-random, but there may be some imprint of the coronal magnetic field, and this problem has been addressed using the PFM. Based on the assumption that the free magnetic energy present when a coronal mass ejection is initiated is transferred almost totally to other forms of energy by the time the CME stops accelerating, the PFM was used to calculated the magnetic orientation in the ejected plasma. The magnetic orientation at the ‘release height’ (height where the front of a CME ceases to accelerate) was calculated and compared with B0 events observed at 1 AU for which solar sources have been identified /38,39/. These studies, for a total of 11 events, show that the PFM application may be appropriate for those driver gas-associated B0 events which have magnetic structures lacking large internal field rotation and are associated with active region CMEs. This, however, is a very preliminary study with a small number of cases, and the results are only suggestive that B0 in a flare-associated CME driver gas may be predictable. This seems to be the only time the PFM has specifically been applied to analyzing transients. Potential extensions to the above analysis are numerous. The relative interplanetary and soI~rcauses of B0 have been considered and it is recognized that there are contributions both from dynamical interactions between transients /40/ and the solar wind and from Alfvén wave trains /36/, as well as from the source region at the Sun. One approach might be to utilize knowledge of the vector magnetic field at a flare site. Another approach might be to incorporate the dynamics of the transient in the interplanetary medium. Flare site correlations have been remarkably unproductive, while specific incorporation of solar wind dynamics is not yet practical for specific event analysis /40/. Empirical studies of magnetic field draping around CMEs have identified the interplanetary source of some southward B0 events, but are not predictive /41,42/. Although of practical importance, this problem has thus far not yielded well to modeling or empirical studies, Topology/Connectivity of IMP Fieldlines This presents a heirarchy of problems. Here, the estimating the amount of magnetic flux being carried away from the Sun will be placed first. Magnetic flux erupts on the Sun at varying rates and locations throughout the solar cycle. Some of the flux re-submerges into the photosphere, but some of it also is carried into the corona and solar wind. It also seems that coronal transient sometimes carry magnetic flux away from the Sun. There are several unknowns in this process. They are: (i) What is the ratio of re-submerged to removed flux? (the uppermost question). (ii) Is the flux removed mainly in large scale transients or by small scale reconnection? A subsidiary question to (ii) is if magnetic clouds and CMEs are suspected of carrying magnetic flux, how can it be determined? This subject involves studies of the structure of magnetic clouds, CMEs, energetic particles, and bidirectional streaming of protons and heat flux in the solar wind. A magnetically disconnected CME, called a plasmoid, was first invoked to explain Forbush decreases /43,44/,

and later used to explain electron heat flux dropouts and bidirectional electron streaming /45,46/. These concepts, although implicity related to flux removal from the Sun, were proposed to explain specific obser-

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vations for other reasons. Up to the present, the geometry of the transient IMF has never been successfully used to infer unambiguous disconnection from the Sun. The evidence for plasmoids has been, and continues to be, all indirect. The twisted flux rope geometry of magnetic clouds might be related to the twisted fields often seen in CMEs and prominences, but this remains a plausibility argument rather than a proof. Figure 8 is a schematic of open magnetic fleidlines as in the PFM/HCS paradigm, along with various possible CME topologies in interplanetary space, including an attached bottle, a detached plasmoid, and a partially attached flux rope. The arrows indicate the direction of the associated electron heat flux. The phenomena in this figure cover the various possibilities that have been suggested for the relationship between observed IMF transients and coronal magnetic fields. They are what is being considered in this section, and the following topics are covered in order: (1) The direct measurement of magnetic flux advection in the interplanetary medium. (2) Evidence for shape of interplanetary transients. (3) Evidence for the connectivity to the Sun of interplanetary transients. To unambiguously measure the magnetic flux content of the solar wind requires 3-D spacecraft coverage. In the absence of this, another attempt has been made to measure the magnetic flux content of solar wind structures using singlespacecraft data /47/. For regions with simple magnetic topologies (i.e. negligible meridional component), the flux integral is equivalent to ~ = fB~ 3’ dt, where B~is the ecliptic plane field component measured perpendicular to the solar wind yelocity 3’. Thus, ~ can be measured entirely from measured quantities. This calculation provides a ‘pseudoflux’ which is a plausible estimate of the actual flux so long as the mendional component ofthe IMF is small. The study covered variations in the magnetic flux over a 16 year interval and addressed questions of opening and closing offlux by comparing q~iof both CMEs and heat flux dropouts (HFDs) - which are suspected of representing fieldlines that have disconnected from the Sun.

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Fig. 8: Schmatic diagram of normal open magnetic field and Variations of more than 60% in an- various possible CME topologies in interplanetary space. The nual averages of q~over the solar cy- possible CME geometries are; (1) attached bottle; (2) detached cle were found and suggest flux is plasmoid; and (3) partially attached flux rope. The large arrows being both opened up and closed off indicate the direction of the electron heat flux /72/. in the IMP and, more significantly, gives an crude estimate of the the minimum rate at which the opening and closing must be happening. This was addressed in more detail by examining the magnetic flux within particular structures, which requires determining the boundaries of that structure. In /47/, existence of bidirectional electron events was used to provide a signature of CMEs in interplanetary space /48/. All such events in an 18 month interval were used to calculate the rate at which newly opening magnetic flux would be added in the ecliptic plane assuming CMEs remain simply tied to the Sun at both ends (bottle geometry). Figure 9 displays the results: the lighter solid line shows the buildup of newly opening magnetic flux assuming all the field encountered in the bidirectional events is simply connected back to the Sun. The solid line with dots is the monthly average of the pseudo-flux. At the rate of buildup of flux showing in this figure, the amount of open magnetic field in the ecliptic would be expected to double over only ca. 9 months. Of course, if CMEs remain only partially attached to the Sun, the estimated rate at which the pseudo-flux builds up would be slower. This investigation in /47/ is not a quantitative calculation, or even a proof, of flux buildup and removal in the IMP, but it does re-emphasizethat this is an important question which depends on the topology and magnetic connectivity of CMEs and other IMP transients, about which disappointingly little is really known in spite ofextensive efforts. A recent review on CMEs and magnetic flux ropes in the interplanetary medium /48/ summarizes the present understanding. Formed in the corona by the ejection of solar material from closed magnetic field regions, CMEs at 1 AU generally have distinct plasma and field signatures. The most common is probably counterstreaming fluxes of suprathermal electrons, indicating that CMEs are typically closed field structures either rooted at both ends in the Sun or entirely disconnected from the Sun.

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About 30% of all CMEs also exhibit internal magnetic field rotations characteristic of magnetic flux ropes which, along with low proton temperature and strong field strength, characterize magnetic clouds /49/. These form as a result of local reconnection within rising, previously sheared coronal fields /48,50/, but there continues to be no way to prove whether this reconnection completely disconnects clouds from the Sun. Besides the above, other common signatures of CMEs in the solar wind include Helium abundance enhancements, ion and electron temperature depressions, electron heat flux dropouts, unusual ionization states, and counterstreaming energetic protons. The interpretation of the the ___________________________________________ data on CMEs is not unique. • ~tOn~i~ Flux Identical data has been used interrated Flux to imply both connection to sooo Average 2.D Flux and disconnection from the Sun. Most of the uncertainty results from the incomplete ~ --—-—-—-—-—-—-data available in any given instance or, equivalently, in am— biguities in interpreting existing data. For example, minimum variance analysis is used 0 I I I . , -r to suggest a magnetic strucA S 0 N D J F M A M J .1 A S 0 N D .1 F tune for magnetic clouds /49/ Month [8/78-2/80] which, although not necessarily used to imply connection to the Sun, has been used to develop a host of cloud modFig. 9: Monthly and integrated ecliptic plane pseudo-fluxes of the magels /49,51,52,53/. The internetic flux carried by CMEs observed by ISEE-3 at 1 AU /73/. The pretation of minimum vandashed line indicates the average pseudo flux for the period indicated. ance analysis using magnetic The CMEs were identified by the streaming of suprathermal electrons in field data requires underlying both directions along the local magnetic field. The pseudo-flux function, assumptions about the char4o, is defined in the text. actenistics offield rotations in clouds. In /54/ a flux rope model with a variable degree ofhelical distortion from axisymmetry was used to shown that even a fractionally small distortion can render a flux rope almost unrecognizable under standard diagnostics. But, the second main result from that study is that the plasma velocity field signatures are also characteristic of flux ropes and may not be as sensitive to dymmetnies as the magnetometer traces are. Instead of directly assessing magnetic field geometry, plasma measurements provide indirect evidence about the nature of magnetic fieldlines far from the point of measurement. Heat flux dropouts are one suggested indication that a fieldline is, for some reason, no longer conducting heat flux from the hot corona /45,46/. However, these can be ambiguous too; in /55/ it was shown that only 2 of 25 electron heat flux dropouts in the solar wind represent disconnection from the Sun, using higher energy electrons with longer mean free paths to identify disconnection. In another approach, the topology of magnetic clouds was probed using solar energetic particles /57/, with the conclusion that the rapid access of solar energetic particles to clouds indicates fieldlines extend back to the Sun and hence are not plasmoids. In yet another approach, halo electrons were used to imply closed magnetic structures exist for a sample of 39 CMEs, all having continued magnetic connection to the corona /58/. This favors a tongue or flux rope scenario rather than a fully detached plasmoid. A direct method of suggesting disconnection is to use SMM coronagraph data to indicate fieldline geometry in the corona. Doing this, a sequence of events was identified /56/ that is consistent with reconnection across the HCS and creation of a detached u-shaped magnetic structure. But, it seems for every example for which disconnection is claimed, there is a counter example using the same type of data. So, although there is some evidence in, e.g. SMM observation of transient that there is occasional reconnection, every time a test using plasma with CMEs/clouds at 1 AU is made the inference is that there is still a connection to the Sun. This cannot always be the case because flux clearly erupts from the Sun over the solar cycle and a strong case can be made for a substantial portion of that flux to be eventually carried into the interplanetary medium. However, in spite of an extensive effort, the advection of magnetic flux away from the Sun is poorly understood today and the work of /47/ just serves to emphasize that point. ALFVEN WAVES AND TURBULENCE The turbulent character of the solar wind fluctuations was established quite early /59/, while examples were soon also found of pure Alfvdn waves /60/. This does not, however, imply a waves versus turbulence controversy. Instead, recent advances in turbulence and Alfvén wave theory are reconciling the different points of view /61,62/. These new analyses generally formulate the problem in terms of Els~sservariables, which are equally helpful for data analysis, simulations ofturbulent processes, and understanding the physics of non-WKB and nonlinear Alfvénic fluctuations.

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S. T. Suess

Alfvénic fluctuations carry energy, momentum, and information on the physical state where they originated. For this reason, studies of coronal magnetic field - IMF relationships presently lead more often to inferences about the state of the magnetic field in the corona based on IMF data, in contrast to the opposite for quasisteady phenomena. However, the interaction of predominantly Alfv~nicfluctuations with high speed solar wind streams and their intrinsic velocity shear is one of the principal subjects of current turbulence research, as reflected by the number ofpapers written on this topic in recent years /62,63,64/. This interaction, and the development ofturbulence in the interplanetary medium, unfortunately maean that the relationship ofAlfvén waves and turbulence in the solar wind to steady and fluctuating magnetic fields in the corona is a problem which may have no solution. This is because IMP fluctuations appear to be undergoing modification by (perhaps intermittent) turbulence which removes information about the source of some temporal variations /65,66/. However, this cannot be known for certain until some aspects of the models can be verified by in siiu measurements made closer to the Sun than the 0.3 AU reached by the Helios spacecraft - e.g. by Solar Probe. The same measurmenta are also required to fully define the interplanetary observational constraints on Alfvén wave acceleration of the solar wind /67,68/. There has been one very timely idea put forward that depends closely on the character of fluctuations and the relationship between coronal and interplanetary fields. This is the suggestion /69/ that polar heliospheric magnetic fields at large heliocentric distances may deviate considerably from the PFM/HCS paradigm both instantaneously and on average. They suggested the polar field may be dominated by randomly oriented transverse magnetic fields of much larger amplitude than the background Archimedean spiral, and although the average field direction is unchanged, the field direction is transverse to the average direction in the paradigm much more often. The origin of the fluctuations is suggested to be fieldline footpoint motion in the photosphere. Neugebauer and Alexander /70/ also support the idea of convection-driven shuffling of magnetic field foot points at the solar surface leading to disturbances in the corona that are carried off by waves (which may also contribute to acceleration of the wind). The existence of the large amplitude fluctuations in the outer heliosphere depends critically on the period and wavelength and the propagation of waves in the corona and solar wind. Too short a wavelength implies the fluctuations are Alfvénic and therefore of much smaller amplitude /71/. The result of this is that a clear understanding of wave and turbulence dynamics in the solar wind and corona is going to be necessary to make any sense at all of what observations at 1 AU say about conditions in the corona. SUMMARY Relationships between coronal and interplanetary magnetic fields have been reviewed in three categories: quasi-steady phenomena, transient phenomena, and wave and turbulent phenomena. The greatest amount of progress has been made in the former. Only a few empirical results exist for transient phenomena. A great body of theory has recently been developed on Alfvénic turbulence, but it has been sparsely used to relate IMF fluctuations to coronal magnetic fields and dynamics - not a little due to the fact that much information is lost by nonlinear interact-ions between the corona and 1 AU. In siju observations close to the Sun may help to improve this situation. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.

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