vortices near the wavy heliospheric current sheet

VORTICES NEAR THE WAVY HELIOSPHERIC CURRENT SHEET

G. A. DRILLIA and X. MOUSSAS Space Group, Astronomy, Astrophysics and Mechanics, Department of Physics, National University

of Athens, GR 15784, Panepistimiopolis, Athens, Greece

(Received 16 August, 1995; in final form 11 January, 1996)

Abstract. We study the heliospheric current sheet structure during the 1979-1982 time period, which includes the sunspot maximum of solar cycle 21 and the 1980 reversal of the polar magnetic field of the Sun. We examine the evolution of the large-scale configuration of the heliospheric current sheet (HCS), as calculated by Hoeksema (1991), and its extent in heliographic latitude during this time period.

We study the fine-scale characteristics of its structure near sector boundaries (SB) detected in the vicinity of the Earth, using interplanetary magnetic field and solar wind velocity data, as well as temperature measurements (mainly from IMP data). We observe small vortices (eddies) of the order of 0.2 to 0.4 AU in diameter, with time scales of several hours to days. Vortices appear frequently in the plasma near the so-called 'thick' sectors. The local orientation of the sector boundaries is distorted by the presence of vortices. The appearance of vortices is evident in the interplanetary magnetic field, plasma velocity, density, and temperature data.

1. Introduction

In 1965, Wilcox and Ness (1965) demonstrated the sector structure as a pattern of alternating regions of interplanetary magnetic field (IMF) having either positive or negative polarity along the Archimedian spiral direction (Parker's model). The heliospheric current sheet (HCS) divides interplanetary space into two hemispheres of opposite polarities. Field lines that leave the Sun with positive polarity appear in one hemisphere because they come from the corresponding polar coronal hole, while field lines having a negative polarity lie in the other hemisphere because they originate from the opposite coronal hole. The dominant polarity of the IMF in either the northern or the southern hemisphere of interplanetary space is approximately the same as that of the bipolar component of the Sun's polar field in the same hemisphere (Rosenberg and Coleman, 1969).

The HCS, which is approximately flat near the Sun, from where it originates, exhibits a large-scale wavy structure moving outwards, due to the Sun's rotation, and sometimes extends to large absolute heliographic latitudes. Smith, Tsurutani, and Rosenberg (1978) studied the observations of IMF made by Pioneer 11, which reached a maximum heliographic latitude of 16 ~ near the sunspot minimum (1976) in order to determine the maximum latitudinal extent of the HCS. They concluded that the sector boundary structure vanishes at about 15 ~ latitude, above which the magnetic field exhibits a dominant (almost constant) polarity (outward-positive for that time period).

Thomas and Smith (1980), using Pioneer 10 and 11 measurements, confirmed that the tilt angle of the HCS during sunspot minimum is about 15 ~ but also

Solar Physics 166: 403-413, 1996. @ 1996 Kluwer Academic Publishers. Printed in Belgium.

404 G.A. DRILLIA AND X. MOUSSAS

suggested that during the declining phase after the sunspot maximum (1972- 1973) it reached latitudes between 25 ~ and 30 ~

During 1977, the current sheet was found almost horizontal (parallel to the solar equator), though during late 1978 it was highly inclined relative to the solar equator and therefore extended to large heliographic latitudes (Behannon and Burlaga, 1983). It seems that the tilt of the current sheet is the smallest near the sunspot minimum and therefore larger than 15 ~ elsewhere in the solar cycle (Hoeksema, 1980; Thomas and Smith, 1981).

It seems that sector boundaries near the Sun have a north-south orientation (Svalgaard et al., 1975). On the other hand, Schultz (1973), Levy (1976), and Alfvrn (1977) argued theoretically that the sector boundary surface might lie near the solar equatorial plane on average. The boundaries are the extension of the mean source surface field in the corona. The Sun's polar field magnitude is important for the potential-field model that determines the form of the HCS (Hoeksema, 1989) near sunspot minimum when it is strong and the low-latitude fields are relatively weak. On the contrary, near sunspot maximum, when the polar fields weaken and the lower-latitude fields become much stronger, the polar fields are not important for the potential-field model.

It seems that there is a solar-cycle variation in the dominant inclination of the solar boundary surfaces; high inclinations with respect to the solar equatorial plane are observed near sunspot maximum, i.e., 1971 and low inclinations near solar minimum, i.e., 1976 (Villante et al., 1979).

The orientation and shape of the sector boundaries depend on the number of coronal holes and also on their position and their polarities that vary throughout the solar cycle. Neubauer (1978), using Helios 1 measurements, showed that the tilt angle of the current sheet could be between 29 ~ and 65 ~ when the sector boundary orientation angle is 43 ~ Generally, we may suggest that a variety of orientations and shapes is possible, depending on the relative positions of the coronal holes and their polarity. We conclude that the latitudinal extent of the HCS and the inclination of sector boundaries observed at the solar equatorial plane might change throughout the sunspot cycle because of the changes in the strength of the Sun's polar field and of the varying positions and characteristics (number, polarity) of the coronal holes (Klein and Burlaga, 1980; Burlaga, 1978).

There is almost conclusive evidence that the 'thickness' of the sector boundaries depends upon the solar cycle phase. The current sheet 'thickness' can be estimated using the time it takes to sweep past an interplanetary spacecraft. Behannon (1981) calculated the boundary layer 'thickness' using the observed time, t, when the IMF is variable, the orientation of the normal, fi, to the discontinuity surface (determined by the minimum variance analysis method), the solar wind velocity, V, and the spacecraft velocity, Vsc, as 7- = ~(V - Vsc) �9 ft. The mean thickness ranged between 4 x 10 4 and 1 x 105 kin. Klein and Burlaga found that the duration of the SBs is either short (less than 10 min) or long (more than 3 hours). Thus they defined the thin and thick boundaries, respectively. Many boundaries are observed

VORTICES NEAR THE WAVY HELIOSPHERIC CURRENT SHEET 4 0 5

in IMF data as reversals of field polarity within 1 min to 1 hour. They correspond to a distance scale of 104 to 106 km (Smith, Tsurutani, and Rosenberg, 1978). For the period of January to April 1974, during the declining phase before the 1976 solar cycle minimum, Behannon (1977) demonstrated that the sector boundary transition regions (from one sector to another) were either very broad (covering 2 days and almost 30 ~ of a solar rotation) or consisted of a series of sharp (less than 10 min) reversals of the IMF that lasted up to 3 days. Neubauer (1978), using Helios 1 observations, also noted that a mixed polarity region existed between two well-defined magnetic sectors of opposite polarity, which lasted for 6 days (near the 1975 minimum). This could be defined as a sector boundary transition region and therefore denoted a boundary 'thickness' of 6 days.

Furthermore, single crossings occurred over time intervals between a few min- utes and several hours as Villante et al. (1979) reported. It also seems that there is no clear relationship between the boundary 'thickness' and the heliographic distance.

Burlaga (1990) detected large-scale eddies at very large heliocentric distances which form a vortex street. Similar vortices are present in the data analysed here near the Earth's orbit, as is shown in our results.

2. The Large-Scale Structure of the Heliospheric Current Sheet during 1979-1982

We have used hourly values of the IMF vector and of the solar-wind velocity at the vicinity of the Earth, covering the 1979-1982 time period. We have considered the configuration of the heliospheric current sheet for the above mentioned time calculated by Hoeksema (1991), who used the potential field model and the photospheric observations for this time period.

At the beginning of 1979 (Carrington rotation 1676), the north pole of the Sun had positive polarity and the configuration of the HCS was complex. The sheet structure is not sinusoidal, and its warping and tilting develops asymmetrically with respect to the equatorial plane. Near CR 1679 the sunspot maximum occurs. The HCS structure begins to be complex about half a year before (CR 1675) and its complexity continuously increases for half a year after the sunspot maximum. During this complex phase, the current sheet configuration seems to evolve rapidly and dramatically and reaches an absolute heliographic latitude of about 70 ~ or sometimes even more; i.e., during CR 1684, 1685, 1686 the HCS extends to the north pole. During most of 1979, segments of the sheet are orientated almost perpendicular to the equatorial plane. This is typical of time periods near solar maximum, in contradiction with periods near solar minimum where the HCS shows very little extent in latitude (about 16 ~ ) and very limited evolution.

The dominant structure of the IMF observed at the Earth, throughout a solar cycle, consists of either two or four sectors, depending on the phase of the solar


cycle, as well as on the heliographic latitude of the observations. In mid 1976 the HCS consisted of four sectors per solar rotation with a 15 ~ extent in latitude.

The latitudinal extent increased with time, reaching 30 ~ in early 1978 and even 90 ~ near the 1979 sunspot maximum, as demonstrated before. The period from the beginning of 1979 to mid-1981 is characterized by a most irregular (compared for example with the mid-1981 to early-1985 period) and a sector pattern asymmetric in latitudinal distribution. The most probable pattern in the northern hemisphere consisted of four sectors, although, more frequently, there was a two-sector pattern in the southern hemisphere. During the maximum period a two-sector pattern dominated in the middle latitudes, although a four-sector pattern was observed mostly near the solar equator.

As the declining phase of the solar cycle begins (June of 1981) the structure of the heliospheric current sheet becomes simpler and the latitudinal distribution of the sector patterns becomes symmetric; a two-sector pattern dominates at middle and high latitudes in both hemispheres. At the equatorial plane, we observe alternative two- and four-sector patterns. The latitudinal extent of the HCS was about 30 ~ reminiscent of the 1978 structure.

In late 1981 and 1982, the form of the surface of the HCS suggests a nearly bipolar geometry (two sectors) extending to 50 ~ heliographic latitude.

In the IMF, the evolution from four sectors to two implies that the negative sector becomes progressively narrower, and the two neighbouring positive sectors form a single positive sector larger than them.

The differences in the structure of the HCS throughout the solar cycle are well explained by the gradual polar field reversal that occurs at the declining phase, just after the sunspot maximum. Then the polar fields weaken and reverse in polarity. During 1980 the polar fields (north and then south) weaken gradually and then increase again having the reverse polarity. Actually, in early 1980 the north polar field changes polarity from positive to negative. The asymmetry of the HCS increases till negative polarity dominates in the northern hemisphere. The reversal is completed at CR 1694 and about four months later the south polar field becomes clearly positive. The greatest complexity of the heliospheric current sheet occurs from CR 1687 to CR 1694, where large positive regions are disconnected from the - at the time - positive north pole and move southwards, then the reversal of the southern polar field occurs. After the reversal of both polar fields (CR 1701) the structure of the HCS begins to evolve slowly, and its configuration begins to reach lower absolute heliographic latitudes than before (70 ~ or less). We then enter the decline to the solar minimum phase of the solar cycle, where the polar field exhibits constant polarity for about ten years, so no sector boundaries exist above or below 16 ~ of the equatorial plane and the HCS surface is nearly flat with only small quadrupole-like warps.

For a solar rotation, the 50 ~ latitude should be defined as the mean latitudinal extent of the current sheet, except for the period which includes the sunspot max-

VORTICES NEAR THE WAVY HELIOSPHERIC CURRENT SHEET 407

imum and the polar field reversal, when the latitude of the HCS reaches even the value of 90 ~ , and the latitudinal variability maximizes.

3. Small-Scale Features of the Heliospheric Current Sheet

Sector boundaries often lie ahead of fast solar streams, which usually exhibit the dominant magnetic polarity of the coronal holes from where they originate. The heliospheric current sheet tends to be deflected by the solar wind streams. These streams originate from the two polar coronal holes, above or below the magnetic solar equator, and because of their very large velocity they create a subpressure, which gives rise to a large-scale deflection of the HCS towards the corresponding solar pole (Moussas et aL, 1995). A possible relation between the shape of the boundary and the coronal hole positions has been investigated (Burlaga, Lemaire, and Turner, 1977). The coronal holes tend to have the polarity of the hemisphere where they were born. This is always valid for the large polar coronal holes. This tendency determines the polarity of their outgoing solar streams. This also explains the observed relation between the sheet configuration and the position of the coronal holes, as well as its asymmetric latitudinal structure; e.g., four sectors can be observed per solar rotation in northern latitudes in contradiction with two observed sectors in southern latitudes.

The large-scale wavy structure of the HCS, which is shaped by solar rotation, develops from a nearly fiat sheet observed near the Sun. The HCS can also be modified in structure and position by the development and existence of the corotating interaction regions (CIR). The CIRs, which are produced near the stream interface by fast solar wind streams compressing the plasma and its frozen-in magnetic field, overtake the nearest fold of the current sheet's wavy structure. The equatorial current sheet extends to higher heliographic latitudes more often within CIR's than in the quiet solar wind. A forward and a reverse shock wave develop at both sides of the stream interface which practically coincides with the warped current sheet, as soon as the velocity difference between the fast and the slow solar wind plasma exceeds the fast magnetosonic wave mode. The three-dimensional shocks of the CIR follow the continuously variable inclination of the warped current sheet until the forward shock of the CIR meets the reverse shock of the preceding CIR.

The velocity difference leads to the development of shear instabilities and Kelvin-Helmholz instabilities (Landau and Lifschitz, 1959; Chandrasekhar, 1961; Shanna and Srivastava, 1992). As a result, various-scale foldings form. For the development of vortices in a three-dimensional MHD turbulence, a series of numer- ical simulations have been performed (Politano, Pouquet, and Sulem, 1995).

The interplanetary current sheet contains warps and ripples and its structure in small scale consists of 'crested waves'. The crests of the waves are broken by the overtaking fast solar stream (shearing) and the vortices generated are released to the interplanetary medium northwards or southwards. Such 'crested waves' and


generated vortices may be detected in the interplanetary magnetic field measurements as well as in the solar wind velocity measurements. What do we expect to see in the measurements? It is well understood that sometimes the angle between magnetic field vectors of opposing sectors was not found to be 180 ~ as expected, but had reached lower values, as small as 170 ~ at sunspot maximum (Svalgaard and Wilcox, 1974; King, 1976). But if we consider the angle between magnetic field vectors for an adequate time period (approximately 3 days) before and after the sector boundary for all the 25 cases observed, we find it to be close to 180 ~ This perhaps means that near sunspot maximum the HCS is locally folded, and the fine-scale warpings of the sheet appear in the turnings of the magnetic field vector measurements, as the spacecraft moves through the corrugated sector boundary considered.

In a sector boundary case, the IMF usually changes direction by rotating in a plane, for example in the (x, y) plane, with a negligible component normal to this plane. In the 25 cases examined, Bx, By, and Bz components have got similar absolute values, so the observed segment of the sector boundary plane is significantly inclined relative to the equatorial plane, as well as to the meridional plane. As a result of the rippled structure of the SB, its orientation varies a lot with time and space and corresponds to the local tilt of the HCS. If we denote the warped current sheet as the extension into interplanetary space of the neutral line in the photosphere, and therefore of the neutral line at the source surface near the Sun, then we would not expect and we do not observe a flat sheet near the Sun. Thus the interplanetary current sheet includes an additional warping.

We conclude that the local tilt of the HCS and therefore the SB orientation are due to multiple warpings of the sheet at its source surface in the photosphere, to the modified IMF and also to the large- and small-scale fluctuations, which develop mainly from shear instability and warp the interplanetary sheet. In this sense the inferred inclination of the current sheet at a certain radial distance from the Sun can be large, for example, at one longitude but small at another.

The rippled structure of the SB and its resulting local orientation variations has often been detected in the past as multiple sector boundaries that were named 'narrow sectors'. Therefore the total number of observed sectors increased. What we truly observe is the multiple spacecraft crossings of the same sector boundary that is tilted to the equatorial plane, rippled, and folded by stream instabilities. This folding frequently develop into vortices by prolonged shearing action.

In a time period of four-and-a-half months, between late 1974 and early 1975 (before solar minimum), Behannon and Burlaga (1983) observed 105 such crossings with durations from 1 to 40 min and typical wavelengths for the corrugations between 0.05 and 0.1 AU.

In our 25 cases of sector boundary crossings covering three and a half years (1979-1982), small-scale features in the current sheet structure exist that are observed throughout the time period around the boundary data set. The charac- teristic length scale of the foldings is 0.2 to 0.4 AU. In some of the cases, where


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a 360 ~ turn of the B vector is observed, we probably detect a vortex or a very complicated circular folding of the HCS (e.g., on 23 March, 1979).

The fact that the observed temperature enhances significantly at the SB, supports the vortex assumption because of the expected turbulence associated with high temperature (Geranios, 1982, 1987). A double peak in the temperature with a minimum between them is present in most cases. The double peaks coincide with the limits of the vortex. The thermalization is probably the result of magnetic reconnection and dissipation, as found in MHD simulations (Politano, Pouquet, and Sulem, 1995). The vortices, rotating, move towards the solar poles due to the subpressure caused by the fast solar wind of the polar coronal hole combined with the Magnus effect. Much larger vortices have been observed, using Ulysses data, at considerably higher latitudes with respect to the solar equator and at various heliocentric distances (Moussas et aL, 1996). An analysis of in-ecliptic IMF data from Ulysses revealed the presence of large-scale vortices associated with corotating structures (Polygiannakis and Moussas, 1996).

It is evident that, because the stream interface and the current sheet surface is characterized by local inclinations and perturbations (foldings, ripples, and vor-


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tices), the minimum variance analysis can only be used to calculate the local orientation of the sector boundary layer. These local tilts are of low significance and completely different from the global orientation of the HCS.

Using the time that takes the SB to sweep past the spacecraft, we would consider most of the boundaries 'thick'. In most of the 25 cases the field vector changes polarity by rotating for more than a day. The so-called 'thickness' could generally represent:

(a) The randomly oriented perturbations and turbulence near the current sheet, part of which are the foldings that generate vortices.

(b) A random motion of the thin current sheet, perpendicular to the equatorial plane that would continuously change the SB plane orientation, as the spacecraft passes the boundary. The assumed dependance of the sector boundary 'thickness'


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from the solar cycle phase really reflects the dependance of the HCS fine-scale structure (degree of folding and complexity) on the solar cycle phase.

4. Conclusions

The heliospheric current sheet is a thin, almost mathematical surface that develops from the tilted, with respect to the equator, sheet that is observed near the sun and outflows, frozen, into the solar wind.

Due to the solar rotation, the large-scale sinusoidal structure of the HCS is perturbed by fine-scale fluctuations. Most commonly such distortions are the results of fast solar wind flows interacting with slow plasma and consist of warps, foldings, crested waves, and vortices.

Vortices are detected by the observed (over 360 ~ ) turnings (frequently multiple) of the interplanetary magnetic field or/and of the solar wind velocity, as well as by the significant increase in the solar wind temperature at the limits of the vortices with a decrease in the temperature in between.


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Figure 2a-b. Illustration of the solar wind velocity vector fluctuations. The average value of the radial component has been subtracted from the Vx time series, in order to sense better the Vx variations. The projection of the V vector to the (x, z) and (x, y) are also shown to denote the turnings of the Vs~o vector.

These fine-scale features, which were observed in the past but were erroneous- ly thought of 'thick' sector boundaries, also determine the spatial and temporal dependance of the orientation of the sector boundaries.

References

Bavassano, B. and Bruno, R.: 1989, J. Geophys. Res. 94, 168. Behannon, K. W. and Burlaga, L. F.: 1983, J. Geophys. Res. 88, 7837. Behannon, K. W., Neubauer, F. M., and Barnstorf, H.: 1981, J. Geophys. Res. 86, 3273. Behannon, K. W., Burlaga, L. F., Hoeksema, J. T., and Klein, L. W.: 1989, J. Geophys. Res. 94, 1245. Burlaga, L. F.: 1990, 3. Geophys. Res. 95, 4333. Burlaga, L. F., Lemaire, J. F., and Turner, J. M.: 1977, J. Geophys. Res. 82, 3191. Chandrasekhar, S.: 1961, Hydrodynamic and Hydromagnetic Stability, Dover Publ., New York. Geranios, A.: 1982, Astrophys. Space Sci. 81, 103. Geranios, A.: 1987, Planetary Space Sci. 35, 722.


Hoeksema, J. T.: 1989, Adv. Space Res. 9, 4141. Hoeksema, J. T.: 1991, in E. Marsch and R. Schwenn (eds.), 'Large-Scale Structure of the Heliospheric

Magnetic Field: 1976-1991', Solar WindSeven, p. 191. Hoeksema, J. T., Wilcox, J. M., and Scherrer, P. H.: 1983, J. Geophys. Res. 88, 9910. Klein, L. and Burlaga, L. F.: 1980, J. Geophys. Res. 85, 2269. Landau, L. D. and Lifschitz, E. M.: 1959, Electrodynamics of Continuous Media, Addison-Wesley,

London. Moussas, X. and Tritakis, B.: 1982, SolarPhys. 75, 361. Moussas, X., Polygiannakis, J. M., Kakouris, A., and Alevizos A.: 1996, Solar Phys., submitted. Olmsted, C. and Akasofu, S. I.: 1986, J. Geophys. Res. 91, 13689. Politano, H., Pouquet, A., and Sulem, P. L.: 1995, Plasma Physics, in press. Polygiannakis, J. M. and Moussas, X.: 1996, Solar Phys. 166, 423. Rosenberg, R. L. and Coleman, P. J.: 1969, J. Geophys. Res. 74, 5611. Sharma, A. C. and Srivastava, K. M.: 1992, J. Geophys. Res. 97, 1294. Smith, E. J., Tsurutani, B. T., and Rosenberg, R. L.: 1978, J. Geophys. Res. 83, 717. Thomas, B. T. and Smith, E. J.: 1981, J. Geophys. Res. 86, 11105. Villante, U., Bruno, R., Mariani, F., Burlaga, L. F., and Ness, N. E: 1979, J. Geophys. Res. 84, 6641. Wilcox, J. M. and Ness, N. E: 1965, J. Geophys. Res. 70, 5793.

vortices near the wavy heliospheric current sheet

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