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An investigation of the heliospheric current sheet (HCS) structure
PIonet. Spuc@ Sci., Vol. 36, No. 2, pp. 105 115, 1988 Printed in Great Britain.
0032-C~i33/88 $3.00+0.00 Peqamon Press
pit
AN INVESTIGATION OF THE HELIOSPHERIC CURRENT SHEET (HCS) STRUCTURE V. G. ESELEVICH and M. A. FILIPPOV SibIZMIR, Irkutsk 33, P.O. Box 4,664033 U.S.S.R.
(Received 5 January 1987) Abstract-A study is made of the flow in the heliospheric current sheet (HCS) with velocities ranging from 300 to 450 km s-‘. It is shown that plasma and the inte~lanetary magnetic field (IMF) in the HCS do not undergo, within the measurement errors, any appreciable compassion in the course of an interaction with high speed streams al R < 1 a.u., i.e. the HCS structure at the Earth’s orbit is determined mainly by the sheet’s parameters near the solar surface. It has been found that the increased value of the &-component in the HCS is attributable to two factors, namely the increased values of IBI in the sheet and the rotation of vector B in the plane of a sheet inclined to the-ecliptic plane.
1. INTRODUCTION
That there exist two classes of quasi-stationary (i.e. averaged over different sporadic processes such as flares, jets, oscillations, etc.) solar wind streams might be considered a well-established fact to date. These are high speed streams with velocities v N 450-800 km s’, on the one hand, and a slow wind with v N 30s 450 km s-‘, on the other. Here u is the averaged, maximum velocity in the central part of the stream. A source for fast streams is provided by coronal holes (Krieger et aI., 1973 ; Nolte et al., 1976; Sheeley et al., 1976; Hundhausen, 1977). Slow wind corresponds to flows in streamers or, accordingly, in the heliospheric current sheet (HCS) (Svalgaard et al., 1974 ; Korzhov, 1977 ; Gosling et al., 1981 ; Borrini et al., 1981 ; Feldman et al., 1981). These streams, whose formation terminates essentially already at R 6 20 R,, are characteristically different in a number of features as follows. Fast screens from coronal holes provide a flow along the magnetic field (at R < 20 R,) of a collisionless (the free path I > L, the size of the inhomogeneity) plasma with /3 = nT/(13*/87~) < 1; such flows have a significant angular size, Arp N 30”-100”. Slow streams are flowing across the magnetic field of a quasi-collisional (J. 4 L) plasma with fi > 1 within a narrow sheet with angular size Acp 6 10”. A consistent MHD theory of fast streams outflowing from coronal holes was developed in Hollweg (1978) on the basis of earlier theoretical studies along this vein (Parker, 1958, 1963 ; Hartle and Barnes, 1970). As well as being in fairly good agreement with experiments, Hollweg’s (1978) theory assumes that the main contribution to plasma acceleration is made 105
by a stream of Alfvkn waves ; observational evidence lends support to this inference (Withbroe et al., 1982, 1985). Eselevich and Filippov (1986) showed, however, that the influence of thermal pressure forces and superradial divergence, f, of magnetic field lines upon wind velocity at R < 3 R, may be comparable with the effect of AIf& waves and may be dominant, on occasions. A promising approach as regards constructing a solar wind model was developed by Ponomarev (1957). It makes it possible not only to calculate the solar wind characteristics with given boundary conditions but also to infer the boundary parameters themselves in the lower corona under rather general assumptions about its heating mechanism. Known collisionless models of solar wind (Aarnodt and Case, 1962; Eviatar and Schulz, 1970; Lemaire and Scherrer, 1971) are still of a fragmentary character and cannot be used in the compa~son with observations. The situation takes a turn for the worse with slow wind flow theory. There is qualitative evidence reported by Parker (1958) that the plasma near the solar equator where the component & of the dipole magnetic field is minimum, has fi > 1 and will, therefore, outflow from the solar surface along the ecliptic plane in a narrow neutral sheet of thickness 6, thus carrying along the magnetic field lines. South- and northward of the ecliptic plane the magnetic field is directed in opposite directions and its reversal occurs on a scale 5. More rigorous calculations on computers confirmed the possibility of formation of such a neutral sheet in the ecliptic plane (Pneuman and Kopp, 1971), while estimates showed that its thickness 6 is determined by plasma conductivity (Pneuman, 1971).
V. G. ESELEVICH and
106
Observational data which have largely confirmed the qualitative picture of the slow wind as suggested by Parker have revealed a number of essential differences as well. For example, near solar minimum the HCS in which a slow wind is flowing looks like a plane, wave-like “skirt” of thickness A << R, which periodically intersects the ecliptic plane near the solar surface at an angle Bos< 15” (Korzhov, 1982). The HCS occupies the medium at large distances, while at Earth orbit HCS intersections with the ecliptic plane form slow wind parcels. Inside these parcels there occurs magnetic field reversal, with an increased plasma density and with decreased proton temperature and decreased content of admixture ions He’+ with respect to H+ ions (Feldman et al., 1981 ; Gosling et al., 1981). Unlike theoretical predictions, the observed width of the HCS is A >> 6 (A will be defined in Section 2). HCS regions observed at the Earth’s orbit generate, while interacting with the magnetosphere, the strongest disturbances in it (Ponomarev, 1957; Ivanov and Mikerina, 1970; Bobrov, 1973 ; Burlaga, 1975). Therefore, questions related to HCS study are important for predicting magnetospheric disturbances. As the HCS slow wind propagates in interplanetary space as far as the Earth’s orbit, it undergoes collisions with fast plasma streams outflowing from coronal holes, and this, according to earlier work (Ivanov, 1968 ; Matsuda and Sakurai, 1972 ; Burlaga, 1974 ; Hundhausen and Burlaga, 1975) can lead to plasma compression in the HCS and a strong transformation of its structure as it moves to the Earth. However, more recent findings indicate that the situation is the opposite, i.e. the HCS structure due to the interaction with fast streams would not change significantly up to the Earth’s orbit (Gosling et al., 1981; Feldman et al., 1981 ; Borrini, 1981). The purpose of this paper is to study the HCS with an emphasis on the following points. (i) The distribution of plasma parameters inside the HCS and its angular width A”. (ii) HCS characteristics at different distances from the Sun to the Earth’s orbit. (iii) The structure of the HCS magnetic field at the Earth’s orbit and discussion of its nature.
2. HELIOSPHERIC
CURRENT
CHARACTERISTICS Despite spheric
the
current
diversity sheet
SHEET @ICS) AND ITS
INSIDE THE EARTH’S of
structures
of
ORBIT the
helio-
(HCS) observed at the Earth’s orbit, it is possible to distinguish six general salient features which characterize the distribution of the parameters inside the HCS, as follows.
M.
A.
FILIPPOV
“p I
(a)
I
I
(b)
FIG. 1. A SCHEME OF TIME DEPENDENCE OF THE QUASISTATIONARY PARAMETERS OF PLASMA AND THE IMF INSIDE THE HCS (SLOW WIND) AT THE EARTH'S ORBIT, OF FRONTRELATED VELOCITY PROFILE (a) OF THE HIGH SPEED STREAM: (~~IMFMODULI~,(C~PLASMADENSITY, (d)-IMF B,-COMPONENT,AND(~~PR~TONTEMPERAT~RE Tp.
(i) The presence of a density maximum nmax and a magnetic field strength maximum, B,,,,,, which exceed the time-averaged values of nmin and Bmin in the “plateau” region of the velocity distribution of the subsequent (in Figs lb, c to the right of the sheet, with respect to time) high speed stream, respectively, by factors of 5-10 for density and 2 or 3 for magnetic field. (ii) A reversal, before n = nmax, of the direction of the BJB,) (Fig. Id) and B,(B,) components of field and the presence of a maximum of lB1 (Fig. 1b) and B,(B,). (The B,, B, and B, components between brackets on spherical coordinates near the Sun cor-
Investigation of HCS structure respond to Cartesian components B,, B,, and LIZat the Earth’s orbit.) (iii) In the general case there is some time lead (and some space lead) of nmax with respect to B,,,,, (Figs lb, c). (iv) The comparatively small solar wind velocities near n = nmax,v N 30@-450 km s-i (Figs la, c). (v) An appreciable value of azimuthal velocity, in the direction of solar rotation, of the stream parcel in the vicinity of point n = nmau, v, = l&100 km s-’ which significantly exceeds v, N_l-2 km s-l in the stream (Siscoe, 1972). (vi) The presence near n,,, of the minimum of the fraction of admixture ions He’+/He+ [min AfHe)], and of the minims of the difference of velocities v, - up of a-particles and protons and the ratio of their temperatures Tz/Tp(Gosling et al., 1981; Feldman et al., 1981). Note that point B,,, of the HCS at the Earth’s orbit is recorded simultaneously with or somewhat earlier than the mean point (A) of the velocity front of the nearest, subsequent stream. This implies that the notion of the HCS involves so called “non-compressive density enhancements” (NCDEs) where the wind velocity does not increase (Gosling et al., 1977) and density enhancements associated with an increase of wind velocity (corresponding in time to the velocity front of the streams, see Figs la, c). In addition to HCS characteristics introduced earlier in Gosling et al. (1981), Feldman et al. (1981) and Borrini et al. (198 l), the characteristics mentioned above involve an IMF modulus whose maximum, as will be shown below, is an important property of the HCS. Let us introduce the notion of HCS width in two different ways, as follows. A, = AS, * v, is the HCS width which is determined from the time width At, of the density profile at height %&I+ f (%,X -n&,) (where v, is the a~muthal rate of solar rotation at R = 215 R,, and n&, is an averaged value of n of the sheet-preceding stream during the next 24 h, in Fig. lc to the left of the sheet). AB = At,* V~is the HCS width which is determined from the time scale of the profile ]B] at height B,,,+ f(&an-%i,) (Fig. lb). Note also that Burlaga er al. (1977) and Klein and Burlaga (1980) investigated the sector boundaries
corresponds to the smallest value of Tpin the current * T*“,m sheet and TpWX corresponds to the largest value of Tpoutside the sheet which is time-coincident with the inflection point of the streamer velocity profiIe at the end of the front (Figs la, e).
107
which characterize the scale 6 = z - u* (see Fig. id) of the change of sign of the B, (or BY) component of field. In the case of the HCS the sector boundary, while lying inside the sheet near n = pt,,,, has a scale S < An, A8 (Figs 1b, c, d). From this it follows that the HCS is a separation boundary between high speed streams (zI,,, -N 45&800 km s-‘) which carry magnetic fields of opposite polarity. In the ecliptic plane the HCS, as the magnetic field lines of the streams, lines up with the Archimedean spiral (Klein and Burlaga, 1980) (see also Section 1). Therefore, the plasma at the front of high speed streams which move radially is capable of overtaking and interacting with, at R > 20 R,, the HCS plasma, the radial velocity of which is below v N 30&450 km s-r. Hence, there exists, as pointed out above, an alternative cause of the observed HCS structure as a compression region of plasma and magnetic field : either a compression in the sheet is caused by fast plasma streams which overtake it at 20 R, < R < 215 R, from the Sun (Ivanov, 1968 ; Ivanov and Mikerina, 1970 ; Matsuda and Sakurai, 1972 ; Burlaga, 1974 ; Hundhausen and Burlaga, 1975) or such a structure is formed mainly near the solar surface (Gosling et ai., 1981 ; Feldman ef al., 1981 ; Borrini et al., 1981). In order to provide an answer to this question, expe~mental plots of ~~~~jn~i~, B,,,IB~i, and T_,/Tmi, (see Figs 2, 3 and 4)* vs R (For R --c215 R,) were constructed using Hellos 1 and 2 measurements (Burlaga et al., 1978; Marsch et al., 1982) and from data in a catalogue (King, 1979) at 1 a.u. sampled in Table 1. The table gives, for each stream identified and for a given solar rotation, data at R = 1 a.u. (King, 1979) and from the range of distances 0.3 a.u. < R G 0.8 a.u., which significantly improves the validity of the plots. Exceptions to this are data denoted by an asterisk which were taken for the stream identified and for two neighbou~ng rotations of the Sun (in other words, every other rotation). Values of ~~~~1~~~~ at R = 1.5 R, and R = 4 R, in Fig. 2 were obtained from K-corona observations in 1972 (Howard et al., 1976) to be the ratio of emission brightness in the streamer region to that in the central part of a polar coronal hole. Relevant dates of nearEarth observations were estimated as rE = t,+ At where At = 11 days is the time delay which is determined by the travelling time of the coronal structure observed on the limb before it intersects the central meridian (one-fourth of a solar rotation c?r7 days) and by the solar wind transport time (N 4 days for HCS plasma). Points 0 shown in Fig. 2 correspond, respectively, to 22 January, 15 May and 4 November
ESELFVICHand M.
V. G.
A. FILIPPOV
FIG. 2.THE
DEPENDENCEONDISTANCE R TOTHE ~UNOFTHERATIOOFDENSITYMAXIMUMfl,,INTHE HCS TO ?rmin, THEAvF.RAGED VALLI OFn DURINCiTIiFFORTHCOMING 24 h IN THESTRRAhI FOLLOWING THESHEET. +--From K-corona observations (Howard et al., 1976) for 1971-1972. O-From K-corona observations (Howard et al., 1976) and a catalogue (King, 1977) for 1972. + and @-From Hellos 1 and 2 data (Burlaga et al., 1978; Marsch et al., 1982) and a catalogue (King, 1979), respectively, for 1975 and 1976 ()rn~~~~ent error).
I
J *E
r
loo
4
+Tl
--_--_-_+ +-+ +------_-_____*~~
2
c---_-.“--
i
1
50
+____“-
e=,‘,-=
---
j_
-x_
-
I
I
150
loo
I
I
I au
200
R % FIG. 3. THE DEPENDENCE ON DISTANCER FROM THE Sus OF THE RATi OF IMF MAXIMUMIN ITIF HCS, B,,, TO TIIF OSCILLATION-AVERAGED VALUE OF &, IN A SUBseQUENT ROTATION FROMHelios I AND 2 DATA (BURLAGAet al., 1978 ; MAWCHet af., 1982) AND A CATALOWE (KING, 19%) MR 1975. Dotscorrespond to the points marked every other rotation because of the lack of data (#-measurement error).
1972 near the Sun and to 2 February, 26 May and 15 November 1972 at 1 a.u. From these representations it follows that the value of r~~~~/rr,,,~,, within the error indicated in the form of a spread to the right in the figure changes little as the current sheet plasma travels as far as the Earth’s orbit and is, in effect, determined by the value of n,,, /nmin near the solar surface which, as follows from K-corona data for 1971-1972 (designated as e in Fig. 2) may assume values in the range from N 2 to z 10. For points * in Fig. 2, respective data at the Earth’s orbit are missing. However, amex/nminin the range 210 are also observed at the Earth’s orbit for some other years (for example, + corresponds to 1975 and @ to 1976 in Fig. 2). In this case, within R = 60-215
1
50
+I 100
I I50
m
,
l0.u.
200 t
-_
R.9
FIG. 4.Tns DEP~D~N~ON ~~STANCE~~OM WE SUNOF THE RATlO OF M.4XIMUh.l PROTONTRMPERATURF TpwxOUTSIUE THI?HCS WHOSR POSITIONROUGHLYCOINCIDFSWITH THF INFZECTlON POINT ON THE VELOCITY PROFILE OF THE HIGH SPEEDSTRRAM (SEEFIGS la, b) TO Tmin,AMINIMUMVALUEOF Tp IN THE HCS FROM Heiios i AND 2 DATA (BURLAGA et at., 1978; MARSCH et ai., 1982)AND A CATAUXXJE (KING, 1979) FOR 1975 (+) and 1976 (83).
Dots correspond to the points marked every other rotation because of the lack of data (+-measurement error). Ro, where the strongest interaction between highspeed streams and current sheet plasma must be occurring, the value of h,,/n,i, which is different for different HCS remains virtually unaltered (+ and @ in Fig. 2). A similar situation applies to the magnetic field .Bma,/Bm, and relative proton temperature TPWIT*& 9 which within the error indicated in the figure do not increase, at least, with distance from the Sun (Figs 3 and 4). Hence it follows that since in the streams values of Bminand h, vary nearly as R - ’ ffor B(R) see also Burlaga et al., 19781, this regularity also applies to the values of B,,, and PZ,,, in the HCS.
109
Investigation of HCS structure TABLE 1. CURRENTSHEETINTERSECTIONSOESERVEDCONSECUTIVELYNEARTHESUNANDATTHE
No.
6 7 8
6 7 8
R
(lO’+K) Min
B Max
(nT) Min
17 29 30 57 56
7 12 15 26 36
Date/ day no.
(a.u.)
Mnax
Min
Max
1975 30.01/30 9.02/40 28.02/59 5.03164 13.03/72
0.78 0.68 0.44 0.37 0.31
30 45 40 70 350
6 8 14 25 35
50 60 40 60 70
1976 15.03175 20.03/80 24.03184
0.66 0.60 0.55
45 40 80
6 20 11
60 8 60
2 3.5 4
-
1975 1.02/32 10.02/41 28.02/59 5.03/64 7.04197
1.00 1.00 1.00 1.00 1.oo
25 27 10 10 35*
5 5 3.5 4 3.5*
45 35 24 16 40*
4 3.5 6 5 3*
10* 14 13* 8* 13*
1976 16.02146 23.03183 26.03186
1.oo 1.oo 1.oo
25* 14 50
3.5* 6 7
50* 6 40
2.5” 2 4
-
(cme3)
Tp
4 5 10 4 6
4* 5 6* 4* 6*
EARTH’SORBIT
Note
The IMF was measured on 1.03 The IMF was measured on 27.03 The IMF was measured on 5.02
-
*The values indicated have been taken every other rotation due to lack of data.
Thus, within the uncertainty of the plots in Figs 2, 3 and 4 which does not exceed +20%, the values of n max,R,,, and Tp,,, observed in the HCS at the Earth’s orbit are formed near the solar surface as streamers, rather than being due to compression of the sheet by approaching velocity streamers. A further test for correctness of this conclusion may be to compare the width A, of the HCS at the Earth’s orbit in angular units with the width A,, of the streamers at R N 3R, as well as to compare the time behaviour of the HCS widths A,, and AB at the Earth’s orbit (Figs 5a, b). The angular width of the HCS, A,,, at the Earth’s orbit was determined using a catalogue (King, 1977) as the time scale At, of the density profile (Fig. lc) and was then calculated by the formula : A, = At;cos$~13.3*sin0,
= 9.44*At,*sin0,8
(1)
because the spiral angle $ at the Earth’s orbit makes up 45”. The O,c-angle of inclination of the HCS plane to the ecliptic plane will be determined in Section 3 of this paper. Part of the values of BO,are given in Table 2. The angular width of the HCS, AB, was also determined by formula (l), where At, was replaced by Ata, the time width of the magnetic field profile B(t), see Fig. lb. (We employ here the result of Section 3 of this paper implying that the inclination of the vector
B to the ecliptic plane coincides with the angle 0,8 of the HCS inclination to it.) The angular width A,, of the streamers was determined from structural drawings of the corona (Vsekhsvyatsky et al., 1965; Nikolsky et al., 1977) as the angular distance between two boundary lines of the streamer at R 3 3 R, (the scheme of determination of A,, is given at the bottom left of Fig. Sa). Figure 5a presents the values of A, and A,, which were determined by the above-mentioned methods for the years for which the required initial data were available. From the data for 1973 it follows, for example, that the mean values of A,, and A,> are close to each other : A,, N 6.5” and A,, II 5.2”. It is also apparent from Fig. 5 that the value of A, undergoes, as time progresses, periodic variations by about factors of 2 or 3 (an exception being the end of 1973 when the increase of A,, is more than by a factor of 5). In this case the period of this variation approaches 1 year. It seems likely that the value of Ans also experiences a similar periodic variation. At least, the magnitude and amplitude of A,,, variations for 195&1970 are both close to the observed values of A,, during the time interval 197&1976. The period of An8variation eludes determination due to lack of more detailed data. The magnetic angular width of the sheet, AB, exceeds by factors of 2 to 5 the A,, ; however, the
V. G. ESELEVICH and M. A. FILIP~OV
110
TABLE2. INCLINATION ANGLESOF THECURRENTSHEET TO EARTH’SORBITDURING Q0 (deg.)
60 (deg.)
Date
Type of transition
at the Sun
at the Earth
1972 10.02 18.02 67.03 15-16.03 34.04 10.04 8-9.05 28-29.05 8-9.10 13.12
R T T T R T T T T T
29 57 72 44 45 36 27 35 24 38
+55 +65 +80 -85 i-62 +60 -75 +80 +65 -90
1973 6.03 19.03 1.04 28.04 27.05 10.06 56.08 20.08 12.09 15.09 27-28.10 13.11 19.12 27-28.12
ECLIPTICPLANENEARTHESUN AND AT THE 1972-1978
THE
T T T T R T T T R T T T T T
64 50 34 54 70 42 8 26 31 39 30 36 17 54
T.-_--__.-
T /*
,I
,I
1950
1960
Date
Type of transition
at the Sun
at the Earth
50 45 30 50 40 59 65 50 26
-70 -80 -33 -42 -55 -66 -80 -77 -50
T T T T
47 45 40 32
-55 +72 -70 +70
T T T T
28 15 14 15
-65 *45 -70 +45
1977 4.11
R
32
+45
1978 2425.08 9-10.09
R R
75 66
-52 -78
1974 25-25.01 30.05 25.06 338.07 22-23.07 2.08 29.08 12-13.10 7.12 1975 7.02 1.08 20.08 16.09
-80 k65 -80 +60 -77 +70 f60 f35 +54 f45 *90 -47 -65 k60
1976 16.08 14.09 25.09 1l-12.10 /
.-- JIE 1 I
197c (b)
;:
Year
:
’ 4 ’, m’E 3 : I a *+I : .++ : I \ ;+ \ a -+\ \+ : +‘,+ +‘-+ + ++ -_ + 0 1973
+ + tF’ 0+‘, ++/ ,$ I + ; f ++ : +4 I
1975
Year FIG. 5. THE TIMEVARIATION OF TYPICALANGULARWIDTHS A. (a) ANDAB (b) OF THEHCS AT THEEARTH’S ORBITASOBTAINED BY FORMULA (1) USINGA CATALOGUE (KING, 1977). +-mean angular thicknesses of the streamers, An, at distance R - 3 R, as determined from structural drawings of the corona (the scheme of determination of A_, is shown at the bottom of the figure, at the left).
Investigation of HCS structure period of its variation coincides with the periodicity of A, (Fig. 5b). This lends further support to the fact that both A,, and AB are different characteristics of the same object, the HCS. To conclude this section, we want to note that whenever HCS interaction with a fast stream does not lead to any appreciable compression of the plasma in the sheet, their collision must result in momentum transfer from the stream to the HCS and, in particular, to transfer of the azimuthal component of momentum. This inference is shown by data, according to which the azimuthal rate of rotation in the W-E direction of point nmax inside the sheet can amount at the Earth’s orbit to values of u, - l&100 km s-’ (Siscoe, 1972), i.e. one or two orders of magnitude in excess of a, N l-2 km ss’ inside the streams.
3. MAGNETIC FIELD STRUCTURE OF THE HELIOSPHERIC
CURRENT SHEET
In order to investigate the magnetic field structure inside the sheet, the method of 8-q diagrams was employed. The method is to indicate on a plot hourly values of 6’ and rp from catalogues (King, 1977, 1979, 1983) for the entire time interval during which the sheet traverses the observation point, also including 1 or 2 days before and after that event. In this case, as the analysis shows, if the extreme point of vector B in space rotates with respect to a certain centre remaining in the same plane, then the 0-cp diagram represents the intersection line of this plane with a fixed-radius sphere, whose centre coincides with the origin of vector B and with the origin of coordinates. The equation for the intersection line has the form : P -B
cosB,*sin@
= -sinO,.cos(cp--cp,).cosO.
Here p is the distance from the plane of rotation of vector B to the origin of coordinates, Ip/BI < 1, angle 0 is counted from the ecliptic plane, - 90” < 0 < 90”, and B0 and qpo characterize, respectively, the inclination of the plane of rotation to the ecliptic plane and the position of the normal projected onto the ecliptic plane where the normal is to the plane of rotation. The method described above was applied in the study of HCS structure at the Earth’s orbit for the time interval 1971-1978 for which we know : first, the HCS configuration near the solar surface (R 2 3 R,) *The transition in the HCS cannot be called a “discontinuity” because it does not satisfy the whole set of requirements and Lifshitz,
that characterize 1959).
the discontinuity
(Landau
111
obtained from white-light corona emission (Korzhov, 1982) and, second, the hourly values of angles 0 and cp at the Earth’s orbit (King, 1977, 1979, 1983) which allow determination of the main structural properties of the HCS mentioned in Section 1. In this case we have excluded from our consideration the events showing a very rapid change of sign of B (or when it occurs within t < 1 h). Thus, the method of 0-q diagrams was utilized in the analysis of 44 HCSs. The analysis revealed that during the movement through the HCS from the appropriate preceding to the subsequent stream a 180” reversal of the magnetic field vector takes place in the form of two different kinds of transitions,* as follows. 1. Rotational transition (P # 0). This implies that, as the current sheet is being traversed, the end of the magnetic field vector B suffers rotation in a plane which makes an angle BO,with the ecliptic plane and the origin of vector B is at a distance P from this plane. 2. Tangential transition (P = 0). This is a particular case of the rotational transition when P = 0 in which vector B lies, as a whole, in the plane of rotation which makes an angle BO,with the ecliptic plane. Examples of a rotational and a tangential transition are shown, respectively, in Figs 6a and 6b. It is interesting to note that in a region of the sheet of width AB experimental points of the &cp diagram with a typical absolute spread A@, Acp N f25” fit the calculated 8-q curves (solid lines in Fig. 6), whereas outside the sheet on both sides of it, the points with the same typical absolute spread A0, Acp N f25” are arranged in a random fashion near points cp,, = 135”, O0 = 0” and cpO= 315”, B0 = O”, and this indicates that outside the sheet there is not any fixed plane of rotation of vector B. As is evident in Table 2, out of 44 events of the HCS being studied, 11 correspond to rotational transitions and 33 correspond to tangential transitions. Table 2 gives the values of the BOXand B,,, angles of inclination of the current sheet to the ecliptic plane, respectively, at R 2 3R, determined from data reported by Korzhov (1982) and at R = 215 R, obtained by the method of 8-q diagrams. From the plot of BO,vs f3,s (Table 2) it is seen that as one moves away from the Sun, the angle of inclination of the HCS to the ecliptic plane increases. Also, as regression analysis shows, the rate of increase is close to B,,, = BO,+ 17”. The great spread of the averaged experimental points indicates the existence of one or several parameters we are not yet aware of, which have a marked influence upon the relation between the quantities B,,, and QO,. In summarizing the aforesaid, we want to note that the presence in the current sheet of:
V. G. E~ELEVICHand M. A. FILIPWV
112
60 -
0.6 -
FIG. 7. THE DEPENDENCE OFTHE MAXIMUM OFTHENORMALIZED IMF &-COMPONENTIN THEHCS ON THEINCLINATIONANGLE 19~. OF THE SHEET TO THE ECLIPTIC PLANE.
determined
by processes in the solar corona and do
not change
-30
substantially
the Sun and the Earth’s
provided
that their production
Sun are well understood,
-
(except,
between
perhaps, orbit.
mechanisms near the
4. DISCUSSION OF THE NATURE OF MAGNETIC FIELD STRUCTURE IN THE CURRENT SHEET For the sake of simplicity, we shall consider a current sheet which represents
increased magnitude of the magnetic field, and rotation
of the end of vector B or full vector in
the sheet’s plane making an angle B,,,with the ecliptic plane, provides
from solar disk
observations.
FIG. 6. EXAMPLESOFTHEa_cPDIAGRAMS INSIDETHEHCS (a), (C) AND OUTSIDE THE HCS (b) : (BFTANGENTIAL TRANSITION, (c)--R~~AII~NAL TRANSITION.
-a
0,)
these HCS characteristics at
the Earth’s orbit may be predicted -60 -
-the
for
Therefore,
a natural
explanation
of the fact that a
an infinite
thickness A and lies symmetrically
flat disk of
with respect to the
ecliptic plane (see Fig. 8a). We
assume, according
model, that the formation
to Parker’s
(1958,
1963)
of the sheet is due to plasma
outflow
from the solar surface where the field com-
ponent
B, perpendicular to the flow direction is mini-
of field is recorded at
mal and fi > 1. As a result, the plasma flow while
the Earth’s orbit in the region of the sheet. This is also
carrying along the field lines makes them extend along
shown by the observed (despite the noticeable
spread
the radius so that sufficiently far from the Sun we have
of points) increase of the largest, normalized
values
B, >>Be (Pneuman,
maximum of the B,-component
of
B,/B inside the sheet from Bo, (Fig. 7).The approxi-
mate equality of the typical spreads of Afl and Acp for
established
points on B-cp diagrams inside and outside the sheet,
B = B, and -B.
as mentioned
occurs a continuous
above,
native explanation,
allows us to exclude an alter-
viz. the increased level of MHD
turbulence in the HCS as compared with the streams. From follows
the discussion in Sections that the main characteristics
2 and
3 it also
of the HCS are
such that Bm,,/Bmi”, nmax/nminand Tm,xITmi,, the rotation of the vector B in the sheet’s plane, the angle of inclination
/3,,of the sheet’s plane to the ecliptic
plane, and the angular width of the sheet A,, are all
1971). As a result, a magnetic
field distribution typical of a neutral sheet (Fig. 8b) is
at
; on the boundaries of the sheet we have between which, inside the sheet, there
B,(e)transition, with a reversal B = 0 on the sheet’s axis. Rotation of the Sun as a
whole will not modify such a distribution but will only add a Q-independent ponent of field, in elongation
value of the azimuthal
com-
B,(B)= constant, and this will result of the sheet along
the Archimedean
spiral (Klein and Burlaga, 1980). The situation may change abruptly
if differential
rotation of the Sun (i.e. dependence of the azimuthal
Investigation of HCS structure
113
(0)
8, (b)
-
t
(d)
ts
I
@
t
i
C
A
8
(f )
8
_-p. 4 [~-.
_.
IO
-0-I *a, Q .-.-0
e_ -a*
Fio.8. ASCHEME EXPLAINING
(e)
'Q
I 0
-
’ ?e
-
-4
--_
e,
T~~C~NISM~ORROTATIONOF~CTOR
B INSIDE
THE
HCS
ASA~O~~Q~NCE
(a) The Sun with the HCS of thickness ABsymmetric with respect to the equator. (b) The field distribution inside the HCS in the absence of differential rotation of the Sun. (c) The dependence on 0 of the azimuthal velocity of solar rotation vV at the base of the HCS on the solar surface between points A and C. (d) Bending (dots B) of the originally meridional field Be, due to the dependence u,(O) of type (c). (e) The azimuthal component of field along 0 which arises due to the dependence v,(O) of type (c). (f) The dependence on 0 inside the HCS of field B = B, +B,, which is obtained by vectorial summation of the (b) and (e) plots, (g) Rotation of vector B’ = B,+B, in the HCS plane rep.
velocity of rotation of the solar surface up on 8) is taken into account (Fig. 8~). Indeed, let the magnetic field on the solar surface in the main HCS be B = Booand let the ends of its field lines be frozen-in to the plasma at latitudes A and C, respectively, northand southward of the equator (Fig. 8d). The presence of a positive gradient of rotation velocity ug of the Sun from latitudes A and C equatorwards will cause the B,-component to bend in the direction of I)~with the largest deviation at the equator (Fig. Sd), and accordingly, will lead to the generation of the B,component of field, whose schematic distribution vs 0 is shown in Fig. 8e. The plasma with p > 1 that outflows from the solar surface along the equator, while carrying along the magnetic field, pulls in its wake the magnetic field lines along the radius ; as a result, sufficiently far from the Sun it appears that B, _ B, >>Be. (According to Pneuman, 1971,
3, N R- ‘, i.e. B, decreases with distance much more rapidly as compared with the B, and B, components.) Adding the B, (Fig. 8b) and BV (Fig. 8e) components gives a net vector B’ = B,+B, which experiences rotation in the HCS plane repby an angle of 180” (Figs 8f, g). In order to explain the similar rotation of vector B in the plane of an inclined sheet which intersects the ecliptic plane at an angle O,, it is necessary to assume in the vicinity of the inclined part of the current sheet the existence of a meridional, differential plasma motion with vg = f(p). 5. CONCLUSIONS (I) It has been shown that both the plasma and the magnetic field in the heliospheric current sheet (HCS) do not undergo any appreciable, additional
114
V. G. ESELEV~CH and M. A. FIL~PPOV
compression during an interaction with high speed streams everywhere at R < 215 R,. Therefore, the HCS structure at the Earth’s orbit is determined mainly by its properties near the solar surface. This is in agreement with findings reported by Gosling et al. (1981), Feldmanet al. (1981) and Borriniet al. (1981), obtained independently by the analysis of the fraction of admixture ions He’+/H+ in the solar wind. (2) The variation of magnetic field B inside the HCS implies a rotational or a tangential transition in which the ends of vector B or full vector B experience, as they move across the sheet, a rotation in the HCS plane making an angle 8, with the ecliptic plane. An analogous conclusion about the rotation of vector B was drawn by Klein and Burlaga (1980) in the analysis of the sector boundaries. (3) MHD turbulence cannot be responsible for the increased values of the IMF &-component in the HCS because the level of random MHD oscillations is nearly the same in both the sheet and the streams. (4) The increased value of the &-component in the HCS is accounted for by two factors : increased values of lB1in the sheet and rotation of vector B (or its end) in the plane of the sheet inclined to the ecliptic plane at angle 8,. (5) A likely reason for the rotation of vector B inside the HCS is the differential rotation of the Sun.
REFERENCES Aamodt, R. E. and Case, K. M. (1962) Density in a simple model of the exosphere. Physics Flui& 5, 1019. Bobrov, M. S. (1973) K,-index correlations with solar wind parameters during the first and second stages of a recurrent geomagnetic storm. Planet. Space Sci. 21, 2139. Borrini, G., Gosling, J. T., Bame, S. J., Feldman, W. C. and Wilcox, J. M. (1981) Solar wind helium and hydrogen structure near the heliospheric current sheet : a signal of coronal streamers at I AU. J. geoplbys. Res. 86,4565. Burlaga, L. F. (1974) Interplanetary stream interfaces. J. qeo&ys. Rex 782028. Buriaga; L. F. (1975) Interplanetary streams and their interaction with the Earth. &ace Sci. Rev. 17.327. Burlaga, L. F., Lemaire,‘J. F. and Turner, J. M. (1977) Interplanetary current sheets at 1AU. J. geophys. Res. 82, 3191. Burlaga, L. F., Ness, N. F., Mariani, F., Bavassano, B., Villante, U., Rosenbauer, H., Schwenn, R. and Harvey, J. (1978) Magnetic fields and flows between 0.3 and 1 AU during the primary mission of Helios 1. J. geophys. Res. 83, 5167. Eselevich, V. G. and Filippov, M. A. (1986) Study of the mechanism for solar wind formation. Planet. &ace Sci. 34,1119. Eviatar, A. and Schulz, M. (1970) Ion-temperature anisotropies and the structure of the solar wind. Planet. Space Sci. 18, 321. Feldman, W. C., Asbridge, J. R., Bame, S. J., Fenimore, E. E. and Gosling, J. T. (1981) The solar origin of solar wind
interstream flows : near~uatori~ coronal streamers, J. geaphys. Res. 86,540X. Gosling, J. T., Borrini, G., Asbridge, J. R., Bame, S. J., Feldman, W. C. and Hansen, R. T. (1981) Coronal streamers in the solar wind at 1 AU. J. geaphys. Res. 86, 5438. Gosling, J. T., Hildner, E., Asbridge, J. R., Bame, S. J. and Feldman, W. C. (1977) Noncomuressive densitv enhancements in the solar wind. J. geopiys. Res. 82, SO&. Hartle, R. E. and Barnes, A. (1970) Nonthermal heating in the two-fluid solar wind model. J. geophys. Res. 75, 6915. Hollweg, J. V. (1978) Some physical processes in the solar wind. Rev. Geophys. Space Phys. 16,689. Howard, R. A., Koomen, M. J., Michels, D. J., Tousev, R., Detwiler, C. R., Roberts, D. E., Seal, R. T,, Wh&ney, J. D., Hansen, R. T.. Hansen. S. F.. Garcia. C. J. and Yasukawa, E. (1976).Synopti~ observations of the solar corona during Carrington rotations 15&J-1596. Report UAG-48A, p. 160. NOAA, Boulder, CO. Hundhausen, A. J. (1977) An interplanetary view of coronal holes, in Coronal Holes and High Speed Solar Wind Streams (Edited by Zirker, J.), p. 225. Colorado Assoc. Univ. Press, Boulder, CO. Hundhausen, A. J. and Burlaga, L. F. (1975) A model for the origin of solar wind stream interfaces. J. geophys. Res. 80, 1845. Ivanov, K. G. (1968) Deformation as the cause for largescale variations of the magnetic field in interplanetary plasma streams. Geomagn. Aeronomiya 8, 1098. Ivanov, K. G. and Mikerina, N. V. (1970) Solar wind deformation velocity, large-scale variations of magnetic fieId and &-index of magnetic activity. Geomagn. Aeronomiya 10,417.
King, J. H. (1977) Interplanetary tedium Data Book. NASA, Greenbelt, Maryland. King, J. H. (1979) Interplanetary Medium Data Baok, Supplement 1. NASA, Greenbelt, Maryland. King, J. H. (1983) Interplanetary Medium Data Book, SuupLment 2. NASA, Greenbelt,Maryland. Klein. L. and Burlasa, L. F. (1980) Intemlanetarv sector boundaries 1971-1973. J. geobhys.‘Res. Sk, 2269.. Korzhov, N. P. (1977) Large-scale three-dimensional structure of the interplanetary magnetic field. Solar Phys. 55, 505. Korzhov, N. P. (1982) Maps of polarities of the large-scale magnetic field of the Sun and the interplanetary current sheet ~on~guration during 197llI978. Preprint SibIZMIR 2-82, Irkutsk, U.S.S.R. Krieger, A. S., Timothy, A. F. and Roelof, E. C. (1973) A coronal hole and its identification as the source of a high velocity solar wind stream. Solar Phys. 29, 505. Landau, L. D. and Lifshitz, E. M. (1959) Electrodynamics of Continuous Media. Izd. FML, Moscow. Lemaire, J. and Scherrer, M. (1971) Kinetic models of the solar wind. J. geophys. Res. 76, 7479. Marsch, E., Miihlhluser, K. H., Schwenn, R., Rosenbauer, H., Pilipp, W. and Neubauer, F. M. (1982) Solar wind protons : three-dimensional velocity distribution and derived plasma parameters measured between 0.3 and 1 AU. J. geophys. Res. 87,52. Matsuda, T. and Sakurai, T. (1972) Dynamics of the azimuthally dependent solar wind. Cosmic Electrodyn. 3,97. Nikolsky, G. M., Sazanov, A. A. and Kishonkov, A. K. (1977) The polarization of the inner solar corona at the eclipse of 10 July 1972. Solar Phys. 53, 79. Nolte, J. T., Krieger, A. S., Timothy, A. F., Gold, R. E.,
Investigation of HCS structure Roelof, E. C., Vaiana, G., Lazarus, A. J., Sullivan, J. D. and McIntosh, P. S. (1976) Coronal holes as sources of solar wind. Solar Phys. 46, 303. Parker, E. N. (1958) Dynamics of the interplanetary gas and magnetic fields. Astrophys. J. 128,664. Parker, E. N. (1963) Interplanetary Dynamical Processes. Interscience, New York. Pneuman, G. W. (1971) On neutral sheets in the solar wind. Solar Phys. 23, 223.
Pneuman, G. W. and Kopp, R. A. (1971) Gas-magnetic field interactions in the solar corona. Solar Phys. 18,258. Ponomarev, E. A. (1957) Concerning the theory of the solar corona. Doctoral Thesis, Kiev. Sheeley, N. R., Jr., Harvey, J. W. and Feldman, W. C. (1976) Coronal holes, solar wind streams and recurrent geomagnetic disturban~s: 1973-1976. S&r Phys. 49, 271.
115
Siscoe, G. L. (1972) Structure and o~entations of solar wind interaction fronts : Pioneer 6. J. geophys. Res. 77,27. Svalgaard, L., Wilcox, 3. M. and Duvail, T. L. (1974) A model combining the polar and the sector structured polar magnetic fields. Solar Phys. 37, 157. Vsekhsvyatsky, S. K., Nikolsky, G. M., Ivanchuk, V. I., Nesmeyanovich, A. T., Ponomarev, E. A., Rubo, G. A. and Cherednichenko, V. 1. (1965) The Solar Corona and Corpuscular Emission in Interplanetary Space. Kiev Univ. Press, Kiev. Withbroe, G. L., Kohl, J. L., Weiser, H. and Munro, R. H. (1982) Probing of the solar wind acceleration region using spectroscopic techniques. Space Sci. Rev. 33, 17. Withbroe, G. L., Kohl, J. L., Weiser, H. and Munro, R. H. (1985) Coronal temperatures, heating and energy flow in a polar region of the Sun at solar maximum. ~strop~ys. J. 297,324.
0032-C~i33/88 $3.00+0.00 Peqamon Press
pit
AN INVESTIGATION OF THE HELIOSPHERIC CURRENT SHEET (HCS) STRUCTURE V. G. ESELEVICH and M. A. FILIPPOV SibIZMIR, Irkutsk 33, P.O. Box 4,664033 U.S.S.R.
(Received 5 January 1987) Abstract-A study is made of the flow in the heliospheric current sheet (HCS) with velocities ranging from 300 to 450 km s-‘. It is shown that plasma and the inte~lanetary magnetic field (IMF) in the HCS do not undergo, within the measurement errors, any appreciable compassion in the course of an interaction with high speed streams al R < 1 a.u., i.e. the HCS structure at the Earth’s orbit is determined mainly by the sheet’s parameters near the solar surface. It has been found that the increased value of the &-component in the HCS is attributable to two factors, namely the increased values of IBI in the sheet and the rotation of vector B in the plane of a sheet inclined to the-ecliptic plane.
1. INTRODUCTION
That there exist two classes of quasi-stationary (i.e. averaged over different sporadic processes such as flares, jets, oscillations, etc.) solar wind streams might be considered a well-established fact to date. These are high speed streams with velocities v N 450-800 km s’, on the one hand, and a slow wind with v N 30s 450 km s-‘, on the other. Here u is the averaged, maximum velocity in the central part of the stream. A source for fast streams is provided by coronal holes (Krieger et aI., 1973 ; Nolte et al., 1976; Sheeley et al., 1976; Hundhausen, 1977). Slow wind corresponds to flows in streamers or, accordingly, in the heliospheric current sheet (HCS) (Svalgaard et al., 1974 ; Korzhov, 1977 ; Gosling et al., 1981 ; Borrini et al., 1981 ; Feldman et al., 1981). These streams, whose formation terminates essentially already at R 6 20 R,, are characteristically different in a number of features as follows. Fast screens from coronal holes provide a flow along the magnetic field (at R < 20 R,) of a collisionless (the free path I > L, the size of the inhomogeneity) plasma with /3 = nT/(13*/87~) < 1; such flows have a significant angular size, Arp N 30”-100”. Slow streams are flowing across the magnetic field of a quasi-collisional (J. 4 L) plasma with fi > 1 within a narrow sheet with angular size Acp 6 10”. A consistent MHD theory of fast streams outflowing from coronal holes was developed in Hollweg (1978) on the basis of earlier theoretical studies along this vein (Parker, 1958, 1963 ; Hartle and Barnes, 1970). As well as being in fairly good agreement with experiments, Hollweg’s (1978) theory assumes that the main contribution to plasma acceleration is made 105
by a stream of Alfvkn waves ; observational evidence lends support to this inference (Withbroe et al., 1982, 1985). Eselevich and Filippov (1986) showed, however, that the influence of thermal pressure forces and superradial divergence, f, of magnetic field lines upon wind velocity at R < 3 R, may be comparable with the effect of AIf& waves and may be dominant, on occasions. A promising approach as regards constructing a solar wind model was developed by Ponomarev (1957). It makes it possible not only to calculate the solar wind characteristics with given boundary conditions but also to infer the boundary parameters themselves in the lower corona under rather general assumptions about its heating mechanism. Known collisionless models of solar wind (Aarnodt and Case, 1962; Eviatar and Schulz, 1970; Lemaire and Scherrer, 1971) are still of a fragmentary character and cannot be used in the compa~son with observations. The situation takes a turn for the worse with slow wind flow theory. There is qualitative evidence reported by Parker (1958) that the plasma near the solar equator where the component & of the dipole magnetic field is minimum, has fi > 1 and will, therefore, outflow from the solar surface along the ecliptic plane in a narrow neutral sheet of thickness 6, thus carrying along the magnetic field lines. South- and northward of the ecliptic plane the magnetic field is directed in opposite directions and its reversal occurs on a scale 5. More rigorous calculations on computers confirmed the possibility of formation of such a neutral sheet in the ecliptic plane (Pneuman and Kopp, 1971), while estimates showed that its thickness 6 is determined by plasma conductivity (Pneuman, 1971).
V. G. ESELEVICH and
106
Observational data which have largely confirmed the qualitative picture of the slow wind as suggested by Parker have revealed a number of essential differences as well. For example, near solar minimum the HCS in which a slow wind is flowing looks like a plane, wave-like “skirt” of thickness A << R, which periodically intersects the ecliptic plane near the solar surface at an angle Bos< 15” (Korzhov, 1982). The HCS occupies the medium at large distances, while at Earth orbit HCS intersections with the ecliptic plane form slow wind parcels. Inside these parcels there occurs magnetic field reversal, with an increased plasma density and with decreased proton temperature and decreased content of admixture ions He’+ with respect to H+ ions (Feldman et al., 1981 ; Gosling et al., 1981). Unlike theoretical predictions, the observed width of the HCS is A >> 6 (A will be defined in Section 2). HCS regions observed at the Earth’s orbit generate, while interacting with the magnetosphere, the strongest disturbances in it (Ponomarev, 1957; Ivanov and Mikerina, 1970; Bobrov, 1973 ; Burlaga, 1975). Therefore, questions related to HCS study are important for predicting magnetospheric disturbances. As the HCS slow wind propagates in interplanetary space as far as the Earth’s orbit, it undergoes collisions with fast plasma streams outflowing from coronal holes, and this, according to earlier work (Ivanov, 1968 ; Matsuda and Sakurai, 1972 ; Burlaga, 1974 ; Hundhausen and Burlaga, 1975) can lead to plasma compression in the HCS and a strong transformation of its structure as it moves to the Earth. However, more recent findings indicate that the situation is the opposite, i.e. the HCS structure due to the interaction with fast streams would not change significantly up to the Earth’s orbit (Gosling et al., 1981; Feldman et al., 1981 ; Borrini, 1981). The purpose of this paper is to study the HCS with an emphasis on the following points. (i) The distribution of plasma parameters inside the HCS and its angular width A”. (ii) HCS characteristics at different distances from the Sun to the Earth’s orbit. (iii) The structure of the HCS magnetic field at the Earth’s orbit and discussion of its nature.
2. HELIOSPHERIC
CURRENT
CHARACTERISTICS Despite spheric
the
current
diversity sheet
SHEET @ICS) AND ITS
INSIDE THE EARTH’S of
structures
of
ORBIT the
helio-
(HCS) observed at the Earth’s orbit, it is possible to distinguish six general salient features which characterize the distribution of the parameters inside the HCS, as follows.
M.
A.
FILIPPOV
“p I
(a)
I
I
(b)
FIG. 1. A SCHEME OF TIME DEPENDENCE OF THE QUASISTATIONARY PARAMETERS OF PLASMA AND THE IMF INSIDE THE HCS (SLOW WIND) AT THE EARTH'S ORBIT, OF FRONTRELATED VELOCITY PROFILE (a) OF THE HIGH SPEED STREAM: (~~IMFMODULI~,(C~PLASMADENSITY, (d)-IMF B,-COMPONENT,AND(~~PR~TONTEMPERAT~RE Tp.
(i) The presence of a density maximum nmax and a magnetic field strength maximum, B,,,,,, which exceed the time-averaged values of nmin and Bmin in the “plateau” region of the velocity distribution of the subsequent (in Figs lb, c to the right of the sheet, with respect to time) high speed stream, respectively, by factors of 5-10 for density and 2 or 3 for magnetic field. (ii) A reversal, before n = nmax, of the direction of the BJB,) (Fig. Id) and B,(B,) components of field and the presence of a maximum of lB1 (Fig. 1b) and B,(B,). (The B,, B, and B, components between brackets on spherical coordinates near the Sun cor-
Investigation of HCS structure respond to Cartesian components B,, B,, and LIZat the Earth’s orbit.) (iii) In the general case there is some time lead (and some space lead) of nmax with respect to B,,,,, (Figs lb, c). (iv) The comparatively small solar wind velocities near n = nmax,v N 30@-450 km s-i (Figs la, c). (v) An appreciable value of azimuthal velocity, in the direction of solar rotation, of the stream parcel in the vicinity of point n = nmau, v, = l&100 km s-’ which significantly exceeds v, N_l-2 km s-l in the stream (Siscoe, 1972). (vi) The presence near n,,, of the minimum of the fraction of admixture ions He’+/He+ [min AfHe)], and of the minims of the difference of velocities v, - up of a-particles and protons and the ratio of their temperatures Tz/Tp(Gosling et al., 1981; Feldman et al., 1981). Note that point B,,, of the HCS at the Earth’s orbit is recorded simultaneously with or somewhat earlier than the mean point (A) of the velocity front of the nearest, subsequent stream. This implies that the notion of the HCS involves so called “non-compressive density enhancements” (NCDEs) where the wind velocity does not increase (Gosling et al., 1977) and density enhancements associated with an increase of wind velocity (corresponding in time to the velocity front of the streams, see Figs la, c). In addition to HCS characteristics introduced earlier in Gosling et al. (1981), Feldman et al. (1981) and Borrini et al. (198 l), the characteristics mentioned above involve an IMF modulus whose maximum, as will be shown below, is an important property of the HCS. Let us introduce the notion of HCS width in two different ways, as follows. A, = AS, * v, is the HCS width which is determined from the time width At, of the density profile at height %&I+ f (%,X -n&,) (where v, is the a~muthal rate of solar rotation at R = 215 R,, and n&, is an averaged value of n of the sheet-preceding stream during the next 24 h, in Fig. lc to the left of the sheet). AB = At,* V~is the HCS width which is determined from the time scale of the profile ]B] at height B,,,+ f(&an-%i,) (Fig. lb). Note also that Burlaga er al. (1977) and Klein and Burlaga (1980) investigated the sector boundaries
corresponds to the smallest value of Tpin the current * T*“,m sheet and TpWX corresponds to the largest value of Tpoutside the sheet which is time-coincident with the inflection point of the streamer velocity profiIe at the end of the front (Figs la, e).
107
which characterize the scale 6 = z - u* (see Fig. id) of the change of sign of the B, (or BY) component of field. In the case of the HCS the sector boundary, while lying inside the sheet near n = pt,,,, has a scale S < An, A8 (Figs 1b, c, d). From this it follows that the HCS is a separation boundary between high speed streams (zI,,, -N 45&800 km s-‘) which carry magnetic fields of opposite polarity. In the ecliptic plane the HCS, as the magnetic field lines of the streams, lines up with the Archimedean spiral (Klein and Burlaga, 1980) (see also Section 1). Therefore, the plasma at the front of high speed streams which move radially is capable of overtaking and interacting with, at R > 20 R,, the HCS plasma, the radial velocity of which is below v N 30&450 km s-r. Hence, there exists, as pointed out above, an alternative cause of the observed HCS structure as a compression region of plasma and magnetic field : either a compression in the sheet is caused by fast plasma streams which overtake it at 20 R, < R < 215 R, from the Sun (Ivanov, 1968 ; Ivanov and Mikerina, 1970 ; Matsuda and Sakurai, 1972 ; Burlaga, 1974 ; Hundhausen and Burlaga, 1975) or such a structure is formed mainly near the solar surface (Gosling et ai., 1981 ; Feldman ef al., 1981 ; Borrini et al., 1981). In order to provide an answer to this question, expe~mental plots of ~~~~jn~i~, B,,,IB~i, and T_,/Tmi, (see Figs 2, 3 and 4)* vs R (For R --c215 R,) were constructed using Hellos 1 and 2 measurements (Burlaga et al., 1978; Marsch et al., 1982) and from data in a catalogue (King, 1979) at 1 a.u. sampled in Table 1. The table gives, for each stream identified and for a given solar rotation, data at R = 1 a.u. (King, 1979) and from the range of distances 0.3 a.u. < R G 0.8 a.u., which significantly improves the validity of the plots. Exceptions to this are data denoted by an asterisk which were taken for the stream identified and for two neighbou~ng rotations of the Sun (in other words, every other rotation). Values of ~~~~1~~~~ at R = 1.5 R, and R = 4 R, in Fig. 2 were obtained from K-corona observations in 1972 (Howard et al., 1976) to be the ratio of emission brightness in the streamer region to that in the central part of a polar coronal hole. Relevant dates of nearEarth observations were estimated as rE = t,+ At where At = 11 days is the time delay which is determined by the travelling time of the coronal structure observed on the limb before it intersects the central meridian (one-fourth of a solar rotation c?r7 days) and by the solar wind transport time (N 4 days for HCS plasma). Points 0 shown in Fig. 2 correspond, respectively, to 22 January, 15 May and 4 November
ESELFVICHand M.
V. G.
A. FILIPPOV
FIG. 2.THE
DEPENDENCEONDISTANCE R TOTHE ~UNOFTHERATIOOFDENSITYMAXIMUMfl,,INTHE HCS TO ?rmin, THEAvF.RAGED VALLI OFn DURINCiTIiFFORTHCOMING 24 h IN THESTRRAhI FOLLOWING THESHEET. +--From K-corona observations (Howard et al., 1976) for 1971-1972. O-From K-corona observations (Howard et al., 1976) and a catalogue (King, 1977) for 1972. + and @-From Hellos 1 and 2 data (Burlaga et al., 1978; Marsch et al., 1982) and a catalogue (King, 1979), respectively, for 1975 and 1976 ()rn~~~~ent error).
I
J *E
r
loo
4
+Tl
--_--_-_+ +-+ +------_-_____*~~
2
c---_-.“--
i
1
50
+____“-
e=,‘,-=
---
j_
-x_
-
I
I
150
loo
I
I
I au
200
R % FIG. 3. THE DEPENDENCE ON DISTANCER FROM THE Sus OF THE RATi OF IMF MAXIMUMIN ITIF HCS, B,,, TO TIIF OSCILLATION-AVERAGED VALUE OF &, IN A SUBseQUENT ROTATION FROMHelios I AND 2 DATA (BURLAGAet al., 1978 ; MAWCHet af., 1982) AND A CATALOWE (KING, 19%) MR 1975. Dotscorrespond to the points marked every other rotation because of the lack of data (#-measurement error).
1972 near the Sun and to 2 February, 26 May and 15 November 1972 at 1 a.u. From these representations it follows that the value of r~~~~/rr,,,~,, within the error indicated in the form of a spread to the right in the figure changes little as the current sheet plasma travels as far as the Earth’s orbit and is, in effect, determined by the value of n,,, /nmin near the solar surface which, as follows from K-corona data for 1971-1972 (designated as e in Fig. 2) may assume values in the range from N 2 to z 10. For points * in Fig. 2, respective data at the Earth’s orbit are missing. However, amex/nminin the range 210 are also observed at the Earth’s orbit for some other years (for example, + corresponds to 1975 and @ to 1976 in Fig. 2). In this case, within R = 60-215
1
50
+I 100
I I50
m
,
l0.u.
200 t
-_
R.9
FIG. 4.Tns DEP~D~N~ON ~~STANCE~~OM WE SUNOF THE RATlO OF M.4XIMUh.l PROTONTRMPERATURF TpwxOUTSIUE THI?HCS WHOSR POSITIONROUGHLYCOINCIDFSWITH THF INFZECTlON POINT ON THE VELOCITY PROFILE OF THE HIGH SPEEDSTRRAM (SEEFIGS la, b) TO Tmin,AMINIMUMVALUEOF Tp IN THE HCS FROM Heiios i AND 2 DATA (BURLAGA et at., 1978; MARSCH et ai., 1982)AND A CATAUXXJE (KING, 1979) FOR 1975 (+) and 1976 (83).
Dots correspond to the points marked every other rotation because of the lack of data (+-measurement error). Ro, where the strongest interaction between highspeed streams and current sheet plasma must be occurring, the value of h,,/n,i, which is different for different HCS remains virtually unaltered (+ and @ in Fig. 2). A similar situation applies to the magnetic field .Bma,/Bm, and relative proton temperature TPWIT*& 9 which within the error indicated in the figure do not increase, at least, with distance from the Sun (Figs 3 and 4). Hence it follows that since in the streams values of Bminand h, vary nearly as R - ’ ffor B(R) see also Burlaga et al., 19781, this regularity also applies to the values of B,,, and PZ,,, in the HCS.
109
Investigation of HCS structure TABLE 1. CURRENTSHEETINTERSECTIONSOESERVEDCONSECUTIVELYNEARTHESUNANDATTHE
No.
6 7 8
6 7 8
R
(lO’+K) Min
B Max
(nT) Min
17 29 30 57 56
7 12 15 26 36
Date/ day no.
(a.u.)
Mnax
Min
Max
1975 30.01/30 9.02/40 28.02/59 5.03164 13.03/72
0.78 0.68 0.44 0.37 0.31
30 45 40 70 350
6 8 14 25 35
50 60 40 60 70
1976 15.03175 20.03/80 24.03184
0.66 0.60 0.55
45 40 80
6 20 11
60 8 60
2 3.5 4
-
1975 1.02/32 10.02/41 28.02/59 5.03/64 7.04197
1.00 1.00 1.00 1.00 1.oo
25 27 10 10 35*
5 5 3.5 4 3.5*
45 35 24 16 40*
4 3.5 6 5 3*
10* 14 13* 8* 13*
1976 16.02146 23.03183 26.03186
1.oo 1.oo 1.oo
25* 14 50
3.5* 6 7
50* 6 40
2.5” 2 4
-
(cme3)
Tp
4 5 10 4 6
4* 5 6* 4* 6*
EARTH’SORBIT
Note
The IMF was measured on 1.03 The IMF was measured on 27.03 The IMF was measured on 5.02
-
*The values indicated have been taken every other rotation due to lack of data.
Thus, within the uncertainty of the plots in Figs 2, 3 and 4 which does not exceed +20%, the values of n max,R,,, and Tp,,, observed in the HCS at the Earth’s orbit are formed near the solar surface as streamers, rather than being due to compression of the sheet by approaching velocity streamers. A further test for correctness of this conclusion may be to compare the width A, of the HCS at the Earth’s orbit in angular units with the width A,, of the streamers at R N 3R, as well as to compare the time behaviour of the HCS widths A,, and AB at the Earth’s orbit (Figs 5a, b). The angular width of the HCS, A,,, at the Earth’s orbit was determined using a catalogue (King, 1977) as the time scale At, of the density profile (Fig. lc) and was then calculated by the formula : A, = At;cos$~13.3*sin0,
= 9.44*At,*sin0,8
(1)
because the spiral angle $ at the Earth’s orbit makes up 45”. The O,c-angle of inclination of the HCS plane to the ecliptic plane will be determined in Section 3 of this paper. Part of the values of BO,are given in Table 2. The angular width of the HCS, AB, was also determined by formula (l), where At, was replaced by Ata, the time width of the magnetic field profile B(t), see Fig. lb. (We employ here the result of Section 3 of this paper implying that the inclination of the vector
B to the ecliptic plane coincides with the angle 0,8 of the HCS inclination to it.) The angular width A,, of the streamers was determined from structural drawings of the corona (Vsekhsvyatsky et al., 1965; Nikolsky et al., 1977) as the angular distance between two boundary lines of the streamer at R 3 3 R, (the scheme of determination of A,, is given at the bottom left of Fig. Sa). Figure 5a presents the values of A, and A,, which were determined by the above-mentioned methods for the years for which the required initial data were available. From the data for 1973 it follows, for example, that the mean values of A,, and A,> are close to each other : A,, N 6.5” and A,, II 5.2”. It is also apparent from Fig. 5 that the value of A, undergoes, as time progresses, periodic variations by about factors of 2 or 3 (an exception being the end of 1973 when the increase of A,, is more than by a factor of 5). In this case the period of this variation approaches 1 year. It seems likely that the value of Ans also experiences a similar periodic variation. At least, the magnitude and amplitude of A,,, variations for 195&1970 are both close to the observed values of A,, during the time interval 197&1976. The period of An8variation eludes determination due to lack of more detailed data. The magnetic angular width of the sheet, AB, exceeds by factors of 2 to 5 the A,, ; however, the
V. G. ESELEVICH and M. A. FILIP~OV
110
TABLE2. INCLINATION ANGLESOF THECURRENTSHEET TO EARTH’SORBITDURING Q0 (deg.)
60 (deg.)
Date
Type of transition
at the Sun
at the Earth
1972 10.02 18.02 67.03 15-16.03 34.04 10.04 8-9.05 28-29.05 8-9.10 13.12
R T T T R T T T T T
29 57 72 44 45 36 27 35 24 38
+55 +65 +80 -85 i-62 +60 -75 +80 +65 -90
1973 6.03 19.03 1.04 28.04 27.05 10.06 56.08 20.08 12.09 15.09 27-28.10 13.11 19.12 27-28.12
ECLIPTICPLANENEARTHESUN AND AT THE 1972-1978
THE
T T T T R T T T R T T T T T
64 50 34 54 70 42 8 26 31 39 30 36 17 54
T.-_--__.-
T /*
,I
,I
1950
1960
Date
Type of transition
at the Sun
at the Earth
50 45 30 50 40 59 65 50 26
-70 -80 -33 -42 -55 -66 -80 -77 -50
T T T T
47 45 40 32
-55 +72 -70 +70
T T T T
28 15 14 15
-65 *45 -70 +45
1977 4.11
R
32
+45
1978 2425.08 9-10.09
R R
75 66
-52 -78
1974 25-25.01 30.05 25.06 338.07 22-23.07 2.08 29.08 12-13.10 7.12 1975 7.02 1.08 20.08 16.09
-80 k65 -80 +60 -77 +70 f60 f35 +54 f45 *90 -47 -65 k60
1976 16.08 14.09 25.09 1l-12.10 /
.-- JIE 1 I
197c (b)
;:
Year
:
’ 4 ’, m’E 3 : I a *+I : .++ : I \ ;+ \ a -+\ \+ : +‘,+ +‘-+ + ++ -_ + 0 1973
+ + tF’ 0+‘, ++/ ,$ I + ; f ++ : +4 I
1975
Year FIG. 5. THE TIMEVARIATION OF TYPICALANGULARWIDTHS A. (a) ANDAB (b) OF THEHCS AT THEEARTH’S ORBITASOBTAINED BY FORMULA (1) USINGA CATALOGUE (KING, 1977). +-mean angular thicknesses of the streamers, An, at distance R - 3 R, as determined from structural drawings of the corona (the scheme of determination of A_, is shown at the bottom of the figure, at the left).
Investigation of HCS structure period of its variation coincides with the periodicity of A, (Fig. 5b). This lends further support to the fact that both A,, and AB are different characteristics of the same object, the HCS. To conclude this section, we want to note that whenever HCS interaction with a fast stream does not lead to any appreciable compression of the plasma in the sheet, their collision must result in momentum transfer from the stream to the HCS and, in particular, to transfer of the azimuthal component of momentum. This inference is shown by data, according to which the azimuthal rate of rotation in the W-E direction of point nmax inside the sheet can amount at the Earth’s orbit to values of u, - l&100 km s-’ (Siscoe, 1972), i.e. one or two orders of magnitude in excess of a, N l-2 km ss’ inside the streams.
3. MAGNETIC FIELD STRUCTURE OF THE HELIOSPHERIC
CURRENT SHEET
In order to investigate the magnetic field structure inside the sheet, the method of 8-q diagrams was employed. The method is to indicate on a plot hourly values of 6’ and rp from catalogues (King, 1977, 1979, 1983) for the entire time interval during which the sheet traverses the observation point, also including 1 or 2 days before and after that event. In this case, as the analysis shows, if the extreme point of vector B in space rotates with respect to a certain centre remaining in the same plane, then the 0-cp diagram represents the intersection line of this plane with a fixed-radius sphere, whose centre coincides with the origin of vector B and with the origin of coordinates. The equation for the intersection line has the form : P -B
cosB,*sin@
= -sinO,.cos(cp--cp,).cosO.
Here p is the distance from the plane of rotation of vector B to the origin of coordinates, Ip/BI < 1, angle 0 is counted from the ecliptic plane, - 90” < 0 < 90”, and B0 and qpo characterize, respectively, the inclination of the plane of rotation to the ecliptic plane and the position of the normal projected onto the ecliptic plane where the normal is to the plane of rotation. The method described above was applied in the study of HCS structure at the Earth’s orbit for the time interval 1971-1978 for which we know : first, the HCS configuration near the solar surface (R 2 3 R,) *The transition in the HCS cannot be called a “discontinuity” because it does not satisfy the whole set of requirements and Lifshitz,
that characterize 1959).
the discontinuity
(Landau
111
obtained from white-light corona emission (Korzhov, 1982) and, second, the hourly values of angles 0 and cp at the Earth’s orbit (King, 1977, 1979, 1983) which allow determination of the main structural properties of the HCS mentioned in Section 1. In this case we have excluded from our consideration the events showing a very rapid change of sign of B (or when it occurs within t < 1 h). Thus, the method of 0-q diagrams was utilized in the analysis of 44 HCSs. The analysis revealed that during the movement through the HCS from the appropriate preceding to the subsequent stream a 180” reversal of the magnetic field vector takes place in the form of two different kinds of transitions,* as follows. 1. Rotational transition (P # 0). This implies that, as the current sheet is being traversed, the end of the magnetic field vector B suffers rotation in a plane which makes an angle BO,with the ecliptic plane and the origin of vector B is at a distance P from this plane. 2. Tangential transition (P = 0). This is a particular case of the rotational transition when P = 0 in which vector B lies, as a whole, in the plane of rotation which makes an angle BO,with the ecliptic plane. Examples of a rotational and a tangential transition are shown, respectively, in Figs 6a and 6b. It is interesting to note that in a region of the sheet of width AB experimental points of the &cp diagram with a typical absolute spread A@, Acp N f25” fit the calculated 8-q curves (solid lines in Fig. 6), whereas outside the sheet on both sides of it, the points with the same typical absolute spread A0, Acp N f25” are arranged in a random fashion near points cp,, = 135”, O0 = 0” and cpO= 315”, B0 = O”, and this indicates that outside the sheet there is not any fixed plane of rotation of vector B. As is evident in Table 2, out of 44 events of the HCS being studied, 11 correspond to rotational transitions and 33 correspond to tangential transitions. Table 2 gives the values of the BOXand B,,, angles of inclination of the current sheet to the ecliptic plane, respectively, at R 2 3R, determined from data reported by Korzhov (1982) and at R = 215 R, obtained by the method of 8-q diagrams. From the plot of BO,vs f3,s (Table 2) it is seen that as one moves away from the Sun, the angle of inclination of the HCS to the ecliptic plane increases. Also, as regression analysis shows, the rate of increase is close to B,,, = BO,+ 17”. The great spread of the averaged experimental points indicates the existence of one or several parameters we are not yet aware of, which have a marked influence upon the relation between the quantities B,,, and QO,. In summarizing the aforesaid, we want to note that the presence in the current sheet of:
V. G. E~ELEVICHand M. A. FILIPWV
112
60 -
0.6 -
FIG. 7. THE DEPENDENCE OFTHE MAXIMUM OFTHENORMALIZED IMF &-COMPONENTIN THEHCS ON THEINCLINATIONANGLE 19~. OF THE SHEET TO THE ECLIPTIC PLANE.
determined
by processes in the solar corona and do
not change
-30
substantially
the Sun and the Earth’s
provided
that their production
Sun are well understood,
-
(except,
between
perhaps, orbit.
mechanisms near the
4. DISCUSSION OF THE NATURE OF MAGNETIC FIELD STRUCTURE IN THE CURRENT SHEET For the sake of simplicity, we shall consider a current sheet which represents
increased magnitude of the magnetic field, and rotation
of the end of vector B or full vector in
the sheet’s plane making an angle B,,,with the ecliptic plane, provides
from solar disk
observations.
FIG. 6. EXAMPLESOFTHEa_cPDIAGRAMS INSIDETHEHCS (a), (C) AND OUTSIDE THE HCS (b) : (BFTANGENTIAL TRANSITION, (c)--R~~AII~NAL TRANSITION.
-a
0,)
these HCS characteristics at
the Earth’s orbit may be predicted -60 -
-the
for
Therefore,
a natural
explanation
of the fact that a
an infinite
thickness A and lies symmetrically
flat disk of
with respect to the
ecliptic plane (see Fig. 8a). We
assume, according
model, that the formation
to Parker’s
(1958,
1963)
of the sheet is due to plasma
outflow
from the solar surface where the field com-
ponent
B, perpendicular to the flow direction is mini-
of field is recorded at
mal and fi > 1. As a result, the plasma flow while
the Earth’s orbit in the region of the sheet. This is also
carrying along the field lines makes them extend along
shown by the observed (despite the noticeable
spread
the radius so that sufficiently far from the Sun we have
of points) increase of the largest, normalized
values
B, >>Be (Pneuman,
maximum of the B,-component
of
B,/B inside the sheet from Bo, (Fig. 7).The approxi-
mate equality of the typical spreads of Afl and Acp for
established
points on B-cp diagrams inside and outside the sheet,
B = B, and -B.
as mentioned
occurs a continuous
above,
native explanation,
allows us to exclude an alter-
viz. the increased level of MHD
turbulence in the HCS as compared with the streams. From follows
the discussion in Sections that the main characteristics
2 and
3 it also
of the HCS are
such that Bm,,/Bmi”, nmax/nminand Tm,xITmi,, the rotation of the vector B in the sheet’s plane, the angle of inclination
/3,,of the sheet’s plane to the ecliptic
plane, and the angular width of the sheet A,, are all
1971). As a result, a magnetic
field distribution typical of a neutral sheet (Fig. 8b) is
at
; on the boundaries of the sheet we have between which, inside the sheet, there
B,(e)transition, with a reversal B = 0 on the sheet’s axis. Rotation of the Sun as a
whole will not modify such a distribution but will only add a Q-independent ponent of field, in elongation
value of the azimuthal
com-
B,(B)= constant, and this will result of the sheet along
the Archimedean
spiral (Klein and Burlaga, 1980). The situation may change abruptly
if differential
rotation of the Sun (i.e. dependence of the azimuthal
Investigation of HCS structure
113
(0)
8, (b)
-
t
(d)
ts
I
@
t
i
C
A
8
(f )
8
_-p. 4 [~-.
_.
IO
-0-I *a, Q .-.-0
e_ -a*
Fio.8. ASCHEME EXPLAINING
(e)
'Q
I 0
-
’ ?e
-
-4
--_
e,
T~~C~NISM~ORROTATIONOF~CTOR
B INSIDE
THE
HCS
ASA~O~~Q~NCE
(a) The Sun with the HCS of thickness ABsymmetric with respect to the equator. (b) The field distribution inside the HCS in the absence of differential rotation of the Sun. (c) The dependence on 0 of the azimuthal velocity of solar rotation vV at the base of the HCS on the solar surface between points A and C. (d) Bending (dots B) of the originally meridional field Be, due to the dependence u,(O) of type (c). (e) The azimuthal component of field along 0 which arises due to the dependence v,(O) of type (c). (f) The dependence on 0 inside the HCS of field B = B, +B,, which is obtained by vectorial summation of the (b) and (e) plots, (g) Rotation of vector B’ = B,+B, in the HCS plane rep.
velocity of rotation of the solar surface up on 8) is taken into account (Fig. 8~). Indeed, let the magnetic field on the solar surface in the main HCS be B = Booand let the ends of its field lines be frozen-in to the plasma at latitudes A and C, respectively, northand southward of the equator (Fig. 8d). The presence of a positive gradient of rotation velocity ug of the Sun from latitudes A and C equatorwards will cause the B,-component to bend in the direction of I)~with the largest deviation at the equator (Fig. Sd), and accordingly, will lead to the generation of the B,component of field, whose schematic distribution vs 0 is shown in Fig. 8e. The plasma with p > 1 that outflows from the solar surface along the equator, while carrying along the magnetic field, pulls in its wake the magnetic field lines along the radius ; as a result, sufficiently far from the Sun it appears that B, _ B, >>Be. (According to Pneuman, 1971,
3, N R- ‘, i.e. B, decreases with distance much more rapidly as compared with the B, and B, components.) Adding the B, (Fig. 8b) and BV (Fig. 8e) components gives a net vector B’ = B,+B, which experiences rotation in the HCS plane repby an angle of 180” (Figs 8f, g). In order to explain the similar rotation of vector B in the plane of an inclined sheet which intersects the ecliptic plane at an angle O,, it is necessary to assume in the vicinity of the inclined part of the current sheet the existence of a meridional, differential plasma motion with vg = f(p). 5. CONCLUSIONS (I) It has been shown that both the plasma and the magnetic field in the heliospheric current sheet (HCS) do not undergo any appreciable, additional
114
V. G. ESELEV~CH and M. A. FIL~PPOV
compression during an interaction with high speed streams everywhere at R < 215 R,. Therefore, the HCS structure at the Earth’s orbit is determined mainly by its properties near the solar surface. This is in agreement with findings reported by Gosling et al. (1981), Feldmanet al. (1981) and Borriniet al. (1981), obtained independently by the analysis of the fraction of admixture ions He’+/H+ in the solar wind. (2) The variation of magnetic field B inside the HCS implies a rotational or a tangential transition in which the ends of vector B or full vector B experience, as they move across the sheet, a rotation in the HCS plane making an angle 8, with the ecliptic plane. An analogous conclusion about the rotation of vector B was drawn by Klein and Burlaga (1980) in the analysis of the sector boundaries. (3) MHD turbulence cannot be responsible for the increased values of the IMF &-component in the HCS because the level of random MHD oscillations is nearly the same in both the sheet and the streams. (4) The increased value of the &-component in the HCS is accounted for by two factors : increased values of lB1in the sheet and rotation of vector B (or its end) in the plane of the sheet inclined to the ecliptic plane at angle 8,. (5) A likely reason for the rotation of vector B inside the HCS is the differential rotation of the Sun.
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Siscoe, G. L. (1972) Structure and o~entations of solar wind interaction fronts : Pioneer 6. J. geophys. Res. 77,27. Svalgaard, L., Wilcox, 3. M. and Duvail, T. L. (1974) A model combining the polar and the sector structured polar magnetic fields. Solar Phys. 37, 157. Vsekhsvyatsky, S. K., Nikolsky, G. M., Ivanchuk, V. I., Nesmeyanovich, A. T., Ponomarev, E. A., Rubo, G. A. and Cherednichenko, V. 1. (1965) The Solar Corona and Corpuscular Emission in Interplanetary Space. Kiev Univ. Press, Kiev. Withbroe, G. L., Kohl, J. L., Weiser, H. and Munro, R. H. (1982) Probing of the solar wind acceleration region using spectroscopic techniques. Space Sci. Rev. 33, 17. Withbroe, G. L., Kohl, J. L., Weiser, H. and Munro, R. H. (1985) Coronal temperatures, heating and energy flow in a polar region of the Sun at solar maximum. ~strop~ys. J. 297,324.