East-west asymmetry in solar wind velocit

Goldstein, B.

Lazarus, A. J.

Siscoe, G. L.

English

NASA Technical Reports Server

https://ntrs.nasa.gov/search.jsp?R=19690015537 2020-03-12T04:12:24+00:00Z
An East-West Asymmetry in the 
Solar Wind Velocity 
G.L. Siscoe? B. Goldstein, A.J. Lazarus 
August, 1968 
*Present address: Department of Meteorology, University 
of California, Los Angeles, California 90024 
A bs tra c t 
An east-west asymmetry may exist in the solar wind velocity due 
to the action of  a well known mechanism, namely, the influence o f  the solar 
rotation on the interaction between fast and slow streams. The mechanism 
predicts fast streams tend to come from the west and slow ones from the east 
with respect to the average solar wind direction. It i s  noted that i f  there i s  
a correlation between density and velocity, a measurement of the average 
azimuthal wind component i s  not sufficient to determine the angular momentum 
flux. 
east-west variations in flow direction with periods around 4 days (the largest 
period studied) may be due to the fast stream-slow stream interaction. The 
percentage decreases for shorter periods. 
Experimental evidence from Pioneer 6 indicates that about SO$ of  the 
Physical principle. The solar wind speed i s  known to be highly variable, for 
example, i t  has been observed to double i n  less than one day [Snyder and 
Neugebaurer (1966)l. Dessler ('1967) has pointed out that one effect o f  the 
solar rotation on the interaction of adjacent streams of different velocity i s  
to produce east-west deflections of the flow. Other aspects of the interaction 
have been described by Parker (1965), Neugebauer and Snyder (1967), and 
Sarabhai (1963). We would l ike briefly to describe the interaction in the 
framework of  f luid mechanics since this framework allows calculation of  
the size of the expected effects (Corovillano and Siscoe, 1969). The main 
purpose of this section i s  to point out that the interaction should produce a 
prevailing east-west asymmetry in the solar wind velocity. 
The asymmetry i s  introduced by the sun's rotation acting on different 
velocity streams through the physical mechanism illustrated i n  Figure 1. The 
figure shows schematically the interaction between fast and slow streams. The 
sun's rotation imposes a spiral pattern on each stream in  the manner familiar 
from rotating lawn sprinklers: the slower the stream, the tighter the spiral. Thus, 
adjacent streams with different speeds w i l l  interact along their interface. For 
simplicity, the figure shows a thin interface, however, the same argument 
holds for a gradual transition between streams. InTigure 1 (a), the slow stream 
precedes, and an increased thermal and magnetic pressure occurs along the 
interface due to compression by the overtaking fast stream. The associated 
pressure gradient can be resolved into radial and azimuthal components; only 
-2- 
the latter i s  shown in the figure. 
radially speed up the slow stream and slow down the fast stream. The azimutha 
stress acts to deflect the slow stream to the west and the fast stream to the easta 
I t  i s  clear that the radial stress must act to 
In  Figure l(b), the fast stream precedes, and the thermal and magnetic pressures 
are reduced along the interface due to the separation of the two streams. Again 
the associated pressure gradient can be decomposed into radial and azimuthal 
components. The radial component again acts to equalize the radial velocity 
of the two streams. The azimuthal stress pulls the fast stream toward the east 
and the other toward the west. Thus, i n  both cases, the fast stream i s  accelerated 
toward the east and the slow stream toward the west which should result i n  the 
asymmetry claimed in the first paragraph. 
In the final section the expected asymmetry i s  shown to be present i n  
that 
been computed. Future comparison i s  planned for Pioneer 7 and IMP 1 data. 
The solar wind velocity asymmetry has been shown to be consistent with an 
observed prevailing east-west asymmetry in  the orientation of tangential 
discontinuities (Siscoe, Turner and Lazarus, 1969). 
North-south component. The correlation between solar wind speed and east- 
west direction w i l l  be degraded to some extent by h e  north-south component 
of the pressure &adient. To recognize the importance of the north-south 
component, consider the case in  which I t  i s  zero. This case occurs only i n  
the special circumstance where the interface between the two streams intersects 
portion of the Pioneer 6 plasma data for which the east-west angles have 
-3- 
the solar equatorial plane a t  right angles. Projected back onto the solar surface, 
the situation requires that the regions generating the fast and slow streams inter- 
face along a l ine of constant solar longitude. However, i t  i s  probable that such 
interfaces are arbitrarily oriented on the solar surface and the special situation 
required for zero north-south component i s  unlikely. Thus, a substantial amount 
of the non radial motion induced by the solar rotation may occur in the north- 
south direction. A fast stream may find it easier to flow north or south of a 
preceding slow stream than to deflect to the east. All  though the east-west effect 
competes with the north-south motion, i t  should be measurably present. 
A contribution to the average azimuthal velocity. Several authors have con- 
sidered the possibility of  a non-zero average azimuthal component of the solar 
wind velocity (Weber and Davis, 1967, see also the review by Dessler, 1967). 
Magnetic and viscous stresses have been invoked to transfer some of  the sun's 
- 
angular momentum to the solar wind. There results a net loss of angular 
momentum from. the sun and an average azimuthal velocity i n  the same direction 
the sun rotates. 
There is,  therefore, a tendency to believe that a measurement of 
average azimuthal velocity gives direct information about the angular momentum 
flux. We point out in this section that correlationz i n  the longitudinal structure 
i n  the solar wind can also produce an average azimuthal component but with 
no angular momentum flux, thus, the assumed association need not be valid. I t  
would avoid a l l  ambiguity i f  the observed average of the product pV,Vr were 
computed by experimenters. 
-4- 
since this is directly proportional to the angular momentum flux at  a fixed solar 
distance. 
A non-zero average azimuthal velocity w i l l  occur as a result of the 
interaction of fast and slow streams i f  there i s  a correlation between speed 
and density. The resulting average velocity can be either from the east or 
from the west, and i t  produces no loss of angular momentum from the sun. Since 
this mechanism i s  independent from those mentioned above, we may isolate i t  
and assume zero net flux of angular momentum away from the sun. For the 
purpose of illustrating the mechanisms, consider the following idealized situation: 
fast streams alternate with slow streams; a l l  north-south velocity components 
are zero, a l l  fast streams have the same velocity and density (Vf, q. ,
slow streams a l l  have velocity and density (Vr, VfD, p ); l e t  the total azimuthal 
f S 
angle occupied by the fast streams be 6 and that of the slow streams be 5 . Recall 
from the discussion about the interaction of  fast and slow streams that V 
have opposite signs. 
sun rotates, Vf i s  positive and V i s  negative. The net flux o f  angular momentum 
) and the 
s s s  
f S 
and V 
cp CP 
I f  we choose the angle Q to decrease in  the direction the 
S 
0 CP 
carried away i n  the solar equatorial plane per unit north-south distance i s  
- 
The average azi,muthaI velocity i s  
-5- 
S 
Eliminating V between equations ( 1 )  and (2), we find 
cp 
Thus, the sign of vcp depends on the mass flux ratio o f  the fast and slow streams. 
f f  
P vr > I sirce vf > vs . For example, in the case of equal densities, p = p , -
psv: 
r r  
I n  this case v 
the sun on average. However, there i s  experimental evidence that the solar 
f s  
wind speed and density tend to be anticorrelated, that is  p < p [see, for 
i s  negative, that i s ,  the wind would appear to come from east of a 
example, Snyder and Neugebauer, 19661. Hence, i t  might be that the mass 
flux ratio i s  less than one, which would produce a positive . I f  this i s  the 
case, the wind might appear to come from west of the sun on average. 
to 
Experimental evidence. Data from the M.I . T .  plasma experiment on Pioneer 6 
have been examined for evidence of the predicted asymmetry. The instrument 
measures the flow direction in the spacecraft equatorial plane (essentially the 
0 
ecliptic plane) with a relative error probably less than k l  . The accuracy of 
the absolute angle with respect to the sun-spacecraft line i s  not yet determined; 
hence, we w i l l  not consider the average direction of flow. 
Three hour averages of the solar wind speed - were correlated against 
the flow angle ,in the ecliptic plane for a 27 day stretch of  data. The 
aberation of the wind due to spacecraft motion was removed. Also the trouble- 
some effects of  long term trends were reduced by subtracting three day sliding averages 
-6- 
The angle was taken positive for flows from the west; thus, there should be a 
positive correlation between angle and speed. 
The correlation coefficient as a function of lag i s  shown in Figure 2 
for lags up to 30 hours. There i s  a conspicuous peak of  +0.45 a t  zero lag, 
which implies an in phase positive correlation as predicted. 
That the peak value i s  considerably less than 1 implies an appreciable 
uncorrelated component to the variations, or another correlation with a different 
phase. To decide which, the cross spectrum shown in Figure 3, was made. 
The coherence falls off with increasing frequency beginning with 0.49 a t  
0.29 x 
a t  zero unti l the coherence falls to 0.1 , and then begins to deviate randomly. 
Thus, the departure from perfrect coherence must be due to uncorrelated 
fluctuations. Whatever coherence i s  present i s  caused by a mechanism that 
produces zero phase such as that described here. The uncorrelated part o f  
the fluctuations, becomes relatively more important for higher frequencies or 
for smaller scale lengths. In addition to the reduction in correlation due to 
the north-south velocity component which was mentioned earlier, part of 
the uncorrelated component might be Alfven waves, which would be unlikely 
to remain coherent over a 27 day period. 
cps or a period of 4 days. However, the phase stays essentially 
/- 
The experimental evidence suggests that part of the variations i n  
angle are due to the mechanism described here. In  fact for variations with 
periods around 4 days about 50$ may be so generated. 
-7- 
Acknowledgements 
This work has been supported in part by the National Aeronautics 
and Space Administration under contract NAS 2-3793 administered by the 
Ames Research Center. One of us (GLS) was supported by the Department of 
Meteorology of the University of California at  Los Angeles during a portion 
of  the research. 
References 
Carovillano, R. L. , and G. L. Siscoe, Corotating structure i n  the solar wind, 
submitted to Astrophysical J. , 1969. 
Neugebauer, M. and C.  W. Snyder, Mariner 2 observations of the solar wind, 
1 , average properties, J . Geophys. Res. - 71, 4469, 1966. 
Neugebauer, M. and C. W. Snyder, Mariner 2 observations of the solar wind I - 
2 ,  relation of plasma properties to the magnetic field, J. Geophys. Res. 
- 72, 1823, 1967. 
Parker, E. N., Dynamical theory of  the solar wind, Space Science Rev., 4, -
666, 1965. 
Sarabhai I V. , Some consequences of nonuniformity of solar wind velocity, 
Siscoe, 
Weber, 
J. Geophys. Res. 68, 1555, 1963. -
G. L. , J. M. Turner, and A .  J. Lazarus, Simultaneous plasma and 
magnetic field measurements of probable tangential discontinuities i n  
the solar wind, Solar Physics, i n  press, 1969. 
- 
E. J., and L. Davis, Jr., The angular momentum of the solar wind, 
Astrophysics J. - 148, 217, 1967. 
Figure Captions 
Figure 1 : A schematic representation of  the interaction between fast and 
slow streams. (a) Slow stream preceding. (b) Fast stream 
preceding . 
Figure 2: Correlation between Pioneer 6 measurements of solar wind speed 
and angle in  the ecliptic plane as a function o f  lag time. 
Figure 3: Cross spectrum between data used in  Figure 2. 
. 
a 
I- 

.5 
.4 
a, 
* 3  c .  
W 
a 
-c 
0 
0 
L 
.2 
.I . 
Pioneer 6 
Angle vs. Speed 180° 
goo 
- 9 O O  
-180' 
0 0.29 0.58 0.87 1.16 1.45 1.74 2.03 2.31 2.59 2.89 
Frequency  cps)  
/ 


An east-west asymmetry in the solar wind velocity

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server