Angular momentum flux carried by solar wind calculated from Mariner 5 dat

Goldstein, B. E.

Lazarus, A. J.

English

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https://ntrs.nasa.gov/search.jsp?R=19710022905 2020-03-11T20:16:00+00:00Z
CENTER FOR SPACE RESEARCH
M AS S ACHUSETTS I NSTITUTE OF TECHNOLOGY
N 71 .32-81
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4JL1DI1il ^.t F.:u to Astropiv-s i c:al Journal, Part 1
Observation of the Angular Momentum Flux
Carried by the Solar Wind
Alan J. Lazarus and Bruce L. Goldstein
Physics Department and
Center for Space Research
Massachusetts Institute of Technology
CSR-P-71-56
	 MarcL 1971
ABSTRACT
Using data from the Mariner 5 spacecraft, we have
measured the annular momentum flux carried by the solar wind
and find it in agreement with earlier estimates based on obser-
vations of the deflection of comet tails.
•In this note we report measurements of the or)n--radial
velocity components of the solar wind flow determined by the
plasma experiment on Mariner 5 during the period from June
to November, 1967. We use those results to estimate the angular
momentum flux transported by the solar wind from the equatorial
region of the sun and find that the magnitude of the flux i:;
similar to that estimated by Weber and Davis (1967, 1970) and
agrees with the most recent estimates from comet tail observa-
tions (Brandt and heise, 1970) . Using his early results, Br:,ridt
(1966) pointed out that the solar wind must be considered as an
important mechanism for slowing the rotation of the sun, and
the recent results imply a slowing down time of ,, 7 x 10 9 years.
It is hard to make an unbiased measurement of the average
solar wind flow direction. At 1 AU the average departure from
radial flow is on t;ie order of 2', and the variation about that
average is .ti ±5° in the course of a solar rotation (e.g. see
hundhausen et al., 1970a). Vela 2 data taken from July 1964 to
0
July 1965 indicates: an average flow coming from 12 east of the
sun (see Coon, 1968 for the data, a discussion of their signifi-
cance, and a caution by Parker). Vela 3A and 3B data (July 1965-
Nov. 1967) give average flow directions of 2.52° and .93° from
east of the sun indicating, as the authors point out, a source
of systematic error (Hundhausen et al., 1970a). Moreover, IMP 1
data (late 1963 to early 1964) give an average flow from 1.5°
west of the sun (Egidi et al., 1969).
6- 2 -
A partial explanation for the observation of an average flow
from the west may come from the fact that during the interaction
of high and low speed streams of solar wind, the higher speed
wind is deflected so that it appears to come from the west while
the lower speed wind appears to come from the east (Siscoe et al.,
1970). There was a chance coincidence between the passages of
such interaction regions and -she location of IMP 1, such that the
spacecraft was inside the magnetosphere during a portion of the
time of lower speed wind and may have missed sor;.e of the wind from
the east. There is, however, no clear indication that the average
speed measured by IMP 1 is unusually hig:i.
The Mariner 5 spacecraft trajectory took it inwarcas to
ti 0.6 AU which increased the magnitude of the expected tangential
velocity component and hopefully reduced the importance of small
systematic errors.
The experiment used a modulated grid Faraday cup similar tc
that flown on Mariner 4 (Lazarus et al., 1966). The spacecraft
was 3-axis stabilized, and the detector directly faced the sun.
The bulk speed, number density, and thermal speed of the proton
component of the plasma were determined by comparing the measured
energy distribution with that expected from a convected, iso-
tropic Maxwellian distribution. The flow direction for an indi-
0
vidual measurement was determined to with-'n ±2( ti ± 4 km/sec
transverse velocity) by comparing the particle fluxes incident
on three 120°-sectors of a circular collector plate with the
fluxes expected from a convected Maxwellian distribution having
the parameters determined above and a particular flow direction.
6The systematic error of the direction determination could
be checked after launch when the spacecraft was in the solar wind
and it rolled about the sun-spacecraft axis for approximately
22
 Hours. The resulting angles were consistent with the solar
wind flow direction being nearly constant during the three roll
0
periods but with an effective detector alignment elrur of 2 .
Such an error is consistent with mounting and coristr.uction un-
certainties, and that error was used to correct the weasured
angles. Unfortunately, no such check was available near the end
of the flight.
T.ae coordinate syst ,=m used in this paper is spacecraft
centered solar equatorial: The radial coordinate, r, is positive
outward along the Sun-spacecraft line; the transverse coordinate,
t, is parallel to the solar equatorial plane and is positive in
the direction corresponding to the orbital motion of the planets;
and the normal coordinate, n, is the third member of the right-
Banded coordinate system. The spacecraft's orbital plane is
inclined 2.7° to the ecliptic, and during the period of these
data the heliographic latitude of the spacecraft varies from
`1-0 ` to 4. 5°14 and back to 0° .
Hourly averages of the velocity components and other quanti-
ties of interest were used to form averages over complete solar
rotations taking into account the changing position of the space-
craft. The velocity of the spacecraft obtained from the JPL
trajectory data was used to correct for aberration effFcts.
The results are given in the first five columns of Table 1.
As the Sun-spacecraft distance decreases, the solar wind comes
more from east of the sure. There is also a consistent southward
flow.
- 4 -
We can estimate the angular momentum flux by using our
measurements of angular momentum flux density near the sun's
equatorial plane: The angular momentum flux density carried by
the protons is given by mp14V rV t R, where N is the number of
protons per cc, m  is the mass of a proton, V  and V  are the
radial and transverse components of the proton bulk velocity,
and R is the Sun-spacecraft distance. The magnetic field also
exerts a torque which is given by the appropriate Maxwell stress
tensor component; and the equivalent angular momentum flux density
is -BrBtR/4-,-, where 
HrHt are the radial and transverse components
of the magnetic field.
Another contribution to the angular momentum flux could
come from the anisotr.opic thermal pressure of the solar wind
(Hundhausen, 1970b). This contribution is small, on the average,
compared to the magnetic stress contribution quoted above
(Eviatar and Schulz, 1970), and therefore we shall neglect the
particle pressure anisotropy in our estimate.
The sixth through eighth columns of Table 1 show the two
contributions to the angular momentum flux density and also the
estimate of the solar equatorial angular momentum flux per unit
solid angle obtained by multiplying the average of the sum of
the two flux densities by R 2 . For reference, the final column
of Table 1 shows the proton flux per sterradian averaged over the
same rotation. We estimate that our systematic error in average
flow direction early in the flight is equivalent to a transverse
velocity of '1, 2 km/sec. We can only assume that no significant
directional bias developed as the flight progressed.
We have only indirect measurements of solar wind properties
outside the ecliptic plane, and in order to estimate the net
6
V
- 5 -
angular momentum loss rate due to the zolar wind, we follow
Brandt and include only the solar wind flow between latitudes
of + 30 0 and assume that its behavior in that region is the
same as we observe near the ecliptic. Assuming an equatorial
angular momentum flux of approximately 1.2 x 10 30 dyne-cm/d
we obtain a net slowing torque of 7 x 10 30 dyne-cm which is the
same as Brandt's estimate.
I	 Our results differ from the theoretical work of Weber and
Davis (1967, 1970) in the observation that the magnetic field
contribution to the angular momentum flux is definitely smaller
than the particle contribution.
Acknowledgement
We thank tae Mariner 5 magnetic field experimenters
(J. Belcher, Y. Coleman, L. Davis, D. Jones, and E. Smith) for
the use of their data prior to publication.
This work was supported in part by the
National Aeronautics and Space Adminis-
tration under grant NGR 22-009-372.
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1RL'FERENCES
Brandt, J.C. 196L,	 A	 .J., 144,	 1221.
Brandt, J.C. and Heise,	 J. 1970,	 AAp.J.,	 159,	 1057.
Coon, J.H. 1968, in Earth's Particles and Fields, 359 (Proceed-
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Germany July 31 - August 11, 1967, edited by B.M. McCormac,
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Egidi, A., Pizzella, G., and Signorini, C. 1969, J. Geophys. Res.,
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Eviatar, A. and Schulz, M. 1970, Planet. and Space Sci., 18, 321.
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1970x, J. Geophys. Rc:s. , 75, 4643.
Hundhau., en, A.J. 1970b, Rev. o f Geophys. ,-id Spaces Physics, 8, 729.
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.	 1970, J. Geophys. Res., 75, 2419.
I


Observation of the angular momentum flux carried by the solar wind

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