The Solar Wind Helium Abundance: Variation with Wind
Speed and the Solar Cycle
Matthias R. Aellig*, Alan J. Lazarus* and John T. Steinberg1^
* MIT Center for Space Research, Cambridge, MA 02139
^Los Alamos National Lab., Los Alamos, NM 87545
Abstract We investigate the helium abundance in the solar wind and variations thereof on a time scale of
years. Data from the WIND/SWE experiment gathered between the end of 1994 and early 2000 are analyzed.
In agreement with similar work for previous solar cycles, we find a clear dependency of the He/H ratio in the
solar wind on the solar cycle. In the slow solar wind, the average He/H rises from a minimum of less than two
percent around solar minimum to about 4.5% in early 2000. The solar cycle dependency is stronger the lower the
speed that is used to sort the data. We observe the strongest dependency of the He/H ratio on the solar wind speed
around solar minimum and it weakens as the solar activity increases. We speculate that the expansion factor of the
magnetic field close to the Sun changes over the solar cycle and thereby changes the efficiency of the Coulomb
drag. Inefficient Coulomb drag leads to a low helium abundance in the solar wind.
INTRODUCTION
DATA
This contribution is a somewhat expanded version of a
poster given at the SOHO-ACE Workshop 2001 in Bern.
A formal paper on our results will be found in Aellig et
al [ 1 ]. Some of the figures and text from that paper have
been used by permission.
The solar wind helium abundance was first reported to
vary over the solar cycle by Ogilvie and Hirshberg [2].
Combining data sets from several spacecraft they found a
solar cycle variation ofna/np of 0.01 ±0.01 with the average helium abundance being higher during periods of
higher activity. Adding data from Imp 6, 7, and 8, Feldman et al. [3] confirmed the solar cycle dependency, but
they found that the maximum difference in helium abundance between the low- and high-speed wind occurred
near solar minimum in contradiction to the results reported by Ogilvie and Hirshberg [2] who reported the
maximum speed variation near the peak of solar activity.
Analyzing ISEE-3 data from the ICI instrument, Ogilvie
et al. [4] reported the solar cycle dependency of the solar
helium abundance for solar cycle 21. They suggested that
the smallest dependence on speed occurs during the period of decreasing activity but before solar minimum. In
this paper we report the abundance variation with wind
speed from one year before solar minimum to nearly solar maximum. An overview of previously reported He/H
in the solar wind plus the work described in this paper is
shown in Figure 1.
For this study we used data from the Faraday Cup portion
of the SWE instrument on the Wind spacecraft, Ogilvie et
al [5]. The Faraday Cup data allow the determination of
the solar wind proton velocity, thermal speed and density.
The same parameters can be derived for solar wind alpha
particles under most circumstances.
Isotropic Maxwellian velocity distributions are assumed for both the protons and the alpha particles, and
every energy/charge sweep (lasting approximately 90
seconds) is fitted individually. Depending upon the quality of the data and how well the two ion populations are
separated, different fitting approaches are taken or some
parameters may be subject to a constraint. In all cases
that are used, the distinction between protons and alphas
is clear.
The data analyzed cover the time period from the
launch of the Wind mission in late 1994 to April 2000,
i.e., about half a solar cycle. The average helium abundance over a certain period was calculated as the ratio of
the integrated number densities of helium and protons.
This corresponds to a weighted average of the He/H ratios where the weights are the proton densities. As a measure of the variability of the individual values we use the
central interval in which 68% of all measurements fall.
We stress that CMEs, current sheet crossings, and shocks
have not been excluded from the analysis since it is our
intention to characterize the solar wind He/H at large.
As a proxy for the solar activity we used the monthly
CP598, Solar and Galactic Composition, edited by R. F. Wimmer-Schweingruber
© 2001 American Institute of Physics 0-7354-0042-3/01/$ 18.00
89
ium abundance in the solar wind.
350
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und a
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gilvie
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WIND SWE FC
Ulysses SWICS In-Ecliptic
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SIDC Sunspot Number
*
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300
250 _o
200 =3
150 Q.
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cu
I
c
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50
0
1960
0
1970
1980
Year
1990
2000
FIGURE 1. Solar wind He/H over several solar cycles (from [1]).
FIGURE 1. From [1]
DATA
For this study we used data from the Faraday Cup portion
of the SWE instrument on the Wind spacecraft. The
Faraday Cup data allow the determination of the solar
wind proton velocity, thermal speed and density. The
same parameters can be derived for solar wind alpha
particles under most circumstances.
Isotropic Maxwellian velocity distributions are assumed for both the protons and the alpha particles, and
every energy/charge sweep (lasting approximately 90
90
seconds) is fitted individually. Depending upon the qual-
with a robust fit are shown in Table 2. Based on the
variation of b over the solar cycle, the speed dependence
is four times stronger around solar minimum than during
1999 and early 2000.
Another way to display the increasing He/H ratio for
lower speed wind as solar activity increases is shown
in Figure 3 which displays a histogram of the measured
ratios in 1996 and 2000.
sunspot number provided by the Sunspot Index Data
Center (SIDC).
The He/H data that fall into a certain speed range
were averaged over 250 days. The speed bins cover the
speed below 350 km/s and then bins 50 km/s wide for
higher speeds up to 600 km/s. Typically those averages
are based on several tens of thousands of measurements.
Since the observation period contains the solar minimum
around 1996, faster streams are not that prominently represented in our study particularly around 1996. Nevertheless averages between 550 km/s and 600 km/s contain
at least 1600 data points (see Table 1).
SUMMARY
We have found a strong variation of the solar wind helium abundance between the end of 1994 and early 2000.
The lowest values are observed around solar minimum
in 1996. Those finding are in agreement with previous
reports about the solar cycle dependency during earlier
activity cycles [2,3,4,6], We find the dependence of the
helium abundance on the solar wind speed to be strongest
during solar minimum which agrees with results reported
by Feldman et al. [3] but that solar cycle speed dependence disagrees with those reported by Ogilvie and Hirshberg [2] and Ogilvie et al. [4]. Our value for He/H
that was averaged over all speeds around solar minimum
is considerably lower than the speed-averaged helium
abundance around previous solar minima. It is not clear,
however, to what degree this is a real effect and to what
degree it is a systematic difference between different sensors.
RESULTS
The result of our analysis is shown in Figure 2. For
the slowest wind considered, i.e., for wind speeds below
350 km/s the average He/H at the beginning of the observation period is 1.8 % and then drops to as low as 1.4 %
close to solar minimum. Then, the average He/H in that
speed range starts to increase and reaches 4 % by the beginning of the year 2000, tripling within three years. For
larger speeds, the average value at the start of the observation period increases as well as does the value observed around solar minimum. Furthermore, the change
over the observation period becomes smaller. While the
uncertainties of the mean values of He/H (indicated by
error bars) in the speed range below 350 km/s shows a
cycle dependency with the smallest uncertainty around
solar minimum, no obvious pattern is observed for the
speeds from 550 km/s to 600 km/s. We also analyzed
the speed range between 600 and 850 km/s in which a
slight linear increase of the average He/H is observed
from 1995 to 2000 although there are only relatively few
measurements in that speed range, especially around solar minimum.
Because the number of observations is large, the mean
values of the He/H ratio are well-determined. Nevertheless, the range of values contributing to each mean
value is also large: the long error bars in Figure 2 show
the ranges of the ratios corresponding to the 16and
84quantiles of the measured He/H The range spanned by
those values contains the central range into which 68%
of the He/H determinations fall.
In summary, throughout the observation period increasing solar wind speed implies increasing helium
abundance in the solar wind. The strength of that speed
dependence also varies over the solar cycle. Using a linear fit to the observed He/H ratio as a function of speed,
we get
He/H =
[He/H] =
DISCUSSION
In the following we discuss a possible explanation for
the solar cycle dependency of the helium abundance that
also would explain the observed speed dependency.
Many theoretical studies indicate that the proton flux
is the most important parameter regulating the behaviour
of the alpha particles in the solar wind Burgi [7] and references therein. Coulomb collisions between the protons
and the alpha particles and the minor ions play an important role in accelerating the latter two constituents Geiss
et al. [8]. The proton flux transfers momentum to helium
ions and accelerates them out of the corona. The larger
the proton flux, the more efficiently helium is accelerated and the more helium is observed in the solar wind. It
turns out that, under coronal conditions, among all heavy
ions 4He couples the least efficiently to the protons.
Although the proton flux at 1 AU varies only by little
over the solar cycle Wang [9], the proton flux in the acceleration region of the solar wind does not necessarily
have to be constant as we shall now discuss. In a stationary case, the continuity equation along a flux tube with
(1)
where the parameter b indicates the strength of the speed
dependence. The resulting values for a and b derived
91
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1995
1996
1997
1998
Year
1999
2000
FIGURE
data.
The
solid
error
shown
FIGURE2.2. The
The solar
solar wind
windhelium
heliumabundance
abundancederived
derivedfrom
fromthe
theWind/SWE
Wind/SWEFaraday
FaradayCup
Cup
data.
The
error
barsbars
shown
for for
each
each
represent
the uncertainty
of the
plotted
mean
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The
dotted
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bars indicate
which
68/the
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represent
the uncertainty
of the
plotted
mean
value.
See
text
for more
of the
the range
rangeinfrom
which
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mean value is
fall;
see text. The
The figure
numbers
across[1]the top of the figure are the values of range error bars when they fall outside the figure. The figure
determined.
is from
is from [1]
close to the Sun and the subsequent depletion of helium
that case, the fast wind cannot serve as a test for the
Alpha
Abundance
Distribution
ions because of inefficient Coulomb
drag. Solar
wind
hypothesis.
streams close to the current
sheet
have
very
large
expanIf
indeed
variations of the proton flux close to the Sun
0.08
sion factors close to the Sun Wang and
Sheely
[13]
which
via
Coulomb
drag cause
Wind speeds between 350 ond 400
km/s the observed helium abundance
lead to a low helium abundance in the solar wind Bürgi
variation over the solar cycle, the same effect should be
Jan-Decpresent in other elemental or even isotopic ratios. In those
[11]. So far, we have discussed a potential 1996
explanation
N=76,532
c 0.06
for the solar cycle variation
in a low speed bin. We can
ratios, we expect a considerably less pronounced effect
<D
apply the same concept
of flux tube expansion close to
since 4 He has the strongest dependency on the proton
D
CT why during solar minimum we
the Sun to the question
flux Bodmer and Bochsler [14].
CD dependence of the helium abunobserve a strong speed
2000 Jon-Apr
dance. Wang and Sheeley0.04
[13] reported an inverse correN= 10,501
lation between the rate
0> of magnetic flux-tube expansion
ACKNOWLEDGMENTS
> at 1 AU. With increasing solar
and the solar wind speed
wind speed at 1 AU they associate smaller expansion facWe are grateful to the many individuals who contributed
•§and0.02
tors close to the Sun
therefore a larger proton flux in
to the success of the Solar Wind Experiment (SWE) on
QL above, that leads to a higher He/H
corona. As discussed
the Wind spacecraft. Furthermore, we thank Yi-Ming
in the solar wind which is observed in Figure 2 around
Wang for valuable suggestions and discussions. This
solar minimum.
work was supported in part by NASA Grant NAG5-7359.
0.00 tu:_____
We tried to verify our hypothesis also for the fast
The figures and tables from [1] are used by permission of
0.00 19770.02
0.04
0.08 Geophysical
0.10 Union.
0.12
wind. In the time interval between
and 1994
there 0.06
the American
was also a solar cycle dependence of the protonAlpha
flux at Abundance
2.5 R for near-Earth wind speeds larger than 550 km/s
FIGURE
[Y.-M. Wang, private communication, 2000]. Following
FIGURE3.3.
REFERENCES
the arguments given above for the slow wind, we should
therefore also expect a solar cycle dependence of the
Aellig,
R, A. J. Lazarus,
andparticles
J. T. Steinberg,
The
2. Ogilvie, K. W. and J. Hirshberg, The solar cycle
11.1.Bürgi,
A.,M.Dynamics
of alpha
in corosolar
wind He/H
the wind
fast wind,
we do J.not
wind type
helium
abundance:
variation
wind
variation
of theforsolar
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abundance,
nalsolar
streamer
geometries,
in Solar
Windwith
Seven,
observe.
Still,Res.,
it can79,
be4595–4602
argued, that(1974).
the fast solar wind is
speedbyand
the solar
cycle,
Geophys.pp.Res.
Lett., in
Geophys.
edited
E. Marsch
and
R. Schwenn,
333–336,
wave-driven and that the helium ions are not accelerated
press,
2001
Pergamon
Press,
Tarrytown,
N.
Y.,
(1992).
3. Feldman,
J. by
R. Asbridge,
S. J.interaction.
Bame, andIn
by
Coulomb W.
dragC.,but
wave-particle
J. T. Gosling, Long-term variations of selected solar
12. Borrini, G., J. T. Gosling, S. J. Bame, W. C. Feldwind properties: Imp 6, 7, and 8 results, J. Geophys.
man, and J. M. Wilcox, Solar wind helium and hyRes. 83, 2177–2189 (1978).
drogen structure near the heliospheric current sheet:
a signal of coronal streamers at 1 AU, J. Geophys.
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Res. 86, 4565–4573 (1981).
J. Geiss, Solar wind observations with the Ion Composition Instrument aboard the ISEE-3/ICE space13. Wang, Y.-M. and N. R. Sheeley Jr., Solar wind
craft, Sol. Phys. 124, 167–183 (1989).
speed and coronal flux-tube expansion, Ap. J. 355,
726–732 (1990).
5. Ogilvie, K. W. et al., SWE, a comprehensive plasma
TABLE 1. The number of spectra contributing to each speed range for the year
centered about the average year indicated. Note that speeds are given in km/s.
Year
1995.3
1996.5
1997.9
1998.6
1999 .4
2000.0
56238
44296
36686
21150
15064
14600
24849
35432
74580
52124
31590
15624
8800
3597
88786
67348
41666
14940
6440
1600
132
34608
55370
45650
25290
13440
9160
7722
40376
46556
41168
21420
13216
8200
7392
21012
35934
30544
20790
17248
16800
15147
Speed range
<350
350-400
400-450
450-500
500-550
550-600
600-850
TABLE 2. Parameters for the speed dependence of He/H given in eq. 1. The mean absolute deviation between the measured He/H and
the linear fit is denoted with 6.
Year, Month
1995, Mar
1995, Nov
1996, Aug
1997, Mar
1997, Dec
1998, Aug
1999, May
2000, Jan
a[%]
-1.4
-2.4
-2.8
-1.9
0.63
-0.62
2.36
3.03
b [% s/km]
8[%]
2
0.19
0.21
0.09
0.09
0.19
0.08
0.18
0.07
1.07 10~
1.20 10~2
1.30 10~2
1.05 10~2
0.54 10~2
0.96 10~2
0.30 10~2
0.32 10~2
and Wang's [9] profiles to calculate the proton flux at
2.5 /?0, we find that during solar minimum it is lower
by a factor of nine assuming a cycle-independent flux at
1 AU. A quantitative study showed that indeed the proton flux at 2.5 RQ varies by about a factor of ten over the
solar cycle between 1977 and 1994 [Y.-M. Wang, private
communication, 2000] when near-Earth wind speeds of
less than 400 km/s were analyzed. A parameter study by
Burgi [11] has shown that with decreasing proton flux
close to the Sun (induced by a locally increasing overexpansion) the helium abundance in the solar wind decreases because of the decreased momentum transfer via
Coulomb collisions. The change of the expansion profile,
i.e., the magnetic structure, over the course of the solar
cycle leads to a decreased proton flux at around 2.5 RQ
during solar minimum. We suggest that this reduction of
the proton flux close to the Sun decreases the efficiency
of the Coulomb drag and therefore reduces the He/H ratio in the solar wind around solar minimum.
Our measurements during solar minimum were taken
close to the heliospheric current sheet. It is known that
the helium abundance drops considerably upon current
sheet crossings Borrini et al. [12]. Indeed, their observation fits the idea of strong reduction of the proton flux
close to the Sun and the subsequent depletion of helium
ions because of inefficient Coulomb drag. Solar wind
streams close to the current sheet have very large expansion factors close to the Sun Wang and Sheely [ 13] which
lead to a low helium abundance in the solar wind Burgi
[11]. So far, we have discussed a potential explanation
for the solar cycle variation in a low speed bin. We can
apply the same concept of flux tube expansion close to
the Sun to the question why during solar minimum we
observe a strong speed dependence of the helium abundance. Wang and Sheeley [13] reported an inverse correlation between the rate of magnetic flux-tube expansion
and the solar wind speed at 1 AU. With increasing solar
wind speed at 1 AU they associate smaller expansion factors close to the Sun and therefore a larger proton flux in
corona. As discussed above, that leads to a higher He/H
in the solar wind which is observed in Figure 2 around
solar minimum.
the areal expansion A (r) — r2 /(r) reads
n(r)v(r)A(r) = const.
(2)
From the measured proton flux at R — 1 AU, the proton
flux O(r) at any given radial distance r can be inferred
using
= n(r)v(r) = <&(/?)
A(K)
A(r)
(3)
The ratio of the expansion factors of the magnetic field
is likely to change over the solar cycle since the large
scale magnetic structure of the corona changes from a
well-organized morphology with polar coronal holes and
an equatorial streamer belt around solar minimum to
a much more complicated structure with small coronal
holes and small streamers at all solar latitudes. The expansion factors of the magnetic field can be inferred using solar magnetograms and the assumption of a potential field model, either with or without a heliospheric current sheet Wang and Sheely [10]. Wang [9] gives two expansion profiles /(r) of the magnetic field for the slow
solar wind during solar minimum and solar maximum.
The expansion profile for solar minimum shows a very
strong over-expansion around 2.5 RQ before it decreases
at larger radii and levels off at about 5. Contrarily, the solar maximum expansion profile monotonically increases
to about 20 at large heliocentric distances. Using eq. 3
93
6. Neugebauer, M., Observations of solar wind helium, Fundamentals of Cosmic Physics 7, 131-199
(1981).
7. Biirgi, A., Proton and alpha particle fluxes in the solar wind: results of a three-fluid model, J. Geophys.
/tes. 97,3137-3150(1992).
8. Geiss, J., P. Hirt, and H. Leutwyler, On acceleration
and motion of ions in corona and solar wind, Sol.
Phys. 12,458-483(1970).
9. Wang, Y.-M., Two types of slow solar wind, Ap. J.
Lett. 437, L67-L70 (1994).
10. Wang, Y.-M. and N. R. Sheeley Jr., The solar origin
of long-term variations of the interplanetary magnetic field strength, J. Geophys. Res. 93, 1122711236(1988).
11. Biirgi, A., Dynamics of alpha particles in coronal streamer type geometries, in Solar Wind Seven,
edited by E. Marsch and R. Schwenn, pp. 333-336,
Pergamon Press, Tarrytown, N. Y, (1992).
12. Borrini, G., J. T. Gosling, S. J. Bame, W. C. Feldman, and J. M. Wilcox, Solar wind helium and hydrogen structure near the heliospheric current sheet:
a signal of coronal streamers at 1 AU, /. Geophys.
Res. 86,4565-4573(1981).
13. Wang, Y.-M. and N. R. Sheeley Jr., Solar wind
speed and coronal flux-tube expansion, Ap. J. 355,
726-732(1990).
14. Bodmer, R. and P. Bochsler, Influence of Coulomb
collisions on isotopic and elemental fractionation
in the solar wind acceleration process, J. Geophys.
Res. 105,47-60,2000.
We tried to verify our hypothesis also for the fast
wind. In the time interval between 1977 and 1994 there
was also a solar cycle dependence of the proton flux at
2.5 RQ for near-Earth wind speeds larger than 550 km/s
[Y.-M. Wang, private communication, 2000]. Following
the arguments given above for the slow wind, we should
therefore also expect a solar cycle dependence of the
solar wind He/H for the fast wind, which we do not
observe. Still, it can be argued, that the fast solar wind is
wave-driven and that the helium ions are not accelerated
by Coulomb drag but by wave-particle interaction. In
that case, the fast wind cannot serve as a test for the
hypothesis.
If indeed variations of the proton flux close to the Sun
via Coulomb drag cause the observed helium abundance
variation over the solar cycle, the same effect should be
present in other elemental or even isotopic ratios. In those
ratios, we expect a considerably less pronounced effect
since 4He has the strongest dependency on the proton
flux Bodmer and Bochsler [14].
ACKNOWLEDGMENTS
We are grateful to the many individuals who contributed
to the success of the Solar Wind Experiment (SWE) on
the Wind spacecraft. Furthermore, we thank Yi-Ming
Wang for valuable suggestions and discussions. This
work was supported in part by NASA Grant NAG5-7359.
The figures, some text, and tables from [1] are copyrighted 2001 by the AGU and are used with permission.
REFERENCES
1. Aellig, M. R, A. J. Lazarus, and J. T. Steinberg, The
solar wind helium abundance: variation with wind
speed and the solar cycle, Geophys. Res. Lett., 28,
2767-2770(2001).
2. Ogilvie, K. W. and J. Hirshberg, The solar cycle
variation of the solar wind helium abundance, J.
Geophys. Res., 79,4595-4602 (1974).
3. Feldman, W. C, J. R. Asbridge, S. J. Bame, and
J. T. Gosling, Long-term variations of selected solar
wind properties: Imp 6,7, and 8 results, J. Geophys.
/tes. 83,2177-2189(1978).
4. Ogilvie, K. W., M. A. Coplan, P. Bochsler, and
J. Geiss, Solar wind observations with the Ion Composition Instrument aboard the ISEE-3/ICE spacecraft, Sol. Phys. 124,167-183 (1989).
5. Ogilvie, K. W. et al., SWE, a comprehensive plasma
instrument for the Wind spacecraft, Space Science
Reviews 71,55-77, 1995.
94