The Polar Coronal Holes and the Fast Solar Wind : Some
Recent Results
S. Patsourakos*, S.-R. Habbalf, J.-C. Vial** and Y. Q. Hu*
*Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey, RH5 6NT,
UK
^University of Wales, Department of Physics, Penglais, Aberystwyth, Ceredigion, SW23,3BZ, UK
**Institut d'Astrophysique Spatiale, Universite Paris XI - CNRS, Bat. 121, F-91405 Orsay Cedex, FRANCE
* University of Science and Technology of China, Hefei, Anhui, Peoples Republic of China
Abstract. We report on recent results on the source regions of the fast solar wind : the Polar Coronal Holes
(PCH). They concern a comparison between the effective temperatures for a large set of different ions obtained
from observations in the inner corona of PCH and from a fast wind numerical model based on the ion-cyclotron
resonant dissipation of high-frequency Alfven waves. We also report on some preliminary results from our
modeling concerning the Fe/O ratio in the inner corona in PCH.
INTRODUCTION
quency. Moreover, this preferential heating and acceleration of low gyrofrequency ions, takes place closer to
the Sun owing to the rapid decrease with distance of the
magnetic field strength. When the dispersion of Alfven
waves by the minor ions is taken into account (e.g., (11)
and (12)) preferential heating and acceleration of minor
ions is even more enhanced: minor ions act as 'channels'
for the wave heating to proceed from one gyrofrequency
to a much faster one.
One of the most useful spectroscopic observables in
the solar corona is the ion effective temperature. It essentially corresponds to a combination of thermal and nonthermal (waves, turbulence) motions along a given line of
sight (LOS) in the corona. Since effective temperatures
are directly associated to ion temperatures, they provide
a powerful means of testing heating mechanisms. For example, in the frame of the models exposed in the previous
paragraph, one can expect an ordering of the ion effective
temperature with the ion gyrofrequency : the smaller the
gyrofrequency the larger the effective temperature. This
has been confirmed by (9) who confronted observations
of the effective temperatures of Mg X and O VI made
by UVCS in the outer corona with model calculations.
SUMER observations of a number of different ions in the
inner corona (14) have also demonstrated the existence
of such a trend even though it is somehow weak. What is
clearly needed is to confront effective temperatures of a
large number of ions which scan a wide range of gyrofrequencies derived from observations and detailed model
predictions. This is the main objective of the present paper. Moreover, we make an initial assessment on the pos-
A major breakthrough in our understanding of the
fast solar wind resulted and still results from observations made by the Solar and Heliospheric Observatory
(SOHO). Is seems that the fast solar wind emanates from
the boundaries of the magnetic network in Polar Coronal Holes (1) and then continues through the interplume
regions its journey into the outer corona (2) and (3). Electrons are rather cool in PCH and their temperature barely
exceed 1 MK (4). On the other hand protons and minor ions are significantly hotter than electrons with minor
ions being preferentially heated and accelerated with respect to protons (5).
The above results gave strong hints on the importance
of the resonant interaction between ion-cyclotron (ic)
waves with solar wind ions, for fast solar wind energetics and dynamics. The potential of the above mechanism for preferential heating and acceleration of the solar
wind ions was recognized by a number of authors (e.g.,
(6), (7) and (8)). The essence of this mechanism is that
high frequency ion-cyclotron waves resulting from either
a turbulent cascade of low frequency Alfven waves towards high frequencies (e.g., (9)) or from microflaring
in the network (10) can dump their energy and momentum into plasma heating and acceleration when their frequency matches the local gyrofrequency of a given ion.
Since the power spectrum of such waves is inversely proportional to the frequency of the waves this means that
ions with a smaller gyrofrequency will be more strongly
heated and accelerated than ions with a larger gyrofre-
CP598, Solar and Galactic Composition, edited by R. F. Wimmer-Schweingruber
© 2001 American Institute of Physics 0-7354-0042-3/017$ 18.00
299
TABLE 1. Initial conditions at 1 RQ used for constructing the
grid of our models described in the text. / m ,rl,a refer to the formulation of flow tube cross-section given in (15). The ion densities
are calculated by using the photospheric elemental abundances of
(16) and ionization equilibrium calculations of (17). The Alfven
waves power spectrum is the same as in (9).
electron density
electron(=proton, oc-particle, ion) temperature
magnetic field strength
2.5 x 108cm~3
8.0x 105 K
8G
fm
5
rl
1.31 R0
a
0.51 R0
helium abundance
wave amplitude
0.06
30 kms"1
sible impact that the physical mechanisms invoked by
the models exposed above may have on elemental abundances in the inner corona of PCH.
The present paper is organized as follows. In the second section we outline the numerical model we used
while in the third section we give some sample results
of the model. In the fourth section we make a comparison between observed effective temperatures and model
calculations concerning a number of different ions. The
fifth section deals with the Fe/O abundance ratio in the
inner corona of PCH as it is derived from the model. In
the sixth section we discuss our results and present our
conclusions.
test-particles in the ambient proton a-particles wind. For
more details, the interested reader should reffer to (9) and
the references therein.
In the present work we constructed a grid of solar
wind solutions, employing the same initial conditions
and comprising a number of different minor ions. As
such we had at hand the radial profiles of the density,
velocity and temperature for protons, a-particles and a
number of minor ions. In Table 1 we give the initial
conditions we used for each run made in the frame of
the present work.
SAMPLE RESULTS
DETAILS OF THE NUMERICAL MODEL
The numerical model used here is described in full detail in (9). It simultaneously solves the time-dependent
conservation equations for mass, momentum, energy and
wave-action for a four-species plasma (protons, electrons, a-particles and one minor ion) in a flow tube
with the relevant physical quantities being functions of
the radial distance only. The flow tube cross-section is
described using the formalism of (15). A Kolmogorov
power-spectrum describes the energy transfer from lowfrequency left-hand-polarized Alfven waves to highfrequency ion cyclotron waves, and with the resulting
resonant interaction with the solar wind ions (solar wind
bulk and minor species) is responsible for coronal heating and the acceleration of the solar wind. The distribution of wave energy to the ions is described by the quasilinear theory of wave-particle interaction and by a coldplasma dispersion relation. Grid points in space are distributed in such a way as to deal with steep gradients. The
corresponding numerical code is run for a sufficient time
(& 35 days in physical time) inorder to reach a steadystate solution i.e. mass, momentum and energy to attain
a constant value and it covers a distance range 1 R© 1.2 AU. Minor ions could approximately be treated as
300
We present in Figures 1 and 2 some sample results from
our modelling. In Figure 1 we show a number of properties of the background wind : protons and a-particles
start to get appreciably heated from a distance of about
1.3 R0, which corresponds to the distance from which
most of the super-radial expansion of the flow tube starts
taking place. To note here, that the a-particles to protons
temperature ratio, is larger than their mass ratio which results from the inclusion of dispersive Alfven waves. Contrary to protons and a-particles, electrons remain cool
since on one hand they receive no direct heating and
on the other hand Coulomb collisions are not sufficient
enough as to sustain a common temperature between ions
and electrons. Finally, after an initial lag a-particles start
to flow faster than the protons.
In Figure 2 we note that the temperature and velocities of the selected iron ions, which correspond to the
dominant ions in the inner corona of coronal holes, are
clearly ordered in a decreasing charge state : the smaller
the charge state (and thus the gyrofrequency) the more
a given ion is heated and accelerated closer to the Sun.
Moreover, iron ions are heated and accelerated more and
closer to the Sun as compared to the solar wind bulk
(protons and a-particles). The iron ions reach their terminal speed at a distance of about 3 R© which is signif-
electron density
temperatures
10
10
10'
10
w4
1.0
10
1.5
2.0
2,5
distance Rs
flow velocities
3.0
1.5
2.0
2.5
distance R_
3.0
1.0
1.5
2.0
2.5
3.0
distance R_
1000
1.0
FIGURE 1. Radial profiles of (a) the electron density (upper left panel), (b) the electron, proton and a-particles temperatures
(upper right panel) and (c) the proton and a-particles flow velocities (lower left panel).
Fe ; ion temperatures
,9^
10
10
Fe X
Fe IX
10C
10
1.0
1.5
2.0
2.5
3.0
Fe : flow velocities
1000 I
2.0
distance R a
FIGURE 2.
ions.
Calculated radial profiles of (a) the temperature (upper panel) and (b) the flow velocity (lower panel) for several iron
icantly smaller than the corresponding distance for protons (w 10R0) and are extremely hot (temperatures of
the order of 100 MK at 1.2 R0). The significant difference in velocity between the different ion stages of iron
in the inner corona (e.g., a factor w 4 at 1.2 R0 between
Fe IX and Fe XII), may have a significant bearing on
301
ionization balance calculations in the solar wind acceleration regions which normally use the assumption of
a common flow velocity for all ionization stages of the
same element,
1.05 FL
1x10' -
4x10°
1,18 FL
108F
10'
10°
q/m
FIGURE 3. Model calculated (rhombs) and observed (triangles) effective temperatures for a series of ions as a function of their
^ ratio. They concern distances 1.05 (upper panel) and 1.18 (lower panel) R0.
TABLE 3. The same as for Table 1, but now at at
a distance 1.18 RQ.
ION EFFECTIVE TEMPERATURES
ion
TABLE 2. Observed versus calculated effective
temperatures at a distance of 1.05 R0. The first column gives the used ion, the second column gives its
corresponding charge over mass ratio, the third column gives the logarithm (base 10) of the observed
Teff, the fourth column the reference from which the
T£$ were extracted ; a : (18), p : (14), y : (19) and
the fifth column gives the logarithm (base 10) of the
calculated Teff.
ion
m
iog(r$)
ref
log(r-f)
MgX
OVI
Ne VIII
NeVII
Mg VIII
Si VIII
Si VII
FeXI
FeX
0.37
0.31
0.29
0.28
0.28
0.24
0.21
0.17
0.16
6.55
6.45
6.55
6.5
6.55
6.4
6.55
6.65
6.75
a
6.23
6.24
6.23
6.24
6.25
6.31
6.42
6.65
6.8
y
P
P
P
P
P
P
P
MgX
OVI
Ne VIII
NeVII
Mg VIII
Si VIII
FeXII
m
iog(r$)
ref
log(T-f)
0.37
0.31
0.29
0.28
0.28
0.24
0.19
6.64
6.61
6.7
6.7
6.6
6.8
6.8
a
6.61
6.69
6.63
6.73
6.76
7.02
7.59
y
P
P
P
P
P
that minor ion species can be approximately treated as
test particles in the background solar wind (maximum
variations of 10-15 % were found between solutions
employing different ions). Effective temperatures Teff
were calculated according to the following relation :
(1)
where 7} is the ion temperature and < 5o)2 > is the velocity variance of unresolved motions along the LOS. For
calculating < 5\)2 > we considered that it is associated
(1) to the velocity amplitude of the Alfven waves which
propagate along the magnetic field lines and it writes as :
From the model results we calculated the effective
temperatures for a number of ions and compared them
with published observations of effective temperatures in
PCH. We note that we checked if the inclusion of a
minor species in the calculations, considerably alters the
properties of the background proton-a wind, in the same
spirit as in (9). We found, as the above authors also did,
(2)
302
Iron vs Protons
4.0x10
3,0x10
^ 2,0X10
LQX1Q
1.0
1.5
2,0
2.5
3,0
2,5
3,0
Oxygen vs Protons
1.0
1,5
2,0
distance
FIGURE 4. Radial variation of the the iron (upper panel) and oxygen (lower panel) abundances with respect to the Hydrogen as
a function of the distance.
where pw is the wave pressure and p the mass density and
(2) to solar wind motions along the LOS that produce
extra line broadening. For (2) we calculated the rms
value of the ion flow velocities distribution along the
LOS, by weighting each point taken into account in the
calculation by the square of the corresponding electron
density. Teff were determined by the observations, by
attributing the line width of the observed spectral lines
of different ion species to an effective temperature.
The results of this comparison are tabulated in Tables 2 and 3 and shown in Figure 3. The calculated Teff
tend to decrease with increasing ^ following the lines of
the ion-cyclotron resonance mechanism. The plateau towards large ^ can be explained by the existence of heavier ions (Fe, Si) in this range of ^ than in the descending
part of the Teff versus ^ curve which tends to compensate the decrease of Tf0n with ^). The observed Teff are
less 'well-ordered' with ^ than the calculated but a trend
is also evident. What we can conclude is that the calculated and observed Teff are in a good agreement to a
factor of maximum 2 in all but one cases. It can also be
noted that while at r = 1.18R© we have T$ > Temeff°fd
t
this trend is reversed for r = 1.05R0. The point of~ ithe
303
maximum disagreement between the observations and
the calculations (a factor w 6) corresponds to observations made in the Fe XII line at 1.18 R©. This line is particularly faint in coronal hole regions and observations
may have underestimated its true width: the poor photon
statistics in the line wings hamper to resolve the full line
and thus the corresponding Teff.
THE FE/O RATIO IN THE INNER
CORONA OF POLAR CORONAL HOLES
Inorder to make a case on the possible implications the
present model and the ic mechanism in general may have
on elemental abundances in the inner corona, we show
here some preliminary results on the Fe/O abundance ratio (Figure 4). In-situ observations (20) of this ratio in
fast solar wind streams have shown that it takes values
comparable to the photospheric ones. We approximated
the iron and oxygen total densities by the sum over the
densities of their dominant ionization stages (Fe IX, X,
XI, XII and O VI, VII, VII correspondingly). It can be
seen from Figure 4 that the iron abundance decreases
with distance in the range 1.0-1.3 R0 while for oxygen this decrease takes place in the range & 1.5-1.8 RQ.
The above behavior is a direct consequence of the different velocity profiles of oxygen and iron : iron is more
massive than oxygen and it is therefore more efficiently
accelerated closest to the Sun owing to the smallest gyrofrequencies of the iron ions as compared to the oxygen
ions. Therefore the iron and oxygen start moving faster
than the protons and thus become depleted at different radial distance regimes. From the above it follows that until
a distance of w 1.3 R0 the Fe/O decreases a result which
may be termed as an 'inverse FlP-effect' for iron and
oxygen. We note here, that at larger distances from the
Sun both elements retain more or less their abundances
at 1 R0.
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DISCUSSION AND CONCLUSIONS
The rather good agreement between the observed and
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ions with ^ ratios from 0.16 to 0.37 provides another
strong argument in favor of the importance of the ic
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It is remarkable to note how well calculations fit the
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same element inferred by modeling along with detailed
observations of the Fe/O ratio in the inner corona of Polar Coronal Holes are needed to settle this issue.
ACKNOWLEDGMENTS
S. Patsourakos is financed by PPARC.
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