Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://star.arm.ac.uk/~ambn/312jgd.ps Äàòà èçìåíåíèÿ: Wed Jun 2 13:24:20 1999 Äàòà èíäåêñèðîâàíèÿ: Mon Oct 1 21:06:29 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: coronal hole

A&A manuscript no.
(will be inserted by hand later)
Your thesaurus codes are:
02.12.1; 02.12.3; 06.01.2; 06.01.3; 06.03.2; 06.19.2
ASTRONOMY
AND
ASTROPHYSICS
June 1, 1999
Coronal Hole Diagnostics out to 8R fi
J.G. Doyle, L. Teriaca and D. Banerjee
Armagh Observatory, College Hill, Armagh BT61 9DG, N. Ireland
emails: jgd@star.arm.ac.uk, lte@star.arm.ac.uk, dipu@star.arm.ac.uk
Received date, accepted date
Abstract. The Si viii line width measurements and N e
estimates based on SUMER observations are combined
with LASCO and UVCS output to provide an overview
of its variations with height above a polar coronal hole.
From the combined dataset we find a radial dependence
of the electron density, in the range 1--2 R fi as r \Gamma8 , from
2 to 4 R fi as r \Gamma4 and then as r \Gamma2 . Combining the Si viii
half width at 1/e of the peak intensity with the UVCS
O vi half width, we find a small increase of the half width
from 1 to 1.2 R fi , then a plateau until 1.5 R fi , thereafter a
sharp increase until 2 R fi , finally a more gradual increase
reaching 550 km s \Gamma1 at 3.5 R fi . Our data suggests that
the MHD waves responsible for the excess line broadening
tends to become non­linear as it reaches 1.2 R fi .
Key words: Sun: Corona ­Ultraviolet; SOHO--Sun:
waves; Sun: Coronal Hole; Sun: Electron Density
1. Introduction
The measurement of line widths can provide information
concerning ion temperatures, sub­resolution turbulent mo­
tions and velocity fluctuations associated with magneto­
hydrodynamic (MHD) waves in the corona. Line width
variations combined with simultaneous electron density
estimates, provides a very powerful diagnostic for the so­
lar corona. In two previous papers we have reported such
observations off the Western limb (Doyle et al. 1998; here­
after DBP) and above a Coronal Hole (Banerjee et al.
1998; hereafter BTDW) based on Si viii lines observed
with SUMER (Wilhelm et al. 1995) onboard SOHO.
Doschek et al. (1997) have derived electron densities as
a function of height in the north and south polar coronal
holes. They find that for distances of a few arc seconds
outside the solar limb, the average line of sight electron
densities in the coronal holes are about a factor of 2 lower
than in quiet sun regions. Electron densities similar to
those derived from the Si viii lines are reported by Fludra
et al. (1999a,b) and Doyle et al. (1999) based on Si ix data
Send offprint requests to: J.G Doyle
obtained with the CDS instrument onboard SOHO (Har­
rison et al. 1995). Wilhelm et al. (1998) have deduced elec­
tron temperatures, densities and ion velocities in plumes
and inter­plume regions of coronal holes. Recently War­
ren & Hassler (1999) have used Si iii, Mg viii, Si viii and
Mg ix line ratios for electron density measurements. In an
earlier study, Hassler et al. (1990) presented line profiles
of coronal lines from Mg x 609/625 š A up to ¸ 140,000 km
above the limb.
In the coronal hole (see BTDW), the line width data
show that the non­thermal line­of­sight velocity increases
from 27 km s \Gamma1 at 27 arc sec above the limb to 46 km s \Gamma1
some 250 arc sec (i.e. ¸180,000 km) above the limb. The
electron density shows a decrease from 1:1 10 8 cm \Gamma3 to
1:6 10 7 cm \Gamma3 over the same distance. It was shown by
DBP and BTDW that the Si viii non­thermal velocity
was inversely proportional to the quadratic root of the
electron density, in excellent agreement with that pre­
dicted for undamped radially propagating Alfv'en waves.
The Western limb data showed a similar trend. Several
questions arise from this work, e.g. how representative are
the Si viii lines of coronal hole conditions near the limb?
How do these observations of line width and electron den­
sity out to 1:25 R fi compare with measurements further
off­limb? We address these issues by looking at additional
SUMER data out to 1.38 R fi coupled with measurements
obtained from LASCO and UVCS. This allows us to in­
vestigate physical conditions of the solar corona and the
coronal­heliospheric interface. Earlier observations of Sky­
lab and more recently SOHO/UVCS observations (Cran­
mer et al. 1999) have established that the fast solar wind
originates from coronal holes, while the slow wind is as­
sociated with bright equatorial streamers and a number
of dramatic transient events such as coronal mass ejec­
tions (CMEs). We concentrate here on the coronal hole
region in the solar minimum phase (during Nov­Dec '96).
All solar wind modelling requires knowledge of both the
electron density and non­thermal velocity at the base of
the coronal hole as boundary conditions. We hope that
our results will provide input parametric values for such
solar wind modelling.

2 Doyle et al.: Coronal hole diagnostics
2. Observations and Data Reduction
SUMER is a normal incidence spectrograph operating over
the wavelength range 450 š A to 1610 š A, details can be ob­
tained from Wilhelm et al. (1995). The dates of the obser­
vations discussed here, their locations, pointing, slit sizes
and exposure times are given in BTDW.
Fig. 1. A sample plot of the Si viii spectral region in the coro­
nal hole. Line fits are given by the dotted line.
Briefly, the data was acquired above a north polar coro­
nal hole (NPCH) on 4 November 1996 and 10 Decem­
ber 1996. Sequences in the NPCH comprised of a tem­
poral series of spectra taken at the same pointing but at
successive times. The images were taken with the 1\Theta300
and 4\Theta300 arc sec slits. Using the individual spectra a
summed spectrum was obtained. Analysis at different po­
sitions along the slit will give us information at different
heights above the coronal hole. Details on the reduction
procedures can be found in BTDW, where they have stud­
ied up to 1.25 R fi off the limb. In the present paper we
extend the analysis further off the limb up to 1.38 R fi .
For each line a Gaussian fit (Fig. 1) was applied us­
ing the Genetic Algorithm (GA) of Charbonneau (1995).
A single Gaussian fit was applied for the analysis of each
line. A complete examination of the reliability of GA with
respect to other algorithms was performed by McIntosh et
al. (1998). An estimation of the errors in the derived pa­
rameters was obtained using the GA­derived parameters
as an input for a ``classical'' IDL­CURVEFIT procedure
(Peter, 1999; Peter & Judge, 1999).
Using the new algorithms we re­analyze the dataset al­
ready presented by BTDW. For the NPCH, we add 3 more
points at 285, 325 and 370 arcsec above the solar limb with
respect to the data presented in BTDW. We find that our
previous estimate of errors around 0.5 km s \Gamma1 for the non­
thermal velocity obtained with the 1 \Theta 300 slit and of 1.0­
1.5 km s \Gamma1 for those obtained with the 4 \Theta 300 slit, are
correct. Slightly larger errors are present towards the end
of each slit (see x3 and Fig. 4. later). For the new 3 points,
errors of 4, 5 & 7 km s \Gamma1 were derived. For the electron
density, the error arises not only from the measured ratio
of the two lines but also from the errors in the atomic CHI­
ANTI (Dere et al. 1997) database that we have used. The
expected error coming from the database is estimated to
be from 12% to 15% (see Laming et al., 1997). The prop­
agation of this error in the ratio through the CHIANTI
database was simply performed introducing the value of
the ratio and the value of the ratio plus/minus the er­
ror. The resulting relative error was summed quadratically
with the error of 15% estimated before. The final error was
practically dominated by the errors in the database up to
200 arcsec (substantially the entire dataset presented in
BTDW). Larger errors are again present for the new 3
points (see Fig. 2, inset).
Inspection of the spectral region around the Si viii
lines revealed a strong feature at 1442.47 š A, (identified as
a second order line at 721.23 š A from a comparison of off­
limb data taken on and off the KBr coated part of the
detector; Feldman et al. 1997). The intensity variation of
this line compared to Si viii 1445.75 š A and 1440.49 š A shows
a similar fall­off implying a similar temperature of forma­
tion. No identification was given by Feldman et al. (1997)
of this line, although they did suggest it to be a hot coronal
feature, perhaps due to Fe viii. We are unable to verify its
identification due to incomplete energy levels for Fe viii.
3. Results & Discussion
In Fig. 2, we plot the electron density as derived from
Si viii, coupled with N e from UVCS (Kohl et al. 1998)
and LASCO (Lamy et al. 1997). The LASCO data was
acquired in February 1996, while the UVCS images were
time­averaged from November 1996 to April 1997.
Guhathakurta & Fisher (1995, 1998) estimated the
electron density distribution in the coronal hole from ob­
servations made with the space based SPARTAN 201­
01,03 instrument. At that phase of the descending solar
magnetic activity cycle the coronal conditions were dif­
ferent from our observing period (during our observing
period the solar activity was in the minimum phase), so
we don't compare our results with SPARTAN, but the es­
sential density profile has a striking similarity. The above
authors obtained the density profile from polarized bright­
ness (pB) measurements between 1.16 ­ 6 R fi . They give
an analytic prescription of the density profile as,
N (r)
N (R fi ) = exp
Ÿ
\Gamma ¯m p g fi R fi
kB (T e + T p )=2
`
1 \Gamma R fi
r
'–
(1)
where N is the number density (= N e + N p ), ¯ is mean
atomic weight (= 0:62), m p the proton mass, kB the Boltz­
mann constant, g fi the solar gravity and the effective tem­
perature is given by T eff = (T e + T p )=2, where T e and T p
are the electron and proton temperature, respectively. The
line fit as a function of (1\Gamma R fi
r ) for all densities out to 8 R fi
is shown as the solid line in Fig. 2 for T eff = 1:2 10 6 K.

Doyle et al. : Coronal hole diagnostics 3
Fig. 2. Variation of the electron density above the polar coronal hole. The circles represent data from SUMER, diamonds data
from LASCO and triangles data from UVCS. The solid line represents Eq. (1) with Teff = 1.2 10 6 K and the dashed line
represents the polynomial Eq. (2).
Thus for a locally isothermal fully ionized two­fluid coro­
nal plasma solution we can either estimate T e or T p . Using
T e of Si viii as 8 10 5 K (i.e. its formation temperature in
ionization equilibrium), we find an estimate of T p as 1.6
10 6 K. Furthermore this formula predicts an electron den­
sity of 4:5 10 3 cm \Gamma3 at 8 R fi in excellent agreement with
observations.
Our results for the ion temperature are in agreement
with observations obtained by UVCS (Kohl et al. 1997;
Cranmer et al. 1999) who find that at larger distances from
the limb the ions in a coronal hole are extremely `hot' and
the electrons are much `cooler'. Thus our observations re­
confirms that in the coronal hole plasma, particularly at
larger distances from the limb the assumption of collisional
ionization equilibrium can not be used any more. This is
also consistent with a study of several ions by Tu et al.
(1998) who found ion temperatures perhaps as high as 2--3
times the formation temperature in ionization equilibrium
even at heights of only a few tens of arcsecs.
Recently, Esser et al. (1999) have combined data from
SPARTAN, White light coronagraph (WLC) from 1.5 ­
5.5 R fi in April '93, with Mauna Loa observations between
1.16 ­ 1.5 R fi (Fisher & Guhathakurta, 1995). We are
unable to fit the data in Fig. 2 with their polynomial as our
data­set is more complete, extending from 1.02 ­ 8 R fi . In­
fact, the expression given by Esser et al. predicts a rather
high electron density at the limb and a density three orders
of magnitude smaller at 1AU. Instead, the data in Fig. 2
suggests a fall­off in density proportional to r \Gamma8 from 1
to 2 R fi , then r \Gamma4 from 2 to 4 R fi and finally as r \Gamma2 . A
polynomial fit of the form
N e = 1 \Theta 10 8
r 8
+ 2:5 \Theta 10 3
r 4
+ 2:9 \Theta 10 5
r 2
(2)
provides an excellent fit to the data as shown by the dotted
line in Fig. 2. The first coefficient in the R.H.S of Eq. (2)
is determined by the electron density close to the limb
(i.e. from our Si viii SUMER data), the last coefficient
determined by the electron density at 1 AU, while only
the middle coefficient was varied in order to provide the
best fit.
In Fig. 3, we plot the half width at 1/e of the peak in­
tensity (V 1=e ) in km s \Gamma1 as measured from Si viii SUMER
data plus O vi UVCS data (Kohl et al. 1998). The effec­

4 Doyle et al.: Coronal hole diagnostics
Fig. 3. Variation of the half width in km s \Gamma1 at 1=e of the peak intensity in the coronal hole. The circles represent data from
SUMER and triangles data from UVCS.
tive (ion kinetic) temperature (T k ) can be obtained from
(Kohl et al. 1998),
V 1=e = c\Delta– 1=e
– 0
=
r
2kBT k
M
(3)
where M is the ion mass and \Delta– 1=e
is the observed 1/e
half width. We have applied a mass correction factor of
1.32 to the Si viii data to make it consistent with O vi.
Note that the kinetic temperature include contributions
both from microscopic thermal motions and unresolved
transverse wave motions. As shown in Fig. 3, this data
suggests a small increase from 1 to 1.2 R fi , then a plateau
up to 1.5 R fi , followed by a sharp increase up to 2 R fi ,
then a more gradual increase further out.
Now we turn our attention to the question of the non­
thermal velocity. The analysis of DBP and BTDW showed
that the non­thermal line­of­sight velocity as derived from
the Si viii line widths increases above the limb while the
electron density decreases. On a closer inspection, the ob­
servations revealed that the non­thermal velocities were
inversely proportional to the quadratic root of the elec­
tron density, in excellent agreement with that predicted
for undamped radially propagating Alfv'en waves. In the
WKB approximation the rms wave velocity amplitude and
density are related by (Hollweg 1990),
! ffi v 2 ? 1=2 / ae \Gamma1=4 (4)
The non­thermal velocity can be deduced from the
standard equation for an optically thin line broadened by
thermal broadening caused by the ion temperature T i and
broadening caused by non­thermal motions as given by,
FWHM =
''
4ln2
`
–
c
' 2 `
2kBT i
M + ¸ 2
' # 1=2
(5)
where M is the ion mass, ¸ is the non­thermal speed, re­
lated to the wave amplitude by ¸ 2 = 1
2
! ffi v 2 ?, where
the factor of 2 accounts for the polarization and direction
of propagation of a wave relative to the line of sight.
Measuring the FWHM of the Si viii 1445 line and
using Eq. (5) with T i ¸ 1:6 10 6 K (as suggested from
the line fitting to N e ), the diamond symbols in Fig. 4
represents the observed non­thermal velocities at different
heights.
Now If we assume the same ion temperature as Si viii
for the 721.23 š A line (as suggested by the intensity fall­off

Doyle et al. : Coronal hole diagnostics 5
compared to Si viii), the Si viii non­thermal widths im­
plies an ion mass of ¸53 for this new feature. This latter
assumption is probably valid as different emission lines are
generated in the same column mass as seen by the spectro­
graph. Although, this can not be taken as absolute proof
it does suggest that the line may be due to Fe, probably
ionization stages vii--viii.
In Fig. 4, the (+) represents the velocities calculated
on the basis of the Eq. (4), using the measured N e from
Si viii. We have used a magnetic field strength of B = 6G
and a proportionality constant so as to match the energy
flux density (see BTDW for details). In both cases, we
find excellent agreement in the inner corona, but for the
outer corona AE 200 arc sec (see Fig. 4), the (+) symbols
starts to deviate from those calculated from the observed
FWHM(diamond symbols in Fig. 4). It is also possible to
estimate the errors in the calculated non­thermal velocity
(+); for the last 4 points, errors of 3, 3, 5 and 15 km s \Gamma1
have been estimated. Despite these large errors we have no
overlap with the error­bars of the observed non­thermal
velocities, suggesting an effective break­down of Eq. (4)
above 1.2 R fi .
Lou & Rosner (1994) have already pointed out that
waves can be reflected against gradients in the Alfv'en
speed and the WKB approximation fails. The reflection is
important as it increases the momentum transfered from
the Alfv'en wave to the medium. Recently Torkelsson et
al. (1998) have shown that the Alfv'en waves steepen and
produce current sheets in the non­linear regime. These
waves are strongly damped by non­linear steepening. They
have also reported density oscillations in their simulations,
which are consistent with observations by Ofman et al.
(1997) who reported quasi periodic variations in the po­
larized brightness in the polar coronal holes between 1.9­
2.45 R fi , as observed from the white light channel (WLC)
of UVCS. It would be interesting to see whether these den­
sity oscillations are also present in the inner corona which
can be due to the presence of non­linear high amplitude
compressional waves as reported by Ofman et al. (1997).
For that one needs a high cadence dataset. We propose
that somewhere around 1.2 ­ 1.3 R fi this non­linearity be­
comes important (as indicated by Figs. 3 & 4). The Alfv'en
waves with an amplitude of 30­50 km s \Gamma1 (as observed) at
the base of the coronal hole can generate non­linear soli­
tary type of waves, which can contribute significantly to
solar wind acceleration in open magnetic field structures.
Note from Fig. 3 that relatively sharp variations occur
around 1.5 R fi . This may be the location where the ther­
malization and the isotropization times of various species
begins to exceed the local coronal expansion time. Esser et
al. (1999) from a study of Mg x and O vi lines (observed
with SOHO/UVCS) found a transition from collisional to
collisionless plasma between 1.75 to 2.1 R fi in a polar
coronal hole. Cranmer et al. (1999) have presented an em­
pirical model of H i and O vi distributions, which also
indicates the presence of this transition. In their model
Fig. 4. Variation of the non­thermal velocity with height in
the north polar coronal hole. The diamonds represent those
measured with Si viii, the plus symbols correspond to theoret­
ical estimates based on Eq. (4) and the measured Ne (see text)
and squared boxes represent those derived from the 721.23 š A
line assuming it's due to an Fe ion.
they found a sharp variation between 1.8 R fi ­ 2.1 R fi
(see their Figs. 5&9). It is also interesting to note that the
electron density variation at 2 R fi has changed to r \Gamma4 from
its earlier r \Gamma8 fall­off. For line width measurements, UVCS
data are not available below 1.5 R fi , so we feel that the
combined SUMER and UVCS datasets allows us to locate
this transition point with better precision suggesting that
the physics of the plasma transport and wave dissipation
diverges from classical Coulomb theory at heights beyond
1.5 R fi . At larger distances, e.g. above 2 R fi , the large
V 1=e can also be due in part to the ion­cyclotron resonant
acceleration by high frequency MHD waves (McKenzie et
al. 1995). We hope that our results will provide more pre­
cise input parameters at the base of the coronal hole for
future solar wind models.
Acknowledgements. Research at Armagh Observatory is grant­
aided by the Dept. of Education for N. Ireland while partial
support for software and hardware is provided by the STAR­
LINK Project which is funded by the UK PPARC. This work
was supported by PPARC grant GR/K43315. We would like
to thank the SUMER team at Goddard Space Flight Center
for their help in obtaining the data. The SUMER project is
financially supported by DLR, CNES, NASA, and PRODEX.
SUMER is part of SOHO, the Solar and Heliospheric Obser­
vatory of ESA and NASA. We would also like to thank Scott
McIntosh for a copy of the GA routine.
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