Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://star.arm.ac.uk/~ambn/364.ps Äàòà èçìåíåíèÿ: Wed Oct 10 13:16:08 2001 Äàòà èíäåêñèðîâàíèÿ: Mon Oct 1 20:14:18 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: coronal hole

A&A 377, 691--700 (2001)
DOI: 10.1051/0004­6361:20011153
c
# ESO 2001
Astronomy
&
Astrophysics
Long period oscillations in the inter­plume regions of the Sun
D. Banerjee 1 , E. O'Shea 2 , J. G. Doyle 3 , and M. Goossens 1
1 Centre for Plasma Astrophysics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, 3001 Heverlee, Belgium
2 ESA Space Science Dept., ESTEC Solar System Div., Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
3 Armagh Observatory, College Hill, Armagh BT61 9DG, N. Ireland
e­mail: eoshea@so.estec.esa.nl; jgd@star.arm.ac.uk
Received 7 March 2001 / Accepted 14 August 2001
Abstract. We examine long spectral time series of inter­plume lanes observed on the 14th and 15th March 2000
with the Coronal Diagnostic Spectrometer (CDS) on­board SoHO. The observations were obtained in lines over
a wide temperature range, from the chromosphere to the corona. The statistical significance of the oscillations
was estimated by using a randomisation method. Our observations indicate the presence of compressional waves
with periods of 20--50 min or longer, both o#­limb and on­disk and up to 70 min further out to at least 25 arcsec
o#­limb. To our knowledge this is the first time that long period oscillations in the inter­plume regions close to the
limb of the Sun have been detected. We interpret these oscillations as outward propagating slow magneto­acoustic
waves which may contribute significantly to the heating of the lower corona by compressive dissipation and which
may also provide some of the enough energy flux required for the acceleration of the fast solar wind. These slow
waves may have been produced at the network boundaries in the coronal hole.
Key words. Sun: corona -- Sun: oscillations -- Sun: UV radiation
1. Introduction
When viewed o#­limb, polar plumes are the most promi­
nent structures in polar coronal holes (DeForest et al.
1997; Koutchmy & Bocchialini 1998). More re­
cently, DeForest et al. (2001) produced images from
LASCO/SoHO, which clearly show polar plumes extend­
ing to altitudes of 30 solar radii or more, very close to the
outer edge of the C­3 field of view and above the likely
Alf’venic point of the wind flow. Plumes are considered
to be bright threads rooted in the network and are
thought to form at the network boundaries where small
bipoles within a coronal hole reconnect with unipolar
flux concentrations (Wang & Sheely 1995; Wang 1998).
It has been known that the density of the plumes are
much higher (3--5 times) than the inter­plume background
(Saito 1965; Ahmed & Withbroe 1977; Young et al. 1999)
implying that the coronal heating rate is not uniform
over the coronal hole.
Plume formation involves magnetic reconnection be­
tween unipolar flux concentrations and nearby bipoles, but
the bipolar fields constitute only a small fraction of the to­
tal magnetic flux within the polar coronal hole. Primarily,
Send o#print requests to: D. Banerjee,
e­mail: dipu@wis.kuleuven.ac.be
coronal holes are overwhelmingly unipolar. This fact fur­
ther suggests that plumes are not the source of the high
speed polar wind (Wang et al. 1997).
The large outflow velocity as measured by Giordano
et al. (2000) and Patsourakos & Vial (2000) also favours
inter­plume lanes as being the main source of the fast solar
wind. The excess broadening of spectral line profiles in the
inter­plumes as compared to the plumes (Hassler et al.
1997; Wilhelm et al. 1998; Banerjee et al. 2000a) further
supports this idea. These authors also reported an anti­
correlation between the intensity and line widths of the
O vi 1032 š A line in both plume and inter­plume regions,
with detailed plume structures being seen out to 1.5 R# .
Thus it is becoming increasingly important to study the
dynamics of the inter­plume regions in polar coronal holes.
There are several reports on the structure, formation,
evolution and dynamics of plumes in the literature, but
there are only a few studies on inter­plume regions, mainly
because of the fact that they are very di#cult to observe
spectroscopically. Banerjee et al. (2000b,c) investigated
the temporal behaviour of polar plumes as observed in the
transition region line, O v 629 š A. In this paper we report
on the temporal behaviour of the inter­plume lanes as ob­
served by the CDS/SoHO instrument. Observations were
performed for lines over a wide temperature range, from

692 D. Banerjee et al.: Long period oscillations in the inter­plumes
Fig. 1. Position of the observing slit for the s18831r00 dataset
(14 March 2000) on an EIT/SoHO image of the south polar
coronal hole in Fe ix/x 171 š A taken 3 hours after the temporal
series (courtesy of the EIT consortium).
the low chromosphere (He i 584 š A), through the transition
region (O iii 599 š A, O iv 554 š A, O v 629 š A) to the corona
(Mg ix 368 š A), in a south polar coronal hole region.
2. Observations and data reduction
The Coronal Diagnostic Spectrometer (CDS) on­board
the Solar Heliospheric Observatory (SoHO) is a dual ex­
treme ultraviolet spectrometer, covering the wavelength
range 150 to 780 š A, comprising of a normal incidence
and a grazing incidence spectrometer (Harrison et al.
1995). The normal incidence spectrometer (NIS), whose
data is the subject of this paper, gives spectral images in
two wave­bands (308--381 š A and 513--633 š A). In order to
get good time resolution, we used the NIS in a sit­and­
stare mode. As the slit location, x = 92, y = -1051, is
the location of the centre of the slit (for the s18831r00
dataset), the coordinates at the top of the slit, x = 92,
y = -931 are on the disk and thus we can work out the
solar rotation expected at these coordinates. We find that
by using the routine ROT-XY in the SoHO software tree
that over one hour the Sun should rotate by 0.82 arcsec
per hour. Therefore over 4 hours at this location we can
thus expect that the Sun will rotate by a maximum of
#3 arcsec through the slit. If the source being observed
has a width of 3 arcsec or greater the e#ect of the so­
lar rotation on the resulting power spectrum will not be
important. Furthermore, we note that the rotation veloc­
ity of 0.82 arcsec per hour is the rotation velocity at the
top of the slit, i.e. this is the maximum rotation veloc­
ity. Therefore at other locations further out along the slit
we would expect the e#ect of the sit and stare mode, on
the resulting power, to be reduced further, and to become
less important in the areas beyond the limb. So for our
inter­plume observations in the polar region the e#ects of
the solar rotation are not considered to be important. For
the data reported here, the 2 â 240 arcsec slit was used.
Figure 1 shows an image of the Southern polar coronal
hole region taken with EIT/SoHO in Fe ix/x 171 š A at
19:00 UT on March 14, 2000, with the slit superimposed
(for dataset s18831r00). This figure confirms that our ob­
servations were pointed at an inter­plume region between
two plume regions. One should also note that the slit is
only a few arcsec away from a plume structure and inter­
sects the plume #40 arcsec o#­limb. The consequences of
this fact will be discussed in the final section.
The data discussed here were selected from
14--15 March 2000. The temporal series datasets were
obtained for the five lines of He i 584 š A (log T = 4.3 K),
O iii 599 š A, (log T = 5.0 K), O iv 554 š A (log T = 5.2 K),
O v 629 š A (log T = 5.4 K) and Mg ix 368 š A
(log T = 6.0 K), all with exposure times of 60 s (see
Table 1 for details). Data were obtained after the recovery
of SoHO and so the lines show the characteristic broad­
ened wings. This broadening has the e#ect of blending the
Mg ix 368 š A line with that of the nearby Mg vii 367 š A
line. We were able to fit the Mg ix component of this
blend satisfactorily by using a double Gaussian, and
by fixing the position of the Mg vii line. We fitted the
O iv 554 š A line with three Gaussians to take account
of the two weaker components of the O iv multiplet at
#553 and 555 š A. In all other cases, fitting was done using
a single Gaussian as the lines were found to be generally
symmetric. Details on the CDS reduction procedure, plus
the Wavelet analysis, may be found in O'Shea et al.
(2001) and Banerjee et al. (2001). The statistical signifi­
cance of the observed oscillations was estimated by using
a Monte Carlo or randomisation method. The advantage
of using a randomisation test is that it is distribution free
or nonparametric, i.e. it is not limited or constrained by
any specific noise models, such as Poisson, Gaussian etc.
We follow the method of Fisher randomisation as outlined
in Nemec & Nemec (1985) and implemented in the UK
Starlink software package, PERIOD (Dhillon & Privett
1997) (details can be found in O'Shea et al. 2001). Briefly,
the randomisation test is based on the assumption that, if
there is no periodic signal in the time series data, then the
measured values (intensity, velocity, etc.) are independent
of their observation times. For example, the intensities I 1 ,
I 2 ,... I n , observed at times t 1 , t 2 ,... t n , are just as likely
to have occurred in any other order I r(1) , I r(2) ,... I r(n) ,
where n is the total number of observations and r(1),
r(2),... r(n) is a random permutation of the subscripts 1,
2,... n. By using the maximum power peak in the global
wavelet spectrum, which is just the average of the wavelet
power over time and similar to a smoothed Fourier
power spectrum (Torrence & Compo 1998), at the ``test
statistic'' (see Dhillon & Privett 1997) it was possible
to test the hypothesis that there was no periodicity in
our data. The proportion of permutations that gave a
value greater or equal to the peak power of the original
time series would then provide an estimate of p, the
probability that no periodic component is present in the
data, i.e. a large value of p suggests that there is little or
no real periodicity in the data whereas a small value of p
suggests that the measured periodicity is likely to be real.
In practise n! is usually so large that it is not possible to
do this, due to computational and time constraints, and
so the peak powers are generally calculated for only a
random sample of m permutations. By carrying out this

D. Banerjee et al.: Long period oscillations in the inter­plumes 693
Fig. 2. Wavelet results for an inter­plume location corresponding to the He i 584 š A line in the s18831r00 dataset at pixel 40.
Panels a) and b) represent intensity and velocity results respectively. The middle left panels show the time frequency phase
plot corresponding to the variations shown in the top panels. The white horizontal lines in the phase plot indicate the power
maxima, corresponding to the maximum probability level for that particular time. The middle right hand panels show the
average of the wavelet power spectrum over time, i.e. the global wavelet spectrum. The continuous dashed horizontal lines in
the wavelet spectra indicate the lower cut o# frequency. The lowest panels show the variation of the probability with time from
the randomisation test.
approximation, for a random sample of 250 permutations,
we were able to obtain a reliable estimate of p. For a
sample of 250 random permutations the standard errors
of the p values are no greater than 0.04 (Nemec & Nemec
1985). Of course, the larger the number of permutations
chosen, m, the lower the standard error of the p value.
The probability levels displayed in this paper are the
values of (1 - p) â 100. We choose a value of 95% as
the lowest acceptable probability level. Occasionally the
estimated p value can have a value of zero, i.e. there
being an almost zero chance that the observed time series
oscillations could have occurred by chance. In this case,
and following Nemec & Nemec (1985), the 95% confidence
interval can be obtained using the binomial distribution,
and is given by 0.0 < p < 0.01, that is, the probability
((1 - p) â 100) in this case is between 99--100%.
To improve the signal­to­noise ratio of this data we
binned by three pixels along the slit (i.e. 3 â 1.68 arcsec),
in e#ect creating new pixels of #5â2 arcsec 2 . To determine
the Doppler shifts, wavelength calibration is needed. We
use the ``limb method'', where we assume that above the
limb all (non­radial) wave or mass motions on average
cancel out. In the absence of radiative transfer e#ects, the
o#­limb Doppler shift must on average be zero.
3. Results
The pointing of the slit was positioned at the south polar
limb (see Fig. 1) in such a way that a major part of the slit
was outside the limb and a part on the coronal hole. We
first present results from the inter­plume regions (o#­limb)
and later on focus on the disk part of the coronal hole. We
choose a 5 â 2 arcsec 2 region (a single binned pixel) in an
inter­plume location about 5 arcsec o# limb (pixel 40, in
our binned scale) for dataset s18831r00. Other regions will
be discussed later.
For the He i 584 š A line, formed in the low chromo­
sphere we present the wavelet results in Fig. 2. The inten­
sity and velocity variations are shown in the top panels.
In the wavelet spectrum, the dark contour regions show
the locations of the highest power. The light white hori­
zontal lines within the dark contour regions indicate the

694 D. Banerjee et al.: Long period oscillations in the inter­plumes
Fig. 3. The results of the wavelet analysis corresponding the O iii 599 š A line at pixel 40 in s18831r00. Representations are the
same as Fig. 2.
Fig. 4. The results of the wavelet analysis corresponding to the O iv 554 š A line at pixel 40 in s18831r00.

D. Banerjee et al.: Long period oscillations in the inter­plumes 695
Fig. 5. The results of the wavelet analysis corresponding to the O v 629 š A line at pixel 40 in s18831r00.
Fig. 6. The results of the wavelet analysis corresponding to the Mg ix 368 š A line and summed pixels 39--40 in s18831r00.

696 D. Banerjee et al.: Long period oscillations in the inter­plumes
Table 1. Details of the temporal sequence CHROM N6.
Date Dataset Pointing Start End Lines Observed
X, Y UT UT
14 March 2000 s18831r00 92, -1051 12:06 15:50 He i, O iii, O iv, O v, Mg ix
15 March 2000 s18854r00 27, -1056 12:09 15:53 He i, O iii, O iv, O v, Mg ix
locations of the maximum wavelet power at each particu­
lar time. The lowest panel shows the variation of the prob­
ability level over the observing time, by which it is possible
to see whether the maximum wavelet power at any time
in the wavelet spectrum has a high or low probability of
being due to noise. Only locations that have a probability
greater than 95% are regarded as being real, i.e. not due to
noise. Cross­hatched regions, on either side of the wavelet
spectrum, indicate the ``cone of influence'' (COI), where
edge e#ects become important (see Torrence & Compo
1998). The dashed horizontal lines in the wavelet spec­
tra indicates the lower frequency cut­o#, in this instance
0.21 mHz (due to edge e#ects), corresponding to oscilla­
tions with periods of #80 min.
The results from Fig. 2 show that the He i 584 š A in­
tensity oscillations are stronger and slightly more reliable
than the velocity oscillations. The time frequency phase
plane plots of intensity (left panels of Fig. 2) shows signif­
icant power around 0.3 mHz for almost the entire observ­
ing period. There is secondary power concentrated around
0.6 mHz for part of the sequence. The global wavelet spec­
trum (on the right of Fig. 2a), which is the average of the
wavelet power spectrum over the entire observing period
shows the strongest intensity power at 0.27 mHz. This
is printed out in Fig. 2 above the global wavelet plot, to­
gether with the probability estimate for the global wavelet
power spectrum. The velocity curve rarely shows power
above the 90% level and thus can not be considered as
being signifcant.
Now we turn our attention to several oxygen lines
formed at transition region temperatures. The wavelet re­
sults of the O iii 599 š A, O iv 554 š A and O v 629 š A
lines are presented in Figs. 3, 4 and 5, respectively. The
O iii 599 š A line shows intensity power in the 0.25--1.2 mHz
range with a peak at 0.25 mHz in the global wavelet spec­
trum at a high probability level (see value in figure and
in Table 2). The velocity oscillation shows a similar trend
with a varying probability level. The strongest global peak
is at 0.41 mHz, with a high probability level. The O iv
line (see Fig. 4) shows strong intensity power in the 0.2--
1.2 mHz range with the strongest power peaks at 0.25 mHz
and 0.41 mHz. The velocity peaks at 0.45 and 0.83 mHz
both with a high probability level. The O v 629 š A inten­
sity shows a similar power distribution with the strongest
power peak at 0.25 mHz, while the velocity shows the
strongest powers at 0.25 and 0.9 mHz. Both are present
with a very high probability level (see Table 2). Note that
the nature and period of oscillations, corresponding to the
three oxygen lines formed over a range of transition region
temperatures, behaves more or less in a similar way.
Next we present the wavelet results for the coronal line
Mg ix 368 š A in Fig. 6. Because of the low signal to noise
ratio in this case we binned over two pixels (39--40). The
global wavelet spectrum shows that the strongest intensity
power peak is around 0.38 mHz, with a high probability
level. The velocity signal for this line is too weak for any
reliable detection of oscillations.
Now, to emphasise the fact that these low frequency
oscillations are not only from this particular pixel location
but rather from all over the inter­plumes across our slit,
and also from the disk part of the coronal hole, we show
the spatial behaviour of the oscillation frequencies mea­
sured from the He i 584 š A & O v 629 š A lines in Figs. 7
and 8, respectively. These figures show the measured fre­
quencies as a function of position along the slit (X­F slice).
The frequencies in the left panels (crosses) correspond to
the maximum power, which have a probability of more
than the 95% after the randomisation test. The total num­
ber of counts in a pixel (summed counts) during the ob­
servation is shown in the right column, and is useful in
identifying the limb (pixel 41 corresponds to the limb). It
also shows the intensity fall o# as we go outside the limb
(pixel 40 and lower). The intensity and velocity results
both show that the primary maxima in the global wavelet
spectra lies in the range 0.23--0.8 mHz. The appearance
of more crosses in the intensity X­F slices as compared to
the velocity also indicates that the intensity oscillations
are stronger and more reliable (>95% probability level).
It might also indicate that the intensity oscillations are
more coherent than the velocity, but it should be borne in
mind that the velocity oscillations are weak, so it might
be that they are there, but the randomisation test does
not allow them to be detected over 95% probability level.
Furthermore it is interesting to note that these low fre­
quency oscillations are also present on the disk part (very
close to the limb, e.g. px 44) just below the inter­plume
lane. This gives an indication that whatever is causing
these oscillations in the inter­plumes, is also present on
the bright part of the disk, presumably in the network
boundaries.
As an alternative method of representing the presence
of these long period oscillations we show in Fig. 9, the
intensity variation of He i 584 š A line at di#erent loca­
tions (o#­limb) in the inter­plumes. Just from a visual

D. Banerjee et al.: Long period oscillations in the inter­plumes 697
Fig. 7. Frequencies measured in the intensity (bottom row)
and velocity (top row) fluctuations of the He i 584 š A line,
as a function of spatial position along the slit. The left pan­
els show the frequencies corresponding to the maximum power
measured above the 95% confidence level, after the randomi­
sation test, in the global wavelet plot. The right panels show
the total number of counts in a pixel (summed counts) over
the observation time.
Fig. 8. Frequencies in the O v 629 š A line, as a function of
spatial position along the slit.
examination of the He i 584 š A light­curves (Fig. 9 and
top panel of Fig. 2) one can see the presence of a long
periodicity of #70 min (notice the three strong peaks),
which becomes more apparent further o#­limb, up to at
least 25 arcsec.
Now we turn our attention to dataset s18854r00. We
first show the space time behaviour (a portion of the slit
which focuses the inter­plume region and the coronal hole)
as observed by He i 584 š A, in the form of a X­T slice
(Fig. 10). The top panel shows the original intensity map.
To bring out the details of the original intensity map
(X­T slice) we have filtered out the bright components
in the image. The intensity map I(y, t) is convolved in
the time direction with a Gaussian G(t). This results in a
smoothed image S(y, t) = I #G which contains no high fre­
quencies. Then dividing the original intensity map by the
Fig. 9. Intensity variation of He i 584 š A line in the s18831r00
dataset at di#erent inter­plume locations (o#­limb) as labelled.
smoothed map results in the contrast enhanced map, i.e.
C(y, t) = I(y, t)/S(y, t) (see Doyle et al. 1999, for details).
In this contrast enhanced image (lower panel of Fig. 10),
the solar north­south (SOLAR-Y) direction is in the ver­
tical axis, the horizontal axis is time. Once again the right
panels show the total number of counts in a pixel. The
grey scale coding has the most intense regions as white.
Note that around the time 20th, 70th and 110th min of
the observing sequence there are very bright features de­
tected in the X­T slice, perhaps spicules? The gradients
of these structures (in X­T slice) can provide information
about their speeds. Banerjee et al. (2000b) have however
studied their structures and dynamics in greater detail so
we do not intend to go any further in that direction here.

698 D. Banerjee et al.: Long period oscillations in the inter­plumes
Fig. 10. Space time behaviour of the intensity in the He i 584 š A
line corresponding to the s18854r00 dataset. The left panels
show the intensity maps (X­T slice) and the right panels show
the summed counts. The gray scale coding has the most intense
regions as white.
The presence of these jet­like features strongly a#ects the
background oscillations and thus our main objective of
studying the oscillations of the inter­plume regions was
not possible for this dataset. However, the disk part of
the slit has not been a#ected by the presence of these fea­
tures and so we use it here to investigate oscillations on
the disk. For a representative case of the coronal hole oscil­
lations, corresponding to a network bright pixel we choose
px 45 of s18854r00 dataset. For He i 584 š A, the intensity
and velocity both show the strongest peak at 0.23 mHz.
For O v 629 š A the intensity and velocity both shows strong
peaks around 0.27 and 0.25 mHz respectively, all with a
high probability level and also lasting for almost the entire
observing period. The detailed results from the other lines
and also from brightest pixel on the disk (px 44) for the
dataset s18831r00, are summarised in Table 3. It is clear
that the long period oscillations are present in all the lines
and in both datasets.
4. Discussion
Recent UVCS/SoHO observations (Giordano et al. 2000;
Patsourakos & Vial 2000) have established that the inter­
plume lanes provide a channel for the acceleration of the
fast solar wind. Patsourakos & Vial (2000) have reported
a total outflow velocity of #67 km s -1 at 1.05 R# , as mea­
sured by SUMER/SoHO. Their result is consistent with
large oxygen ion outflow velocities of 105 and 150 km s -1
at 1.7 R# as measured by UVCS/SoHO (Giordano et al.
2000). They have also shown that in the inter­plume lanes
the outflow is much faster than in the plumes, where the
outflow velocity is between 0 and 65 km s -1 . Thus it is
becoming important to know whether one can find di#er­
ent type of waves in these two regions, namely the plume
and the inter­plume. Furthermore since inter­plume and
network seems to be the main source for the fast solar
wind when viewing o#­limb and on disk respectively, it
is also important to study them individually and finally
to find a connection between these two regions. High­
cadence EIT/SoHO observations indicate that quasi pe­
riodic fluctuations with periods of 10--15 min are present
in polar plumes (DeForest & Gurman 1998) with a fil­
amentary structure within the plume, on a spatial scale
of 3--5 arcsec. These authors conclude that the waves are
either sound waves or slow magneto­acoustic waves, prop­
agating along the plumes at #75--150 km s -1 . Recently,
Ofman et al. (2000a) detected quasi periodic variations
in the polarization brightness (pB) at 1.9 R# , in both
plume and inter­plume regions. Their Fourier power spec­
trum shows significant peaks around 1.6--2.5 mHz and ad­
ditional smaller peaks at longer and shorter time­scales.
Their wavelet analysis of the pB time series shows that
the coherence time of the fluctuations is about 30 min.
Compressional modes reveal themselves in the form
of intensity oscillations, through variations in the emis­
sion measures, and because of density fluctuations they
are detected as velocity oscillations as well. This fact al­
lows us to interpret the oscillations measured here as being
due to slow magneto­acoustic waves. We should also point
out that the wavelet analysis su#ers from edge e#ects at
both ends of the time series. Some of our low frequency
oscillations in the phase plots are very close to the COI,
but at the same time the primary and secondary peaks in
the global wavelet spectra are above the lower frequency
cut o# of 0.21 mHz. So our detected oscillation frequen­
cies above 95% probability level (see Tables 2 and 3) are
quite reliable. Also note that the velocity oscillations are
not always reliable (e.g. Table 2, He i, Mg ix). It is fur­
ther interesting to note that these long period slow waves
are present all the way from the chromosphere, through
the transition region to the corona (although the coro­
nal Mg ix line is much less reliable). It is likely that the
waves detected at 1.9 R# by Ofman et al. (1997, 2000a)
using UVCS/SoHO and the waves detected by DeForest
& Gurman (1998) around 1.2 R# using EIT/SoHO are
the same as those reported here and as also observed by
CDS/SoHO in the polar plumes, very close to the solar
limb and in the network boundary of the coronal holes,
by Banerjee et al. (2000b,c).
It is therefore interesting to note that we are detect­
ing similar types of waves (compressional and with long
periodicities) in plumes and inter­plume regions close to
the limb and also in the network boundaries in the coro­
nal hole. Ofman et al. (2000a) have also observed these
long period waves in plumes and inter­plumes at 1.9 R# .
The periodicity in the inter­plumes seems to be slightly
longer than in the plumes. Linear slow magneto­acoustic
waves propagate at a speed close to the sound speed in a
low # coronal plasma. The long periodicity in the inter­
plume may be just a temperature e#ect on the slow waves.
Plumes are cooler than the background plasma (DeForest
et al. 1997). However, we should also point out that, be­
cause of line of sight e#ects and the proximity of the polar
plumes to our slit locations, we can not rule out contribu­
tions from both regions being present. Another possibility

D. Banerjee et al.: Long period oscillations in the inter­plumes 699
Table 2. Oscillation frequencies observed in the inter­plume a few arcsec o#­limb (px 40 in our binned scale corresponding to
the s18831r00 dataset). By using the wavelet method and the randomisation test the frequencies corresponding to primary and
secondary peaks in the global wavelet spectrum and their corresponding probability levels are listed.
Lines Intensity Results Velocity results
Primary Prob. level Secondary Prob. level Primary Prob. level Secondary Prob.level
He i 0.27 mHz 99--100% 0.58 mHz 99--100%
O iii 0.25 mHz 99--100% 0.64 mHz 99--100% 0.41 mHz 98.0%
O iv 0.25 mHz 99--100% 0.41 mHz 99--100% 0.45 mHz 99--100% 0.83 mHz 99--100%
O v 0.25 mHz 99--100% 0.35 mHz 99--100% 0.25 mHz 99--100% 0.9 mHz 99.2%
Mg ix 0.38 mHz 96.8%
Table 3. Summary of the oscillation frequencies observed corresponding to the brightest pixel on­disk (px 44 in our binned
scale for s18831r00 dataset and px 45 of s18854r00 dataset).
Dataset Lines Intensity Results Velocity results
Primary Prob. level Secondary Prob. level Primary Prob. level Secondary Prob. level
s18854r00 He i 0.23 mHz 99--100% 0.38 mHz 99--100% 0.23 mHz 95.6% 0.58 mHz 99--100%
O iii 0.25 mHz 99--100% 0.64 mHz 99--100% 0.29 mHz 98.8% 0.83 mHz 99.6%
O iv 0.27 mHz 99--100% 0.98 mHz 99--100% 0.32 mHz 99--100% 0.76 mHz 99--100%
O v 0.27 mHz 99--100% 0.58 mHz 99--100% 0.25 mHz 99--100% 0.58 mHz 99--100%
s18831r00 He i 0.32 mHz 99--100% 0.9 mHz 99--100% 0.23 mHz 99--100%
O iii 0.58 mHz 97.2% 0.98 mHz 99.2%
O iv 0.58 mHz 95.6% 0.29 mHz 99--100% 0.23 mHz 98.0% 0.29 mHz 98.0%
O v 0.58 mHz 97.2% 0.29 mHz 99--100% 0.45 mHz 99--100%
Mg ix 0.41 mHz 96.8%
is that the waves detected adjacent to a plume structure
could simply be waves which just leaked out of the plume
cavity and are propagating through the inter­plume.
Patsourakos & Vial (2000) concluded that a solar wind
outflow starting from the network and then continuing
in the inter­plume is a reasonable conceptual description.
Our observation of a long periodicity in the network and
in the inter­plumes (as presented here) supports this de­
scription. The likely detection of compressional waves in
the south polar coronal hole close to the limb (as presented
here) and well above the limb (Ofman et al. 2000a) may
provide the additional momentum and heat required for
the acceleration of the fast solar wind in coronal holes.
From our observation it is clear that the velocity ampli­
tudes are quite small and they appear to be sub­sonic,
thus the linear theory may well be applicable (at least
close to the limb). The energy flux carried by the slow
magneto­acoustic waves can be estimated as #[(#v) 2 /2]v s ,
in WKB approximation, where #v is the wave velocity am­
plitude, and c s is the sound speed. Using c s = 150 km s -1
in the low # coronal plasma, # = 1.67 â 10 -15 gm cm -3 ,
and #v = 10 km s -1 , we get a wave energy flux of
#1.25 â 10 4 ergs cm -2 s -1 . This is almost an order of
magnitude less than #10 5 ergs cm -2 , the energy flux re­
quired to accelerate the fast solar wind. These waves can
be further damped by compressive viscosity (Ofman et al.
2000b).
Finally our possible detection of long period slow waves
in plume and inter­plume regions raises further questions
on the magnetic topology of these regions and the influ­
ence of magnetic field. Most of the theoretical progress so
far has been devoted to waves in plumes (Ofman et al.
2000b; Nakariakov et al. 2000), where the linear and non­
linear e#ects have been included for the study of the wave
propagation. Such numerical simulations for inter­plumes
are very much warranted.
Acknowledgements. We would like to thank the referee for
his valuable suggestions. Research at Armagh Observatory
is grant­aided by the N. Ireland Dept. of Culture, Arts and
Leisure. D. B. wishes to thank the ONDERZOEKSRAAD
of K.U. Leuven for a fellowship (F/99/42) and EOS is
a member of the European Solar Magnetometry Network
(www.astro.su.se/ # dorch/esmn/). We would like to thank
the CDS and EIT teams at Goddard Space Flight Center
for their help in obtaining the present data. CDS and EIT
are part of SOHO, the Solar and Heliospheric Observatory,
which is a mission of international cooperation between ESA
and NASA. This work was supported by PPARC grant
PPA/G/S/1999/00055. The original wavelet software was pro­
vided by C. Torrence and G. Compo, and is available at URL:
http://paos.colorado.edu/research/wavelets/.
References
Ahmed, I. A., & Withbroe, G. L. 1977, Sol. Phys., 53, 397
Banerjee, D., O'Shea, E., Doyle, J. G., & Goossens, M. 2001,
A&A, 371, 1137
Banerjee, D., Teriaca, L., Doyle, J. G., & Lemaire, P. 2000a,
Sol. Phys., 194, 43

700 D. Banerjee et al.: Long period oscillations in the inter­plumes
Banerjee, D., O'Shea, E., & Doyle, J. G. 2000b, A&A, 355,
1152
Banerjee, D., O'Shea, E., & Doyle, J. G. 2000c, Sol. Phys., 196,
63
DeForest, C. E., Plunkett, S. P., & Andrews, M. D. 2001, ApJ,
546, 569
DeForest, C. E., Hoeksema, J. T., Gurman, J. B., et al. 1997,
Sol. Phys., 175, 393
DeForest, C. E., & Gurman, J. B. 1998, ApJ, 501, L217
Doyle, J. G., van den Oord, G. H. J., O'Shea, E., & Banerjee,
D. 1999, A&A, 347, 335
Giordano, S., Antonucci, E., Noci, G., Romali, M., & Kohl,
J. L. 2000, ApJ, 531, L79
Harrison, et al. 1995, Sol. Phys., 162, 233
Hassler, D. M., Wilhelm, K., Lemaire, P., & Sch˜uhle, U. 1997,
Sol. Phys., 175, 375
Koutchmy, S., & Bocchialini, K. 1998, Solar Jets & Polar
plumes ESA, SP­421, 51
Nakariakov, V. M., Ofman, L., & Arber, T. D. 2000, A&A,
353, 741
Nemec, A. F., & Nemec, J. M. 1985, AJ, 90, 2317
Ofman, L., Romali, M., Poletto, G., Noci, G., & Kohl, J. L.
1997, ApJ, 491, L111
Ofman, L., Romali, M., Poletto, G., Noci, G., & Kohl, J. L.
2000a, ApJ, 529, 592
Ofman, L., Nakariakov, V. M., & Selegals, N. 2000b, ApJ, 533,
1071
O'Shea, E., Banerjee, D., Doyle, J. G., Fleck, B., & Murtagh,
F. 2001, A&A, 368, 1095
Patsourakos, S., & Vial, J.­C. 2000, A&A, 359, L1
Saito, K. 1965, PASJ, 17, 1
Torrence, C., & Compo, G. P. 1998, Bull. Amer. Meteor. Soc.,
79, 61
Wang, Y.­M. 1998, ApJ, 501, L145
Wang, Y.­M., Sheeley, N. R., & Dere, K. D., et al. 1997, ApJ,
484, L75
Wang, Y.­M., & Sheeley, N. R. 1995, ApJ, 452, 457
Wilhelm, K., Marsch, E., Dwivedi, B. N., et al. 1998, ApJ,
500, 1023
Young, P. R., Klimchuk, J. A., & Mason, H. E. 1999, A&A,
350, 286