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Astronomy & Astrophysics manuscript no.
(will be inserted by hand later)
Signatures of very long period waves in the polar coronal holes
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, NL-2201 AZ, Noordwijk, The Netherlands
3 Armagh Observatory, College Hill, Armagh BT61 9DG, N. Ireland
emails: dipu@wis.kuleuven.ac.be; eoshea@so.estec.esa.nl; jgd@star.arm.ac.uk;
Marcel.Goossens@wis.kuleuven.ac.be
Received date, accepted date
Abstract. We examine long spectral time series of a coronal hole observed on the 7th March 2000 with the Coronal
Diagnostic Spectrometer (CDS) on-board SoHO. The observations were obtained in the chromospheric He i, and
a series of higher temperature oxygen lines. In this letter we report on the presence of long period oscillations in a
polar coronal hole region on the disk. Our observations indicate the presence of compressional waves with periods
of 20-30 minutes or longer.
Key words. Sun: Polar coronal holes -Ultraviolet: SoHO{Sun: Oscillations
1. Introduction
Coronal holes in the solar atmosphere have been identi-
ed as the source regions of the fast solar wind. Recent
observations from SUMER/SoHO have also shown that
the coronal velocity structure is linked with the chromo-
spheric magnetic network, with the largest out ow veloc-
ities occurring along network boundaries (Hassler et al.
1999). Wilhelm et al. (2000) reported more blue-shifts in-
side than outside coronal holes. They also showed that
the out ow of material, which must occur through open
eld lines, occurs mostly in the darker regions. Thus it is
becoming increasingly important to study the dynamics
of the polar coronal hole regions. Banerjee et al. (2000)
investigated the temporal behaviour of polar plumes as
observed in the transition region line O v 629 A line, not-
ing the presence of long period (20-30 min) compressional
waves. In a follow-up paper, Banerjee et al. (2001) ex-
tended this study to the inter-plume regions and reported
on even longer periodicities (up to 70 min) over a wider
temperature range. It is also becoming important to know
whether one can nd dierent types of waves in these dif-
ferent regions, namely the plume, the inter-plume and the
coronal hole. Also, one needs to address the question of
whether the long period waves observed outside the limb
(in the plume and inter-plume) originate from the disk
part of the coronal hole? In this letter we report on the
temporal behaviour of a polar coronal hole as observed by
the CDS/SoHO instrument.
Send oprint requests to: D. Banerjee
2. Observations and data reduction
For these observations we have used the normal inci-
dence spectrometer (NIS) (Harrison et al. 1995), which
is one of the components of the Coronal Diagnostic
Spectrometer (CDS) on-board the Solar Heliospheric
Observatory (SoHO). In order to get good time resolu-
tion the rotational compensation was switched o (sit-
and-stare mode) and so it is important to calculate the
lowest possible frequency we can detect from this long time
sequence after taking the solar rotation into account (see
Doyle et al. 1998 for details). For our dataset, s18778r00
(coordinates x = 127; y = 781), this rotation amounts to
3 arcsec per hour. Thus for a 2 arcsec wide slit width, the
lowest frequency resolution is 0.42 mHz. The temporal se-
ries dataset was obtained on 7th March 2000 for the four
lines of He i 584 A, O iii 599 A, O iv 554 A and O v 629 A,
with exposure times of 60 sec and using the 2 240 arc-
sec slit. The formation temperature of these lines range
from 20,000K to 250,000K. We t the O iv 554 A line
with three Gaussians to take account of the two weaker
components of the multiplet at 553 and 555 A. In all
other cases, tting was done using a single Gaussian as
the lines were found to be generally symmetric. Details
on the CDS reduction procedure, plus the wavelet anal-
ysis, may be found in O'Shea et al. (2001). Before ap-
plying the wavelet analysis we rst removed the trend of
the data (i.e. the very lowest frequency oscillations) us-
ing a 30 point running average. By dividing the results
of this running average (or trend) into the original data
and subtracting a value of one we obtained the resulting

2 D. Banerjee et al.: Waves in the polar coronal holes
Fig. 1. Wavelet results corresponding to the He i 584 A line in the s18778r00 dataset at pixel 22. Panels (a) and (b) represent
intensity and velocity results respectively. The middle row left panels show the time frequency phase plot corresponding to the
variations shown in the top panels. The middle row 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 ( 0:42 mHz). The lowest panels show the variation of the probability with time from the randomisation test, with
the dot-dash line indicating the 95% signicance level.
detrended data used in the analysis. The statistical sig-
nicance of the observed oscillations was estimated 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 specic noise models, such as Poisson, Gaussian etc.
We follow the method of Fisher randomisation as outlined
in Nemec & Nemec (1985), performing 250 random per-
mutations to calculate the probability levels. The levels
displayed here are the values of (1 p) 100, where p is
the proportion of the permutations that show a null test
result (see O'Shea et al. 2001). 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 oscil-
lations could have occurred by chance. In this case, and
following Nemec & Nemec (1985), the 95% condence in-
terval can be obtained using the binomial distribution,
and is given by 0.0 < p < 0.01, that is, the probability
((1 p) 100) in this case is between 99{100%. To im-
prove the signal-to-noise ratio of this data we binned by
three pixels along the slit, in eect creating new pixels of
52 arcsec 2 . The velocity values presented in this letter
are relative velocities, that is, they are calculated relative
to an averaged prole, obtained by summing over all pixels
along the slit and all time frames.
3. Results
The He i 584 A results are presented in Fig 1. In the
wavelet spectrum, the dark contour regions show the lo-
cations of the highest powers. Only locations that have a
probability greater than 95% are regarded as being real,
i.e. not due to noise. Cross-hatched regions, on either
side of the wavelet spectrum, indicate the `cone of in u-
ence' (COI), where edge eects become important (see
Torrence & Compo, 1998). The dashed horizontal lines in
the wavelet spectra indicate the lower frequency cut-o, in
this instance 0.42mHz, corresponding to oscillations with
periods of 40 minutes. The results from the phase plots
show that the He i 584 A intensity and velocity both show
signicant power in the 0.5-0.8 mHz range, for almost the
entire observing period. The global wavelet spectra (on
the right of Fig 1(a) & (b)), which are the average of the
wavelet power spectrum over the entire observing period,
show the strongest intensity power at 0.54 mHz (31 min-

D. Banerjee et al.: Waves in the polar coronal holes 3
Fig. 2. Intensity wavelet results for the O iii 599 A line corre-
sponding to pixel location 28.
Fig. 3. Intensity wavelet results for the O iv 554 A line corre-
sponding to pixel location 28.
utes) and the strongest velocity power at 0.64 mHz (26
minutes). This is printed out in Fig 1 above the global
wavelet plots, together with the probability estimate for
the global wavelet power spectrum.
Turning to the higher temperature oxygen lines, the
intensity wavelet results of O iii 599 A, O iv 554 A and
O v 629 A are presented in Figs. 2, 3 & 4 respectively, for
a single pixel location, px 28. All three oxygen lines show
intensity power around 0.7 mHz, with a peak at 0.64 mHz,
in the global wavelet spectrum plots, at a very high prob-
Fig. 4. Intensity wavelet results for the O v 629 A line corre-
sponding to pixel location 28.
ability level (see value in gures). The velocity oscillation
shows a similar trend but with a much smaller probabil-
ity level. For the O v velocity data, the strongest global
peak is at 0.7 mHz, with a 99.6% probability level. For the
other two oxygen lines the velocity oscillations are much
weaker and are not considered to be signicant. Note that
the nature and period of the intensity oscillations, corre-
sponding to the three oxygen lines, formed over the tem-
perature range 100,000 to 250,000K, behave more or less
in a similar way.
To emphasize the fact that these low frequency oscilla-
tions are not only coming from one or two particular pixel
locations but rather from all over the coronal hole across
our slit, we show, in Fig. 5, the spatial behaviour of the
oscillation frequencies measured from the O v 629 A line
for a section of the slit. This gure shows the measured
frequencies as a function of position along the slit (X-F
slice). The frequencies in the left panels, crosses and plus
symbols, correspond to the primary and secondary max-
ima (from the global wavelet spectrum) respectively. The
total number of counts in a pixel (summed counts) dur-
ing the observation is shown in the right column, and is
useful in identifying the network brightening (the peaks
correspond to the network pixels). The intensity and ve-
locity results both show that the primary maxima in the
global wavelet spectra lies in the range 0.5-1.0 mHz. The
secondary maxima of intensity often appears in the 1.2-1.4
mHz range. The appearance of a few more crosses in the
intensity X-F slice as compared to the velocity also indi-
cates that the intensity oscillations are slightly stronger
and more reliable (> 95% probability level). Note that
these low frequency oscillations come from both bright
and dark pixels, implying that they are present both in

4 D. Banerjee et al.: Waves in the polar coronal holes
Fig. 5. Frequencies measured as a function of spatial position
along the slit (X-F slice) for the O v 629 A line (left panels).
The right panels show the total number of counts in a pixel
(summed counts) over the observation time.
the network and internetwork, if that structure is present
in the coronal hole.
4. Conclusion
High-cadence EIT/SoHO observations indicate that quasi
periodic uctuations with periods of 10-15 minutes are
present in polar plumes (DeForest & Gurman 1998). These
authors conclude that the uctuations are caused either
by sound waves or slow magneto-acoustic waves propa-
gating along the plumes at 75{150 km s 1 . Ofman
et al. (2000) detected quasi periodic variations in the
polarization brightness (pB) at 1.9 R , in both plume
and inter-plume regions. Their Fourier power spectrum
shows signicant peaks around 1.6-2.5 mHz and addi-
tional smaller peaks at longer and shorter time-scales.
Recently, Banerjee et al. (2000, 2001) reported on the
existence of long period slow magneto-acoustic waves in
the plumes and inter-plumes respectively, as observed by
CDS/SoHO. Compressional modes reveal themselves in
the form of intensity oscillations, through variations in
the emission measure, and also as velocity oscillations
through uctuations in the plasma density. This fact al-
lowed them to interpret the measured oscillations as being
due to slow magneto-acoustic waves. It is likely that the
waves detected at 1.9 R by Ofman et al. (2000) us-
ing UVCS/SoHO and the waves detected by DeForest &
Gurman (1998) around 1.2 R using EIT/SoHO are the
same as those reported by Banerjee et al. (2000, 2001) in
the polar plumes and inter-plumes very close to the so-
lar limb (o-limb). Thus it is important to nd a source
region for these long period waves.
It was conjectured that these waves can originate from
the network boundaries in the polar coronal hole. In this
short contribution we show that these long period waves
do indeed originate from the disk part of the coronal hole
but the important point to note is that they are also
present at several locations in the coronal hole, namely in
the network and internetwork regions. We nd the pres-
ence of long period oscillations in bright pixels (corre-
sponding to the network locations) and also in the darker
pixels corresponding to the inter-network. The nature of
the waves are very similar to the ones reported by Banerjee
et al. (2000, 2001) and thus we also interpret these waves
as slow magneto-acoustic. We should also point out here
that we do not have information about the phase speed,
k and the phase relations, which conrms if the waves are
slow or fast. But since we do not observe any steepening
of the wave amplitudes or shocks we suggest that these
waves are slow waves. Furthermore, it is interesting to note
that these long period slow waves are detected in plasma
ranging in temperature from 20,000K to 250,000K, which
implies that theses waves are present much lower in the
atmosphere and are able to propagate upwards. However,
we have not been able to pin-point the location where
these waves originate and whether they are present in the
corona. We hope to address these questions in a wider
diagnostic study in a future observing campaign.
Acknowledgements. DB wishes to thank the
ONDERZOEKSRAAD of K.U.Leuven for a fellowship
(F/99/42). 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. Research at Armagh
Observatory is grant-aided by the N. Ireland Dept. of Culture,
Arts and Leisure. This work was supported by PPARC grant
PPA/G/S/1999/00055. The original wavelet software was
provided by C. Torrence and G. Compo, and is available at
URL: http://paos.colorado.edu/research/wavelets/.
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