Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://star.arm.ac.uk/preprints/460.ps Äàòà èçìåíåíèÿ: Mon Oct 3 13:50:14 2005 Äàòà èíäåêñèðîâàíèÿ: Mon Oct 1 21:30:46 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: coronal hole

Astronomy & Astrophysics manuscript no. 3826 September 27, 2005
(DOI: will be inserted by hand later)
Repetitive occurrence of explosive events at a coronal hole
boundary
J. G. Doyle 1 , M. D. Popescu 1,2 and Y. Taroyan 1
1 Armagh Observatory, College Hill, Armagh BT61 9DG, N. Ireland
2 Astronomical Institute of the Romanian Academy, RO­040557 Bucharest 28, Romania
Received / accepted
Abstract. SUMER/SoHO data taken at a coronal hole boundary show a repetitive explosive event occurrence rate of around
3 min increasing to over 5 min towards the end of the activity. We suggest that the neighbouring oppositely directed closed
and open field lines at the coronal hole boundary undergo repetitive reconnection seen as a sequence of explosive events.
The repetitive reconnection may be triggered by transverse oscillations of the flux tubes in the closed field line region. These
oscillations periodically separate and bring together the closed and open field lines on the two sides of the coronal hole boundary.
An important indicator favouring the interpretation in terms of a kink mode is the observed increase in the oscillation period.
Key words. Sun: activity: -- Sun: oscillations -- Sun: transition region -- Sun: UV radiation -- Line: profiles
1. Introduction
Explosive events (also called bidirectional jets) are small re­
gions of a few arcseconds size with strong blue­ and red­shifted
emission reaching Doppler shifts of up to 150 km s -1 . Over the
past decade, there have been many studies of explosive event
(EE) activity. For example, Chae et al. (1998) found that EEs
appear preferably in regions with weak fluxes of mixed polar­
ity or on the border of regions with large concentration of mag­
netic flux. Madjarska & Doyle (2002) investigated time delays
between the chromospheric and transition region lines. Teriaca
et al. (2004) estimated that the average size of an EE was
1 800 km with a birthrate of 2 500 s -1 over the entire Sun based
on the O ## 1032 å line. The jets' number density along coronal
hole (CH) boundaries was found by Madjarska et al. (2004) to
be about 4­5 times higher with respect to the quiet Sun, while
Doyle et al. (2005) reported on EEs which were clearly visible
in N # 1238 å yet were very weak or absent in O # 629 å.
Dere (1994) was the first to note that EEs are often observed
in bursts lasting up to 30 minutes in regions undergoing mag­
netic cancellation. This was confirmed by P’erez et al. (1997),
Chae et al. (1998) and Ning et al. (2004). It is this point that
the present study is directed towards. Here, we look at time se­
ries data taken with SUMER (Solar Ultraviolet Measurements
of Emitted Radiation) onboard SoHO (Solar & Heliospheric
Observatory) in a polar CH region over a period of more than
4 hr and in particular, we search for evidence of whether these
bursts are random or have a periodical nature.
Send o#print requests to: J.G. Doyle
e­mail: jgd@arm.ac.uk or http://star.arm.ac.uk/preprints
Fig. 1. The coronal hole region from the Sun's north pole in the light
emitted by Fe ##/# 171 å observed with EIT on 23 October 1996. The
white line shows the fixed position of the SUMER slit. The image was
taken 21 min after the beginning of the SUMER time series.
2. Data
The data presented here were acquired with the SUMER spec­
trometer (Wilhelm et al. 1995, Lemaire et al. 1997) in the
north polar CH on 23 October 1996. Slit no. 8 (0.3 ## wide and
120 ## long) with detector B was fixed at x = 0 ## ; y = 950.25 ## .
Fig. 1 shows the position of the slit on an EIT (Extreme ultra­
violet Imaging Telescope) image taken during our time series.
The SUMER dataset was taken between 12:39:01--16:51:19
UT, with an exposure time of #10.5 s. SUMER data has a spa­
tial resolution of 1 ## (i.e. the pixel size along the slit).
The line in which the observation was transmitted to Earth
is O ## 1032 å (originating at #300,000 K in the transition re­
gion). This line shows a very good response to EEs (Teriaca
et al. 2004). We applied the standard procedures for correct­
ing and calibrating the raw data: decompression, reversal, flat­
field, dead­time, local­gain and geometrical correction (e.g. see
Xia et al. 2005 for further details or the SUMER/SoHO home­
page).

2 Doyle et al.: Repetitive occurrence of explosive events at a coronal hole boundary
Fig. 2. Top: A sequence of #122 min (700 exposures of 10.5 s each) and 40 ## on solar­y from the time series flux map of O ## 1032 å
observed with SUMER on 23 October 1996 (logarithmic scale). Over­plotted are the contours of the line widths. The white rectangle represents
the selected burst of EEs (77 min; 10 ## ) shown in more detail on the bottom panels: (a): the flux map (logarithmic scale); (b) line widths
(logarithmic scale); (c) the Doppler velocity (linear scale; ±20 km s -1 ).
3. Results
In this contribution, we only focus on the location with the
biggest concentration of EEs, e.g. towards the base of the slit.
The upper panel in Fig. 2 shows the O ## 1032 å flux for a
40 ## section over #122 min (700 exposures of 10.5 s each).
Over­plotted are the contours of the full width at half maximum
(FWHM) which give an indication of where EEs take place. It
is obvious that the largest EE activity is at the base of the time
series map. If we check the EIT image, we see that the base of
the slit is located right on the intersection between the base of
the dark CH and the top of a bright feature (a CH boundary).
We consider solar­y=0 as the base of our slit (y = 890.25 ## in
solar coordinates, #70 ## down from the solar limb).
We further select only one example where a sequence of
EE repetition is seen (the white rectangle, 10 ## high; 60 min
time length) which is shown in more detail in the bottom pan­
els of Fig. 2. In (a) we plot the O ## integrated flux, which is
done by summing all 50 spectral pixels of the SUMER window
and subtracting the continuum background. In (b) we show the
FWHM, and in (c) the Doppler velocity. These two parameters
were computed by fitting the line with a single Gaussian profile.
Although this is a good approximation for the ``quiet'' transition
region, a single profile is not really what we see when an EE
occurs. The Doppler map is hence only an indication of excess
blue/red wings in the line. As noted by Teriaca et al. (2004),
line profiles which show at least one of the fitted parameters
(or the # 2 ) diverging by more than 3 # from the average of its
distribution are potential EEs.
During the whole observation (#4 h 12 min), the base of the
slit moved #9 ## on the solar disk (the rotational compensation
was switched o#, as we are very close to the limb). Inspecting
the EIT image, we see that only in the initial stage was the slit
located on a CH boundary; as we progress in time, the slit en­
ters a `dark' region in the CH. This is why towards the second
part of the observation the high EE activity from the base of
the slit vanishes. During the #60 min interval of our selected
EE sequence, the base of the slit moved #2.1 ## . From Fig. 2
it is obvious that these EEs undergo a repetitive sequence. In
order to estimate what is the repetition rate of the EEs occur­

Doyle et al.: Repetitive occurrence of explosive events at a coronal hole boundary 3
Fig. 3. Panel (a) is a sequence of 20 min for the flux (in counts/10.5 s, the thin line) and the FWHM (in arbitrary units, the thick line) variation
(averaged over 3 ## at solar­y=3--5). Panel (b) is the spectral radiance, L, integrated over 5 min in a ``quiet'' region (position 44 to 49 in panel a).
Panel (c) is the spectral radiance integrated over #30 s (an average of 3 exposures of 10.5 s each) over an interval of 5 min (position 53 to 58
in panel a), showing how rapidly it changes during the EE activity. In panel (b) and (c), the average spectral radiance in a quiet region from the
CH is plotted as a thin line.
rence, we applied the wavelet transform to the FWHM variation
with time at solar­y=3--5 (see Fig. 2). Details on the wavelet
analysis were originally given by Torrence & Compo (1998) 1 .
We basically apply the transform as described in Popescu et
al. (2005). For the convolution of the time series, we chose the
Morlet function, and to establish if the oscillations found are
real, we implemented the Linnell Nemec & Nemec (1985) ran­
domization method, which estimates the significance level of
the peaks in the wavelet spectrum. The use of the randomiza­
tion technique was done according to O'Shea et al. (2001). In
Fig. 3 we show some examples of the spectral profile of these
EEs which clearly have a secondary blue­shifted component,
sometimes with little or no increase in the intensity.
The top panel of Fig. 4 shows the time variation of the
FWHM in spectral pixels averaged over 3 ## on solar­y. The left
bottom panel is the wavelet spectrum; and the right panel is the
global wavelet spectrum, which is the sum of the wavelet power
over time at each oscillation period. The dark­coloured regions
from the wavelet spectrum show the locations of the highest
power. Cross­hatched regions indicate the ``cone of influence'',
where edge e#ects become important. Only periods less than
11 min are considered.
For the series of EEs starting around t = 50 min, the wavelet
analysis detects two classes of periods. A weak, less signifi­
cant ``constant'' period of around 8 min plus a stronger signal
which increases in period with time. The repetitive rate is ini­
tially around 3 min increasing to over 5 min towards the end
1 http://paos.colorado.edu/research/wavelets/
of the activity. We clearly see six cycles in an interval of # 25
min (from t = 50 up to 75 min). The weaker `constant' period
is present throughout the observations and is not related to the
increasing period.
4. Discussion
As outlined in the Introduction, several previous investigations
have indicated that EEs sometimes tend to occur in bursts. For
example, Ning et al. (2004) found that events can occur 3--5
min apart and suggested that oscillations due to some wave mo­
tion could play a role in triggering the individual events. Fan et
al. (2004) adopted a 2D MHD approach involving anomalous
resistivity. Although such an approach can produce a burst­like
appearance, it is di#cult to see how it could produce the period­
like events seen in Fig. 4.
CH boundaries are regions where the magnetic field
changes its configuration. In particular, oppositely directed
closed and open field lines may co­exist at the boundary.
Therefore, favorable conditions for the occurrence of magnetic
reconnection are present. The reconnection between the neigh­
bouring and oppositely directed field lines is likely to be ob­
served as an EE or a bidirectional jet, as shown by the in­
creased rate of EE activity at a CH boundary by Madjarska et
al. (2004). The repetitive character of these events and the 3--5
min periodicities seen in Fig. 4 imply that MHD waves could
be involved in this process. Recent SoHO/TRACE observations
have revealed the presence of a great variety of MHD waves in
the solar atmosphere. Observational and theoretical aspects of

4 Doyle et al.: Repetitive occurrence of explosive events at a coronal hole boundary
Fig. 4. Wavelet results for the time variation of O ## 1032 å over 60 minutes, at solar­y=3­5 (averaged over 3 ## ). The top panel shows the
variation of the FWHM in spectral pixels. The corresponding wavelet power spectrum is shown in the bottom middle panel. In the global
wavelet power spectra the top dashed line represents the maximum allowed period (#29 min). The other lines represent the periods that appear
in the selected example of FWHM variation with time.
MHD waves in the solar atmosphere are discussed in review
papers by Aschwanden (2003) and Roberts (2004). In the fol­
lowing discussion, we assess the likelihood of di#erent types
of waves to trigger EEs and modulate their occurrence rate.
Three di#erent classes of MHD waves may exist: Alfv’en
waves and slow/fast magnetoacoustic waves. The solar at­
mosphere essentially represents a low­# plasma environment
where the magnetic pressure dominates the plasma pressure.
Therefore, the slow waves are essentially acoustic waves con­
strained to propagate along the strong magnetic field lines.
These waves have negligible e#ect on the strength and orien­
tation of the magnetic field and are unlikely to play an impor­
tant role in the above described reconnection process. Alfv’en
waves are nevertheless believed to be relevant to many pro­
cesses occurring in the solar atmosphere. These waves twist the
field lines along which they propagate. In the present situation,
however, it is unclear how the twisting could create more favor­
able conditions for the reconnection between the neighbouring
closed and open oppositely directed field lines. We therefore
examine the possibility of a mechanism involving fast waves.
The CH boundary region separates the tenuous CH region
from the denser quiet sun region. The equation of magnetohy­
drostatic pressure balance requires the total pressure (plasma
and magnetic) to remain constant across the boundary:
p +
B 2
2µ = const. (1)
Eq. (1) can be rewritten in the form
# # # # # # #
c 2
s
#
+
c 2
A
2
# # # # # # = const, (2)
where # is the density and
c s =
#p
#
# 1
2
, c A =
B 2
µ#
# 1
2
(3)
are the sound and Alfv’en speeds. Eq. (2) implies that the Alfv’en
speed in the CH region exceeds the Alfv’en speed in the neigh­
bouring quiet sun region provided they have the same tem­
perature. The fast waves are ducted by the inhomogeneity in
the Alfv’en speed and may propagate in the region where the
Alfv’en speed is lower (Edwin & Roberts 1983). The field lines
in this region are closed. The observations presented in this
paper were done in the O ## line which has a peak formation
temperature of about 300,000 K. Assuming that the electron
temperature is approximately the same as the ion temperature,
we find a sound speed of about # 85 km s -1 . This gives a lower
estimate for the phase speed of the fast waves (the phase speed
of the fast waves exceeds the minimum Alfv’en speed which, in
turn, exceeds the sound speed). The observed period P in Fig. 4
is in the range of 3­5 min. Taking a typical flux tube width of
d = 1 Mm and assuming that c A # 2c s , we find that the corre­
sponding dimensionless wavenumber is small:
kd <
2#d
c A P # 0.2, (4)
and, therefore, the thin flux tube approximation can be ap­
plied. Three di#erent types of waves can be generated in thin
flux tubes: slow (longitudinal), Alfv’en (torsional) and kink
(transverse) waves. These waves are governed by the Klein­
Gordon equation and have their characteristic cut­o# frequen­
cies (Roberts 2004). As we eliminated the first two types of
waves, we discuss the kink mode.
The kink mode oscillations shake the field lines of the flux
tube in the transverse direction. Such transverse motions could
periodically separate and bring together the closed and open
field lines at the boundary and thus trigger magnetic reconnec­
tion between oppositely directed field lines. Another important
indicator favouring the interpretation of the repetitive EEs in
terms of a kink mode is the period increase seen in Fig. 4. The
fact that the tube oscillates does not contradict the requirement
of hydrostatic pressure balance as the amplitude of the oscil­
lations decreases exponentially outside the tube. The thinner

Doyle et al.: Repetitive occurrence of explosive events at a coronal hole boundary 5
the tube, the smaller the wave amplitude away from the tube
(Edwin & Roberts 1983).
It is well­known that EEs are associated with the cancel­
lation of the magnetic flux. On the other hand, the frequency
of the kink mode is proportional to the Alfv’en frequency. The
Alfv’en speed would gradually decrease due to the flux can­
cellation and this would result in an increase in the period of
the kink mode, i.e. as the outer field lines of the flux tube get
reconnected, they are substituted by the inner field lines. This
is a continuous process during which the Alfv‘en speed gradu­
ally decreases because the outer field lines ``wear o#'', i.e., the
strength of the magnetic field decreases.
Standing and propagating kink mode oscillations are read­
ily observed in the higher regions of the solar atmosphere.
Standing kink mode oscillations could be excited impulsively.
They have damping times of about 3 wave periods (e.g.
Aschwanden et al. 1999). The kink modes could also be ex­
cited at photospheric heights due to the interaction between the
flux tubes embedded in the convection zone and the external
motions (see, e.g., Musielak & Umlschneider 2001; De Pontieu
et al. 2004). Provided the series of EEs seen in Fig. 2 (from t =
50 min to 75 min) were consecutively triggered by kink mode
oscillations, the damping time of these oscillations should be
long (about 5­10 wave periods). A possible candidate for the
damping of standing kink modes is the mechanism of resonant
absorption (Ruderman & Roberts 2002). The damping time is
given by the expression
# =
d
#l
# 0 + # e
# 0 + # e
, (5)
where # 0 is the density inside the tube and # e is the density out­
side the tube, the transition being accomplished over a distance
l # d to the boundary of the tube. Eq. (5) shows that the thin­
ner the transitional layer where the Alfv’en speed decreases, the
longer the damping time. In the present case, this layer could
become thin due to the continuous interaction of the flux tube
with the external magnetic field. An alternative explanation for
the observed long damping time is the presence of a continu­
ous/intermittent driver.
5. Conclusions
In summary, the following picture has emerged. The neigh­
bouring oppositely directed closed and open field lines at the
CH boundary undergo repetitive reconnection seen as explo­
sive events. The repetitive reconnection is triggered by trans­
verse oscillations (i.e. the kink mode) of the flux tubes in the
closed field line region. These oscillations periodically sepa­
rate and bring together the closed and open field lines on the
two sides of the coronal hole boundary. This picture is some­
what similar to what is seen in the magnetosphere: a sudden
increase in the solar wind pressure during southward interplan­
etary magnetic field orientation leads to enhanced magnetic re­
connection on the dayside magnetopause (Boudouridis et al.
2005). Hence, the proposed mechanism explains the repetitive
nature of the observed EEs, however, other possibilities should
not be excluded.
Acknowledgements. Armagh Observatory's research is grant­aided
by the N. Ireland Dept. of Culture, Arts & Leisure. This work
was partially supported by the Program for Research in Irish Third
Level Institutions for Grid­enabled Computational Physics of Natural
Phenomena (Cosmogrid) & by PPARC grant PPA/G/S/2002/00020.
SUMER is financially supported by DLR, CNES, NASA & ESA
PRODEX programme (Swiss contribution). SUMER & EIT are part
of SoHO which is a mission of international cooperation between ESA
and NASA. We thank the referee for valuable comments.
References
Aschwanden, M., 2003, `Review of coronal oscillations', in
(eds) Erd’elyi et al., Turbulence, Waves and Instabilities in the
Solar Plasma, NATO Sci Ser., vol. 124, pp.215­237
Aschwanden, M.J., Fletcher, L., Schrijver, C.J., & Alexander,
D. 1999, ApJ, 520, 880
Boudouridis, A., Zesta, E., Lyons, L. R., et al., 2005, J
Geophys Res 110, A05214
Chae, J., Wang, H., Lee, C. ­Y., Goode, P. R., & Sch˜uhle, U.,
1998, ApJ, 497, L109
De Pontieu B., Erd’elyi, R., & James, S. P. 2004, Nat, 430, 536
Dere, K.P., 1994, Adv. Space Res. 14, 13
Doyle, J.G., Ishak, B., Ugarte­Urra, I., Bryans, P. & Summers,
H.P., 2005, A&A 439, 1183
Edwin, P. M., & Roberts, B., 1983, Solar Phys., 88, 179
Fan, Q., Feng, X., Xiang, C., 2004, Communications in
Theoretical Physics, 2004, 41 (5): 790
Lemaire, P., Wilhelm, K., Curdt, W., et al., 1997, Sol. Phys.,
170, 105
Linnell Nemec, A.F. & Nemex, J.M., 1985, AJ 90, 2317
Madjarska, M.S. & Doyle, J.G., 2002, A&A 382, 319
Madjarska, M.S., Doyle, J.G. & van Driel­Gesztelyi, L., 2004,
ApJ 603, L57
Musielak, Z. E., Ulmschneider, P. 2001, A&A 370, 541
Ning, Z., Innes, D.E. & Solanki, S.K., 2004, A&A 419, 1141
P’erez, M.E., Doyle, J.G., Erd’elyi, R. & Sarro, L.M., 1997,
A&A 342, 279
O'Shea, E., Banerjee, D., Doyle, J.G., Fleck, B. & Murtagh,
F., 2001, A&A 368, 1095
Popescu, M.D., Banerjee, D., O'Shea, E., Doyle, J.G.
& Xia, L.D., 2005, A&A (in press) doi:10.1051/0004­
6361:20053714
Roberts, B. 2004, `MHD Waves in the Solar Atmosphere' in
R. Erd’elyi, J.L. Ballester & B. Fleck (sci. eds.) ESA­SP 547,
1
Ruderman, M.S. & Roberts, B. 2002, ApJ, 577, 475
Teriaca, L., Banerjee, D., Falchi, A., Doyle, J.G. & Madjarska,
M.S., 2004, A&A 427, 1065
Torrence, C. & Compo, G.P., 1998, Bull. of the American
Meteorological Soc., 79, 61
Wilhelm, K., Curdt, W., Marsch, E., et al., 1995, Sol. Phys.,
162, 189
Xia, L.D., Popescu, M.D., Doyle, J.G. & Giannikakis, J.,
2005, A&A 438, 1115