M. Temmer 1 - J. Rybák 2 - A. Veronig 1 - A. Hanslmeier 1
1 - Institute of Physics/IGAM,
Universität Graz, Universitätsplatz 5, 8010
Graz, Austria
2 - Astronomical Institute/SAS, 05960 Tatranská Lomnica,
Slovak Republic
Received 11 August 2004 / Accepted 3 December 2004
Abstract
Previous studies report a 24-day (synodic) period
in the occurrence rate of solar flares for each of the solar
cycles studied, Nos. 19-22 (Bai 1987, ApJ, 314, 795;
Temmer et al. 2004, Sol. Phys. 221, 325). Here we study
the 24-day period in the solar flare occurrence for solar cycles 21 and 22
by means of wavelet power spectra together with the solar flare
locations in synoptic magnetic maps. We find that the 24-day
peak revealed in the power spectra is just the result of a particular
statistical clumping of data points, most probably caused
by a characteristic longitudinal separation
of about
to
of activity complexes in
successive Carrington rotations. These complexes appear as parallel,
diverging or converging branches in the synoptic magnetic maps and are
particularly flare-productive.
Key words: Sun: flares - Sun: activity - Sun: magnetic fields
A 24-day synodic period in the solar flare occurrence has
been reported in various studies, but its origin is still far from
being understood. Explanatory statements most often refer to the
rotational behavior of the solar interior, i.e. deeper lying zones
of activity connected to sunspots rotate faster than the solar
photosphere (Pap et al. 1990; Bai 1987; Pap 1985). In the frame of the
anchoring hypothesis (Balthasar et al. 1982), specifically new-born spots
are connected to deeper and thus faster-rotating layers. However,
from solar rotation studies based on tracing sunspots only a small
fraction (of the order of 1%) of sunspots is reported with
sidereal velocities as high as 16 deg/day corresponding to a
24-day synodic period
(e.g. Pulkkinen & Tuominen 1998; Godoli et al. 1998; Suzuki 1998).
A 23.8-day
period in the solar flare occurrence was first reported by
Bai (1987) for high-energetic hard X-ray events during cycle 21
for the years 1980-1985. It is worth noting that similar periods
were also identified in other solar data sets. Pap (1985) and
Pap et al. (1990) found a 23.5-day period in solar irradiance
measurements for the time span 1980-1988 and in the occurrence
rate of very young, hence active, sunspot groups. Temmer et al. (2003)
found a prominent 23.8-day periodicity in the occurrence rate of
major solar flares observed in H
during 1975-2001 which
could not be established for sunspot relative numbers analyzed for
the same time span. However, after the removal of predominant
periods, Zieba et al. (2001) identified a 23.8-day period in sunspot
relative numbers during the rising phase of solar cycle 23. A
slightly higher period of 24.4 days was found by Henney & Harvey (2002)
in magnetic flux time series for the time span 1977-2001.
Recently, Temmer et al. (2004) performed a systematic study regarding a
possible 24-day synodic period in the occurrence rate of
solar flares for the time span 1955-1997. It was found that the
24-day period in solar flare rates is not an isolated phenomenon
but occurred in all four solar cycles studied (Nos. 19-22),
predominantly during narrow time ranges around the cycle maxima.
For flares of H
importance classes
1, the
appearance of the 24-day period was more prominent but it could
also be seen in subflares. In 3 out of 5 studied cases where a
24-day period was seen in major flare occurrence, a corresponding
period was also found in the occurrence rate of magnetically
complex active regions (including classification
and/or
), whereas it could not be established in magnetically non-complex (
,
)
sunspot groups. These findings are
suggestive of a close connection of the 24-day period seen in
flare occurrence with the magnetic field evolution of complex
active regions, which produce most large flares
(e.g. Sammis et al. 2000).
In the present paper we aim to clarify the type of relation of the
24-day flare period to the magnetic field evolution, and therefore
combine the statistical results from wavelet power spectra with
active region magnetic data. Specifically, we analyze synoptic
magnetic maps from the National Solar Observatory at Kitt Peak
together with the occurrence rate of major H
flare events
for times in which a peak at
24 days was revealed in the
wavelet power spectra. As we will demonstrate in this study, the
24-day period manifested in the power spectra is a statistical
result of the interplay between a characteristic longitudinal
separation of
to
of active region
complexes and the solar rotation period. Thus, we are not dealing
here with a period properly, and will use the term
"quasi-period'' instead of "period'' in the following.
We analyze time intervals in which a 24-day quasi-period in the
occurrence rate of major solar flares is reported by
Temmer et al. (2004) for solar cycles 21 and 22. These are within the
years 1982-1983 for the northern, and 1980-1981, 1989-1990 and
1991-1992 for the southern solar hemisphere. We also analyze the
time span 1987-1989 for which we found a 24-day quasi-period for
the northern hemisphere when considering only times of minimum
solar activity (whereas in the study of Temmer et al. 2004
wavelet power spectra for an entire solar cycle were
investigated). The exact time spans used for the analysis are
listed in Table 1. Note that in order to reduce edge
(cone of influence) effects, for the calculation of the wavelet
power spectra somewhat larger (about 0.5 years) time
intervals than reported in Temmer et al. (2004) were used for
estimating the 24-day quasi-period.
Daily numbers of H
flare events for importance classes
1 ("major'' flares) are derived separately for the northern
and southern hemisphere, using the flare compilation from the
Solar Geophysical Data. The magnetic synoptic maps employed are
from the National Solar Observatory at Kitt Peak (NSO/KP). Each
synoptic map is made from daily full-disk line-of-sight
magnetograms of the Sun for a full Carrington Rotation (CR), i.e. 27.2753 days, and approximates the magnetic flux density in the photosphere as a function of heliographic longitude and latitude
under the assumption that the magnetic fields are vertical
(cf. Harvey et al. 1980; Worden & Harvey 2000; Gaizauskas et al. 1983, and references therein). Since NSO/KP synoptic maps are not available before
1973, only solar cycles 21 and 22 are studied.
Wavelet power spectra are an appropriate tool for investigating time series that contain non-stationary power at many different frequencies (Daubechies 1990). In particular, they can be used to determine predominant periods in a time series together with their times of appearance.
We use the Morlet wavelet (Grossman & Morlet 1984) as analyzing wavelet
function
,
where
is a non-dimensional time
parameter. The continuous wavelet transform can be written as
Table 1: Time spans for which the wavelet power spectra were calculated together with the solar cycle number and hemisphere (N - North, S - South).
![]() |
Figure 1:
Top: WPS derived from daily rates of major flares for the
northern hemisphere during CR 1720-1732 (cycle 21: 1982 March-1983 February) with angular frequency values
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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The data analysis is performed as follows. For each time period
listed in Table 1 we calculated wavelet power spectra
from daily numbers of H flares
1 with a) high
angular frequency (
)
in order to obtain a high
frequency resolution, and b) low angular frequency (
)
in order to obtain a high temporal resolution. The derived WPS are
shown in the top panels of
Figs. 1-5 (left:
,
right:
). For a clearer representation, we did not plot
the total time range for which the WPS was calculated (i.e. the
times listed in Table 1) but only narrow ranges in
which the 24-day quasi-period distinctly shows up. After locating
the appearance of the
24-day quasi-period precisely in time
(using the WPS calculated with
), the synoptic
magnetic maps of the relevant time span were selected. The
heliographic coordinates and times of the associated flares were
mapped to the corresponding Carrington rotation number and
Carrington longitude (L), and superimposed on the synoptic
magnetic maps (bottom panels of
Figs. 1-5). Since the
determination of the heliographic longitude of a flare close to
the limb is very sensitive to small errors, only flares with a
distance
from the central meridian were taken into account.
![]() |
Figure 2:
Same as Fig. 1 but for the southern hemisphere
during CR 1693-1706 (cycle 21: 1980 March-1981 March).
Red and blue bars indicate time ranges where strong and faint
power occurs in the WPS, respectively. Strips of synoptic magnetic
maps are for the belt S0![]() ![]() |
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Figures 1-5 show the WPS
calculated from time series of daily numbers of H flares
with importance classes
1 (cf. Table 1 for the exact time
ranges analyzed) with high frequency (top left) and high time (top
right) resolution together with the corresponding synoptic
magnetic maps including the individual flare positions (bottom).
Here we draw attention to high amplitudes in the WPS within a
confidence level of at least 95% observed for the period range
23.8
0.5 days (a 23.8-day quasi-period is reported
by Bai 1987; Temmer et al. 2004; Zieba et al. 2001; Temmer et al. 2003). Note that we do not
concentrate on periods related to the solar differential rotation
(which are also present in the WPS shown in
Figs. 1-5). Mean synodic periods
reported for the differential rotation of the Sun are within
26.5 days near the solar equator and
29.5 days
around 40
latitude (e.g., Howard 1984; Balthasar et al. 1986).
For the interpretation of synoptic maps it is important to note that
active regions forming a vertical band in successive CRs have
rotational periods close to the CR period of
27.3 days,
whereas bands revealing a slope to the left (i.e. toward smaller
Carrington longitudes) have periods longer than the CR period and
bands inclined to the right (i.e. toward higher Carrington
longitudes) have shorter periods than the CR rate.
The high-frequency resolution WPS in Fig. 1 (top
left panel) shows a broad range within the spectrum where local
peaks of from 23.5 to
28.7 days are revealed above the
significance level of 95%. At a significance level of 99%, two
dominant peaks centered at
24.7 and
28.0 days can be
distinguished. As can be seen from the high-time-resolution WPS
calculated for the same time span (top right panel), these peaks
appear during CR 1723 to CR 1726 (on a 99% significance level).
The corresponding synoptic maps (bottom panel) reveal that the
majority of flares occurs in a diverging active region with the
intersection point centered at Carrington longitude
at CR 1720.
Using the flare locations as tracers, the longitudinal separation
of the two branches of the diverging active region is
45
between the successive Carrington rotations
1723/1724,
52
between CR 1724/1725, and ends up
with
51
between CR 1725/1726 (indicated by white
arrows in Fig. 1).
It is important to note that longitudinal differences between
successive CRs in the range +
to +
correspond to a difference of -3.0 to -3.8 days with respect
to the Carrington rotation rate of
27.3 days, i.e.
quasi-periods in the range 23.5 to 24.3 days. This can be
interpreted in terms of a rotational period only in cases
where such a longitudinal shift between consecutive CRs is
observed for the same feature. In the synoptic maps in
Fig. 1, however, this shift is observed between
the two branches of a flare-productive diverging active region
complex, and thus has nothing to do with rotation at all. However,
it seems to be the cause of the
24-day quasi-period revealed
in the WPS during the same time. As will be shown in the
following, a similar outcome is obtained for the other samples.
![]() |
Figure 3:
Same as Fig. 1 but for the northern hemisphere
during CR 1786-1799 (cycle 22: 1987 February-1988 February).
Strips of synoptic magnetic maps are for the belt
N0![]() ![]() |
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The wavelet power spectra in Fig. 2 reveal a
quasi-period of about 23.3 days during CR 1696-1698 (faint
signal) and CR 1700-1702 (strong signal), respectively.
Additionally, for CR 1700-1702 enhanced power in the wavelet
spectra is observed at 28 days. During these two time spans,
in the synoptic maps patterns of parallel bands of active regions
responsible for a significant fraction of major flares are
observed. These bands are separated in longitude by about
45
-50
,
which corresponds to a quasi-period in the
range of 23.5-23.9 days, similar to what is actually observed in
the WPS.
![]() |
Figure 4:
Same as Fig. 1 but for the southern hemisphere
during CR 1812-1825 (cycle 22: 1989 February-1990 January). Strips
of synoptic magnetic maps are for the belt
S0![]() ![]() |
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In Fig. 3 the occurrence of major flares during
the initial phase of solar cycle 22 is studied. This sample
differs from the others as it covers a time of minimum solar
activity. In the WPS, a quasi-period of about 23.5 days is
revealed very sharply in time during CR 1788-1789. Only few
active regions are present on the Sun, and during the considered
interval only two active regions were observed that produced major
flares; these regions were separated in longitude from CR 1788 to
CR 1789 by about 43
which corresponds to a quasi-period
of
24.0 days.
From the WPS in Fig. 4 a significant (95%
confidence level) power signal is obtained with a quasi-period of
23.8 days during CR 1818-1820. During this time, the synoptic
maps reveal two converging branches of active regions which are
responsible for the majority of solar flares. The two branches are
separated by 45
in longitude in successive CRs
corresponding to a quasi-period of 23.9 days, again close to what
is observed in the WPS.
In Fig. 5 a clear quasi-period in the range of
about 23.8 days is revealed from the WPS within CR 1838-1840.
During this time span the synoptic magnetic maps show two nearly
parallel bands of high flare activity shifted by
46
,
35
,
and 47
within the
successive rotations 1838/1839, 1839/1840, and 1840/1841,
respectively. This would cause quasi-periods of
23.8, 24.7,
and 23.7 days.
![]() |
Figure 5:
Same as Fig. 1 but for the southern hemisphere
during CR 1836-1848 (cycle 22: 1990 November-1991 October). Strips
of synoptic magnetic maps are for the belt
S0![]() ![]() |
Open with DEXTER |
The combined analysis of wavelet power spectra and synoptic
magnetic maps provides us with the possibility to locate the
appearance of the 24-day quasi-period in solar flare occurrence
both statistically and individually. The flare location in the
synoptic maps suggests that peaks in power spectra of 24 days
which were found in the occurrence of flares observed in hard
X-rays (Bai 1987) and H
(Temmer et al. 2004,2003), in
magnetic flux time series (Henney & Harvey 2002), in active region time
series (Pap et al. 1990; Pap 1985; Zieba et al. 2001) and in the occurrence rates
of magnetically complex active regions (Temmer et al. 2004) can be
explained by the spatial distribution of complex, flare-productive
active regions. In general, active regions are not randomly
distributed but are clustered within so-called complexes ("nests'')
of activity (Bumba & Howard 1965). These clusters typically evolve
within one month and are sustained by the fresh emergence of
magnetic flux for about 3-6 months (Gaizauskas et al. 1983).
Flare-producing nests separated by about +40
to +50
in longitude within successive rotations would cause
periods shorter than the Carrington rotation by -3.0 to -3.8 days, i.e. the corresponding quasi-periods are in the range 23.5
to 24.2 days. Our analysis showed that when flare-productive
activity nests with such characteristics are observed in the
synoptic maps, these quasi-periods are indeed observed
simultaneously in the wavelet power spectra. (Actually, our
approach was the other way round, as we first checked the WPS for
the occurrence of a
24-day quasi-period and then inspected
the synoptic maps during the times of appearance of the 24-day
quasi-period.) If this interpretation is correct, then the WPS
should also reveal a peak in the range of
3-4 days which
reflects directly the characteristic separation in longitude. We
checked this by calculating WPS for the same time spans as listed
in Table 1 but ranging from 2 to 30 days. In "simple''
situations (i.e. clearly separated activity branches and low
flare activity from other active regions), indeed peaks in the
range 3-4 days are revealed in the WPS above a confidence level of 95%.
Clearly separated nests of activity are evident in Figs. 1, 3, and 5. The synoptic maps of Figs. 2 and 4 show more loose-activity complexes of ambiguous separation and thus are less convincing samples. On the other hand, it is apparent, e.g., from the synoptic maps in Fig. 2, that the absence of such spatially divided activity nests (cf., CR 1698-1700) coincides with the absence of a 24-day quasi-period in the WPS.
Gaizauskas et al. (1983) described exemplary shapes of multiple
complexes of activity, namely "great complexes'' consisting of
two parallel main branches separated by about 40
in
longitude as well as "diverging and merging complexes'' with two
branches that diverge and converge, respectively, within
successive rotations. These patterns are attributed to a
regularity in the spacing between the complexes with distances
that depend on the characteristic sizes of the regions
(Gaizauskas et al. 1983). Thus, these spatial separations are supposed
to be a non-random phenomenon which might be related to typical
size scales of giant (convective) cells which have typical
longitudinal extensions of
and are assumed
to play an important role in structuring the Sun's large-scale
magnetic field (Beck et al. 1998; Bumba & Howard 1965). It is also worth noting
that Pojoga & Cudnik (2002) found that
70-75% of all flares occur
within activity nests, and that parallel, converging and diverging
activity nests exhibit enhanced flare productivity.
Following the reports from the Mount Wilson Observatory, most
active regions within the studied synoptic maps are classified as
magnetically complex, i.e. include
and/or
groups. There are no spatially divided patterns causing a
quasi-period of 24 days that consist solely of magnetically non-complex groups.
The 24-day quasi-period was statistically found in the occurrence
of major solar flares in each of solar cycles 19 to 22
(Bai 1987; Temmer et al. 2004). In this paper, we have compared the
statistical appearance of the 24-day quasi-period in wavelet power
spectra (with high temporal resolution) with the occurrence of
individual major flare events in synoptic magnetic maps. From this
analysis we conclude that the 24-day peak revealed in power
spectra is just the result of a particular statistical clumping of
data points. The 24-day quasi-period in fact results from the
interplay between the solar rotation period and a typical
separation in longitude by +40
to +50
of large
parallel, diverging, or converging activity nests in successive
CRs. Such regions are known to be particularly flare-productive
(Pojoga & Cudnik 2002). It is worth noting that these longitudinal
separations are of the same size as those reported for giant
convective cells (Beck et al. 1998).
Acknowledgements
M.T., A.V., and A.H. gratefully acknowledge the Austrian Fonds zur Förderung der wissenschaftlichen Forschung (FWF grant P15344) and J.R. the Slovak grant agency VEGA (2/3015/23) for supporting this project. J.R. is member of the European Solar Magnetism Network (ESMN) supported by the EC (EC/RTN contract HPRN-CT-2002-00313). M.T., A.H., and J.R. thank the Austrian and Slovak Academies of Sciences for financing the exchange of scientists. We also want to thank the referee J. Pelt for his constructive comments. NSO/Kitt Peak data used here are produced cooperatively by NSF/NOAO, NASA/GSFC, and NOAA/SEL. Wavelet software was provided by C. Torrence and G. Compo (http://paos.colorado.edu/research/wavelets/).