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Contents lists available at ScienceDirect
Planetary and Space Science
journal homepage: www.elsevier.com/locate/pss
Short- and mid-term oscillations of solar, geomagnetic activity
and cosmic-ray intensity during the last two solar magnetic
cycles
Y.P. Singha,⁎, Badruddinb
a IAS, Mangalayatan University, Aligarh 202145, Indiab Astronomy
Department, Faculty of Science, King Abdulaziz University, Jeddah,
Saudi Arabia
A R T I C L E I N F O
Keywords:Solar periodicitySolar activityGeomagnetic
activityCosmic raysWavelet analysis
A B S T R A C T
Short-and mid-term oscillations of the solar activity (sunspot
number and 10.7 cm solar flux), geomagneticactivity (Ap index) and
cosmic-ray intensity (neutron monitor count rate) are analysed
during the past two solar-magnetic cycles (1968–1989 and
1989–2014). We have implemented the wavelet analysis on the daily
timeresolution data of sunspot number (SSN), 10.7 cm solar flux,
geomagnetic Ap index and Oulu neutron monitorcount rate. Results
suggest that few quasi and intermittent oscillations are observed
with remarkable powerdensity in addition to fundamental periods,
like 27 day (synodic period), 154 day (Rieger period),
semi-annual,annual, 1.3 year, and 1.7 year. We have consistently
observed first (27 day), second (13.5 day) and third(9.0 day)
solar-rotation harmonics in the geomagnetic Ap-index during both
the magnetic cycles. Rieger periodis more pronounced in SSN and
solar flux during 1980-82 and 1990-92. Semi-annual variation of
Ap-index isconsistently observed during both the magnetic cycles.
The annual and ~1.85 year variation are also observed inall the
considered parameters with good signatures in CRI.
1. Introduction
The Sun has been a composite object that reflects
abnormalbehavior because of its complex features. The fundamental
ingredientbehind this complex system is its magnetic field. The
solar magneticfield directly or indirectly disturbs the
interplanetary space, ionosphere,and magnetosphere and even in
lower atmosphere. The study of solarvariability and its influence
on the Earth and Earth's environment hasalways been a challenging
problem to researchers. When solar activitytriggers geomagnetic
activity, the geomagnetic storms of variousmagnitudes occur.
Investigations of time series of solar and solar windplasma,
geomagnetic activity indices and galactic cosmic ray intensityhave
unveiled a large range of periodic and aperiodic behaviours
(e.g.Bazilevskaya et al., 2014; Kudela and Sabbah, 2016 and
referencestherein). Study of the periodicities in the solar and
geomagnetic activityparameters have been useful in relating solar
variability to variationsobserved in various interplanetary
phenomena in order to search for thesolar cause and effects in the
near-earth space environment.
The observation of sunspots, a useful indicator of solar
activity, hasstarted long back and variability in sunspot number
has been studiedsince long. However, the variations of cosmic-ray
intensity, solar windand geomagnetic activity have started since
their systematic ground-based and/or space-based observations
started. The observed variations
periodic or non-periodic have been related directly or
indirectly tochanges in the magnetic activity of the sun (e.g.
McIntosh et al., 2014).The variations of cosmic ray particles are
reported e.g. by Maeda(1967), Akioka et al. (1987), Hill et al.
(2001), Rybak et al. (2001),Kudela et al. (2002), Mavromichalaki et
al. (2003), Singh et al. (2012),Modzelewska and Alania (2013),
Potgieter (2014), Singh andBadruddin (2015a, 2015b), Aslam and
Badruddin (2015), Badruddinand Kumar (2016), Chowdhury et al.
(2016), Kudela and Sabbah(2016), and Rieger et al. (1984) reported
periodicities in solar flaresand Mclntosh et al. (1992) examined
periodicities in coronal observa-tions. Periodic and quasi-periodic
variations of solar wind parameterswas reported by many researchers
e.g. Mursula and Zieger (2000),Nayar et al. (2002), Valdes-Galicia
and Velasco (2008), Chowdhury andDwivedi (2011), Katsavrias et al.
(2012), Singh et al. (2012), Singh andBadruddin (2014), and
Chowdhury et al. (2015), while the oscillationsof geomagnetic
indices by Gonzalez et al. (1993), Paularena et al.(1995), Nayar et
al. (2002), Mursula et al. (2003), Singh and Badruddin(2014), and
Chowdhury et al. (2015) and many others. These oscilla-tions may be
classified in three categories, short-term, mid-term andlong-term
oscillations. The mid-term periodicities are referred to
asintermediate quasi-periodicities (Lou et al., 2003;
Valdes-Galicia andVelasco, 2008; Kudela et al., 2010) or
quasi-biennial oscillations(QBOs) as reported by Bazilevskaya et
al. (2014).
http://dx.doi.org/10.1016/j.pss.2017.02.011Received 31 December
2016; Received in revised form 2 February 2017; Accepted 16
February 2017
⁎ Corresponding author.E-mail address:
[email protected] (Y.P. Singh).
Planetary and Space Science 138 (2017) 1–6
Available online 22 February 20170032-0633/ © 2017 Elsevier Ltd.
All rights reserved.
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It has been reported that the geomagnetic activity depends
stronglyon the solar wind velocity and interplanetary magnetic
field at theEarth's orbit (Burton et al., 1975; Echer et al., 2008;
Gopalswamy et al.,2008; Alves et al., 2011; Constantin, 1989;
Bothmer and Schwenn,1995; Badruddin, 1998; Badruddin and Singh,
2009; Badruddin andAslam, 2013 and references therein). The
mechanism of reconnectionbetween the interplanetary magnetic field
(IMF) and Earth's magneticfield due to interaction between the
solar wind plasma and themagnetosphere was established by Dungey
(1961). Garrett et al.(1974) reported the influence of solar wind
variability on geomagneticactivity, while an empirical relationship
between interplanetary condi-tions and geomagnetic disturbance
parameter was given by Burton(1975).
The fluctuations in the solar wind plasma parameters
includingtemporal shift in these variations play a vital role in
the solar-magnetosphere coupling efficiency (Garrett et al., 1974;
Kane andEcher, 2007; Singh and Badruddin, 2012; Katsavrias et al.,
2016 andreferences therein). The periodicities and fluctuations in
the cosmic rayintensity are intimately related to
behavior/variations in solar andinterplanetary magnetic activity
(e.g. Mavromichalaki et al., 2003;Modzelewska and Alania, 2013;
Aslam and Badruddin, 2015; Singh andBadruddin, 2015a; Bazilevskaya,
2014 and references therein). Themagnetic field that appears at the
solar surface is generated by the solardynamo located at the base
of the convection zone and the differentialrotation of the sun is
one of the fundamental constituent of the dynamo.The ~1.7 year
periodicity is also an important phenomenon that mightbe closely
linked to the solar dynamo. All the variations originate fromwithin
the Sun and hence directly or indirectly reflect the
internalfeatures of the Sun (Howe et al., 2000). Hence, study of
the variabilityof the solar, interplanetary and geomagnetic
parameters as well as thecosmic ray intensity has become an area of
intense research.
2. Data and analysis technique
We have used the sunspot number, solar radio flux (10.7
cm),cosmic ray data (Oulu neutron monitor, location: 65.05°N,
25.47°E, cut-off rigidity: 0.81 GV), geomagnetic activity index Ap
for the period1968–2014. The sunspot number come from
http://www.sidc.be/silso/,10.7 cm solar flux from
http://www.ngdc.noaa.gov/stp/solar/, geo-magnetic Ap index from
http://www.ngdc.noaa.gov/stp/GEOMAG/and cosmic ray data from
http://www.cosmicrays.oulu.fi/. The selecteddata was then divided
into two solar magnetic cycles, one from 1968 to1989 and other from
1989 to 2014. As the solar magnetic polarityreverses around each
solar maximum and the polarity repeats atalternate or subsequent
maximum, therefore, we selected periods fromone maximum to an
alternate maximum, which is essentially a solarmagnetic cycle (Hale
cycle). Daily average data were then subjected towavelet
analysis.
We used Morlet wavelet for wavelet analysis (Torrence and
Compo,1998) to study the short- and mid-term periodicities of
solar, geomag-netic and cosmic ray intensity. The results are
obtained using a singleselected mother function and scaling
parameters.
3. Results and discussion
Fig. 1 depicts the wavelet power spectrum (WPS), global
waveletanalysis (GWS) and daily averaged time series of sunspot
number (SSN)during the period of 1968–2014 (upper panel), 1968–1989
(middlepanel) and 1989–2014 (lower panel). The complete period
covers twocomplete magnetic cycles (maximum to maximum). The
contours in thewavelet power spectrum (WPS), provide information
about the levels ofspectral power corresponding to each variation
at different timeperiods. In each wavelet figure, yellow and green
(light) areascorrespond to lower power regions and red color (light
dark) areascorrespond to the regions of larger power. The colored
(moderatelydark) regions, however, in all of the figures indicate
the region of the
spectrum below the 95% confidence level and thick black contours
arethe regions of the spectrum at the 95% confidence level. In the
waveletspectrum of each wavelet figure, the variation of power is
shown; thethick dashed line in the panel is the line at 95%
confidence level. In allthe wavelet power spectra the Cone of
Influence (COI) is also shown asit describes the region influenced
by the zero padding or shows edgeeffect.
Three fluctuations (local peaks in the power spectrum)
appearduring the period as seen in GWS of the figure (upper panel).
In thestudy of wavelet analysis during the two magnetic cycles
(middle andlower panels), we observe that 1.85 year (675 day)
period is prominentvariation appears during the solar maximum and
during the decreasingphases of the solar cycles; also the period is
significant during the latermagnetic cycle (1989–2014). The synodic
period, Rieger period, semi-annual and annual fluctuations are also
observed in the time series ofsunspot number. The observed
periodicities along with the peak powervalues of all the considered
parameters during both the magnetic cyclesare tabulated in Table 1
and Table 2.
Fig. 1. Wavelet power (WPS), global wavelet (GWS) spectrum and
variation of daily timeseries of sunspot number during 1968–2014
(upper panel), during 1968–1989 (middlepanel) and during 1989–2014
(lower panel). The cone of influence is also shown in eachWPS. The
dashed line in the GWS represents the 95% significant level. The
color bar ofthe figure is also shown. (For interpretation of the
references to color in this figure legend,the reader is referred to
the web version of this article.)
Y.P. Singh, Badruddin Planetary and Space Science 138 (2017)
1–6
2
http://www.sidc.be/silso/http://www.ngdc.noaa.gov/stp/solar/http://www.ngdc.noaa.gov/stp/GEOMAG/http://www.cosmicrays.oulu.fi/
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Wavelet analysis and variation of daily average time series of
solarflux (10.7 cm) is shown in Fig. 2. This band of emission
originates highin the chromospheres and low in the corona of the
solar atmosphere.Solar radio flux at 10.7 cm (2800 MHz) is an
excellent indicator of solaractivity and the importance to study
the 10.7 flux parameter forpredicting the characteristics of solar
cycles (Lampropoulos et al.,2016); hence its variability is
important from the earth perspective.Three local maxima in the
power spectrum are appearing in the globalwavelet spectrum (GWS) of
the solar flux time series of the figure(upper panel). The wavelet
power spectrum of the figure appear as thestacking of the power
columns around the solar maximum, indicatingthat all the variations
are more pronounced during increasing, max-imum and decreasing
phase of the solar cycle. The 27 days variation ismore pronounced
during the solar maximum, when the solar activity ishigh. Rieger
period is more pronounced during the maximum and thedecreasing
phases of solar cycles 21 and 22, while ~300 day period isactive
during the solar cycles 21, 22 and during the decreasing phase
ofsolar cycle 23 (middle and lower panels of the figure). A
quasi-variation~1.91 year (697 day) period is also appeared during
the solar cycle 22and decreasing phases of the cycles 20 and
23.
Fig. 3 depicts the wavelet analysis of geomagnetic storm
measuringparameter Ap index. It shows a number of fluctuations
during theexamined magnetic cycles. Four periods (27 day and its
secondharmonic, semi-annual and 1.61 (in former)/1.45 (in latter
magneticcycle) year) are appeared as prominent fluctuation during
the examinedperiod (Fig. 3, upper panel). In WPS, the signatures of
second harmonicand one solar rotation variations are found
throughout the periodhowever signatures of these variations are
become faint during theincreasing phase of the solar cycle 24.
Figure shows that the semi-annual variation is more pronounced
during the 1972–2006 period. The1.61 year (586.9 day) period is one
of the prominent mid-termvariations of Ap index in the former
magnetic cycle (middle panel),while 1.45 year (528.9 day) period
during the later magnetic cycle(lower panel). These variations are
more active during the solarmaximum and decreasing phases of the
solar cycles. A broad and anextended region appear around 1990,
which is focused around 1.3 year
(474.5 day) period and seems to be significant as seen in the
GWS ofupper panel of the figure.
Energetic charged particles travelling through the interstellar
spacenearly at the speed of light are known as galactic cosmic ray
particles.The wavelet analysis of cosmic ray particles during the
examined periodis shown in Fig. 4. The signature of synodic period
is continuouslyobserved throughout the period. The second and third
harmonics ofsynodic period are observed in later magnetic cycle
with weeksignatures. The good signature of Rieger period is found
in formermagnetic cycle while a variation of 325.6 day is observed
in latermagnetic cycle. Extended significant regions corresponding
to mid-termperiods are continuously observed during the examined
period in theWPS of the upper panel of the figure and more this
region ispronounced during the maximum and decreasing phases of the
solarcycles 20, 21 and 23 (upper panel). The power in these
contours variesfrom ~1.3 year period to more than 1.9 year period,
a significantvariation of 1.72 year (629 day) period is observed in
all the panels ofthe figure.
Quasi-periodic variability due to solar magnetic activity
bandinteraction and instabilities was discussed by Mclntosh et al.
(2014).Recently, Singh and Badruddin (2015b) reported the third
(9.0 days),fourth (7.0 days), fifth (5.5 days) and sixth (4.5 days)
harmonics ofsynodic period of various solar wind plasma and
geomagnetic para-meters. Sabbah and Kudela (2011) observed the
third harmonics ofsynodic period in CR intensity. Earlier, Bai and
Sturrock (1991, 1993)reported the period of 25.5 days as the
fundamental period of solar flareoccurrence time and 51.0, 76.5,
102.0, 127.5 and 153.0 days oscilla-tions are the sub harmonics of
the fundamental period. Valdes-Galiciaet al. (1996) gave a clue to
understand the nature of solar cycle by the1.68 year period of
cosmic ray. Krivova and Solanki (2002) suggested acommon origin of
Rieger (154 days) and 1.3 year fluctuation and Riegerperiod is
third harmonic of the 1.3 year period. The 1.7 year period isan
integral multiple of Rieger period and these two variations
mayappear at the same time Howe et al. (2000) hence Rieger period
may bethe fourth harmonics of fundamental 1.7 year period.
In this work, we report the signature of the harmonics both
lower
Table 1Observed short- and mid-term periodicities of sunspot
number, 10.7 cm solar flux, ap index and cosmic ray intensity (Oulu
NM) and corresponding power during the 1968–89 period.
S. No. SSN Solar flux Ap index Oulu NM
Periodicity Time Power [104] Periodicity Time Power [104]
Periodicity Time Power [103] Periodicity Time Power [106]
1 9.2 d 0.342 13.6 d 0.53 27.8 d 0.10 27.8 d 0.67 26.9 d 0.72
28.8 d 0.544 45.2 d 0.415 73.4 d 0.416 157.2 d 0.13 157.2 d 1.11
180.6 d 1.27 151.9 d 0.957 337.1 d 0.19 314.5 d 1.48 1.14 yr 2.008
1.61 yr 1.88 1.72 yr 4.12
Table 2Observed short- and mid-term periodicities of sunspot
number, 10.7 cm solar flux, ap index and cosmic ray intensity (Oulu
NM) and corresponding power during the 1989–2014 period.
S. No. SSN Solar flux Ap index Oulu NM
Periodicity Time Power [104] Periodicity Time Power [104]
Periodicity Time Power [104] Periodicity Time Power [104]
1 9.5 d 0.30 7.7 d 0.062 13.6 d 0.38 11.3 d 0.083 25.1 d 0.77
26.9 d 0.74 26.9 d 0.56 25.9 d 0.154 63.9 d 0.315 100.2 d 0.486
180.6 d 0.87 162.8 d 0.66 187.0 d 1.207 374.0 d 1.74 303.8 d 1.78
325.6 d 1.068 1.45 yr 2.329 1.85 yr 3.68 1.91 yr 4.02 1.72 yr
3.56
Y.P. Singh, Badruddin Planetary and Space Science 138 (2017)
1–6
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and higher side of synodic period in geomagnetic index Ap during
boththe magnetic cycles. The Rieger period is consistently observed
in solardata (SSN, 10.7 cm solar flux) and cosmic ray data during
the firstmagnetic cycle. Results show that a ~337 day quasi
periodicity isobserved in SSN in addition to annual variation and
near annual(~326 day) and 1.14 year periods are observed in Oulu NM
time series.A quasi period of ~300 day is found in solar flux
series in both themagnetic cycles besides the synodic period. The
~1.45 and ~1.72 yearperiod are observed in Ap index and Oulu NM
time series respectivelyduring both the magnetic cycle and
significant ~1.85 and ~1.91 yearperiods are found in SSN and solar
flux in the latter magnetic cycle.Results also suggest that the
observed periodicities of considered timeseries are more active
during the time of solar maximum and decreasingphases of the solar
cycles.
Although all the reported periodicities are not significant at
95%confidence level, however, the possibilities of their existence
in otherrelated solar/interplanetary parameters needs to be
explored.
4. Conclusions
In this work, we have examined short- and mid-term oscillations
inthe time series of sunspot number, solar flux (10.7 cm),
geomagneticindex Ap and cosmic ray intensity. For this purpose, the
waveletanalysis of all the considered parameters has been performed
duringthe period 1968–2014 consisting two solar magnetic cycles.
Thefollowing conclusions have been drawn:
i) The sub harmonics of 27 days period both on the lower (13.5
daysand 9.0 days) and higher (51 days, 76 days and 101 days) side
arepresent in the Ap index.
ii) All the short- and mid-term variations of Ap index are
smoother andclear during the examined period.
iii) Solar maximum period and decreasing phases of the solar
cycles aremore appropriate to study short- and mid-terms
variations.
iv) Mid-term variations 1.85 year of sunspot number, 1.91 year
of solar
Fig. 2. Wavelet power (WPS), global wavelet (GWS) spectrum and
variation of daily timeseries of 10.7 cm solar flux during 1968 –
2014 (upper panel), during 1968–1989 (middlepanel) and during
1989–2014 (lower panel). The cone of influence is also shown in
eachWPS. The dashed line in the GWS represents the 95% significant
level. The color bar ofthe figure is also shown. (For
interpretation of the references to color in this figure legend,the
reader is referred to the web version of this article.)
Fig. 3. Wavelet power (WPS), global wavelet (GWS) spectrum and
variation of daily timeseries of geomagnetic index Ap during
1968–2014 (upper panel), during 1968–1989(middle panel) and during
1989–2014 (lower panel). The cone of influence is also shownin each
WPS. The dashed line in the GWS represents the 95% significant
level. The colorbar of the figure is also shown. (For
interpretation of the references to color in this figurelegend, the
reader is referred to the web version of this article.)
Y.P. Singh, Badruddin Planetary and Space Science 138 (2017)
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flux, 1.45 year of Ap index and 1.72 year of cosmic ray
intensity aresignificant variations.
v) The observed mid-term variations ~1.3 year and ~1.7 year
areintegral multiples of Rieger period. Hence, 1.3 year variation
is firstand Rieger period be fourth harmonics of fundamental period
~1.7year. Moreover, there is mixing of these observed
mid-termsoscillations of the time series.
Acknowledgements
We gratefully acknowledge the use of OMNI data from the
NationalSpace Science Data Centre
(http://www.omniweb.gsfc.nasa.gov). Wealso gratefully acknowledge
the use of Oulu neutron monitor data. Wethank the Station Manager
of Oulu NM (Ilya Usoskin) for making thedata available. Wavelet
software provided by C. Torrence and G.Compo is acknowledged with
thanks. We also thank anonymousreviewers for their helpful and
constructive comments.
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Fig. 4. Wavelet power (WPS), global wavelet (GWS) spectrum and
variation of daily timeseries of cosmic ray intensity (Oulu NM)
during 1968–2014 (upper panel), during 1968–1989 (middle panel) and
during 1989–2014 (lower panel). The cone of influence is alsoshown
in each WPS. The dashed line in the GWS represents the 95%
significant level. Thecolor bar of the figure is also shown. (For
interpretation of the references to color in thisfigure legend, the
reader is referred to the web version of this article.)
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Short- and mid-term oscillations of solar, geomagnetic activity
and cosmic-ray intensity during the last two solar magnetic
cyclesIntroductionData and analysis techniqueResults and
discussionConclusionsAcknowledgementsReferences