# Solar-Cycle Characteristics in Kodaikanal Sunspot Area: North–South
Asymmetry, Phase Distribution and Gnevyshev Gap

B. Ravindra  Partha Chowdhury  J. Javaraiah  Indian Insititute of
Astrophysics, Koramangala, Bangalore 560034, INDIA  University College of
Science and Technology, Department of Chemical Technology, University of
Calcutta, 92, A.P.C. Road, Kolkata, 700009, West Bengal, India  No. 58, 5th
Cross, Bikasipura, Bengaluru-560 078. Formerly with Indian Institute of
Astrophysics, Koramangala, Bengaluru - 560034, India

###### keywords:

Solar Cycle, Observations, Active Regions, Magnetic Fields; Photosphere,
Sunspots

##  1 Introduction

sec:intro Sunspots are dark and are most easily visible features on the Sun,
even with a moderate-sized telescope. Most solar-activity phenomena are
connected to sunspots. The sunspot record goes back to the time of Galileo
(Vaquero, 2007). However, the daily record of the sunspot observations started
in 1874. These observations started in several observatories around the world
at different times (Ravindra et al., 2013, 2020), and until now, the sunspot-
area and number have the longest record compared to any other data available
in history (Ermolli et al., 2014; Usoskin et al., 2017). This longest record
of data is useful to understand solar irradiance, space climate, the Earth’s
atmospheric chemistry, and rain pattern (Haigh, 2007; Gray et al., 2010; Yeo,
Krivova, and Solanki, 2017).

An eleven-year periodicity is observed in the sunspot activity. Solar dynamo
believed to be operating at the base of the convection zone is assumed to be
responsible for the observed solar activity on the Sun (Charbonneau, 2017).
There are several dynamo models proposed starting from the flux-transport
dynamo model of Babcock–Leighton (Wang and Sheeley, 1991; Choudhuri,
Schussler, and Dikpati, 1995; Dikpati and Charbonneau, 1999) to 3D MHD dynamo
models (Karak and Miesch, 2017). All are able to describe the 11-year
periodicity with uncertainity in their cycle amplitudes (Jiang et al., 2013;
Passos et al., 2014).

Solar cycles show the dominance of one of the hemispheres compared to the
other (Norton, Charbonneau, and Passos, 2014). The north–south asymmetry in
the sunspot-area is reported as small during the maximum period compared to
the minimum period (Roy, 1977). It is reported that sometimes during the
minimum period of the cycle, large sunspot groups appear in one of the
hemispheres, close to the Equator, that could cause the imbalance in the N–S
asymmetry in the area and magnetic flux. It is also found that the northern
and southern hemisphere peak at a different time of the activity cycle. This
phase difference between the two hemispheres is part of asymmetry in their
activity (Waldmeier, 1957, 1971). According to dynamo theory, the stochastic
fluctuations in the dynamo mechanism can lead to the asymmetry in the two
hemispheres (Choudhuri, 1992; Choudhuri, Chatterjee, and Jiang, 2007).

It is now well accepted that the N–S asymmetry exists in a variety of solar
activity indices, but most or all of them are related to the sunspot activity.
The asymmetry in the activity indices is reported in sunspot-area data having
more than 145 years (Vizoso and Ballester, 1990; Carbonell, Oliver, and
Ballester, 1993; Chowdhury, Choudhary, and Gosain, 2013; Zhang and Feng, 2015;
Badalyan and Obridko, 2017). It is also observed in sunspot-number data as
well as in Joy’s law for a few solar cycles (Temmer et al., 2006; Badalyan and
Obridko, 2011; McClintock and Norton, 2013; Leussu et al., 2017; Chowdhury et
al., 2019). Apart from these, the asymmetry is reported in plage index
(Dorotovič et al., 2007; Seguí et al., 2019), magnetic flux (Knaack, Stenflo,
and Berdyugina, 2005; Mordvinov, 2007; Svalgaard and Kamide, 2013; Vernova et
al., 2004, 2018), filaments or prominences observed (Duchlev, 2001; Li et al.,
2010; Hao et al., 2015), differential rotation (Javaraiah and Gokhale, 1997;
Gigolashvili et al., 2005; Xie, Shi, and Qu, 2018), etc. It is also reported
in energetic events such as X-ray and Hα flare index (Ataç and Özgüç, 1996;
Deng et al., 2013a, b, 2017, 2019), coronal mass ejections, radio bursts
(Verma, 1987; Gao, Li, and Shi, 2009; Gonçalves et al., 2014), energetic-
proton events (Richardson, von Rosenvinge, and Cane, 2016), coronal-hole area
(Nisticò et al., 2015) solar wind (Tokumaru, Fujiki, and Iju, 2015; Zirnstein
et al., 2020), coronal green-line index (Sýkora and Rybák, 2010), etc. Some of
the properties of N–S asymmetry can be used to understand the observed
periodicities in cycles, and North–South asymmetric properties of low-latitude
sunspot area can be used to predict the amplitude of the next cycle
(Javaraiah, 2007).

The sunspot-area data are available from the Royal Greenwich Observatory (RGO:
2015LRSP…12….4H), the longest data set. Most of the N–S asymmetry related
studies were carried out using this data set. The next available data set is
from the Debrecen Observatory (Baranyi, Győri, and Ludmány, 2016), which is
about 62 years long. Studies on N – S asymmetry have also been done using this
data set (Javaraiah, 2019). Apart from these, such studies are done using the
Mt. Wilson white-light data set (Howard, Gilman, and Gilman, 1984; Dasi-Espuig
et al., 2010; Baranyi, 2015), Michelson Doppler Imager (MDI:
1995SoPh..162..129S) white-light image data set (Watson et al., 2009; Ravindra
and Javaraiah, 2015). Another observatory that has the longest white-light
data series is from the Kodaikanal Solar Observatory (KOSO: 2010ASSP…19…12H).
The data have been obtained from a single telescope since 1905, and it has
collected more than 110 years of data. The data have been digitized in the
past, and several studies on solar activity are made (Gupta, Sivaraman, and
Howard, 1999; Sivaraman et al., 2003, 2010).

In the present study, we use the KOSO digitized data to study the N–S
asymmetry in the sunspot group area for eight solar cycles. These data make up
another large data set that can be used independently to study several
properties of solar cycles (Mandal et al., 2017; Hiremath et al., 2020). In
the next section, we describe the data and analysis methods adopted. In
Section 3, we present the results of the study, and we end the paper with a
summary and discussion.

##  2 The White-light Images and Method of Analysis

sec:cda

###  2.1 Kodaikanal Sunspot-Area Data

In the present study, we have used the daily white-light sunspot observations,
from 1921 to 2011. These images were recorded with the help of a 6-inch lens
mounted on an equatorial-mount telescope installed at the KOSO. The images of
the sunspots were recorded on lantern photographic plates starting in 1904
(Sivaraman, Gupta, and Howard, 1993) using the aforementioned telescope and
continued until today without any change of its optical set-up since 1918
(Ravindra et al., 2013; Mandal et al., 2017). However, from 1975, these
photographic plates were replaced with high-contrast films. These century-long
sunspot data were digitized and calibrated. To extract the different features
of sunspots, a semi-automated algorithm version of the STARA code (Watson et
al., 2009) was used. The area occupied by the sunspots (in the units of a
millionth of a hemisphere: $\mu$Hem) and the information corresponding to
their latitude and longitude measurements was extracted. This has been done
for each observation starting from 1921, and the measured area was corrected
for the projection effect (e.g. 2013A&A…550A..19R, 2017AA…601A.106M). The
sunspot-area during this time span was averaged over a month and we obtained
the time series of the monthly averaged sunspot-area in both the hemispheres
separately. The detailed explanation of the images, whole calibration process,
including data reduction and digitization of this time series was described by
Ravindra et al. (2013). The Kodaikanal data archive of digitized white-light
images is hosted at kso.iiap.res.in/new/white$\\_$light.

Figure 1.: The Sun’s image taken on 03 August (left) and 14 (right) 1947 at
the Kodaikanal Observatory. The detected sunspots in the white-light digitized
images are shown with contours.

fig:1

After digitization and calibration following Ravindra et al. (2013), the
sunspots are detected. Figure 1 depicts the two solar images taken on 03 and
14 August 1947, at the Kodaikanal Solar Observatory with the detected sunspots
marked with contours on white-light images.

###  2.2 Methods for Kodaikanal Sunspot Area Analysis

Figure 2.: Left: The monthly mean KOSO sunspot-area of the opposite
hemispheres is plotted from 1921 to 2011. Right: The same time series with
13-month smoothed data.

fig:2

Figure 2(a) shows the monthly averaged sunspot-area of both the hemispheres.
The 13-month smoothed sunspot-area plotted against time is shown in Figure
2(b). Both figures indicate a regular cyclic pattern of about 11 years, and
the figure also exhibits the characteristic property of each solar cycle, that
is different from others. We have quantified the sunspot-area asymmetry
between the opposite hemispheres by using the definition of the normalized
north–south asymmetry index [$A_{\mathrm{a}}$ = ( $A_{\mathrm{n}}$ –
$A_{\mathrm{s}}$ ) / ( $A_{\mathrm{n}}$ \+ $A_{\mathrm{s}}$ )], where
$A_{\mathrm{n}}$ and $A_{\mathrm{s}}$ represent the monthly mean northern and
southern hemispheric sunspot area respectively. We have made a plot of the
temporal evolution of $A_{\mathrm{a}}$ data set for each of the Solar Cycles
16 – 23 separately. Then, by looking at the trend, we have plotted the oblique
straight line. This is to examine the change in the trend of asymmetry in the
course of any solar cycle under study.

Solar activities are found to have a phase shift or time lag/lead between the
northern and southern hemispheres in a sunspot cycle (Li, 2009; Muraközy and
Ludmány, 2012; Li et al., 2019). To investigate the time lead or lag between
the opposite hemispheres, we have calculated the cross-correlation (CC)
between the 13 months smoothed monthly mean sunspot-area data of northern and
southern hemispheres. This is done for each of Cycles 16 – 23.

We have also determined the periodic variations of the asymmetry in time
series using the spectral decomposition technique of the wavelet-analysis
method. However, to detect periodicities in sunspot-area asymmetry, we have
used monthly values of north–south difference of area
$\Delta$=$A_{\mathrm{n}}$ – $A_{\mathrm{s}}$. This is because there is some
confusion about the existence of an $\approx$11-year periodicity in the
relative asymmetry:
$(A_{\mathrm{n}}-A_{\mathrm{s}})/(A_{\mathrm{n}}+A_{\mathrm{s}})$ (Javaraiah
and Gokhale, 1997; Ballester, Oliver, and Carbonell, 2005; Javaraiah, 2020).
Yi (1992) for the first time suspected the 11-year periodicity in the relative
asymmetry might be an artifact of the numerator. However, we have also applied
the wavelet technique on the relative asymmetry time series to examine the
similarity and differences between the two time sequences.

The wavelet technique (Farge, 1992) is a useful tool for identifying
oscillatory components within a given signal or time series, which converts a
1D signal into a 2D signal in the time–frequency domain and also provide
information about the exact location of the detected periods. We applied a
complex Morlet wavelet (Morlet et al., 1982) function to both absolute and
relative asymmetry time series as,

$\psi_{n}(\eta)=\pi^{-1/4}\mathrm{e}^{\mathrm{i}\omega_{0}n}\mathrm{e}^{-\eta^{2}}/2$
(1)

Here, $\omega_{0}$ is a non-dimensional frequency and we have adopted
$\omega_{0}$ = 12 for mid-term frequency (low periodic zone) range and
$\omega_{0}$ = 6 for the low-frequency range (long periods) (Torrence and
Compo, 1998; Knaack, Stenflo, and Berdyugina, 2005; Chowdhury et al., 2019).
The wavelet spectrum suffers from edge effects as wavelet power decreases by a
factor $\mathrm{e}^{-2}$ at the edges (Grinsted, Moore, and Jevrejeva, 2004),
which gives rise to a cone-of-influence (COI). This COI is plotted with a bold
dashed line to represent the edge effects. The thin black contours show the
periods above 95 % confidence level inside the COI, assuming red-noise
background and detected using the recipe by Grinsted, Moore, and Jevrejeva
(2004). “Global Wavelet Power Spectra” (GWPS) are computed for all of these
local wavelet plots, representing wavelet power at each period scaled and
averaged over time. The working principle of this method is similar to that of
Fourier power spectra, and the confidence level (95 %) of the GWPS plots are
determined using the method provided by Torrence and Compo (1998).

To investigate the phase shift and common quasi-periods between the monthly
sunspot-area data of the northern and southern hemisphere, we have employed
the cross-wavelet transform (XWT) and wavelet coherence (WTC) techniques. For
two series $X_{n}$ and $Y_{n}$, the quantity $\mid$ $W^{XY}_{n}$ $\mid$ shows
the amount of common power between the two time series in the XWT spectrum as
a function of time and frequency (Grinsted, Moore, and Jevrejeva, 2004). The
phase relation between the two time series is represented by arrows in the XWT
spectrum, with the following convention: arrows pointing right are in-phase;
pointing left are in anti-phase; pointing up are the second series leads by
90∘; pointing down are the first series leads by 90∘. A random distribution of
the arrows represents phase mixing between the two time series under study.
The wavelet transform coherence (WTC) between two time series $X_{n}$ and
$Y_{n}$ is defined as

$R^{2}_{n}=\frac{\mid S(s^{-1}W^{XY}_{n}(s))\mid^{2}}{S(s^{-1}\mid
W^{X}_{n}(s)\mid^{2})S(s^{-1}\mid W^{Y}_{n}(s)\mid^{2})}.$ (2)

Here, $S$ is a smoothing operator, considered as a localized correlation
coefficient in time–frequency space, and its value lies between 0 and 1. WTC
measures the cross-correlation between two time series, even though the common
power is low in the XWT spectrum (Maraun and Kurths, 2004; Grinsted, Moore,
and Jevrejeva, 2004; Chang and Glover, 2010). To draw both the XWT and WTC
plots using the Morlet wavelet technique under the red-noise approximation, we
have utilized the MATLAB code developed by Grinsted, Moore, and Jevrejeva
(2004), which is available at grinsted.github.io/wavelet-coherence/. Finally,
we have investigated the presence of the Gnevyshev Gap (GG:
1963SvA…..7..311G,1967SoPh….1..107G), in both N and S hemispheres separately
using monthly averaged sunspot-area time series. We used a methodology similar
to the one described by Norton and Gallagher (2010) to identify the GG in each
solar cycle.

##  3 Results

###  3.1 N–S Asymmetry and its Temporal Variations

Figure 2(a) shows the temporal variation of the monthly averaged sunspot area
of both the N and S hemispheres for the time span of 1921 to 2011, covering
complete Solar Cycles 16 – 23 and a small part of the rising branch of Cycle
24. Mandal et al. (2017) mentioned that in the KOSO area data the amplitude of
Cycle 23 is large in KOSO data compared to the RGO data. Similarly, the Cycle
18 amplitude is smaller than the RGO measured amplitude. In order to balance
this, we identified the dates where the data is not present in the KOSO data
set in Cycles 18 and 23. If the gap between the consecutive observing days is
more than two days then we filled those data points from the RGO data. The
resulting plot is shown in Figure 2(a). This plot shows that the nature and
amplitude of each cycle are different from others. It is clearly seen that
sunspot-area data sets used in this study show about 11-year solar-activity
cycle with some differences. Similar results are found in the 13-month
smoothed sunspot-area plot (Figure 2(b)). It is observed that in the course of
a sunspot cycle, the peak in the sunspot-area occurs in different time
intervals with different amplitudes in the opposite hemispheres. Figure 2(b)
shows that the sunspot-area possesses maximum and minimum amplitude during
Cycles 19 and 16, respectively, and also shows a double peak during the cycle
maximum. The southern hemisphere is dominant over the North in Cycles 18, 22,
and 23 and this difference is marginal for Cycles 16 and 19. From Figure 2(a),
we find that the odd-numbered cycles like 17, 19, and 21 have higher
amplitudes compared to the preceding even-numbered cycles like 16, 18, and 20.
This is in line with the odd–even cycle rule or Gnevyshev–Ohl rule (Gnevyshev
and Ohl, 1968).

Figure 3.: The total area occupied by the sunspots in the northern (plus
($+$)) and southern (star ($\ast$)) hemisphere over each cycle from 16 – 23.
The value of the total sunspot-area is divided by 10 to show the other curves
in the same plot. The diamond ($\diamond$) and triangle($\triangle$) symbols
represent the maximum area occupied by the monthly averaged sunspot-area in
each cycle in both the northern and southern hemispheres respectively.

fig:3

Figure 3 shows the maximum amplitude of sunspot-area in both hemispheres
during the maximum of the eight solar cycles under study. From the plot, we
found that the sunspot areas in both the northern and southern hemispheres
achieved maximum and minimum values during Cycles 19 and 20, respectively.
Solar Cycle 16 also showed the weakest value. Total sunspot-area in the
southern hemisphere showed a significant rise from Cycle 20 to 21 and
maintained nearly the same trend in Cycle 22 with a jump in Cycle 23, again.
On the other hand, total sunspot-area in the northern hemisphere exhibited a
steady rise from a Cycle 20 to 21 with a drop of its value in Cycle 22. During
Cycles 17, 20, 21, 22, and 23, maximum sunspot-area occupied by the opposite
hemispheres was nearly the same.

Figure 4.: Left: The relative north–south asymmetry in monthly mean sunspot
areas is plotted against time. The solid lines indicate the trends during each
cycle. Right: Same as the left side but for the absolute north–south
asymmetry.

fig:4

Figure 4(left) shows the temporal evolution of the relative N–S asymmetry
index $A_{\mathrm{a}}$ in the monthly averaged sunspot area for each Solar
Cycle, 16 to 23. It has been found that unlike during the minimum period of
the cycles, the area asymmetry values lie between –0.5 and $+$0.5. However,
around the minimum and the onset period of the solar cycles, the sunspot-area
asymmetry index has somewhat large values, close to $+$1 or –1 depending on
which hemisphere dominates over the other. Further, this plot shows that the
slope of the line changes in each cycle, indicating some long-term (about
eight cycle period) systematic change in dominance of the sunspot-area
activity from one hemisphere to another. The right hand side plot in Figure
4(right) shows the temporal evolution of the absolute asymmetry. The data
points are normalized by the maximum value in the cycle series. As for the
relative-asymmetry, also found the eight-cycle period. We have only eight and
a half cycles of data, and the pattern of the inclination of the lines
indicates that this could be an eight-cycle period.

###  3.2 Dominant Hemispheres

Following Carbonell et al. (2007), we applied Student’s t-test to determine
the dominant hemisphere in each solar cycle under study and the results are
shown in Table tab:1. We consider preselected error probability in the
t-distribution as $<$ 0.025, i.e. the difference between northern and southern
hemispheric sunspot-area is statistically significant at a 95 % level.
Otherwise, the difference in sunspot areas in two hemispheres for any cycle
should be regarded as marginal. Such types of solar cycles are marked with “–”
in the table.

Table 1.: Cumulative sum of the monthly averaged northern and southern
hemisphere sunspot-area data, probability of finding the asymmetry by chance,
asymmetry index, and dominant hemispheres in sunspot-area for Cycles 16 to 23.

tab:1  Cycle No. SSA N-hemi SSA S-hemi Probability Asymmetry Dominant
hemisphere 16 33920 29829 1.16 $\times$10-1 0.064 – 17 46061 47234 4.15
$\times$10-1 – 0.013 – 18 57417 52043 1.65 $\times$10-1 0.049 – 19 87263 67575
2.01 $\times$10-3 0.127 N 20 59256 42950 2.04 $\times$10-4 0.159 N 21 62863
59076 2.61 $\times$10-1 0.031 – 22 54349 57989 2.55 $\times$10-1 – 0.032 – 23
64156 72056 5.17 $\times$10-2 – 0.058 –

Table tab:1 shows that the asymmetric nature is statistically significant for
the northern hemisphere in Cycles 19 and 20. The southern hemisphere is
preferred in Solar Cycles 17, 22, and 23, but the difference is not
statistically significant. We also noticed that the normalized asymmetry is
more pronounced at the beginning of a new cycle when the number of spots on
the solar disk is small.

From Mandal et al. (2017), it is clear that there is a difference in the cycle
amplitude of the Kodaikanal data compared to the RGO data. This could be
because of missing data, the contrast of the photographic plates, semi-
automated detection of sunspots, and the software’s ability to detect smaller
sunspots in images. The RGO data have been cataloged using sunspot
observations from different observatories around the world (Cape of Good Hope,
Kodaikanal, and Mauritius) to supplement missing days or bad data. Thus, the
RGO data are affected by different scaling to incorporate data points from
various observatories. This may also lead to differences in values of KOSO
data in comparison to the RGO data.

Many of the earlier statistical studies (Li et al., 2002) used the yearly
averaged data to study the dominant hemisphere. We have used the monthly
averaged data, and the large difference in the amplitudes of the North–South
shows as significant asymmetry. Some studies used the probability distribution
function (Li et al., 2002), and some others have used the overlap of the
North–South time series to identify the dominant hemisphere in the cycle
(Norton, Charbonneau, and Passos, 2014). It appears that the hemispheric
amplitude of the KOSO data in some cycles is different than other observatory
data and hence the difference in the results of the dominant hemisphere.

Figure 5.: Cumulative monthly counts of KOSO sunspot-areas in the northern and
southern hemispheres for Cycles 16 – 23.

fig:5

Figure 5 shows the cumulative sum of the sunspot-area against time in the
northern (solid line) and southern (dashed line) hemispheres for each cycle 16
– 23 separately by utilizing the monthly averaged sunspot-area values. This
indicates that Cycle 16 shows approximately equal activity levels in both the
hemispheres. However, in Cycles 18, 19, 20, and 21 the northern hemisphere
dominated in activity over the southern hemisphere. On the other hand, in
Cycles 17, 22, and 23, the southern hemisphere is more active than the
northern hemisphere. This plot also shows the time period when the dominance
of activity occurs during the progress of any cycle. It has been found that
during Cycle 20 the northern hemisphere’s activity is always highly dominant,
which is a unique property of this cycle. During Cycles 22 and 23, although
the activity of the northern hemisphere was higher than the southern one in
the ascending phase, the situation was shifted to the southern one around the
maximum epoch. This property of the Kodaikanal sunspot-area data set is
consistent with the results previously obtained by Zhang and Feng (2015) for
ESAI sunspot-area database and Chowdhury et al. (2019) for sunspot-numbers.
The bottom-right plot in Figure 5 shows the cumulative sum of the sunspot-area
for the northern and southern hemispheres for the Cycles 16 – 23. This plot
shows that a small or vanishing asymmetry before Cycle 19, and after that,
there is a dominance of the northern hemisphere is seen. This difference could
be because in Cycles 19, 20, and 21 the activity was higher in the northern
hemisphere than the southern hemisphere. During these cycles, the northern
hemisphere is dominant.

Figure 6.: The cumulative N–S asymmetry index is plotted for each Cycle, 16 –
23. The bottom right plot is the cumulative N–S asymmetry index for all the
cycles.

fig:6

The north–south asymmetry is small around the solar-cycle maximum phase when
large numbers of spots are present in the photosphere, and it is large during
the cycle minimum when a small number of spots present on the disk (Li, 2009;
Ravindra and Javaraiah, 2015). Figure 6 shows the variation of cumulative
asymmetry during each cycle under investigation. As can be seen in this
figure, except for Cycle 21 all of the remaining cycles end up a with large
value of the cumulative asymmetry during the end of the cycle. The pattern of
variations of the cumulative asymmetry is considerably different from one
cycle to another. The upward and the downward trends in the values of the
cumulative asymmetry imply the dominance of the northern- and southern-
hemispheres, respectively. In some cycles (Cycles 16, 17, and 22) there are
trends of about 6 – 7 year periodicity. The trends in other cycles suggest the
existence of longer than a 11-year periodicity. The cumulative index of all
the cycles (bottom right-most plot in Figure 6) shows there is steady increase
in the index until the Cycle 19. There is a sudden jump in the cumulative
index during the declining phase of Cycle 19. This is consistent with the
pattern seen in Figure 4, suggesting that there could be a long periodic
(about eight-cycle period) change in the N–S asymmetry. However, we need to
have more data to conclude this result firmly.

###  3.3 Periodicities in the N–S Asymmetry of Sunspot Areas

Figure 7.: Panels a and b exhibit the local and global power spectra of the
monthly mean absolute-asymmetry data series from KOSO sunspot-area for the
range 4 – 32 months. Panels c and d are similar to panels a and b for the
range 16 – 130 months. The 95 % confidence level in all GWPS is indicated by
red dotted lines. Panels e and f are the same as panels a and b but for the
relative-asymmetry data series. Similarly, panels g and h are the same as
panels c and d but for the relative-asymmetry time series.

fig:7

Intermediate-term quasi-periodic variations in the absolute and relative
asymmetry time series of sunspot area studied using the Morlet wavelet
technique and the results are displayed in Figure 7. We find several short-
and mid-term quasi-periodicities during Cycles 16 – 23 in the sunspot
asymmetry data. Figure 7(a) shows that Rieger and near-Rieger type periods are
present in all solar cycles including the recent Cycles 22 and 23 with a
varying length between four to eight months. We have detected the presence of
a quasi-annual period in Cycles 18, 19, 21, 22, and 23. Quasi-biennial
oscillations (QBO) in the range of 1.3 to 2 years were present during
different phases in Cycles 18, 19, 20, 21, and 23 in both of the data sets.
Other long-term QBOs in the range of 2.5 to 4 years were significant
approximately from 1935 to 1972, covering Cycles 17 to 20 and from 1988 to
2002, which covers Cycles 22 and 23 in absolute-asymmetry data. In relative-
asymmetry data, a period in the range of 2 – 2.5 years was present mainly from
1935 to 1955 and from 1970 to 1990. Thus the observed Rieger-type periods and
QBOs show intermittent behavior in asymmetry data. A quasi-period in the range
of five years was also detected in Cycles 18 to 20 and again in Cycles 22 and
23 in absolute-asymmetry data. However, this period was absent in Cycle 22 for
relative-asymmetry data and its presence in Cycle 23 is also weak. Along with
these intermediate-term periodicities, the signatures of the 11-year period of
sunspot cycle was also seen in both types of asymmetry data. However, the
temporal evolution of this Schwabe-cycle period is different in each time
series. The plots of GWPS (Figure 7(b), (d), (f), and (h)) of the asymmetry
time series also exhibit statistically significant periodicities of Rieger
type, QBOs, $\approx$ 5, and $\approx$ 10 years.

###  3.4 Time Delay and Phase Shift between the Hemispheres

Figure 8.: The phase lag between the occurrence of peak between the northern
and southern hemisphere in each cycle. The phase lag is shown in months. The
solid vertical line represents the time of maximum correlation. The peaks at
positive and negative values of lag indicate north and south lead
respectively.

fig:8

We have adapted a cross-correlation technique to detect the degree of how
sunspot areas in the two hemispheres are related (Hagino, Sakurai, and
Miyazawa, 2004; Deng et al., 2016), and the results are shown in Figure 8.
These plots indicate the time lead or lag of sunspot-area time series
separately for Cycles 16 to 23. The results are listed in Table tab:2. The
bottom-right plot in the same figure shows the overall phase lead of the
northern hemisphere by two months, if one considers the eight Cycles 16 – 23.

Table 2.: Time difference between the northern and southern hemisphere
sunspot-area to reach their peak values and the maximum values of correlation
(Max Cor) in Solar Cycles 16 – 23. The zero means there is no time delay
between the two hemispheres in reaching their maximum. The positive value of
time difference indicates the lead of the northern hemispheric activity over
the southern hemisphere expressed interms of months.

tab:2  Solar Cycle No. Time lag/lead [months] Max Cor 16 0 0.90 17 0 0.73 18 0
0.85 19 0 0.91 20 12 0.80 21 15 0.90 22 2 0.93 23 0 0.90

Table tab:2 shows that in Cycle 20, 21, and 22, the northern hemispheric
activity leads the southern by about 12, 15, and 2 months, respectively.
However, in other cycles no delay in the activity levels is observed between
the hemispheres. Compared to the earlier results (Li, 2009; McIntosh et al.,
2013) there is a difference in the phase-leading hemisphere in KOSO data. This
is due to the difference in the measured area in the KOSO data compared to RGO
data. Since we do not have long-term data, we can not conclude that the eight-
cycle pattern exists in the hemispheric phase difference.

Figure 9.: (a) XWT and (b) WTC power spectra for the KOSO hemispheric area for
Cycles 16 to 23. The solid black contours represent 95 % confidence level in
both panels and the thin line indicates the cone of influence (COI). Phase
relationship is represented by arrows.

fig:9

The cross-correlation method used here accounts for the total length of any
solar cycle, but the phase shift may take place at any time during the cycle
(Norton and Gallagher, 2010). Therefore, we have utilized the wavelet
coherence method to realize better the relative-phase relationship and common
quasi-periods of sunspot area between the opposite hemispheres (Chowdhury et
al., 2019; Oloketuyi, Liu, and Zhao, 2019; Javaraiah, 2020), and the results
are shown in Figure 9. From the XWT plot, it is evident that Rieger and
Rieger-type periods (130 – 190 days) are prominent and common in both
hemispheres along with QBOs in the range of 1.2 to 4 years. However, the
arrows are randomly distributed, indicating there exists strong phase mixing
in these periods. Hence, no regular oscillatory pattern has been found in
those periodic regions. The WTC spectrum reveals that this periodic zone is
highly correlated. Both of the wavelet-coherence plots indicate that within
the periodic zone of 9 – 11 years (Schwabe cycle), directions of the arrows
are mainly toward the right, indicating that the solar-cycle length in the
opposite hemispheres is unequal. However, this region is common to both the
hemispheres and is strongly correlated, as seen by the WTC plot. A quasi-
period in the range of 5 – 7 years is common and statistically significant
between 1940 to 1985 with phase variations.

###  3.5 Determination of the Gnevyshev Gap (GG)

Table 3.: The detected Gnevyshev gap for the whole disk, the northern- and
southern-hemisphere data. The $\times$ symbol represents the presence of the
gap and “–” symbol represents that there is no Gnevyshev gap.

tab:3  Solar Cycle No. Whole disk N-hemisphere S-hemisphere 16 $\times$
$\times$ $\times$ 17 $\times$ – $\times$ 18 $\times$ $\times$ $\times$ 19 –
$\times$ – 20 – $\times$ – 21 $\times$ $\times$ $\times$ 22 $\times$ $\times$
$\times$ 23 $\times$ $\times$ $\times$

Figure 10 shows the four month smoothed sunspot area plotted against time for
Cycles 20 and 21. In this figure the existence of Gnevyshev gaps in the whole
disk and also in both of the hemispheres data is clearly seen. We have noticed
that six out of eight solar cycles have shown a detectable Gnevyshev gap in
the total sunspot-area time series. Seven (six) cycles have this gap in the
data of northern (southern) hemisphere. We may conclude that this double-
peaked nature of solar cycles, and the ensuing Gnevyshev gap, is not an
artifact generated by averaging data from hemispheres that are slightly out of
phase. Rather, we confirm earlier results (Norton and Gallagher, 2010) that it
is an inherent property in each hemisphere and must be caused by some physical
mechanism occurring within each hemisphere.

Figure 10.: The four-month smoothed sunspot-area data are used to identify the
Gnevyshev gaps and is shown here for the whole Sun (top), northern hemisphere
(middle) and southern hemisphere (bottom) for Cycles 20 and 21.

fig:10

##  4 Discussion and Conclusions

Sunspot area is a key indicator of the solar-surface magnetic field and its
variation (Hathaway, 2015). Long-term study of sunspot-area helps us better
understand the solar-cycle evolution of the magnetic field, which is the main
source of all types of activity in the Sun. We have utilized the newly
digitized Kodaikanal Observatory sunspot-area data to investigate the
characteristics of north–south asymmetry in solar activity during Solar Cycles
16 – 23, which may provide us valuable information about the nature of the
solar dynamo between the opposite hemispheres in different solar cycles. So
far, to the best of our knowledge, this is the first analysis of the
asymmetric behavior, dominant hemisphere, phase asynchronicity, and the
Gnevyshev Gap (GG) of this Kodaikanal data covering the eight Solar Cycles 16
to 23. Below, we have made a summary about the main findings with discussions:
i) It is observed that both the strength and temporal variation of the KOSO
sunspot-area are not the same in the northern and southern hemispheres. The
peak time is also different in both hemispheres in many cycles. In both
hemispheres the maximum and minimum strength of sunspot-areas were found
during Cycles 19 and 20, respectively. The monthly mean sunspot-area favors
the northern hemisphere during Solar Cycles 16, 19, and 20. However, 13-month
average data indicated that both hemispheres had nearly equal strength in
Cycles 17 and 18. ii) N–S asymmetry is maximum around the minima or the onset
of any new cycle, and it has a cyclic trend. The northern hemisphere was
dominant during Cycle 19 and 20. The hemispheric asymmetry was not
statistically significant in other cycles. Our cumulative analysis revealed
that the northern hemisphere was more active in all cycles except in Cycle 20.
iii) Sunspot activity in the northern hemisphere leads in Solar Cycles 20, 21,
and 22 by 12, 15, and 2 months, respectively. We did not find any time delay
in Cycles 16, 17, 18, 19, and 23. iv) By using the wavelet technique, we have
detected several midterm quasi-periodicities, along with the 11-year
variations in the asymmetry. Our cross-wavelet analysis indicated that these
periods are common and statistically significant in both the hemispheres with
phase mixing. The presence of periods in the range of five years in both local
wavelet and wavelet coherence plots may be assumed as a manifestation of the
asymmetric nature of solar cycles or due to the double-peak structure of solar
cycles (Georgieva, 2011). We found that phase coherency exists only in a
narrow period belt of 9 – 12 years, including the 11-year Schwabe cycle. v)
Finally, we have detected the Gnevyshev Gap in both of the hemispheres
separately for individual Cycles 16 to 23. We have noticed that the Gnevyshev
Gap is common in the sunspot-area data of the whole solar disk, northern, and
in the southern hemisphere during Cycles 16, 18, 21, 22, and 23. This gap is
absent during Cycle 17 in the northern hemisphere and during Cycle 19 and 20
for the southern hemisphere. Our results are consistent with the earlier
detection of this phenomenon in the Greenwich sunspot-area data set (Norton
and Gallagher, 2010).

There is currently no clear physical explanation about the origin of different
types of quasi-periods in various solar proxies. We have detected Rieger-type
and QBOs in the present study, which has also been reported in the literature
(Krivova and Solanki, 2002; Cadavid et al., 2005; Knaack, Stenflo, and
Berdyugina, 2005; Fletcher et al., 2010; Badalyan and Obridko, 2011; Vecchio
et al., 2012; Chowdhury, Choudhary, and Gosain, 2013; Kilcik et al., 2014;
Mandal and Banerjee, 2016; Gurgenashvili et al., 2017; Chowdhury et al., 2019;
Deng et al., 2020 and references therein). Probably the midterm periods are
manifested by emergence of magnetic flux at regular intervals from below the
solar surface (Ballester, Oliver, and Carbonell, 2002) or by the excitation of
Rossby-type waves, (e.g. 2003MNRAS.345..809L, 2005A&A…438.1067K,
2009MNRAS.392.1159C, 2010ApJ…724L..95Z, 2016ApJ…826…55G). Recently, such
Rossby-type waves in both solar upper and interior layers were detected and
diagnosed (McIntosh et al., 2017; Hanson, Gizon, and Liang, 2020).
Zaqarashvili et al. (2015) and Zaqarashvili (2018) have suggested that slow
magneto-Rossby waves could be responsible for long-term variations of solar
activity. Thus, the periods observed in the hemispheric asymmetry might
correspond to different harmonics of global slow magneto-Rossby waves. The
QBOs were detected in the deep solar interior and on different solar surfaces
and considered a global phenomenon (e.g. 2014SSRv..186..359B). However, the
origin of QBOs due to the second dynamo’s presence near the solar surface has
also been suggested (Benevolenskaya, 1998; Obridko and Badalyan, 2014;
Beaudoin et al., 2016; Strugarek et al., 2018). Recently, Inceoglu et al.
(2019) indicated that turbulent $\alpha$-dynamos with the Lorentz force are
mainly responsible for generating the spatio-temporal behavior of the QBOs.
However, to shed more light on the physical mechanisms behind these midterm
quasi-periodicities, more investigation on solar interior dynamics is
required.

We have found asynchronous behavior and time lead/lag in hemispheric solar
activity. This phase shift is probably related to the hemispheric asymmetry
with a connection to the variation of the about 11-year Schwabe cycle (Temmer
et al., 2006; Zolotova and Ponyavin, 2006; McIntosh and Leamon, 2014;
Schüssler and Cameron, 2018 and references therein). However, our findings of
cycle-wise dominant hemispheres and time delay between the hemispheres are not
entirely in agreement with the previous results with ESAI sunspot-area data
(Zhang and Feng, 2015) and sunspot numbers (Chowdhury et al., 2019). But, our
cumulative plots with KOSO data for different solar cycles are totally
consistent with other recent long-term studies for sunspot-related activities
measured at other observatories (e,g. Li et al., 2019; Chowdhury et al., 2019,
etc.). Moreover, our finding of phase coherency only in the small region of
the Schwabe cycle period satisfies the conclusions of Donner and Thiel (2007).

The reason behind the N–S asymmetry is still unclear. Our findings of time
delay (phase difference) and different dominant hemispheres are probably
caused by the unusual behavior of the dynamo mechanism in the opposite
hemispheres. Attempts to explain the hemispheric asymmetry have been proposed
in dynamo simulations in different ways such as asymmetric meridional
circulation (Hathaway and Rightmire, 2010; McIntosh et al., 2013); fluctuation
and randomness in the formation of polar field (Norton, Charbonneau, and
Passos, 2014); asymmetry in dipole and quadrupole components in solar polar-
field reversal (Shukuya and Kusano, 2017). Recently, Hazra and Nandy (2019)
explained the hemispheric asymmetry as a nonlinear coupling between the
dipolar and quadrupolar components of the solar magnetic fields and noticed
that global parity flips and hemispheric asymmetry is closely related. They
particularly noted that if one hemisphere is stronger over another hemisphere
for a sufficiently long time, parity change takes place. At the same time, an
asymmetric variation of subsurface zonal flows in different latitude bands
(Komm et al., 2014; Zhao, Kosovichev, and Bogart, 2014; Komm, Howe, and Hill,
2020) might be related with this N–S asymmetry. However, these speculations
are still far from determining the exact cause of the results obtained from
our analysis. More observations and numerical simulations are required to
understand this phase asynchrony better.

To conclude, we have analyzed about 100 years of digitized white-light data
observed from Kodaikanal Observatory and extracted sunspot area to investigate
the properties of the northern and southern hemispheres separately. We found
some noticeable differences between the northern and southern hemisphere
temporal behavior during the different phases of the solar cycle. In the
future, we would like to investigate other long-term sunspot-related studies
using Kodaiakanal white-light sunspot-area data and compare the results with
other data sets, which may help us understand the underlying physical
processes responsible for the observed long-term behaviour of sunspots.

Acknowledgements We thank the reviewer for fruitful comments. We thank all of
the observers at the Kodaikanal Solar Observatory who have observed
continuously over a century. We also thank the people who have initiated the
digitization program at Kodaikanal Observatory.

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