Characteristics of latitude variations of sunspots in the northern and southern hemispheres are investigated using the daily sunspot area and its latitude during the period from 1874 to 2009. Solar magnetic activity is portrayed in the form of sunspot, regions of concentrated fresh magnetic fields observed on the surface of the Sun. By defining center-oflatitude(COL) as an area-weighted latitude, we find that COL is not
monotonically
decreasing as commonly assumed.In fact, small humps (or short plateaus) between solar minima can be seen around every solar maxima. We also find that when the northern (southern) hemisphere is magnetically dominant, COL is positive (negative), except the solar cycle 23, which may give a hint that these two phenomena are consistently regulated by one single mechanism. As a result of periodicity analysis, we find that several significant periodicities, such as, of ~5.5, ~11, ~49, and ~167 years.
1. INTRODUCTION
Sunspots represent one of the most obvious manifestations of magnetic fields on the solar surface. The complexity of the physical models that explain how the solar magnetic flux is generated and works is mainly due to observational constraints set by temporal and spatial distributions of sunspots (Parker 1955, Babcock 1961, Leighton 1969). That is, any potential model should explain the latitude distribution and drifts of sunspots, the tilt angle and the polarity reversal of the bipolar groups, and so on. The cyclic behavior of the solar large-scale magnetic field has also provided invaluable information about the physical processes involved. The sunspot cycle itself has two main aspects: the periodic variation in the number(including polarity) of sunspots and the migration of the appearance position of sunspots.
Sunspot latitude is an indication of the phase of the sunspot cycle: within a cycle, the higher the latitude, the earlier the phase in the cycle. The progressive change in latitude of sunspot groups is best presented by plotting their latitudes against appearance time. In 1904 Maunder published the first version of such a diagram displaying the sunspot group distribution in latitude for each synodic rotation of the Sun (Maunder 1904). That diagram was soon named ‘butterfly diagram’ and became one of the most popular tools for a compact description of the spot zone evolution. The migration of the sunspot activity belt toward the equator is a direct consequence of the passive transport of the toroidal magnetic field by the meridional circulation (Choudhuri et al. 1995, Nandy &Choudhuri 2001).
One thing that must be kept in mind here is that the diagram takes no account of the sunspot lifetime, nor the spatial size. Since all groups are given equal weight,regardless of their temporal and spatial extention, the diagram is dominated by small sunspots, which scatter over wider latitude ranges than larger ones. That makes the butterfly diagram appear noisy and hard to be understood.This is the first reason why we revisit the butterfly diagram in the present paper. By replotting the butterfly diagram by weighting the sunspot with its area, we would like to check general concepts, such as, 'the distance of the sunspot to the equator
monotonically
decreases as the solar cycle proceeds'. One may also wish to check its validity of some research on the latitudinal migration of solar activity. For example, some researchers have reported that latitudinal migration of sunspots asynchronously occur in the northern and southern hemispheres (Waldmeier 1971, Swinson et al. 1986, Zolotova & Ponyavin 2006, 2007, Donner & Thiel 2007, Zolotova et al. 2009, Li et al. 2009a, b, 2010). They have attempted to explain the solar North-South asymmetry with such a phase difference between paired wings of the butterfly diagram instead of appreciating the real asymmetry in two hemispheres. They have drawn the conclusion by taking a mean latitude from the butterfly diagram without taking due care into account. Furthermore, if such is the case, it is very important since it gives a hint that solar dynamo in two hemispheres is only weakly connected. As a consequence, solar dynamo theory should explain the relative phase shift of the paired wings of the butterfly diagram in the future (Goel & Choudhuri 2009). Until now, magnetic flux transport dynamo models of the Sun’s global magnetic field have been shown to reproduce the amplitude and duration fairly well, but not the relative phase difference in the solar activity.
The North-South asymmetry of activity phenomena in the solar atmosphere also represents an important detail of the solar dynamo action. This is why various solar activity indices, such as, sunspot number, sunspot area, flare index, are studied. Asymmetries between the northern and southern hemispheres have been previously found in various solar indices (Waldmeier 1971, Roy 1977, White & Trotter 1977, Ichimoto et al. 1985, Swinson et al. 1986, Ozgüc & Ucer 1987, Verma 1987, Tritakis et al. 1988, Vizoso & Ballester 1989, 1990, Antonucci et al. 1990, Mouradian & Soru-Escaut 1991, Schlamminger 1991, Yi 1992, Carbonell et al. 1993, Verma 1993, Oliver & Ballester 1994, Javaraiah & Gokhale 1997, Li et al. 1998, 2002, Atac & Ozgüc 1996, 2001, Temmer et al. 2001, 2002, Krivova & Solanki 2002, Vernova et al. 2002, Berdyugina & Usoskin 2003, Knaack et al. 2004, 2005, Ballester et al. 2005, Gigolashvili et al. 2005a, b, Javaraiah & Ulrich 2006, Zaatri et al. 2006, Chang 2007a, b, 2008, 2009). This is the second motivation for the present study. We would like to see if one can find the North-South asymmetry of the time series of the area-weighted latitudinal variation of sunspots and related periodicities.
This paper begins with descriptions of data and how the center-of-latitude (COL) is defined in Section 2. We present results obtained with the Lomb-Scargle periodo2gram and the wavelet transform in Section 3. Finally, we discuss and conclude in Section 4.
2. CENTER-OF-LATITUDE OF SUNSPOT
We have used for the present analysis the Greenwich sunspot group data during the period from 1874 to 1976, and the sunspot group data from the Solar Optical Observing Network (SOON) of the US Air Force (USAF)/ US National Oceanic and Atmospheric Administration (NOAA) during the period of from 1977 to 2009. The daily sunspot area and its latitude have been downloaded from the NASA website
1
.
In
Fig. 1
we show the averaged COL as a function of time during the period from 1874 to 2009. The COL is basically defined by
where
Ai
is the
i
-th sunspot’s area and
Li
is its latitude. Thick and thin curves represent the yearly averaged COL and the monthly averaged COL, respectively. The summation is carried out over a calendar month or a calendar year, instead of the Carrington month. In the first and the second panels, we separately plot the averaged
The averaged center-of-latitude (COL) as a function of time during the period from 1874 to 2009. Thick and thin curves represent the yearly averaged COL and the monthly averaged COL respectively. Positive and negative COL represents the northern and southern latitudes respectively. In the first and the second panels we separately plot the averaged COL for sunspots appeared in the northern and southern hemispheres respectively. In the third and fourth panels we show fitting results from the distributions of COL of sunspots appeared in both hemispheres with signed and unsigned latitudes respectively.
COL for sunspots appeared in the northern and southern hemispheres, respectively. Positive and negative COL represents the northern and southern latitudes, respectively. In the third panel, the averaged COL for sunspots appeared in both hemispheres is plotted. If the mean latitude where sunspots appear in both hemispheres is symmetrical, COL should be in a form of the random noise. However, we observe that the difference is large every time when the solar cycle begins. What is also barely seen is what is expected when there is a relative phase lag between the two wings. What we see is rather that the wings of the butterfly diagram is not symmetric, nor steadily drifts to the equator. In the last panel we plot the averaged COL of average of two hemispheres defined by
such that the absolute value of the latitude is used rather than the latitude itself. It is shown that the solar cycle begins when COL is high. And as the solar cycle proceeds COL decreases in general. We note, however, that COL is not
monotonically
decreasing as commonly assumed. Small humps (or short plateaus) between solar minima can be seen. Actually humps appear around every solar maxima.
1http://solarscience.msfc.nasa.gov/greenwch.shtml
3. NORTH-SOUTH ASYMMETRY AND PERIODICITIES
In
Fig. 2
, we show the difference between the north-
The difference between the northern and southern hemispheres both in sunspot area and in center-of-latitude (COL). In the upper panel we plot the difference in the sunspot area between the northern and southern hemispheres. In the lower panel we plot the scaled difference of COL between the northern and southern hemispheres.
rern and southern hemispheres both in sunspot area and in COL. In the upper panel, we plot the difference in the sunspot area between the northern and southern hemispheres, which is averaged over the whole period for a given solar cycle. Therefore, the upper panel shows the asymmetrical behavior of the solar cycle and thereby which one is the dominant hemisphere. The difference is defined by
where Σ
AN
and Σ
AS
are thus the whole sunspot area appearing in the northern and southern hemispheres during a given solar cycle, respectively. In the lower panel, on the other hand, we plot the scaled difference of COL between the northern and southern hemispheres, which is also averaged over the period for a given solar cycle. The difference is defined by
where ΣCON
N
and ΣCOL
S
are the averaged COL in the northern and southern hemispheres during a given solar cycle as a whole, respectively. We note that COL is positive (negative), when the northern (southern) hemisphere is magnetically dominant. The exception occurs in the cycle 23.
Generally, there is no obvious reason why these two plots look similar, since the first panel tells us how large areas are covered by sunspots for a given hemisphere during the particular solar cycle while the second panel tells us the latitude where large sunspots are distributed for a given hemisphere during the particular solar cycle. For instance, supposed a bigger sunspot is at low latitude in the northern hemisphere and smaller sunspot is at high latitude in the southern hemisphere, it is not impossible that one can observe the positive D
A
(northern dominance) and negative COL (southern dominance). Therefore, the fact that this kind of ‘odd’ thing does not happen for 11 solar cycles may give a clue that these two phenomena are regulated by a consistent mechanism.
In
Fig. 3
, we show Lomb-Scargle periodograms (Press & Rybicki 1989) of COL in units of month
-1
. The power shown here is in an arbitrary unit. In the upper left panel, we show the result of COL in the northern hemisphere. In the upper right one, we show the result of COL variation in the southern hemisphere. Not surprisingly, main peak corresponds to ~11 years. The secondary, yet significant, peak we also see here corresponds to ~5.5 years (confidence level is greater than 90%). We consider this period-
Lomb-Scargle periodograms of center-of-latitude (COL) in units of month-1. The power shown here is in an arbitrary unit. In the upper left panel we show the result of COL in the northern hemisphere. In the upper right one we show the result of COL variation in the southern hemisphere. In the lower left and right ones we show results from COL of sunspots appeared in both hemispheres obtained by taking the unsigned COL and the signed latitude into account respectively.
icity is due to humps between the minima we have seen in
Fig. 1
. In the lower left and right ones, we show results from COL of sunspots appeared in both hemispheres obtained by taking the unsigned COL, and the signed latitude into account, respectively. The power spectrum in the lower left panel is somewhat similar to power spectra in upper panels. In the lower right panel, one might expect a peak corresponding to ~ 9 year periodicity if s/he expects the solar North-South asymmetry (Chang 2007a, b). Instead, the periodicity of ~12 years (frequency ≈0.007 month-1) can be found, which appears in the periodogram of the reciprocal of the total sunspot number,
(Ballester et al. 2005). This can be understood since we take the sunspot area as the weight function in COL calculations. It should be noted that the the highest peak corresponds to ~49 year periodicity (frequency ~0.0017 month
-1
). It can also be understood in terms of a long term variation seen in
Fig. 2
. A similar periodicity of of ~44 years has been reported in the solar North-South asymmetry by Javaraiah (2003) and Zolotova & Ponyavin (2007), who suggested the existence of a '44-yr' cycle or 'double Hale cycle' and further ~80 year periodicity (Gleissberg 1971).
The power distribution in time obtained by the wavelet transform technique. The power is apparently maintained for the almost entire period of data set. One may find peaks corresponding to periodicities of ~49 and ~167 years.
To see how its phase keeps consistently we analyze the same time series data using the wavelet transform technique (Chang 2006), which shows the power distribution in time. The power is normalized in terms of the mean level of noise so that the plot contains the signal-to-noise ratio by itself. As shown in
Fig. 4
, the power is apparently maintained for the almost entire period of data set. We have to conclude therefore that the oscillating component of ~49 year periodicity is significant and consistent. Moreover, one may also see another component with ~167 year periodicity (frequency ~0.0005 month
-1
), which is also found in Javaraiah (2003) where the Sun’s motion about the center of mass of the solar system is related to the long term modulation in the differential solar rotation velocity derived by the sunspot observation.
4. DISCUSSION AND CONCLUSIONS
Since the butterfly diagram is introduced to the field of solar study, the accepted paradigm has pretended that spots are scattered around a mean latitude, which
monotonically
drifts equatorward. For the sunspot activity a second order polynomial curve is widely used to give a fit to the monthly mean latitudes of sunspot activity. Accordingly, most of theoretical calculations have been aimed at developing models predicting the location of such a monotonic latitudinal migration of sunspots. On the other hands, some
nonstandard
solar magnetic models are introduced to describe non-steady equatorward progression (Bell 1960, Antalova & Gnevyshev 1983, Solanki et al. 2008).
We have examined the latitudinal variation of COL of sunspots in each hemisphere. As a fine structure of the butterfly diagram interests some researchers (Solanki et al. 2008, Ternullo 2010) an issue of how one may take care of different size sunspots will become more important. In this work we have suggested one way of doing this. By taking the area of sunspots into account, one may draw a more reliable conclusion on the evolution and distribution of sunspots, such as, 'active latitude' recently suggested. Another example of use of COL is a new diagnostic of the solar cycle and of models of the generation of the Sun’s magnetic field. As Solanki et al. (2008) demonstrated the latitudinal variation of position of sunspots can be used in distinguishing some dynamo models. On doing so, we may take care of the area of sunspots by using COL.
The summary of what we have found is as follows:(1) It is shown that the solar cycle begins when COL is high and that as the solar cycle proceeds COL decreases in general. COL in both hemispheres is not, however,
monotonically
decreasing as commonly pictured in theoretical calculations. Small humps (or short plateaus) between every solar minima can be seen around solar maxima.
(2) When the northern (southern) hemisphere is magnetically dominant, COL is positive (negative), except the solar cycle 23. The fact that this kind of ‘odd’ thing does not happen for 11 solar cycles may give a clue that these two phenomena are consistently regulated by a mechanism.(3) The periodicities of ~5.5 and ~11 years are found in each hemisphere. The periodicity of ~49 years are found in the power spectrum of the averaged COL. A possible periodicity of ~167 years is also noticed.
Acknowledgements
HYC is grateful to Sasha Kosovichev and Philip Scherrer for constructive discussions and hospitality while visiting Hansen Experimental Physics Laboratory, Stanford University where most of work has been done. This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2010-013-C00017).
Antalova A
,
Gnevyshev MN
1983
Latitudinal distribution of sunspot areas during the period 1874-1976
CoSka
11
63 -
93
Antonucci E
,
Hoeksema JT
,
Scherrer PH
1990
Rotation of the photospheric magnetic fields: a North-South asymmetry
ApJ
360
296 -
304
DOI : 10.1086/169120
Babcock HW
1961
The topology of the Sun’s magnetic field and the 22-year cycle
ApJ
133
572 -
DOI : 10.1086/147060
Ballester JL
,
Oliver R
,
Carbonell M
2005
The periodic behaviour of the North-South asymmetry of sunspot areas revisited
A&A
431
L5 -
L8
DOI : 10.1051/0004-6361:200400135
Bell Bell
1960
On the structure of the Sunspot zone
SCoA
5
17 -
28
Carbonell M
,
Oliver R
,
Ballester JL
1993
On the asymmetry of solar activity
A&A
274
497 -
Choudhuri AR
,
Schussler M
,
Dikpati M
1995
The solar dynamo with meridional circulation
A&A
303
L29 -
Donner R
,
Thiel M
2007
Scale-resolved phase coherence analysis of hemispheric sunspot activity: a new look at the north-south asymmetry
A&A
475
L33 -
L36
DOI : 10.1051/0004-6361:20078672
Gigolashvili MSh
,
Japaridze DR
,
Kukhianidze VJ
2005a
Variations of the solar differential rotation associated with polarity reversal
SoPh
231
23 -
28
DOI : 10.1007/s11207-005-1532-5
Gigolashvili MSh
,
Japaridze DR
,
Mdzinarishvili TG
,
Chargeishvili BB
2005b
N-S asymmetry in the solar differential rotation during 1957-1993
SoPh
227
27 -
38
DOI : 10.1007/11207-005-1214-3
Goel A
,
Choudhuri AR
2009
The hemispheric asymmetry of solar activity during the last century and the solar dynamo RAA
9
115 -
126
DOI : 10.1088/1674-4527/9/1/010
Ichimoto K
,
Kubota J
,
Suzuki M
,
Tohmura I
,
Kurokawa H
1985
Periodic behaviour of solar flare activity
Nature
316
422 -
424
DOI : 10.1038/316422a0
Javaraiah J
,
Gokhale MH
1997
Periodicities in the North-South asymmetry of the solar differential rotation and surface magnetic field
SoPh
170
389 -
410
Javaraiah J
,
Ulrich RK
2006
Solar-cycle-related variations in the solar differential rotation and meridional flow: a comparison
SoPh
237
245 -
265
DOI : 10.1007/s11207-006-0130-5
Knaack R
,
Stenflo JO
,
Berdyugina SV
2004
Periodic oscillations in the North-South asymmetry of the solar magnetic field
A&A
418
L17 -
L20
DOI : 10.1051/0004-6361:20040107
Knaack R
,
Stenflo JO
,
Berdyugina SV
2005
Evolution and rotation of large-scale photospheric magnetic fields of the Sun during cycles 21-23. Periodicities north-south asymmetries and r-mode signatures
A&A
438
1067 -
1082
DOI : 10.1051/0004-6361:20042091
Krivova NA
,
Solanki SK
2002
The 1.3-year and 156-day periodicities in sunspot data: wavelet analysis suggests a common origin
A&A
394
701 -
706
DOI : 10.1051/0004-6361:20021063
Li K-J
,
Gao PX
,
Zhan LS
2009a
Synchronization of hemispheric sunspot activity revisited: wavelet transform analyses
ApJ
691
537 -
546
DOI : 10.1088/0004-637X/691/1/537
Li K-J
,
Schmieder B
,
Li Q-Sh
1998
Statistical analysis of the X-ray flares (M >= 1) during the maximum period of solar cycle 22
A&AS
131
99 -
104
DOI : 10.1051/aas:1998254
Li K-J
,
et al.
,
Wang JX
,
et al.
,
Xiong SY
,
et al.
,
Liang HF
,
et al.
,
Yun HS
,
et al.
2002
Regularityof the North-South asymmetry of solar activity
A&A
et al.
383
648 -
652
DOI : 10.1051/0004-6361:20011799
Maunder EW
1904
Note on the distribution of sun-spots in heliographiclatitude 1874-1902
MNRAS
64
747 -
761
Mouradian Z
,
Soru-Escaut I
1991
On the dynamics of the large-scale magnetic fields of the sun and the sunspot cycle
A&A
251
649 -
654
Nandy D
,
Choudhuri AR
2001
Toward a mean field formulation of the babcock-leighton type solar dynamo. i. α-coefficient versus Durney’s double-ring approach
ApJ
551
576 -
585
DOI : 10.1086/320057
Oliver R
,
Ballester JL
1994
The North-South asymmetry of sunspot areas during solar cycle 22
SoPh
152
481 -
485
DOI : 10.1007/BF00680451
Özgüç A
,
Ücer C
1987
North-South asymmetries in the green corona brightness between 1947 and 1976
SoPh
114
141 -
146
Press WH
,
Rybicki GB
1989
Fast algorithm for spectral analysis of unevenly sampled data
ApJ
338
277 -
280
DOI : 10.1086/167197
Roy JR
1977
The North-South distribution of major solar flare events sunspot magnetic classes and sunspot areas 1955-1974
SoPh
52
53 -
61
DOI : 10.1007/BF00935789
Schlamminger L
1991
Hemispherical asymmetries in sunspot areas and auroral frequencies
SoPh
135
407 -
413
DOI : 10.1007/BF00147510
Solanki SK
,
Wenzler T
,
Schmitt D
2008
Moments of the latitudinal dependence of the sunspot cycle: a new diagnostic of dynamo models
A&A
483
623 -
632
DOI : 10.1051/0004-6361:20054282
Swinson DB
,
Koyama H
,
Saito T
1986
Long-term variations in North-South asymmetry of solar activity
SoPh
106
35 -
42
DOI : 10.1007/BF00161351
Temmer M
,
Veronig A
,
Hanslmeier A
2002
Hemispheric sunspot numbers Rn and Rs: catalogue and N-S asymmetry analysis
A&A
390
707 -
715
DOI : 10.1051/0004-6361:20020758
Ternullo M
2010
The butterfly diagram internal structure
MSAIS
14
202 -
Tritakis VP
,
Petropoulos B
,
Mavromichalaki H
1988
Asymmetric variations of the coronal green line intensity
SoPh
115
367 -
384
DOI : 10.1007/BF00148734
Verma VK
1987
On the increase of solar activity in the Southern hemisphere during solar cycle 21
SoPh
114
185 -
188
Verma VK
1993
On the North-South asymmetry of solar activity cycles
ApJ
403
797 -
800
DOI : 10.1086/172250
Vernova ES
,
Mursula K
,
Tyasto MI
,
Baranov DG
2002
A new pattern for the North-South asymmetry of sunspots
SoPh
205
371 -
382
DOI : 10.1023/A:1014264428300
Vizoso G
,
Ballester JL
1989
Periodicities in the North-South asymmetry of solar activity
SoPh
119
411 -
414
DOI : 10.1007/BF00146187
Vizoso G
,
Ballester JL
1990
The North-South asymmetry of sunspots
A&A
229
540 -
546
White OR
,
Trotter DE
1977
Note on the distribution of sunspots between the North and South solar hemispheres and its variation with the solar cycle
ApJS
33
391 -
DOI : 10.1086/190432
Yi W
1992
The North-South asymmetry of sunspot distribution
JRASC
86
89 -
98
Zaatri A
,
Komm R
,
Gonzá lez-Herná ndez I
,
Howe R
,
Corbard T
2006
North South asymmetry of zonal and meridional flows determined from ring diagram analysis of gong ++ data
SoPh
236
227 -
244
DOI : 10.1007/s11207-006-0106-5