A Model of the Double Magnetic Cycle of the Sun

It has been argued that the solar magnetic cycle consists of two main periodic components: a low-frequency component (Hale's 22-year cycle) and a high-frequency component (quasi-biennial cycle). The existence of the double magnetic cycle on the Sun is confirmed using Stanford, Mount Wilson and Kitt Peak magnetograph data from 1976 to 1996 (solar cycles 21 and 22). In the frame of the Parker's dynamo theory a model of the double magnetic cycle is presented. This model is based on the idea of two dynamo sources separated in space. The first source of the dynamo action is located near the bottom of the convection zone, and the second operates near the top. The model is formulated in terms of two coupled systems of non-linear differential equations. It is demonstrated that in the case of weak interaction between the two dynamo sources the basic features of the double magnetic cycle such as existence of two component and observed temporal variations of high-frequency component can be reproduced.Comment: 6 pages, 2 figure

The G-O Rule and Waldmeier Effect in the Variations of the Numbers of Large and Small Sunspot Groups

We have analysed the combined Greenwich and Solar Optical Observing Network (SOON) sunspot group data during the period of 1874-2011 and determined variations in the annual numbers (counts) of the small, large and big sunspot groups (these classifications are made on the basis of the maximum areas of the sunspot groups). We found that the amplitude of an even-numbered cycle of the number of large groups is smaller than that of its immediately following odd-numbered cycle. This is consistent with the well known Gnevyshev and Ohl rule or G-O rule of solar cycles, generally described by using the Zurich sunspot number (Rz). During cycles 12-21 the G-O rule holds good for the variation in the number of small groups also, but it is violated by cycle pair (22, 23) as in the case of Rz. This behaviour of the variations in the small groups is largely responsible for the anomalous behaviour of Rz in cycle pair (22, 23). It is also found that the amplitude of an odd-numbered cycle of the number of small groups is larger than that of its immediately following even-numbered cycle. This can be called as `reverse G-O rule'. In the case of the number of the big groups, both cycle pairs (12, 13) and (22, 23) violated the G-O rule. In many cycles the positions of the peaks of the small, large, and big groups are different and considerably differ with respect to the corresponding positions of the Rz peaks. In the case of cycle 23, the corresponding cycles of the small and large groups are largely symmetric/less asymmetric (Waldmeier effect is weak/absent) with their maxima taking place two years later than that of Rz. The corresponding cycle of the big groups is more asymmetric (strong Waldmeier effect) with its maximum epoch taking place at the same time as that of Rz.Comment: 13 pages, 5 figures, 1 table, accepted by Solar Physic

A solar cycle lost in 1793--1800: Early sunspot observations resolve the old mystery

Because of the lack of reliable sunspot observation, the quality of sunspot number series is poor in the late 18th century, leading to the abnormally long solar cycle (1784--1799) before the Dalton minimum. Using the newly recovered solar drawings by the 18--19th century observers Staudacher and Hamilton, we construct the solar butterfly diagram, i.e. the latitudinal distribution of sunspots in the 1790's. The sudden, systematic occurrence of sunspots at high solar latitudes in 1793--1796 unambiguously shows that a new cycle started in 1793, which was lost in traditional Wolf's sunspot series. This finally confirms the existence of the lost cycle that has been proposed earlier, thus resolving an old mystery. This letter brings the attention of the scientific community to the need of revising the sunspot series in the 18th century. The presence of a new short, asymmetric cycle implies changes and constraints to sunspot cycle statistics, solar activity predictions, solar dynamo theories as well as for solar-terrestrial relations.Comment: Published by Astrophys. J. Let

Solar-Cycle Characteristics Examined in Separate Hemispheres: Phase, Gnevyshev Gap, and Length of Minimum

Research results from solar-dynamo models show the northern and southern hemispheres may evolve separately throughout the solar cycle. The observed phase lag between the hemispheres provides information regarding the strength of hemispheric coupling. Using hemispheric sunspot-area and sunspot-number data from Cycles 12 - 23, we determine how out of phase the separate hemispheres are during the rising, maximum, and declining period of each solar cycle. Hemispheric phase differences range from 0 - 11, 0 - 14, and 2 - 19 months for the rising, maximum, and declining periods, respectively. The phases appear randomly distributed between zero months (in phase) and half of the rise (or decline) time of the solar cycle. An analysis of the Gnevyshev gap is conducted to determine if the double-peak is caused by the averaging of two hemispheres that are out of phase. We confirm previous findings that the Gnevyshev gap is a phenomenon that occurs in the separate hemispheres and is not due to a superposition of sunspot indices from hemispheres slightly out of phase. Cross hemispheric coupling could be strongest at solar minimum, when there are large quantities of magnetic flux at the Equator. We search for a correlation between the hemispheric phase difference near the end of the solar cycle and the length of solar-cycle minimum, but found none. Because magnetic flux diffusion across the Equator is a mechanism by which the hemispheres couple, we measured the magnetic flux crossing the Equator by examining magnetograms for Solar Cycles 21 - 23. We find, on average, a surplus of northern hemisphere magnetic flux crossing during the mid-declining phase of each solar cycle. However, we find no correlation between magnitude of magnetic flux crossing the Equator, length of solar minima, and phase lag between the hemispheres.Comment: 15 pages, 7 figure

North-South Distribution of Solar Flares during Cycle 23

In this paper, we investigate the spatial distribution of solar flares in the northern and southern hemisphere of the Sun that occurred during the period 1996 to 2003. This period of investigation includes the ascending phase, the maximum and part of descending phase of solar cycle 23. It is revealed that the flare activity during this cycle is low compared to previous solar cycle, indicating the violation of Gnevyshev-Ohl rule. The distribution of flares with respect to heliographic latitudes shows a significant asymmetry between northern and southern hemisphere which is maximum during the minimum phase of the solar cycle. The present study indicates that the activity dominates the northern hemisphere in general during the rising phase of the cycle (1997-2000). The dominance of northern hemisphere is shifted towards the southern hemisphere after the solar maximum in 2000 and remained there in the successive years. Although the annual variations in the asymmetry time series during cycle 23 are quite different from cycle 22, they are comparable to cycle 21.Comment: 6 pages, 2 figures, 1 table; Accepted for the publication in the proceedings of international solar workshop held at ARIES, Nainital, India on "Transient Phenomena on the Sun and Interplanetary Medium" in a special issue of "Journal of Astrophysics and Astronomy (JAA)

Hemispheric Sunspot Numbers R_n and R_s: Catalogue and N-S asymmetry analysis

Sunspot drawings are provided on a regular basis at the Kanzelhoehe Solar Observatory, Austria, and the derived relative sunspot numbers are reported to the Sunspot Index Data Center in Brussels. From the daily sunspot drawings, we derived the northern, R_n, and southern, R_s, relative sunspot numbers for the time span 1975-2000. In order to accord with the International Sunspot Numbers R_i, the R_n and R_s have been normalized to the R_i, which ensures that the relation R_n + R_s = R_i is fulfilled. For validation, the derived R_n and R_s are compared to the international northern and southern relative sunspot numbers, which are available from 1992. The regression analysis performed for the period 1992-2000 reveals good agreement with the International hemispheric Sunspot Numbers. The monthly mean and the smoothed monthly mean hemispheric Sunspot Numbers are compiled into a catalogue. Based on the derived hemispheric Sunspot Numbers, we study the significance of N-S asymmetries and the rotational behavior separately for both hemispheres. We obtain that about 60% of the monthly N-S asymmetries are significant at a 95% level, whereas the relative contributions of the northern and southern hemisphere are different for different cycles. From the analysis of power spectra and autocorrelation functions, we derive a rigid rotation with about 27 days for the northern hemisphere, which can be followed for up to 15 periods. Contrary to that, the southern hemisphere reveals a dominant period of about 28 days, whereas the autocorrelation is strongly attenuated after 3 periods. These findings suggest that the activity of the northern hemisphere is dominated by an active zone, whereas the southern activity is mainly dominated by individual long-lived sunspot groups.Comment: 9 pages, 8 figures, data catalogue online available at http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/390/70

Sun's retrograde motion and violation of even-odd cycle rule in sunspot activity

The sum of sunspots number over an odd numbered 11 yr sunspot cycle exceeds that of its preceding even numbered cycle, and it is well known as Gnevyshev and Ohl rule (or G--O rule) after the names of the authors who discovered it in 1948. The G--O rule can be used to predict the sum of sunspot numbers of a forthcoming odd cycle from that of its preceding even cycle. But this is not always possible because occasionally the G--O rule is violated. So far no plausible reason is known either for the G--O rule or the violation of this rule. Here we showed the epochs of the violation of the G--O rule are close to the epochs of the Sun's retrograde orbital motion about the centre of mass of the solar system (i.e., the epochs at which the orbital angular momentum of the Sun is weakly negative). Using this result easy to predict the epochs of violation of the G--O rule well in advance. We also showed that the solar equatorial rotation rate determined from sunspot group data during the period 1879--2004 is correlated/anti-correlated to the Sun's orbital torque during before/after 1945. We have found the existence of a statistically significant $\sim$ 17 yr periodicity in the solar equatorial rotation rate. The implications of these findings for understanding the mechanism behind the solar cycle and the solar-terrestrial relationship are discussed.Comment: 13 pages, 4 figures, accepted by MNRA

Predicting the Amplitude of a Solar Cycle Using the North-South Asymmetry in the Previous Cycle: II. An Improved Prediction for Solar Cycle~24

Recently, using Greenwich and Solar Optical Observing Network sunspot group data during the period 1874-2006, (Javaraiah, MNRAS, 377, L34, 2007: Paper I), has found that: (1) the sum of the areas of the sunspot groups in 0-10 deg latitude interval of the Sun's northern hemisphere and in the time-interval of -1.35 year to +2.15 year from the time of the preceding minimum of a solar cycle n correlates well (corr. coeff. r=0.947) with the amplitude (maximum of the smoothed monthly sunspot number) of the next cycle n+1. (2) The sum of the areas of the spot groups in 0-10 deg latitude interval of the southern hemisphere and in the time-interval of 1.0 year to 1.75 year just after the time of the maximum of the cycle n correlates very well (r=0.966) with the amplitude of cycle n+1. Using these relations, (1) and (2), the values 112 + or - 13 and 74 + or -10, respectively, were predicted in Paper I for the amplitude of the upcoming cycle 24. Here we found that in case of (1), the north-south asymmetry in the area sum of a cycle n also has a relationship, say (3), with the amplitude of cycle n+1, which is similar to (1) but more statistically significant (r=0.968) like (2). By using (3) it is possible to predict the amplitude of a cycle with a better accuracy by about 13 years in advance, and we get 103 + or -10 for the amplitude of the upcoming cycle 24. However, we found a similar but a more statistically significant (r=0.983) relationship, say (4), by using the sum of the area sum used in (2) and the north-south difference used in (3). By using (4) it is possible to predict the amplitude of a cycle by about 9 years in advance with a high accuracy and we get 87 + or - 7 for the amplitude of cycle 24.Comment: 21 pages, 7 figures, Published in Solar Physics 252, 419-439 (2008

Photospheric Magnetic Field: Relationship Between North-South Asymmetry and Flux Imbalance

Photospheric magnetic fields were studied using the Kitt Peak synoptic maps for 1976-2003. Only strong magnetic fields (B>100 G) of the equatorial region were taken into account. The north-south asymmetry of the magnetic fluxes was considered as well as the imbalance between positive and negative fluxes. The north-south asymmetry displays a regular alternation of the dominant hemisphere during the solar cycle: the northern hemisphere dominated in the ascending phase, the southern one in the descending phase during Solar Cycles 21-23. The sign of the imbalance did not change during the 11 years from one polar-field reversal to the next and always coincided with the sign of the Sun's polar magnetic field in the northern hemisphere. The dominant sign of leading sunspots in one of the hemispheres determines the sign of the magnetic-flux imbalance. The sign of the north-south asymmetry of the magnetic fluxes and the sign of the imbalance of the positive and the negative fluxes are related to the quarter of the 22-year magnetic cycle where the magnetic configuration of the Sun remains constant (from the minimum where the sunspot sign changes according to Hale's law to the magnetic-field reversal and from the reversal to the minimum). The sign of the north-south asymmetry for the time interval considered was determined by the phase of the 11-year cycle (before or after the reversal); the sign of the imbalance of the positive and the negative fluxes depends on both the phase of the 11-year cycle and on the parity of the solar cycle. The results obtained demonstrate the connection of the magnetic fields in active regions with the Sun's polar magnetic field in the northern hemisphere.Comment: 24 pages, 12 figures, 2 table