Solar activity parameters and their interrelationship: Continuous decrease in flare activity from solar cycles 20 to 23

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 112,, doi: /2006ja012076, 2007 Solar activity parameters and their interrelationship: Continuous decrease in flare activity from solar cycles 20 to 23 Meera Gupta, 1 V. K. Mishra, 1 and A. P. Mishra 1 Received 14 September 2006; revised 23 November 2006; accepted 11 January 2007; published 18 May [1] The paper gives an insight regarding the interrelationship among a variety of solar activity (SA) parameters. A detailed correlative study has been performed using the monthly data of various solar activity parameters, for example, sunspot numbers (SSN), solar flux (SF, 10.7 cm), grouped solar flares (GSF), solar flare index (SFI), coronal index (CI), and tilt angle (TA) for the solar cycles 19 to 23, the present cycle. Though in general SSN shows a high degree of correlation with other SA parameters, the relationship between SSN and flare indices (GSF and SFI) is not straightforward. The slope of the regression lines between SSN and GSF (for cycles 20 to 23) and those between SSN and SFI (for cycles 21 to 23) is found to decrease continuously with the progression of cycles, without any associated unidirectional change in the correlation coefficient between these indices. In conformity, the similar feature is also observed from the peak values of SSN and flare indices. It is not seen, however, in the case of other SA parameters. The different trend of regression lines between SSN-GSF and SSN-SFI has been explained on the basis of the duration of the major solar flares. The present analysis also includes the statistical/numerical investigations of the occurrence of flares (imp 1B) over the span of solar cycles 20 to 23. These findings shed new light on the underlying physical processes responsible for solar activity and their generic relationship. Citation: Gupta, M., V. K. Mishra, and A. P. Mishra (2007), Solar activity parameters and their interrelationship: Continuous decrease in flare activity from solar cycles 20 to 23, J. Geophys. Res., 112,, doi: /2006ja Introduction [2] In order to study the characteristic features of solar activity (SA), one needs suitable parameters that can be used to depict the various forms of solar output and its variation. The various features of solar activity considering different indices have been studied, without any essential distinction between them [Kuklin, 1976]. The frequency time aspect of solar activity involves the consideration of a set of time variation in different solar activity indices and determination of the power spectrum of the cyclic variation. The spatial aspect implies the study of spatial distribution of solar activity phenomena and degree of homogeneity or inhomogeneity in the characteristic features of solar activity indices according to their heliographical position. Finally, the individual events, which directly depend on the importance and time span of particular phenomena, have also been studied [Heras et al., 1990; Mordvinov, 1995; Vernova et al., 2005]. [3] The various solar activity phenomena and related indices have been divided into two large classes. One of them belongs to indices, which reflect, how frequently new active center formations appear on the Sun. The main variation is characterized as the 11-year solar cycle and the time variation in the spatial distribution pattern, 1 Department of Physics, A.P.S. University, India. Copyright 2007 by the American Geophysical Union /07/2006JA which are influenced by the differential rotation of the Sun. The indices belonging to second category contain information on the importance of particular phenomena or event. Their spatial distribution corresponds to substantial inhomogeneity in longitude and concentration in the low latitude region below 20. Time variation of these indices is represented by a secular (80 90 years) cycle. The presence of two classes of indices requires a different approach to classify them, according to frequency and importance of the phenomena. [4] The variety of solar activity phenomena represented by various indices is coded in a compact numerical form. These indices are classified in different ways and can be subdivided into basic physical indices and derived indices. Basic indices represent numerical characteristics of solar activity, which are observed and measured directly, for example, sunspot numbers, sunspot area, flare brightness, and so on. All other indices are derived from the processing of basic indices or their combination, for example, Wolf number, flare indices, fluctuation indices, etc. Obviously, the indices for which determination and computation of active region area, lifetime, and intensities that are considered, will predominantly reflect the behavior of importance indices. Frequency indices represent the similar number of observed active region formations during specified period [Bhatnagar et al., 1999]. [5] Finally, indices used for various investigations can be divided into standard and nonstandard classes. Standard indices are widely used indices determined according to 1of10

2 standard programs and published in various catalogues, bulletin, etc. Usually, they provide the database for the different kind of studies to be performed. Nonstandard indices are those which are particularly used by different researchers as per their required criteria. [6] Although the number of SA indices such as faculae, flares, coronal holes, and electromagnetic radiation in various bands (10.7 cm radio flux, green corona, etc.), and sunspot numbers on the solar disk, showing the level of sunspot activity, are widely used index of SA; however, the sunspot number (SSN) series is the most analyzed time series in the solar physics. The most pronounced feature of SA is the 11-year cycle (also called the Schwabe cycle), which shows the long-term variation of solar activity which is far from a simple sinusoidal wave. Earlier, the majority of investigators have generally used SSN as a representative solar index for various studies associated with solar-terrestrial relationship (STR) or Sun-Earth connection [Dorman and Dorman, 1967; Pomerantz and Duggal, 1971; Rao, 1972; Webber and Lockwood, 1988]. Later, with the availability of variety of solar indices, various authors have used arbitrarily one index or a combination of some solar indices for their investigation [Dodson et al., 1974; Mavromichalaki et al., 1988, 1990; Ahluwalia, 1998, 2003; Van Allen, 2000; Usoskin et al., 2001, 2003; Hathway et al., 2002; Chattopadhyay et al., 2003; Kane, 2005; Gupta et al., 2006a, 2006b]. The most commonly used indices are sunspot numbers (SSN), 10.7-cm solar flux (SF, 2800 MHz radio emission), grouped solar flares (GSF), solar flare index (SFI), coronal index (CI), and tilt angle (TA). [7] Earlier, Badruddin et al. [1983] have reported a different trend of regression lines, dealing with the solar cycle relationship between SSN and the frequency of major flare occurrence by considering flares of higher importance only on a yearly basis. Recently, the long-term variation of several solar, interplanetary, and geomagnetic parameters during the last many solar cycles has been reported and it is found that SSN and SF show similar 11-year fluctuation of varying amplitude. However, CI has a monotonically increasing amplitude by almost a factor of two [Kane, 2006]. [8] In the present paper, we have made an attempt to study the relative merits of various solar indices (SF, GSF, SFI, CI, and TA) in relation to SSN and their interrelationship. The observed peculiarities/abnormalities, particularly in the relationship between SSN and flare indices have also been discussed. It is quite new approach to analyze and correlate the characteristic features of different solar activity parameters in relation to sunspot numbers. Now there is a need to develop a suitable model to explain the various features of long-term solar activity. 2. Data and Method of Analysis [9] Most of the solar indices data (SSN, 10.7-cm SF, GSF, SFI, and CI) have been taken from the Web site of NOAA (fttp://fttp.ngdc.noaa.gov/stp/solar_data/...html) available in public domain, which have been available for a long period of time through the Solar Geophysical Data, the monthly publication of NOAA, Boulder Colarado, USA. The tilt-angle data have been obtained from the Wilcox solar observatory. The brief introduction about the different solar activity parameters, used in the present investigation, is as follows Solar Flux [10] In the light of large database and correlation studies, it has been recognized that SSN and SF (10.7 cm) are highly correlated even on a monthly average basis [Hathway et al., 2002]. Nevertheless, many investigators still prefer to use both of these solar indices (monthly or yearly averages) for their correlative studies of the solar-terrestrial phenomena [Hathway et al., 2002; Chattopadhyay et al., 2003] Grouped Solar Flares [11] Solar flares are the result of complex magnetic phenomena, seen as a sudden and intense increase in brightness on the solar disk. They occur when magnetic field loops undergo reorganization, releasing energy into the solar corona through chromospheric plasma. It is widely accepted that solar flares are the result of the rapid conversion of a large amount of magnetic energy, stored for a while in the solar corona, and dissipated through magnetic reconnections. The release of energy takes place in a matter of minutes to hours and can amount to values up to J (10 33 erg). The term grouped means all observations made in different locations to the same flare event were lumped together and counted as one. The flare parameters (such as its heliographic coordinates, the start, maximum and end time of the flare, duration, apparent and corrected areas, optical importance) are deduced using the data of all observations. This procedure is used for any importance flares including subflares. [12] Solar flare index. The solar flare index Q, was defined by Kleczek [1952] for describing the Ha flare over a 24-hour period as: Q ¼ i t; where i represents the intensity scale of importance of a flare in Ha and t the duration of the flare in minutes. It is assumed that this relationship evaluates roughly the total energy emitted by flares in the Ha line. Recently, the SFI has been reported as one of the best solar parameters for explaining the heliospheric physical changes with respect to time [Ozguc and Atac, 2003; Mishra and Tiwari, 2003; Mishra et al., 2006] Coronal Index [13] The CI represents an average daily power (irradiance) emitted through the green corona from the entire solar corona, as observed from the Earth into one sterradian toward Earth [Rybansky et al., 2001]. The intensity of the green coronal line (Fe XIV, 5303A ) is routinely measured at several stations across the world. The measurements of these data are used to calculate the CI of solar activity. The CI of SA reflects both the daily changes as well as the presence of long-lived (3 to 6 months) coronal structures. CI, which represents the full-disk solar index, can be very easily compared to solar indices that arise under different physical conditions. Recently, the values of CI provided by Rybansky et al. [2001] has been reported to have data errors and hence their long-term trend is incorrect. Rybansky et al. 2of10

3 Figure 1. The 30-month smoothed series of SSN, GSF, and SFI from 1950 to The differences in the peak values of SSN and GSF/SFI are clearly apparent from the figure. [2005] have explained this error and published the revised values. This revised data set of CI has been considered for the present investigation Tilt Angle [14] Recently, features of the interplanetary medium have been explained on the basis of the heliospheric neutral current sheet, which separates the whole heliosphere into two regions of opposite polarity of the magnetic field. In each hemisphere, the field is well approximated by a Parker Archimedian spiral with the sense of the field being outward in one hemisphere and inward in the other. The field direction in each hemisphere alters in each 11-year sunspot cycle. At the solar minimum, the current sheet is nearly equatorial with the Northern Hemisphere s magnetic field being in one direction and the southern magnetic field s having the opposite sign. The solar magnetic field structure near the sunspot maxima is complex: it corresponds roughly to the increase in the inclination of the current sheet. The inclinations of the heliosphere neutral current sheet along the equatorial plane of heliosphere are often named as tilt angle [Cliver et al., 1996; Cliver and Ling, 2001; Gupta et al., 2006a, 2006b]. [15] In the present paper a running cross-correlation method has been used to study the momentary relationship between SSN and flare activity parameters GSF and SFI [Usoskin et al., 2001; Mishra and Tiwari, 2003]. In this method, we have used a time window of width T centered at time t: [t T / 2, t + T / 2]. The cross-correlation coefficient r(t) is calculated for the data within this window. Then the window is shifted in time by a small time step Dt < T, and the new value of the cross correlation coefficient is calculated. Here the time shifting of 1 month has been taken into account to calculate the correlation coefficient for each month between SSN and flare activity parameters (GSF and SFI), for the entire period of investigation. The time window covers 50-month period. This value was chosen to match two contradictory requirements: (1) the uncertainty of the calculated r(t) are smaller for large T and (2) T should be small in order to reveal the fine temporal structure of the cross correlation function. The selection of period for the time window in the present analysis has been made after testing the several time periods (for example, 40, 50, 60, and 70 months) and it is found that 50-month period for the time-window is appropriate, as it satisfies both contradictory requirements mentioned above. 3. Results and Discussion [16] For most of the studies in the field of STR, SSN were basically used as a prime solar activity parameter, as they were available for a long period of time. Later on, 10.7-cm flux was also been used for STR studies, particularly for ionospheric studies. In the last 50 years, many other solar indices have also been routinely published in Solar Geophysical Data, and hence other indices have also been used for various investigations of STR. With the availability of solar data through the various web sites, it is pertinent to investigate the relationships among these solar indices and to evaluate the best-suited solar parameter for different studies in STR. For this purpose, we have used the monthly average values of the solar indices mentioned in the earlier section SSN and SF Relationship [17] The solar activity parameters SSN and SF show a high degree of correlation, which has been found to be 0.96 for the solar cycles 19 to 23. Therefore it is obvious that for STR studies, either SSN or SF can be used as an 3of10

4 Figure 2. Crossplot between SSN and GSF for the solar cycles 20 to 23. The different trend of regression lines (continuously tending toward x axis) is clearly seen. equally good parameter and will yield the similar result. While deriving the correlation coefficient for the solar cycles 19 to 23, we have plotted the regression lines for all the solar cycles, and find that the regression lines between SSN and SF generally overlap for all the solar cycles, except for 23 (a lower activity cycle than the other solar cycles). Thus to investigate the relationship with other solar indices, only SSN have been considered as a basic parameter Sunspot and Solar Flare Indices [18] In the present analysis, we have studied the longterm relationship among various solar activity parameters. Therefore to compare the qualitative behavior of various solar indices, the 30-month moving average has been calculated to filter out the short-term fluctuations of the data series. The monthly data of GSF and SFI are available from 1966 onward. The 30-month moving average of SSN, GSF, and SFI is depicted in the Figure 1. The differences in the peak values of SSN and GSF are clearly seen to continuously decrease from solar cycles 20 to 23, and the situation reverses in cycle 23 (the peak of GSF is upward in cycles 20 to 22 while the peak of SSN dominates in solar cycle 23). In general, the GSF series follows the SSN series except during the maxima, where the occurrence of solar flares depends on the local sunspot-region activity rather than the general level of solar activity. The occurrence of solar flares needs to meet certain required conditions in various active regions in addition to a general level of activity, which has been further verified in the crossplot between SSN and GSF. The differences between the peak values of SSN and SFI are also found to continuously decrease for solar cycles 21 to 23, while the difference is large and opposite (the peak of SSN is upward) for the solar cycle 20. The large differences between the peaks of GSF and SFI during the solar cycles 20, in comparison to other cycles could be due to two reasons: either the lack of flare occurrences of higher importance, or the large duration of flares during the said cycle showing abnormal relationship between SSN and SFI. [19] The crossplot between SSN and GSF for the solar cycles 20 to 23 is shown in Figure 2. Here the correlation coefficient is not as high as found in the case of SSN and SF. Nevertheless, here again the correlation coefficients are 0.84 or more, with the highest value being 0.96 for solar cycle 21. Moreover, it is observed that the regression lines are significantly different from each other and tend to the x axis as the slope of the lines (the value of m in the straightline equation, y = mx + c) decreases continuously. The regression line for cycle 20 signifies that for SSN (=100), GSF is high (=551), whereas for cycle 23 at the same SSN, GSF is significantly low (=208), also evident from the Table 1. Total/Average Value of GSF for Solar Cycles 20 to 23 Solar Cycles Total/Average Value of GSF Total/Average Value of SFI Total/Average Value of the Solar Flares With the Importance 1b, SC / / /31.62 SC / / /37.37 SC / / /24.28 SC / / /4.34 4of10

5 Figure 3. The occurrence of GSF in relation to SSN (GSF/SSN) from 1965 to Decreasing trend of GSF/SSN ratio with respect to time is observed throughout the investigation period. Figure 2. Furthermore, we have calculated the total/average value of GSF for solar cycles 20 to 23, which is also showing continuously decreasing trend, and hence verifies the above results (Table 1). Moreover, as is apparent from the slope of the trend line in Figure 3, the value of GSF in relation to SSN (the ratio of GSF and SSN) continuously decreases for solar cycles 20 to 23. During the year 1986 (the minima of cycle 22) the value of GSF was exceptionally high (=51) in comparison to SSN (=2.5). This has not been observed in the minima of other solar cycles and needs further investigation on a short-term basis as to why, during the minimum activity period, such a high value of GSF is obtained. [20] Occurrences of energetic flares are better defined through SFI than GSF, as they give an idea of the amount of energy released. We have plotted the scattered graph between SSN and SFI for solar cycles 20 to 23. The correlation between SSN and SFI is 0.66 (lowest) for solar Figure 4. The crossplot between SSN and SFI for the solar cycles 20 to 23. The different trend of regression lines (continuously tending toward x axis from cycle 21 to 23) is clearly seen. 5of10

6 Figure 5. The 50-month running cross-correlation function between SSN and GSF as well as between SSN and SFI for the period cycle 20 and (maximum) for solar cycle 21. The regression lines continuously tend toward the x axis from solar cycles 21 to 23, except for solar cycle 20 (Figure 4). The total/average value of SFI continuously decrease from solar cycles 21 to 23 except for solar cycle 20; this observation again supports the idea that the flare activity decreases continuously in relation to SSN (Table 1). The regression line for solar cycle 20 cuts across all the regression lines (for cycles 21, 22, and 23) and continuous closer to the x axis as seen in Figure 4; the value of c of the regression line for cycle 20 is higher than others. Solar cycle 20 has been reported to be very peculiar with regard Figure 6. The 30-month smoothed series of SSN and CI from 1950 to The close correspondence between SSN and CI is clearly apparent from the figure. 6of10

7 Figure 7. The crossplot between SSN and CI for the solar cycles 19 to 23. Almost similar trend of regression lines for odd and even cycles is clearly seen. to various activities on the Sun. Moreover, we have sorted out solar flares of importance 1B (higher importance) for solar cycles 20 to 23, finding that the occurrence of solar flares of higher importance during solar cycle 20 are as expected in comparison to GSF. This finding indicates that the flares were of short duration, which result to a low value of SFI. [21] Moreover, we have calculated the 50-month running cross-correlation between SSN and GSF as well as between SSN and SFI for the investigation period (Figure 5). We find that the correlation between SSN and GSF is better during the ascending and descending phases. Moreover, the lowest value of cross-correlation coefficient has been obtained during the maximum of solar cycle or just after it (i.e., during , 1980, , and 2000). This result is in conformity with the various findings regarding local solar disturbances during the maximum activity period. During the maxima, peak differences continuously decrease (Figure 1), and the correlation between SSN and flare activity parameters (GSF and SFI) becomes Figure 8. A 30-month smoothed series of SSN and TA from 1976 to of10

8 Figure 9. The crossplot between SSN and TA for the solar cycles 21 to 23. better, which further verifies the above results. An almost similar behavior has been observed with respect to the correlation between SSN and SFI for solar cycles 21 to 23, except for solar cycle 20, where the regression line shows a different behavior (Figure 4) SSN and CI Relationship [22] Furthermore, we have used another solar activity parameter known as CI. CI represents the total irradiance from the Sun through the nm coronal emission line as observed by means of the ground-based coronagraph around the world. Long-term variations have been found in the values of CI. The graph has been plotted between the monthly mean values of SSN and CI, considering a 30- month moving average of both the series. The 30-month moving average of data series has been considered, as it is close to the first zero of the autocorrelation function and roughly one-fourth of the main period (11 years). We find that there is a close correspondence in the long-term variation of SSN and CI, where CI closely tracks the SSN all the time. However, the differences in the peak values of SSN and CI are larger for even cycles in comparison to odd cycles, which further confirms the characteristic differences between even and odd cycles. The significant differences in the amplitude and behavior of odd and even CI cycles are observed in accordance with the SSN cycles (Figure 6). The correlation between SSN and CI are maximum 0.96 for the solar cycles 19 and 22. Almost similar trend of regression lines for odd solar cycles (19 and 21) and for even solar cycles (20 and 22) is obvious in Figure 7. The regression line for solar cycle 23 is quite different, crosses the regression lines of solar cycles 19, 20, and 21 and attains the lowest position in the graph SSN and TA Relationship [23] Furthermore, we have chosen another solar activity parameter, the waviness of a heliospheric neutral current sheet or tilt angle. The 30-month smoothed variation of TA in comparison with the SSN from 1976 to 2005 (cycles 21 to 23) is depicted in Figure 8. The differences between the peak values of SSN and TA are similar for solar cycles 21 and 22, whereas it is relatively small for solar cycle 23. A time lag in the peak values of SSN and TA is also observed. Solar cycle 23 is observed as low activity solar cycle with some peculiarities. The crossplot between both the series has also been performed and found that the regression lines are parallel to each other for solar cycles 21 and 22 with slight difference during solar cycle 23 (Figure 9). The correlation coefficient is better for solar cycle , as shown in Table 2. [24] Observational results presented in this paper show a decreasing flare activity in relation to the level of sunspot activity, which has been observed in terms of the total numbers of flares (GSF) from respective cycles 20 to 23 and SFI, which is the measure of total energy (roughly) emitted by the solar flares (from cycles 21 to 23). In fact, the magnetic field of sunspot groups is mainly responsible for the occurrence of solar flares. When the magnetic field of sunspots in the active region becomes twisted and sheared, the magnetic field lines may cross and reconnect with a huge amount of explosive energy, which extends up to several thousand of miles from the surface of the sun. Table 2. Correlation Coefficient for Solar Cycles 19 to 23 Correlation Coefficient (r) Solar Cycles SSN-SF SSN-GSF SSN-SFI SSN-CI SSN-TA SC NA a NA NA SC NA SC SC SC a NA, data not available. 8of10

9 The solar output and its variability depend on the general level of solar activity; however, the flare occurrence is specifically related to the local sunspot active region, where the magnetic field lines are very complex and twisted. Thus the results obtained in the case of SSN- GSF/SFI relationship are peculiar as they depict the dominance of local sunspot disturbances rather than following the general level of sunspot activity. These results may provide a clue for understanding the local solar disturbances in relation to the general level of activity. Various researchers have tried to search for an index that provides straightforwardly all the information about the flare phenomena, especially to evaluate the energy output during the flare. The assessment of the flare energy through an index, as accurately as possible, is useful for understanding the dynamical processes of the different phases of the solar activity cycle [Maris and Popescu, 2004, and references therein]. 4. Conclusions [25] The significant differences in the amplitude and behavior of odd and even solar cycles have been reported time to time [Wilson, 1988; Mursula et al., 2001]. The observed differences between odd and even cycles are the outcome of the nonlinear interaction that provide the stabilizing mechanism for the cycle s amplitude [Durney, 2000]. If the magnetic field is larger than the average value for a cycle (say odd), the nonlinear feed back mechanism may cause a magnetic field that is smaller than the average for the next cycle (even). Consequently, the odd cycles generally have larger amplitude than the even cycles. In fact, the solar toroidal field is generated at the base of solar convection zone (SCZ). Eruptions of toroidal flux tubes generate a poloidal magnetic field at the surface that is transported to the lower SCZ by meridional motions. [26] The existence of the 22-year solar magnetic cycle is presently best identified by alternating magnetic field polarities of the bipolar sunspot groups in the neighboring 11-year cycles and by the solar corona magnetic field topology as well, when extrapolated from the direct field measurement at the level of the solar photosphere. The 22-year solar magnetic cycle is also observed in the longterm variation of the SSN and the solar corona brightness [Sykora and Storini, 1997] basically due to solar midlatitude active region zones. [27] Observational results presented in this paper clearly indicate the different behavior of even and odd solar cycles in the case of SSN-CI relationship, which is in good agreement with earlier reported results. The shape of cycles and the trend of regression lines for odd and even cycles can be defined as a comprehensible consequence of the 22-year magnetic solar cycle. Here mostly statistical results have been presented regarding the relationship of widely used solar activity parameters; however, the attention of theoreticians are required to explore the physical mechanism of the relationships among various solar activity parameters in the different phases of the solar cycles. On the basis of the statistical results and discussion presented above, the following conclusions can be drawn. [28] 1. It is found that the correlation coefficient between SSN and SF is as high as for solar cycle 19 and is always 0.96 for all other solar cycles (cycles 20 to 23). Naturally, the effects of SSN or SF on terrestrial/interplanetary phenomena are expected to show similar results. In fact, when the correlation coefficient between SSN and SF is 0.95, one can use either of the two solar indices. [29] 2. It is noticed that the correlation coefficient between SSN and GSF is not as high as that found between SSN and SF. Nevertheless, here again, the correlation coefficients are 0.87 or more, with the highest value being 0.96 for solar cycle 21. The regression lines are significantly different from each other and tend to the lower side (the slope of the lines continuously decreasing). The total/ average values of GSF are continuously decreasing for solar cycles 20 to 23. The continuous decrease in the occurrence of GSF in relation to SSN (GSF/SSN) from solar cycles 20 to 23 further verifies the results derived as above. [30] 3. The correlation between SSN and SFI is better for solar cycle 22, which is The regression lines are continuously tending to the down side except for solar cycle 20. A continuous decrease in the energy emitted by Ha flares is observed (registered in optical Ha lines), for solar cycles 21 to 23, as seen through the total/average value of SFI, except for solar cycle 20. During solar cycle 20, there are more flares of higher importance (flares of importance 1B), but due to short duration, their resulting effect has become less. [31] 4. The correlation between SSN and CI is better for solar cycles 19 and 22, which is 0.95, and it is observed that the trend of regression lines for odd (19 and 21) and even (20 and 22) solar cycles are almost similar but the differences in the peak values of SSN and CI are larger for even cycles in comparison to odd solar cycles. [32] 5. In the case of SSN and TA, the correlation is better for solar cycle 22, which has been found to be 0.902, and it is observed that the regression lines are parallel to each other for solar cycles 21 and 22. There is a slight difference for solar cycle 23, which shows similar variational pattern of SSN-TA relationship for solar cycles 21 to 23 (a change in the value of tilt angle is proportional to the change in the value of SSN). [33] Acknowledgments. 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