Comparison of geomagnetic indices during even and odd solar cycles SC17-SC24: Signatures of Gnevyshev gap in geomagnetic activity

We show that the time series of sunspot group areas has a gap, so-called Gnevyshev gap (GG), between ascending and descending phases of the cycle and especially so for the even cycles. For the odd cycles this gap in less obvious, and is only a small decline after the maximum of the cycle. We resample the cycles to have same length of 3945 days (about 10.8 years), and show that the decline is between 1445-1567 days after the start of the cycle for the even cycles, and extending sometimes until 1725 days from the start of the cycle. For the odd cycles the gap is a little earlier 1332-1445 days after the start of the cycles with no extension. We analyze geomagnetic disturbances for solar cycles 17-24 using Dst-index, related Dxt- and Dcx-indices and Ap-index. In all of these time series there is a decline at the time or somewhat after the GG in the solar indices, and as deepest between 1567-1725. The declines are significant at 99 % level for both even and odd cycles of the Dst-index and for Dxt-, Dcx- and Ap-indices for even cycles. For odd cycles of Dxt-index the significance is 95 %, but insignificant for odd cycles of Dcx- and Ap indices. We, however, show that for the cycles 21 and 23, for which Dst exists, the GG is more intense than for the earlier odd cycles. The analyzes of OMNI2 data for 1964-2020 (SC20-SC24) show that these gaps during the maxima of the solar cycles can be seen also in the near-Earth solar wind velocity and IMF magnetic field intensity, and the energy function BV^2.


Introduction
The solar cycle has basically three phases, an ascending phase, a descending phase and between them a so-called Gnevyshev gap (GG) (Antalova and Gnevyshev, 1965;Gnevyshev, 1967Gnevyshev, , 1977Feminella and Storini, 1997;Storini et al., 2003;Ahluwalia and Kamide, 2004;Kane, 2005;Bazilevskaya, Makhmutov, and Sladkova, 2006;Kane, 2008;Norton and Gallagher, 2010;Du, 2015;Takalo and Mursula, 2018), which is kind of a separatrix between the first two (main) phases. The time of the the Gnevyshev gap is 45-55 months after the start of the nominal cycle length, that is, approximately 33-42% into the cycle after its start (Takalo and Mursula, 2018). Storini et al. (2003) gave a review of the effects of GG in different space weather parameters. There are many studies about the overall correlation of the solar and interplanetary activity measure with different aspects of geomagnetic activity. Some of the recent analyzes are mentioned in the next discussion. Feminella and Storini (1997) examined long-term behavior of several solar activity parameters (spots, flares, radio, and X-ray fluxes), confirmed the double peaks and found that the peaks are more distinct with a clear gap in between, when intense and/or long-lasting events are considered. On the other hand, lowenergy and short-duration events tend to follow a single-peaked 11-year cycle. The double peaks are reported to be detected in all the solar atmospheric layers (photosphere, chromosphere, and corona) up to interplanetary space and are linked with the heliomagnetic cycle. Double peaks have been also been detected in geomagnetic activity (Gonzalez, Gonzalez, and Tsurutani, 1990;Kane, 1997;Echer et al., 2004). Interestingly (according to our study) Ahluwalia (2000) found, while studying the connection between IMF parameters, that solar polar field reversals may be responsible for the existence of the Gnevyshev gap in Ap data. An energy function proportional to BV 2 describes the time variations of Ap quite well. Kane (2002), showed that the evolution of various solar indices around sunspot maximum occur almost simultaneously (within a month or two) and the gap between the two peaks is shown to be sharper for more energetic events. Takalo and Mursula (2020) and Takalo (2020) have also shown that the larger the sunspot groups the more clearly their overall distribution during the solar cycle is double-peaked. Verbanac et al. (2011) analyzed the correlation (during 1960-2001) of several solar activity indices: sunspot number, group sunspot number, cumulative sunspot area, solar radio flux F10.7, and interplanetary magnetic field strength (IMF) with geomagnetic activity indices: Ap, Dst and Dcx, and the regional geomagnetic index RES, specifically estimated for the European region. The geomagnetic indices Ap, Dcx, Dst, and RES are all well correlated with the considered solar indices. Interestingly, RES showed the most prominent correlation with solar indices. All geomagnetic indices were found to have the best correlation with the IMF. The highest correlation was found for RES vs. IMF (R = 0.77) for one-year time lag. Ap is also delayed for one year after IMF, while Dcx and Dst are synchronized with IMF. A two-year lag is found between all solar indices (except IMF) and Ap. Kilcik et al. (2017) studied different data sets from January 1996 to March 2014 and found that the best correlation between the sunspot counts and the Ap index is obtained for the large group time series, but they noted that for the highest correlation Ap index delays 13 months compared to all kind of sunspot count series and International sunspot number (ISN) data. They also found that the best correlation between the sunspot counts and the Dst index is obtained for the large sunspot group time series. The Dst index delays with respect to the large group by about 2 months. Furthermore, the correlation coefficients between the geomagnetic indices (Ap, Dst) and X-Ray solar flare index are a little higher than the correlation coefficients between these geomagnetic indices and ISN. Le et al. (2013) examined occurrence of intense storms at the level of 200 nT < Dst ≤ 100 nT, great storms at 300 nT < Dst ≤ 200 nT, and super storms at Dst ≤ 300 nT during the period of 1957 -2006, based on Dst indices and smoothed monthly sunspot numbers. Their statistics showed that 76.9 % of the intense storms, 79.6 % of the great storms and 90.9 % of the super storms occurred during the two years before a solar cycle reached its peak, or in the three years after it. The histograms of yearly number of intense geomagnetic storms have a dual-peak distribution in solar cycles 2122, and three peaks in cycles 20 and 23. The first peak in yearly number of intense geomagnetic storms occurred one year before the solar cycle maximum in solar cycles 20, 21 and 23, but only in solar cycle 22 did the first peak occur at the solar maximum. The second peak for solar cycles 20 to 23 all occurred two years after the solar maximum. The gap between the the first and second peaks for intense geomagnetic storms is 13 years. Note, however, that their histograms are very scarce, and the width of each bin is one year.
Less attention have been paid to the effects of GG on the geomagnetic activity at the Earth. Richardson (2013) and Richardson and Cane (2012a) have, however, performed several studies about the drop of geomagnetic disturbance during the maximum of the solar cycle. They found, especially, a tendency for the Kp-index storm rate to fall during 4th year of the cycle. They also associated several occasions of decline in geomagnetic activity aa-index around solar maximum to the Gnevyshev gap during solar cycles 20 -24 (Richardson and Cane, 2012b) In this study we analyze the strength of geomagnetic activity using daily time series of Dst for years 1957-2009, extended Dst, Dxt, for 1933-2009, corrected and extended Dst, Dcx, for 1933-2009 and Ap-index for years 1933-2020. We first find the interval of the Gnevyshev gap in sunspot number and sunspot area data, and then analyze the statistical significance for the decline during or after the same interval in geomagnetic indices. (Note especially that we do not study cross-correlation of the solar and geomagnetic indices themselves.) This article is organized as follows. Section 2 presents the data and methods used. In Section 3 we study sunspot number and sunspot area data for cycles SC17 -SC23, and also for longer period SC12 -SC23 to get better statistics. In Section 4 we analyze the Dcx, Dxt and Dst during cycles SC17 -SC23, and in Section 5 the Ap-index during cycles SC17 -SC24. In Section 6 we discuss the signatures of GG in the near-Earth interplanetary magnetic field and solar wind velocity using OMNI2 daily data. In Section 7 we consider the sequence of group areas, IMF B and Ap-index for the cycles SC20 -SC24 and give our conclusions in Section 8.

Solar group area and OMNI2 data
In the analysis of sunspot groups for the cycles 12 -24 we use recently published catalogue of sunspot groups by Mandal et al. (2020). The main data for this data set are the Royal Greenwich observatory (RGO) measurements between 1874-1976. The years after 1976 until October 2019 were constructed from the data sets from Kislovodsk, Pulkovo and Debrecen observatories. This data set contains daily appearance of the sunspot groups. Thus the lifetime of each group also affects to the number of the groups. The minima and length of the sunspot cycles used in this study for solar and also geomagnetic indices are listed in Table  1. (We are aware that geomagnetic indices lag somewhat the solar indices, but for this study using the same cycles is appropriate.) OMNI2 data set contains the hourly mean values of the interplanetary magnetic field (IMF) and solar wind plasma parameters measured by various spacecraft near the Earth's orbit, as well as geomagnetic and solar activity indices, and energetic proton fluxes. In our analysis we use daily averages of absolute value of the magnetic field intensity B and solar wind bulk velocity for the years 1964-2020 (SC20 -SC24).

Geomagnetic indices
The Dst (storm-time disturbance) index has been calculated at the World Data Center C2 at Kyoto, Japan, since the International Geophysical Year 1957, using data from four observatories at low latitudes (Hermanus, Honolulu, Kakioka and San Juan). Table 1. Sunspot cycle lengths (in years) and dates (fractional years, and year and month) of (starting) sunspot minima for cycles 12-23 (except the end of data for cycle 24). (NGDC, 2013 The Dxt-index is an extension of Dst using data from the original set of four low-latitude stations for 1941-1956, and using the nearby Cape Down station as a predecessor of the Hermanus station for 1932-1940  . Despite some open questions related to the composition of the original Dst index, the reconstructed index is quite similar to the original one during the overlapping time interval . However, the reconstructed Dxt index corrects for some known errors in the original Dst index, such as the erroneously large daily UT variation in 1971 Karinen et al., 2002).
Dcx index is an extended and corrected version of the Dst index such that it also corrects the Dst (and Dxt) index for the excessive, seasonal varying quiettime level, the so-called "non-storm component" which is unrelated to magnetic storms. Thus the Dcx index has smaller seasonal variation than the other indices Karinen and Mursula, 2006).
Planetary geomagnetic activity index, Ap, is derived from a range of geomagnetic field variations over period of 3 h from measurements provided by 13 geomagnetic observatories between -44 o and 60 o southern and northern geomagnetic latitude. We use here daily averages of the Ap-index, which is a measure of the daily level of the mid-latitude magnetic activity. The Ap-index exists for solar cycles 17 -23, and nowadays also, at least, as a preliminary values for cycle 24.

Two-Sample T-Test
The two-sample T-test for equal mean values is defined as follows. The null hypothesis assumes that the means of the samples are equal, i.e. µ 1 = µ 2 . Alternative hypothesis is that µ 1 = µ 2 . The test statistic is calculated as where N 1 and N 2 are the sample sizes, µ 1 and µ 1 are the sample means, and s 2 1 and s 2 2 are the sample variances. If the sample variances are assumed equal, the formula reduces to where The rejection limit for two-sided T-test is |T | > t 1−α/2,ν , where α denotes significance level and ν degrees of freedom. The values of t 1−α/2,ν are published in T-distribution tables (Snedecor and Cochran, 1989;Krishnamoorthy, 2006;Derrick, Deirdre, and White, 2016). Now, if the value of p< α = 0.05, the significance is at least 95%, and if p< α = 0.01, the significance is at least 99%.

Sunspot area data for cycles SC12-SC23
Figures 1a and b show the total sunspot areas during of SC12 -SC23 for the even and odd cycles, respectively. The area data are smoothed using trapezoidal smoothing over 61 points (rectangular moving average smoothing with window end points having only half of the weight of the inner points). Also all other data are smoothed similarly if not otherwise mentioned. It is evident that the average even cycle is double-peaked such that there is a clear decline between the peaks at about 1445-1567 (marked with blue dashed lines) and fainter decline for the prolonged interval 1567-1725 (end point with fainter black dashed line). This is especially true for the longer period of cycles SC12 -SC22. We believe that the gap is related to the Gnevyshev gap (GG). On the contrary, the average odd cycle has only one maximum (peak), after which (at about 1322) the sunspot index gradually decreases, having a sudden short gap between 1322-1445 (the red dashed lines). The prolonged interval marked for odd cycles is 1445-1567. We could, however, say that the GG is only the start of the descending phase for the odd cycles. One reason, why the GG is more intense in the even cycles is that the even cycles maximize on the average at different time in the southern and northern solar hemispheres, and although GG exists in both hemispheres, there is a longer and deeper GG for the even cycles (Takalo and Mursula, 2020;Takalo, 2020). Note also a (quasi)periodic structure in the average daily area time series. The mean period of this fluctuation is about 150 days, which has  been found to be the period of various activities of the sun (Rieger et al., 1984;Lou, 2000;Richardson and Cane, 2005). The decline near the cycle maximum is usually due to larger groups, which have this double-peak pattern during the solar cycle. Figure 2a and b shows the number of smaller groups (area<500 µHem, millionths of hemisphere) for the even and odd cycle of SC17-SC24 as a function of normalized time (all cycles are normalized such that T norm = (T i − T min ) /L , where T i is the original time of each group, T min is the time for the leading minimum of the cycle, and L is the length of the cycle). The data are calculated from monthly averages and smoothed using 13 month trapezoidal method. It is seen that all odd cycles have only one clear maximum, and only cycle 20 from the even cycles has distinct two-peak structure. This results is in line with the earlier studies mentioned in the Introduction.

Dst, Dxt and Dcx during cycles SC17-SC23
Positive values of the Dst are mainly due the compression of the dayside magnetosphere in the initial phase of storm, while negative values are due to magnetic reconnection and the formation of the storm-related currents, in particular the ring current. Therefore positive and negative values of the Dst index arise from different physical processes. That is why, we use in the next analysis only negative values of the Dst and related indices (the positive values are dealt as zero. We verified that this does not affect the results in this study. If the original time series is used, it is separately mentioned.) We then resampled Dcx − , Dxt − and Dst − indices for each solar cycle 17 -23 (Dst only for cycles 20 -23) such that they all had same length 3945 time steps (days). This is about 10.8 years, which is the average of cycles since the beginning of the 20th century. Figures 3a and  3b show the averages of the absolute values of the Dcx, Dxt and Dst for even and odd cycles, respectively. Here the indices are smoothed using trapezoidal smoothing over 61 points. Note that Dst index exists only since 1957, and that is why we can show only total cycles 20-23 for Dst. The vertical dotted lines are at 1445, 1567 and 1725 days, and at 1322, 1445 and 1567 for the average even and odd cycle, respectively. It is evident that for the even cycles the indices have a decline in the whole interval 1445-1725 days, but as deepest at the end of the nine month period. This interval starts about 37 % after the start of the average cycle. It is evident that the deepest decline lags some months the Gnenyshev gap (GG) in the sunspots, which is located between the lines 1445 and 1567 (see Fig.  1). For odd cycles there is a decline but somewhat earlier, i.e., between 1322-1567, and slightly deeper in the latter half (1445-1567) of the marked interval. However, the decline is not so clear for the odd cycles than for the even cycles. We calculated, using two sided T-test, that the significance of the decline (average Dst is-12.7) for the raw (unsmoothed) Dst-index is 99% for even cycles (C20 and C22) with p < 10 −15 compared to nine months earlier (avg Dst -23.8) and nine months after the marked interval (avg Dst -23.6). For odd cycles (C21 and C23) the decline between 1322-1527 is -11.9 on the average with p=3 × 10 −5 compared to eight months earlier (avg Dst -17.3) and p=9 × 10 −9 compared to eight months after the marked interval (avg Dst is -19.5). For Dxt-index the similar 99% significance exists with p-value < 10 −18 for even cycles, C18, C20 and C22 between 1445-1725 (average Dxt is -11.2)compared to the interval before (avg Dxt -20.9) and after (avg Dxt -22.2). However, for odd cycles C17, C19, C21 and C23, the significance is only at 95% level with p-value 0.017 (the average Dxt values are -17.2, -15.1 and -17.4 for before, during and after the interval 1322-1567, respectively). This is probably because the odd cycles C21 and C23 have more clear double-peaks than the earlier odd cycles, and consequently the decline is pronounced during these cycles (note that Dst-index exists only during odd cycles 21 and 23). For the raw Dcx-index, the two sample T-test shows 99% significance with p< 10 −9 for the even cycles between 1445-1725. The values of average Dcx are -19.3, -11.9 and -18.4 before, during and after the interval, respectively. For the odd cycles the decline in the interval 1322-1567 is insignificant with the average values being -14.6, -14.8 and -16.8 for Dcx before, during and after the interval 1322-1567, respectively. It seems that the equinoctial correction changes the profile during this interval for the Dcx. However, for Dcx index< −50nT there is a significant decline compared to the interval after the marked period with p=0.0093. Figure 4a and b depict an example what the decline looks like in the original indices for cycle 22 and cycle 21, respectively. Here we use the original unsmoothed indices with positive values included. Note that the time axis is similar to Fig. 3, but only the interval 1165-2005 for even cycle and 1077-1812 for odd cycle are shown. Note that the vertical dashed lines show the same intervals as in the earlier figure for the sum of the cycles. It is evident that the indices have smaller values between the dashed lines and especially in the latter interval of those lines. For the odd cycle 21 there is a strong magnetic storm just around the line at 1438, which lasts totally about 20 days and is also seen in the Fig. 3b. This storm changes notably the behavior of the average curve at that site. Otherwise, the intervals between the dashed line are very quiet considering that it was time of the maximum of the solar cycle 21.
We have also divided the disturbed time indices to two categories: strong, index<-50 nT and medium, -50 nT<index≤-15 nT. (We define category strong as quite low level to get better statistics for our research. Note, however, that -50 nT is about mean plus twice the standard deviation for original indices and -15nT is near the mean for the original Dst). Figures 5a and b show the histograms of the two categories, index<-50 nT and -50 nT≤index<-15 nT for the even and odd cycles 20 -23, respectively (Note that one bin is about two months). The vertical dotted lines are at 1445 and 1725 (nine months) for even cycles and 1322 and 1567 (eight months) for odd cycles. In both the even and odd cycles there is a decline between these lines, but it is emphasized in the latter part of this interval, and as clearer for the even cycles than the odd cycles. Note that the minimum of the distribution lags about four months in the medium sized index category that of the GG decline in the sunspot indices. Figure 6a and b show the histograms of the same categories for Dxt index. (Note that here we have twice as many cycles and the histograms show the total number of counts in each category.) For the odd cycles there is no decline neither in index≤-50 nT nor -50 nT≤index<-15 nT category. This seems, however, be due to the cycles 17 and 19, which fill the gaps seen in odd Dst cycles (21 and 23). For even cycles the figures 5a and 6a do not differ very much from each other. Figures 7a and  b show the histograms of the same categories for Dcx index. The histograms in both categories of disturbances are very much similar to those for the Dxt-index.   Figure 8 shows the resampled (3945 days) averages of the smoothed Ap-index for the even and odd cycles for SC17 -SC24. (Vertical lines are again the same as in the earlier figures.) There is a decline in the even cycles, but mainly during the last interval between 1567-1725. While the decline in solar sunspot number and sunspot group area data is between 1445-1567, this means that the decline in Ap is on the average about four months later than in the sun. The two-sided T-test shows that the whole interval 1445-1725 (nine months) has lower mean value of Ap-index with p< 10 −10 compared to both the nine month before and nine months after the interval (as calculated from the raw unsmoothed data). The mean value of Ap for the interval 1445-1725 is 12.7, while for nine months earlier (later) Ap is 18.0 (18.4). In contrast to this, the difference in odd cycles between interval 1322-1567 and eight months earlier or after the interval is not statistically significant. The value of Ap for interval of odd cycles is 13.9, while for eight months earlier (later) it is 14.7 (14.5).

Ap index during cycles SC17-SC24
We have also divided the Ap index in two categories: strong, index>45 nT (mean plus twice standard deviation) and medium, 15 nT<index≤45 nT. Figures  9a and b show the histograms of the two categories for the even and odd cycles 17 -24, respectively. (Note that we have included cycle 24 to 9a). For the even cycles there seems to be a decline about four months after the GG interval in sunspots, but not significant decline for odd cycles. Note that the profile of Ap index greater than 15 nT reminds very much that of aa index (Cliver, Boriakoff, and Bounar, 1996), i.e., for the even cycles the distribution is highest in the declining phase of the sunspot cycle, which maximizes at about 40-50 months after the sunspot cycle maximum. For the odd cycles the maximum is earlier some 10-20 months after the sunspot cycle maximum. These maxima are related to high-speed streams and coronal mass ejections, respectively, during the declining phase of solar cycle (Gosling, Asbridge, and Bame, 1977;Legrand, 1986, 1989;Cliver, Boriakoff, and Bounar, 1996;Echer et al., 2004). Note also that the same phenomenon is seen also in the distributions of Dst, Dxt and Dcx indices (see Figs. 5, 6 and 7) but as a fainter feature. These phenomena affect the overall cross-correlation between the solar indices and geomagnetic disturbance indices such that the delay in the correlation is usually, at least 1-2 years.
6. IMF B and SW velocity during cycles SC20-SC24 Figure 10 shows the smoothed interplanetary magnetic field magnitude average |B|-component from the daily OMNI2 data for the even cycles SC20, SC22  and SC24, and for the odd cycles SC21 and SC23. The values were resampled similarly with the earlier solar and geomagnetic data. The vertical lines are also plotted similarly to earlier figures. There is a decline in IMF absolute value of magnetic field intensity B-component for even cycles, and as deepest between 1567-1725 days from the start of the resampled average cycle. This resembles a lot the decline in Dst-related indices in Fig. 3. For the even cycles the decline is between lines at 1322-1567, with a little spike after 1445. This behavior is also similar to the Dst, Dxt and Dcx curves for odd cycles in Fig. 3. The T-test shows that the gap in B for the even cycles between 1445-1725 has significantly different (smaller) mean value (6.42 nT) at least at level 99 % with p<10 − 6 than nine months earlier (7.15 nT) or later that interval (7.23 nT). These values are calculated from the daily raw data, not from smoothed data. For the odd cycles the significance of the mean B between 1322-1567 (6.79 nT) is at 99 % level with at least p=4.1 × 10 −4 compared to eight months before (7.41 nT) and after the period (7.43 nT). While the OMNI2-data has been measured near Earth in geocentric or L1 (Lagrange point) orbits, it is not surprising that the changes in solar activity and later in IMF soon appear as geomagnetic responses at the Earth. Figure 11 shows the solar wind average velocity during the even and odd solar cycles SC20 -SC 24. Surprisingly, there is now the decline for the odd cycles between the whole interval lines at 1322-1725 (404.3 km/s), but for even cycles as deepest at the end of the earlier used intervals, i.e., between 1567-1725 (403.6 km/s). Note also that solar wind velocity maximizes similarly to Ap-index in the descending phase of the cycles, and earlier for the odd cycles than for the even cycles. As mentioned earlier these maxima are related to coronal mass ejections, and high-speed streams in the solar wind. Significance for different mean of the even cycles in the interval 1567-1725 compared to five months before the interval (445.4 km/s) is clear with p< 10 −13 , and still significant at 99 % level with p=1.7 × 10 −5 to five months after the interval(430.0 km/s). For the odd cycles the significance nine months before (435.2 km/s) and nine months after (436.7 km/s) the interval 1322-1725 is very clear with p< 10 −11 for both periods. Note that the SW behaves differently than the magnetic field intensity such that the average level of the velocity is much higher with occasional high peaks during the descending phase of the cycle. 7. The GA, IMF BV 2 and Ap sequence for the cycles SC20-SC24 Before conclusion we draw-up together the whole sequence of the group areas, an energy function IMF BV 2 (Ahluwalia, 2000) and Ap-index during the intervals 1445-1725 and 1322-1567 for the even and odd cycles between SC20-SS 24, respectively. Figure 12 depicts the sequence of the GG phenomenon from the sun through IMF to the Earth for the even cycles. Here all the curves are calculated only for the even cycles 20, 22 and 24. Note that there are two drops in the GG interval for the groups areas: first between 1445-1567 and second between 1567-1725. The first drop has only a small response in BV 2 and Ap-index, but the second one has a strikingly similar decline in both BV 2 and geomagnetic activity. Both BV 2 and Ap-index reach the smallest values at the end of this interval (except of course at the beginning and end of the cycle). Note, however, that the Ap-minimum is sharper than IMF BV 2 minimum. Figure 13 depicts the sequence of the GG phenomenon for the odd cycles 21 and 23. For these two cycles the decline in areas between 1322-1445 is larger than for the average area for odd cycles between 13 -23 (see Fig. 1b). This is due to the fact, that the cycles 21 and 23 are more double-peaked than the earlier odd cycles. There are also a two-fold drop between 1322-1567 days after the cycle start for IMF BV 2 and Ap-index: first drop between 1322-1445 and second drop between 1445-1567. Here the first drop is larger than the second drop for both BV 2 and Ap-index. Note that the decline in the energy function BV 2 continues still after the line 1567 and this maybe leads to a third drop in the Ap-index.

Conclusions
We have shown that the time series of sunspot group areas has a gap, so-called Gnevyshev gap (GG), between ascending and descending phases of the cycle and especially so for the even cycles. For the odd cycles this cap in less obvious, and is only a short but sudden decline after the maximum of the cycle. We resampled the cycles to have same length of 3945 days (about 10.8 years), and showed that the decline is between 1445-1567 days after the start of the cycle for the even cycles, and extending sometimes until 1725 days from the start of the cycle. For the odd cycles the gap is a little earlier 1332-1445 days after the start of the cycles with no extension. We also find about 150 day periodicity from the time series of the sunspot area data. We believe that this is the same period, which have been reported in several articles, especially in solar flare events (Rieger et al., 1984;Lou, 2000;Richardson and Cane, 2005). Furthermore, we showed that the smaller sunspot groups do not contribute significantly to this double-peak pattern in the solar cycle.
We analyzed geomagnetic disturbances for solar cycles 17 -24 using Dst-index, related Dxt-and Dcx-indices and Ap-index. In all of these time series there is a decline at the time or somewhat after the GG in the solar indices. These declines are 46% smaller for Dst-and Dxt-indices during 1445-1725 than in the surrounding intervals for the even cycles, and are significant at 99 % level for both even and odd cycles of the Dst-index and for Dxt-, Dcx-and Ap-indices for even cycles. For odd cycles of Dxt-index the significance is 95 %, but insignificant for odd cycles of Dcx-and Ap indices. We have plotted histograms for the Dst-,Dxtand Dcx-indices in two categories: Index<-50 nT and -50 nT≤Index<-15 nT, and  for Ap index in categories: Ap>45 nT and 15 nT<Ap≤45 nT. The histograms show much less counts for the even cycles between 1445-1725 days (nine month interval) from the start of the average cycles for all index and in both categories. For odd cycles we discovered significantly less counts in both categories only for Dst-index, and slightly less counts in the "stronger" disturbance categories for other indices. Note that Dst-index exists only for two odd cycles SC21 and SC23, which partly affects this behavior.
The analyzes of OMNI2 data for 1964-2020 (SC20 -SC24) showed that these gaps during the maxima of the solar cycles also exist in the near-Earth solar wind velocity, IMF magnetic field intensity B and the combined energy function BV 2 . It is, however, not surprising that the GG phenomenon exists in the solar originated IMF and solar wind data. The significance of the decline during GG interval is high for both even cycles and odd cycles in |B| and in BV 2 .
Interestingly, the solar wind velocity behaves in a different way. There is a fall in the values simultaneously of the GG in the sun, but the depression lasts longer than in IMF B values and in geomagnetic indices for the odd cycles (between 1322-1725), and shorter for the even cycles (only between 1567-1725). If we divide the average cycle of SW in two halves, the first half has mean velocity 434.0 km/s and 419.7 km/s for even and odd cycles and second half 465.4 km/s and 467.5 km/s for even and odd cycles, respectively. Especially for odd cycles this difference is much larger than the GG related decline in the solar wind velocity. As we have discussed earlier the fast velocities during descending phase of the cycle are due to the coronal mass-ejections and high-speed streams in the solar wind.