1.
Introduction
It is well-known that solar activity affects the Earth, but only within the past two centuries did people realize that geomagnetic storms, presenting themselves through magnificent auroras, are caused by eruptions on the Sun. However, the relationship between solar activity and geomagnetic storms is not straightforward; as Table 1 reveals, some solar activity generates powerful solar flares that do not translate into powerful geomagnetic storms, while some geomagnetic storms follow rather puny solar flares. Nor is there a simple correspondence between coronal mass ejections and geomagnetic storms. Some authors, e.g. [1,2], and references therein, suggested that the Earth's magnetic field is affected by the tidal forces created by the Moon and Sun; their view was echoed by several websites, e.g. [3,4]. There have been attempts to predict upcoming maxima of geomagnetic indices based on the previous maxima and sunspot numbers, e.g. [5,6]. Most, if not all, authors considering the relationship between the tidal forces and geomagnetic activity discuss the proximity of geomagnetic events to different phases of the Moon. In this article we consider the annual aa index, defined at [7], as a proxy for the background geomagnetic field with short-term geomagnetic variations smoothed out. We will show that the maxima of the annual aa index occur at the time when New/Full Moon is augmented by a close perigee, a close lunar node, or a close perihelion; it is the confluence of two or more of these factors that seems to determine the maxima of the annual aa index.
2.
Discussion
Let us first start with a few definitions. New/Full Moon recurs on average every 29.530588 days, while the perigees recur on average every 27.55455 days; and, since 29.530588×14≈413.428,27.55455×15≈413.318, the 413-day time interval is considered as the average common period of New/Full Moon and perigee. As [10] reveals, on average every 413 days New/Full Moon comes within 11 hours of a perigee. As usually, we will use syzygy to denote either New or Full Moon, and syzygy-perigee to denote a pair of a syzygy and a perigee separated by ⩽11 hours. Although the average time between two adjacent New Moon-perigees or two adjacent Full Moon-perigees is close to 413 days, the exact number of days varies. We further define the spread of a syzygy-perigee to be the time between the syzygy and perigee in the syzygy-perigee. A syzygy-perigee is said to be synchronized within 140 minutes, or for the purpose of this article simply synchronized, if its spread is ⩽140 minutes. A series of several consecutive synchronized syzygy-perigees will be referred to as a 140-minute synchronization period, or for the purpose of this article simply synchronization period, due to the synchronized appearance of perigees and syzygies. The core syzygy-perigee, or simply the core, of a synchronization period is the syzygy-perigee with the smallest spread. All other things being equal, the tidal force should increase during synchronization periods, reaching its maxima near the core. However, "other things" are never equal. One of the most obvious things affecting the tidal force other than syzygies and perigees, is the Earth-Moon-Sun alignment; the closer to a straight line is the alignment, the stronger is the tidal force. Thus a non-core syzygy-perigee close to an eclipse, or even a lunar node, may exert a stronger tidal force than a core syzygy-perigee removed from lunar nodes.
Figure 1 compares the annual aa index, as a measure of the Earth's magnetic field, to sunspot numbers (SSN), as a measure of solar activity. Although the aa index overall follows the solar activity, the aa maxima seem to appear rather randomly relative to the SSN maxima. However, that is not the case. The 1870–2007 portion of Table 2 reveals that all aa maxima in 1870–2007 occurred within a year of a synchronization period. We may test the hypothesis on the 2007–2020 period, following the period of Figure 1. Indeed, the graph of the aa index in 2007–2020 available in [6,12] shows that the maximum of the annual aa index is attained in 2015 which, as Table 2 shows, was inside the 2011/3/19–2016/11/14 synchronization period. Twelve calendar years of the 14 annual aa maxima in Table 2 contained a synchronized syzygy-perigee, while two calendar years of annual aa maxima (1991, 1960) were ⩽20 days away from a synchronized syzygy-perigee. What are the chances of that? Of the 152 years 281 days ≈152.8 calendar years in 1869/2/26–2021/12/4, approximately 83.8 years, or ≈55%, fall within a year of a synchronization period and ≈69 years, or ≈45%, are more than a year away from a synchronization period; one would expect at least some of the annual aa maxima to occur more than a year away from the synchronization periods but none did.
Table 2 reveals that not only all 14 aa maxima occurred within a year of a synchronization period, but also 10 of them (2003, 1943, 1892; 1991, 1982, 1974, 1960, 1930, 1910, 1882), or ≈71%, occurred either in the year of a core syzygy-perigee, or the year before, or they year after; such years make up ≈3×152020−1868≈30% of all years. The 1951 and 1872 aa maxima were ≈2 years from the, correspondingly, 1952/8/5 and 1870/4/15 core syzygy-perigees; yet the secondary aa maxima of 1952 and 1870 were of almost the same value as the 1951 and 1872 aa maxima and within a year of the 1952/8/5 and 1870/4/15 core syzygy-perigees. Only the 2015 and 1919 aa maxima were removed from corresponding core syzygy-perigees by ⩾2 years; again the secondary aa maxima of 2012 and 1922 were within a year of the, correspondingly, 2012/5/6 and 1923/11/8 core syzygy-perigees.
We conclude that the aa maximum during a solar cycle is determined not just by SSN but also by the tidal force during the solar cycle, and the tidal force appears to be more important in creating the annual aa maximum of a given solar cycle than SSN.
The maxima of the smoothed monthly mean given in Figure 1 of [6] also fall within a year of the corresponding synchronization periods from 1868 onwards.
Other than primary aa maxima, Figure 1 also shows secondary maxima marked by pink lines. Table 3 shows that all but three of the secondary maxima coincided with the years containing simultaneous syzygy, perigee, and eclipse; the three exceptions coincided with solar maxima. Notice that the 1894 secondary maximum was merely 8 days away from the 1893/12/23 synchronized Full Moon-perigee. The 1919 aa maximum is the aa maximum farthest removed from the core syzygy-perigee of the corresponding synchronization period; castling it with the 1922 secondary maximum would have eliminated this somewhat exceptional case.
Synchronization periods recur almost periodically, the average time between the cores of synchronization periods is ≈3,706 days or ≈10.15 years, obtained by dividing 51, 886 days between 1870/4/15 and 2012/5/6 by 14. The number is very close to the average time of 3, 944 days, or ≈10.8 years, between solar maxima in Figure 1 obtained by dividing 47, 329 days between 1870/8/15 and 2000/3/15 by 12. Although synchronization periods and solar cycles appear usually in tandem, occasionally there pops up an orphaned synchronization period unattached to a solar cycle, i. e. the 1900/3/1–1904/9/9 synchronization period which appeared between two solar cycles and did not produce an aa maximum. Yet, the 1900/3/1–1904/9/9 synchronization period produced a secondary aa maximum in 1905 and the 1903/10/31 powerful geomagnetic storm. All but one aa maxima in Figure 1 are well-defined, the only exception is the 1910 maximum, it is almost indistinguishable from the aa index in 1908–1909; it is as if the 1910/11/17–1913/2/21 synchronization period lost some might to its 1900/3/1–1904/9/9 predecessor.
3.
Conclusions
Table 2 and Figure 1 show that all aa maxima occurred within a year of a synchronization period, and 12 out of 14 aa maxima occurred within 2 years of a core syzygy-perigee; it is hard to attribute this to a mere coincidence. Table 3 shows that all but three secondary aa maxima occurred in years when the tidal force was amplified by New/Full Moon, perigee, and eclipse coming together. We may infer that within a solar cycle the tidal force plays a significant role in the formation of primary and secondary aa maxima. We may speculate that first, the solar activity fills up the Van Allen Belts with energetic particles; and then, the tidal force generated by the Moon and Sun "shakes" the Van Allen Belts somewhat similarly to how one shakes a dried up Christmas tree. Just like the Christmas tree drops its needles when shaken, the Van Allen Belts disperse energetic particles. Of course, the tidal force is only one of several components determining the aa maxima, but it is certainly an important one.
The 2021/12/4–2024/3/10 synchronization period is upcoming; it is in the first half of solar cycle 25 that started in 2019. The aa annual maximum during solar cycle 25 is expected to occur either in 2021–2024 or, if solar cycle 25 is sufficiently long, or in 2029–2031; the most likely years of the annual aa maximum are 2022–2023. This is somewhat better than April 2025±32 months predicted in [6].
Conflict of interest
The author declares no conflict of interest.
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