**1. Introduction**

Solar activity is usually classified by the numbers of sunspots appearing on the solar surface as locations of magnetic loops generated by electro-magnetic solar dynamo in the solar interior [1] with the number of sunspots on the solar surface to change periodically over an eleven-year cycle [2, 3]. Babcock [4] found that a solar background magnetic field (SBMF) surrounding sunspots has the polarities opposite to the leading sunspot polarities, and these are changing also periodically every 11 years.

The magnetic polarities of SBMF and leading polarities of sunspots are shown to be in anti-phase, e.g. having opposite polarities, as found by comparing solar background and sunspot magnetic fields for cycle 21 [5], and 23 [6]. Furthermore, the SBMF was found to be the leading force defining timing and locations of sunspot

occurrences on the solar surface and migration to the equator accounting for north– south asymmetry of solar activity [6]. This investigation highlighted the important role of SBMF in generation of sunspots by dynamo actions and their appearance on the solar surface, thus, defining the solar activity. The link between SBMF (poloidal field) and sunspot (toroidal) magnetic field defines the action of the solar dynamo [1] and it would be beneficial to link a proxy of solar activity to the solar background magnetic field as it is systematically measured in the past 45 years.

(1645–1715) [16]. Such dramatic reductions in solar activity, which are longer than a single eleven-year sunspot cycle, are known as grand solar minima (GSMs). The timings of previous GSMs are found to closely fit the Maunder minimum (1645–1715) [16] and Wolf minimum (1280–1350), and to predict the two upcoming modern GSMs (2020–2053 and 2375–2415). Furthermore, by extrapolating the summary curve backwards to 1000 BC the further GSMs are fit by the curve: Oort's (1040–1080), Homeric (780–710 BC) and many others [17]. This restoration of summary curve [17] clearly gives a better accuracy of solar activity definition, in comparison with the prediction of sunspot activity restored from the past TSI

*Millennial Oscillations of Solar Irradiance and Magnetic Field in 600–2600*

Then, as the next step, Zharkova and co-authors [19] derived the magnitudes of a baseline (zero-line) magnetic field for each 22-year sets and discovered rather rigid periodic variations of this baseline magnetic field with a period of about 2000– 2100 years. This period resembles the period of 2200 years of Hallstatt's cycle reported from the restoration of solar irradiance in the Holocene [20–22]. It is rather difficult to find any mechanism in the solar interior that can account for much weaker and longer oscillations of the baseline of magnetic field. This led us to look for a some kind of periodic forcing linked to the orbital motion of the planets.

Jose [23] first suggested that solar activity on a longer timescale can be affected by the motion of large planets of the solar system. This suggestion was later developed by many researchers (see for example [24–27]) who found that the Sun, as a central star of the solar system, is a subject to the inertial motion around the centerof mass, or barycentre, of the solar system induced by the motions of the other planets (mostly large planets, e.g. Neptune, Jupiter, Saturn and Uranus).

Solar inertial motion (SIM) is the motion of the Sun around this barycenter of the solar system inside the circle with a diameter of about Δ ¼ 4*:*3*RSun*, or Δ = <sup>4</sup>*:*<sup>3</sup> � <sup>6</sup>*:*<sup>95</sup> � <sup>10</sup><sup>5</sup> =2*:*<sup>9885</sup> � <sup>10</sup><sup>6</sup> km, where *RSun* is a solar radius as shown in **Figures 4** and **5** in [19] reproduced from [27, 28]. This schematic drawing (see Fig. 4 in [19]) illustrates sudden shifts in the Sun from the location in the ellipse focus, where it is supposed to reside by Kepler's laws, because the Sun travels in an epitrochiodshaped orbits about the center-of mass (barycentre) of the solar system.

The SIM orbits are induced the tri-fall positions of large planets achieved for different planet configurations changing approximately within different periods of 370 or 2200–2400 years related to the planet positions and their rotation around the Sun [29, 30]. Hence, a joint effect of the orbital effects introduced by the combined motion of the Earth on the orbit and the Sun about the barycentre of the solar system can be the important factors in defining the observed long timescale variations of solar irradiance at the Earth and terrestrial temperature, which has not been explored

yet, despite the Sun is the main source of energy of all the planets (**Table 1**).

*The solar irradiance in W=m*<sup>2</sup> *restored and measured since Maunder minimum.*

**Table 1.**

**29**

Solar irradiance is accepted to be one of the important factors defining temperature variations on the Earth and other planets as it is the main source of the energy

**Authors Maunder minimum 2000–2012** Lean et al.1995 [31] 1363 1366 Steinhilber et al., 2012 [22] 1364 1366 Shirley et al., 1990 [26] — 1370 Wolff and Hickey, 1987 [32] — 1371 Lee et ak, 1985 [33] — 1372

derived with carbon-14 isotope dating [18].

*DOI: http://dx.doi.org/10.5772/intechopen.96450*

Zharkova et al. [7] explored the solar background magnetic field and found the eigen values of the own oscillations of the Sun, by applying Principal Component Analysis (PCA) to the low-resolution full disk magnetograms captured in cycles 21– 23 by the Wilcox Solar Observatory. This approach allowed authors to replace a complex magnetic field seen on the solar surface, the photosphere, with the separate wave components, eight plus eigen vectors, which appeared in pairs [8]. The pair of the two principal components (PCs) are the strongest waves of solar magnetic oscillations covering about 67% of the data by standard deviation, with the nearly-equal largest eigen-values, which oscillate with not equal periods of about 11 years [9, 10]. The PCs are shown to be two magnetic waves generated by the dipole magnetic sources produced by the double solar dynamo action [10, 11] in the inner and outer layers of the solar interior [12].

These waves start in the opposite hemispheres while travelling with an increasing phase shift to the Northern hemisphere (in odd cycles) and to the Southern hemisphere (in even cycles) [7, 10]. The summary curve of these two waves is found close to the averaged sunspot numbers, which define the current solar activity index [9, 10]. This summary curve of solar magnetic waves is proposed as a new proxy of solar activity, which allows us to predict solar activity on any timescale and also to add a magnetic polarity of the background field for a given cycle, known to be opposite to leading polarity of sunspots [6]. The maximum of solar activity for a given cycle (or double maximum for the double waves with a larger phase shift) occurs at the times when each of the waves approaches its maximum, so that at the equal amplitudes the two waves can have a resonant interaction, naturally accounting for often-reported North–South asymmetry of solar activity [6, 13–15].

In order to test further predictions of solar activity with the summary curve of two magnetic waves generated by double dynamo in the Sun in two layers, the summary curve was extended using the mathematical formula from the current time forwards to 3200 and backwards to 1200 [10] (see **Figure 1**). This led to a discovery of grand solar cycles (GSCs) of solar activity with a duration of 350– 400 years, evidently caused by the interference (beating effect) of the two magnetic waves with close but not equal frequencies [10]. There were far fewer sunspots seen during some periods, for example, during the Dalton minimum (1790– 1820), and practically none during the period known as the Maunder minimum

#### **Figure 1.**

*The summary curve (in arbitrary units) of solar activity calculated for 1200 to 3200 years from the 'historical' period (1976–2008, cycles 2123). Positive magnitudes of the summary curve represent northern magnetic polarity while the negative ones - southern magnetic polarity. Reproduced from the data of Zharkova et al. [10].*

### *Millennial Oscillations of Solar Irradiance and Magnetic Field in 600–2600 DOI: http://dx.doi.org/10.5772/intechopen.96450*

(1645–1715) [16]. Such dramatic reductions in solar activity, which are longer than a single eleven-year sunspot cycle, are known as grand solar minima (GSMs).

The timings of previous GSMs are found to closely fit the Maunder minimum (1645–1715) [16] and Wolf minimum (1280–1350), and to predict the two upcoming modern GSMs (2020–2053 and 2375–2415). Furthermore, by extrapolating the summary curve backwards to 1000 BC the further GSMs are fit by the curve: Oort's (1040–1080), Homeric (780–710 BC) and many others [17]. This restoration of summary curve [17] clearly gives a better accuracy of solar activity definition, in comparison with the prediction of sunspot activity restored from the past TSI derived with carbon-14 isotope dating [18].

Then, as the next step, Zharkova and co-authors [19] derived the magnitudes of a baseline (zero-line) magnetic field for each 22-year sets and discovered rather rigid periodic variations of this baseline magnetic field with a period of about 2000– 2100 years. This period resembles the period of 2200 years of Hallstatt's cycle reported from the restoration of solar irradiance in the Holocene [20–22]. It is rather difficult to find any mechanism in the solar interior that can account for much weaker and longer oscillations of the baseline of magnetic field. This led us to look for a some kind of periodic forcing linked to the orbital motion of the planets.

Jose [23] first suggested that solar activity on a longer timescale can be affected by the motion of large planets of the solar system. This suggestion was later developed by many researchers (see for example [24–27]) who found that the Sun, as a central star of the solar system, is a subject to the inertial motion around the centerof mass, or barycentre, of the solar system induced by the motions of the other planets (mostly large planets, e.g. Neptune, Jupiter, Saturn and Uranus).

Solar inertial motion (SIM) is the motion of the Sun around this barycenter of the solar system inside the circle with a diameter of about Δ ¼ 4*:*3*RSun*, or Δ = <sup>4</sup>*:*<sup>3</sup> � <sup>6</sup>*:*<sup>95</sup> � <sup>10</sup><sup>5</sup> =2*:*<sup>9885</sup> � <sup>10</sup><sup>6</sup> km, where *RSun* is a solar radius as shown in **Figures 4** and **5** in [19] reproduced from [27, 28]. This schematic drawing (see Fig. 4 in [19]) illustrates sudden shifts in the Sun from the location in the ellipse focus, where it is supposed to reside by Kepler's laws, because the Sun travels in an epitrochiodshaped orbits about the center-of mass (barycentre) of the solar system.

The SIM orbits are induced the tri-fall positions of large planets achieved for different planet configurations changing approximately within different periods of 370 or 2200–2400 years related to the planet positions and their rotation around the Sun [29, 30]. Hence, a joint effect of the orbital effects introduced by the combined motion of the Earth on the orbit and the Sun about the barycentre of the solar system can be the important factors in defining the observed long timescale variations of solar irradiance at the Earth and terrestrial temperature, which has not been explored yet, despite the Sun is the main source of energy of all the planets (**Table 1**).

Solar irradiance is accepted to be one of the important factors defining temperature variations on the Earth and other planets as it is the main source of the energy


**Table 1.**

*The solar irradiance in W=m*<sup>2</sup> *restored and measured since Maunder minimum.*

occurrences on the solar surface and migration to the equator accounting for north– south asymmetry of solar activity [6]. This investigation highlighted the important role of SBMF in generation of sunspots by dynamo actions and their appearance on the solar surface, thus, defining the solar activity. The link between SBMF (poloidal field) and sunspot (toroidal) magnetic field defines the action of the solar dynamo [1] and it would be beneficial to link a proxy of solar activity to the solar background magnetic field as it is systematically measured in the past 45 years.

Zharkova et al. [7] explored the solar background magnetic field and found the eigen values of the own oscillations of the Sun, by applying Principal Component Analysis (PCA) to the low-resolution full disk magnetograms captured in cycles 21– 23 by the Wilcox Solar Observatory. This approach allowed authors to replace a complex magnetic field seen on the solar surface, the photosphere, with the separate wave components, eight plus eigen vectors, which appeared in pairs [8]. The pair of the two principal components (PCs) are the strongest waves of solar magnetic oscillations covering about 67% of the data by standard deviation, with the nearly-equal largest eigen-values, which oscillate with not equal periods of about 11 years [9, 10]. The PCs are shown to be two magnetic waves generated by the dipole magnetic sources produced by the double solar dynamo action [10, 11] in the

These waves start in the opposite hemispheres while travelling with an increasing phase shift to the Northern hemisphere (in odd cycles) and to the Southern hemisphere (in even cycles) [7, 10]. The summary curve of these two waves is found close to the averaged sunspot numbers, which define the current solar activity index [9, 10]. This summary curve of solar magnetic waves is proposed as a new proxy of solar activity, which allows us to predict solar activity on any timescale and also to add a magnetic polarity of the background field for a given cycle, known to be opposite to leading polarity of sunspots [6]. The maximum of solar activity for a given cycle (or double maximum for the double waves with a larger phase shift) occurs at the times when each of the waves approaches its maximum, so that at the equal amplitudes the two waves can have a resonant interaction, naturally account-

ing for often-reported North–South asymmetry of solar activity [6, 13–15].

In order to test further predictions of solar activity with the summary curve of two magnetic waves generated by double dynamo in the Sun in two layers, the summary curve was extended using the mathematical formula from the current time forwards to 3200 and backwards to 1200 [10] (see **Figure 1**). This led to a discovery of grand solar cycles (GSCs) of solar activity with a duration of 350– 400 years, evidently caused by the interference (beating effect) of the two magnetic waves with close but not equal frequencies [10]. There were far fewer sunspots seen during some periods, for example, during the Dalton minimum (1790– 1820), and practically none during the period known as the Maunder minimum

*The summary curve (in arbitrary units) of solar activity calculated for 1200 to 3200 years from the 'historical' period (1976–2008, cycles 2123). Positive magnitudes of the summary curve represent northern magnetic polarity while the negative ones - southern magnetic polarity. Reproduced from the data of Zharkova et al. [10].*

inner and outer layers of the solar interior [12].

*Solar System Planets and Exoplanets*

**Figure 1.**

**28**

for all planets. During the Maunder minimum, solar activity was significantly reduced for six solar cycles of 11 years and so was the terrestrial temperature in the Northern hemisphere. This was considered to be a result of a reduction of solar irradiance during the Maunder Minimum.

More recent reconstruction of the cycle-averaged solar total irradiance back to 1610 suggests that since the end of the Maunder minimum in 1710 until 2010 there was the increase of the irradiance by a magnitude about 1 <sup>1</sup>*:*<sup>5</sup> *<sup>W</sup>=m*<sup>2</sup> [34]. This increase is correlated somehow with the increase of the baseline terrestrial temperature since the Maunder minimum (e.g. recovering from the little ice age) [35]. Although, it is not clear yet if this trend in variations of the terrestrial temperature and solar irradiance is caused by the increased solar activity itself, which, in fact, started to decrease in the past decades, or by some other factors of the solarterrestrial interaction and by human activities, or by the combination of all the three factors.

In the current chapter we analyse the observational variations of Sun-Earth distances derived from the published ephemeris in the two millennia 600–2600 and relate them to the variations of solar irradiance at the Earth and explore their possible links oscillations of the baseline solar magnetic field and with the reported planetary motions.
