**2. Observed millennial oscillations of solar irradiance and baseline solar magnetic field**

#### **2.1 Millennial oscillations of solar irradiance**

Reconstruction of cycle-averaged total solar irradiance (TSI) back to 1610 suggests an increase of the solar irradiance by a value of about 3 *W=m*<sup>2</sup> (see **Figure 2**) [31, 37], or about 0.22% of the total solar irradiance since the end of the Maunder minimum (see **Figure 2**, left plot).

The space observations in 80s of the total solar irradiance obtained by NIMBUS 7 instruments show pretty wide range of magnitudes varying up to 1370 *W=m*<sup>2</sup> [26], to 1371 *W=m*<sup>2</sup> [32] or 1372 *W=m*<sup>2</sup> [33]. The wide variety of the measured magnitudes of solar irradiance indicates that this physical parameter from the Sun is not as constant as many researchers assume. Although, these changes of solar irradiance from the MM until present times are, in general, small, compared to the tens of watts occurring during seasonal and latitude differences, which may have a noticeable impact on the Earth temperature.

oscillation periods are very close to the 2200 year period called Hallstatt's cycle reported from the other observations of the Sun and planets [21, 22, 24, 44].

*The variations of solar irradiance (left) [31] and terrestrial temperature (right) [36] recovered from the Maunder minimum, which demonstrates a significant drop of the solar irradiance and terrestrial temperature*

Recently, Zharkova et al. [19] reported the similar millennial oscillations of the baseline (zero-line) of the solar background magnetic field (SBMF) calculated from the summary curve obtained with Principal Component Analysis (PCA) [10]. The baseline magnetic field is defined from filtering out large-scale 22 year oscillations, or finding the mean point between two 11 year cycles for the expanded summary curve of 120 thousand years. As result, we detect weak two millennial oscillations of the SBMF baseline with a period of 2000 95 years [19] shown by the navy curve in **Figure 3** (bottom plot). Although, the scale of these baseline oscillations is much smaller (ranging from 10 to 10) than the 11 year magnetic field variations of the summary curve (ranging in 400,400) that is shown in **Figure 3** (bottom plot) for the redacted summary curve (cyan curve) calculated backwards between 70 and 90 thousand years [19]. Note, the summary curve presented by cyan curve in **Figure 3** (bottom plot) has different appearance from that in **Figure 1** (top plot) [19]

**2.2 Millennial oscillations of the baseline magnetic field**

*during the previous GSM, Maunder minimum (see the text for details).*

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

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

**Figure 2.**

**31**

Note, we do not include in this comparison the most recent restorations of the solar irradiance [34, 38], who considered the re-normalised solar irradiance after Maunder minimum and used a magnetic flux transport model with strongly averaged past solar magnetic fields, which make rather difficult to compare these magnitudes of solar irradiance with the non-normalised early observations.

The variations of the solar irradiance recovered for the Holocene from the variations of the carbon <sup>14</sup>*C* isotope abundance in the terrestrial biomass [39] (see **Figure 3**, top plot), demonstrate weak oscillations with a period of about 2200 years, or Hallstatt's cycle [20, 21], which are imposed onto the longer-term (16-20 K years) orbital oscillations (possibly, one of Milankovich cycles) [40, 41]. The solar irradiance oscillations restored over the past 12 000 years [20, 42] were also tested with the wavelet transform spectral analysis, which clearly demonstrate the similar period of 2200 years [22] or up to 2400 years [43]. These baseline

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

#### **Figure 2.**

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

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

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

**2. Observed millennial oscillations of solar irradiance and baseline solar**

Reconstruction of cycle-averaged total solar irradiance (TSI) back to 1610 suggests an increase of the solar irradiance by a value of about 3 *W=m*<sup>2</sup> (see **Figure 2**) [31, 37], or about 0.22% of the total solar irradiance since the end of the Maunder

The space observations in 80s of the total solar irradiance obtained by NIMBUS 7 instruments show pretty wide range of magnitudes varying up to 1370 *W=m*<sup>2</sup> [26], to 1371 *W=m*<sup>2</sup> [32] or 1372 *W=m*<sup>2</sup> [33]. The wide variety of the measured magnitudes of solar irradiance indicates that this physical parameter from the Sun is not as constant as many researchers assume. Although, these changes of solar irradiance from the MM until present times are, in general, small, compared to the tens of watts occurring during seasonal and latitude differences, which may have a notice-

Note, we do not include in this comparison the most recent restorations of the solar irradiance [34, 38], who considered the re-normalised solar irradiance after Maunder minimum and used a magnetic flux transport model with strongly averaged past solar magnetic fields, which make rather difficult to compare these magnitudes of solar irradiance with the non-normalised early

The variations of the solar irradiance recovered for the Holocene from the variations of the carbon <sup>14</sup>*C* isotope abundance in the terrestrial biomass [39] (see

**Figure 3**, top plot), demonstrate weak oscillations with a period of about 2200 years, or Hallstatt's cycle [20, 21], which are imposed onto the longer-term (16-20 K years) orbital oscillations (possibly, one of Milankovich cycles) [40, 41]. The solar irradiance oscillations restored over the past 12 000 years [20, 42] were also tested with the wavelet transform spectral analysis, which clearly demonstrate the similar period of 2200 years [22] or up to 2400 years [43]. These baseline

irradiance during the Maunder Minimum.

*Solar System Planets and Exoplanets*

factors.

planetary motions.

**magnetic field**

**2.1 Millennial oscillations of solar irradiance**

minimum (see **Figure 2**, left plot).

able impact on the Earth temperature.

observations.

**30**

*The variations of solar irradiance (left) [31] and terrestrial temperature (right) [36] recovered from the Maunder minimum, which demonstrates a significant drop of the solar irradiance and terrestrial temperature during the previous GSM, Maunder minimum (see the text for details).*

oscillation periods are very close to the 2200 year period called Hallstatt's cycle reported from the other observations of the Sun and planets [21, 22, 24, 44].

#### **2.2 Millennial oscillations of the baseline magnetic field**

Recently, Zharkova et al. [19] reported the similar millennial oscillations of the baseline (zero-line) of the solar background magnetic field (SBMF) calculated from the summary curve obtained with Principal Component Analysis (PCA) [10]. The baseline magnetic field is defined from filtering out large-scale 22 year oscillations, or finding the mean point between two 11 year cycles for the expanded summary curve of 120 thousand years. As result, we detect weak two millennial oscillations of the SBMF baseline with a period of 2000 95 years [19] shown by the navy curve in **Figure 3** (bottom plot). Although, the scale of these baseline oscillations is much smaller (ranging from 10 to 10) than the 11 year magnetic field variations of the summary curve (ranging in 400,400) that is shown in **Figure 3** (bottom plot) for the redacted summary curve (cyan curve) calculated backwards between 70 and 90 thousand years [19]. Note, the summary curve presented by cyan curve in **Figure 3** (bottom plot) has different appearance from that in **Figure 1** (top plot) [19]

#### **Figure 3.**

*Top plot: The millennial oscillations with a period (2100–2200) (Hallstatt cycle) of the carbon* <sup>14</sup>*C isotope abundances reported in parts per thousand (per mille,* %*) used for solar irradiance dating in the IntCal09 data from Reimer et al. [39]. This period is similar to that derived from the solar irradiance restored in the past 12,000 years with a wavelet transform by Steinhilber et al. [22] (see their Figure 4). The positive sign means excess and the negative sign means deficit of abundances. Bottom plot: The oscillations of the baseline (zero line, see for details section 2.2) of solar background magnetic field (left Y axis, arbitrary units, navy line) with a period of about 2000*�*95 years over-plotted on the oscillations of the reduced summary curve (right Y-axis, arbitrary units, cyan line). Positive magnitudes of the summary and baseline curves represent northern magnetic polarity while the negative ones - southern magnetic polarity. Adopted from Zharkova et al. [19].*

because it was redacted to a single point per year instead of 13 points (for Carrington rotations) originally used [10, 17].

Hence, the baseline magnetic field in **Figure 3** (bottom plot) reveals the very stable oscillations with a period of *Tbase* ¼ 2000 � 95 years [19]. Evidently, these baseline oscillations are normally incorporated into the magnetic field measurements of the summary curve (cyan curve) and, thus, are not detected in the unfiltered observations. The baseline oscillations of magnetic field have a very stable period maintained during the whole duration of simulations of 120 thousand years meaning these oscillations of the baseline magnetic field on a millennial timescale to be induced by a rather stable process either inside or outside the Sun.

reduced summary curve of magnetic field (cyan line). The irradiance curve was reduced in magnitude by factor 3, in order to distinguish this curve from the baseline oscillations (e.g. Spearman's correlation coefficient between these two curves is about 0.68). After the MM the magnetic baseline curve is growing towards northern polarity, while the solid dark line showing the rate of increase of the

*solar cycle (thin lines) and the one averaged per cycle (thick lines) derived by [45].*

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

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

*Top plot: The close-up view of the current cycle of the baseline magnetic field (dark blue curve, arbitrary units, see for details section 2.2) with the minimum occurring during Maunder minimum. The scale of the baseline variations are shown on the left hand side of Y axis, the scale of the summary curve variations - on the right hand side Y-axis. The irradiance curve (magenta line) taken from [20, 39], their Figure 3 (top plot), overplotted on the summary curve of magnetic field (cyan curve) [19]. The irradiance curve had to be reduced in magnitude to avoid full overlapping with the baseline magnetic field curve. The black line defines the slop of the baseline terrestrial temperature from [35]. Adopted from Zharkova et al. [19]. Bottom plot: The variations of terrestrial temperature (red lines) and total solar irradiance (measured in W=m*<sup>2</sup>*) (blue lines) during each*

From the close-up plot of the current millennial baseline cycle in **Figure 4** (top plot) it becomes evident that from 1600 the baseline magnetic field was shifting towards the northern polarity approaching its maximum in about 2600. This

baseline terrestrial temperature [35].

**Figure 4.**

**33**

The variations of the magnetic field baseline oscillations for the current Hallstatt's cycle are shown in **Figure 4** (top plot, navy line) (from [19]) indicatng that it started at Maunder minimum and is in ascending phase now [20, 42] and the *Millennial Oscillations of Solar Irradiance and Magnetic Field in 600–2600 DOI: http://dx.doi.org/10.5772/intechopen.96450*

#### **Figure 4.**

because it was redacted to a single point per year instead of 13 points (for

*polarity while the negative ones - southern magnetic polarity. Adopted from Zharkova et al. [19].*

stable oscillations with a period of *Tbase* ¼ 2000 � 95 years [19]. Evidently, these baseline oscillations are normally incorporated into the magnetic field measurements of the summary curve (cyan curve) and, thus, are not detected in the unfiltered observations. The baseline oscillations of magnetic field have a very stable period maintained during the whole duration of simulations of 120 thousand years meaning these oscillations of the baseline magnetic field on a millennial timescale to be induced by a rather stable process either inside or

The variations of the magnetic field baseline oscillations for the current Hallstatt's cycle are shown in **Figure 4** (top plot, navy line) (from [19]) indicatng that it started at Maunder minimum and is in ascending phase now [20, 42] and the

Hence, the baseline magnetic field in **Figure 3** (bottom plot) reveals the very

*Top plot: The millennial oscillations with a period (2100–2200) (Hallstatt cycle) of the carbon* <sup>14</sup>*C isotope abundances reported in parts per thousand (per mille,* %*) used for solar irradiance dating in the IntCal09 data from Reimer et al. [39]. This period is similar to that derived from the solar irradiance restored in the past 12,000 years with a wavelet transform by Steinhilber et al. [22] (see their Figure 4). The positive sign means excess and the negative sign means deficit of abundances. Bottom plot: The oscillations of the baseline (zero line, see for details section 2.2) of solar background magnetic field (left Y axis, arbitrary units, navy line) with a period of about 2000*�*95 years over-plotted on the oscillations of the reduced summary curve (right Y-axis, arbitrary units, cyan line). Positive magnitudes of the summary and baseline curves represent northern magnetic*

Carrington rotations) originally used [10, 17].

outside the Sun.

**32**

**Figure 3.**

*Solar System Planets and Exoplanets*

*Top plot: The close-up view of the current cycle of the baseline magnetic field (dark blue curve, arbitrary units, see for details section 2.2) with the minimum occurring during Maunder minimum. The scale of the baseline variations are shown on the left hand side of Y axis, the scale of the summary curve variations - on the right hand side Y-axis. The irradiance curve (magenta line) taken from [20, 39], their Figure 3 (top plot), overplotted on the summary curve of magnetic field (cyan curve) [19]. The irradiance curve had to be reduced in magnitude to avoid full overlapping with the baseline magnetic field curve. The black line defines the slop of the baseline terrestrial temperature from [35]. Adopted from Zharkova et al. [19]. Bottom plot: The variations of terrestrial temperature (red lines) and total solar irradiance (measured in W=m*<sup>2</sup>*) (blue lines) during each solar cycle (thin lines) and the one averaged per cycle (thick lines) derived by [45].*

reduced summary curve of magnetic field (cyan line). The irradiance curve was reduced in magnitude by factor 3, in order to distinguish this curve from the baseline oscillations (e.g. Spearman's correlation coefficient between these two curves is about 0.68). After the MM the magnetic baseline curve is growing towards northern polarity, while the solid dark line showing the rate of increase of the baseline terrestrial temperature [35].

From the close-up plot of the current millennial baseline cycle in **Figure 4** (top plot) it becomes evident that from 1600 the baseline magnetic field was shifting towards the northern polarity approaching its maximum in about 2600. This

increase of the baseline magnetic field of northern polarity is likely to coincide with the increase of solar irradiance curve [20, 42]. The baseline terrestrial temperature curve is shown increasing by 0.5<sup>∘</sup> C per 100 years [35] and has a slope (shown by the black line in **Figure 4** top plot) close to that of the magnetic field baseline increase (navy line) [19]. At the same time, the variations of the terrestrial temperature versus solar activity shown in **Figure 4** (bottom plot) [45] reveal that in the past few decades the Earth temperature increase goes against the solar activity showing the signs of decrease. This raised some reasonable questions about the cause of the terrestrial temperature increase and led to suggestions of substantial extra-heating of the Earth atmosphere caused by greenhouse gases.
