Did Open Solar Magnetic Field Increase During The Last 100 Years? A Reanalysis of Geomagnetic Activity

Long-term geomagnetic activity presented by the aa index has been used to show that the heliospheric magnetic field has more than doubled during the last 100 years. However, serious concern has been raised on the long-term consistency of the aa index and on the centennial rise of the solar magnetic field. Here we reanalyze geomagnetic activity during the last 100 years by calculating the recently suggested IHV (Inter-Hour Variability) index as a measure of local geomagnetic activity for seven stations. We find that local geomagnetic activity at all stations follows the same qualitative long-term pattern: an increase from early 1900 to 1960, a dramatic dropout in 1960s and a (mostly weaker) increase thereafter. Moreover, at all stations, the activity at the end of the 20th century has a higher average level than at the beginning of the century. This agrees with the result based on the aa index that global geomagnetic activity, and thereby, the open solar magnetic field has indeed increased during the last 100 years. However, quantitatively, the estimated centennial increase varies greatly from one station to another. We find that the relative increase is higher at the high-latitude stations and lower at the low- and mid-latitude stations. These differences may indicate that the fraction of solar wind disturbances leading to only moderate geomagnetic activity has increased during the studied time interval. We also show that the IHV index needs to be corrected for the long-term change of the daily curve, and calculate the corrected IHV values. Most dramatically, we find the centennial increase in global geomagnetic activity was considerably smaller, only about one half of that depicted by the aa index.     

Long-term predictive assessments of solar and geomagnetic activities made on the basis of the close similarity between the solar inertial motions in the intervals 1840–1905 and 1980–2045

The solar inertial motions (orbits) (SIMs) in the years 1840–1905 and 1980–2045 are of a disordered type and they are nearly identical. This fact was used for assessing predictive capabilities for the sizes of three future sunspot cycles and for the time variation of the geomagnetic aa-index up to 2045. The author found that the variations in sunspot numbers in the interval 1840–1867 and in the interval 1980–2007 are similar, especially after 1850 (1990). The differences may be ascribed to the lower quality of the sunspot data before 1850. A similarity between the variations in geomagnetic aa-index in the intervals 1844–1867 and 1984–2007 is also found. Moreover, the aa-index in these intervals have the same best fit lines (the polynomials of the fourth order) with close positions of the extrema. The extrema of the best fit line for the aa-index in the interval 1906–1928 which corresponds to the first half of the ordered, trefoil interval of the SIM have the opposite positions to them. The correlation coefficient between the aa-indices in the interval 1844–1866 and in the interval 1984–2006 is 0.61. In contrast, the correlation coefficient between the aa-indices in the interval 1844–1866 and in the interval 1906–1928 is ?0.43. Cautious predictions have been made: the author believes that the cycles 24–26 will be a repeat of cycles 11–13, i.e. they could have heights around 140 (100), 65 and 85, they will have lengths of 11.7, 10.7 and 12.1 years. The maxima of the cycles should occur in 2010, 2023 and 2033, the minima in 2007, 2018, 2029 and 2041. Up to 2045, the aa-index could repeat its values for the interval 1868–1905. The results indicate that solar and geomagnetic activities are non random processes. If these predictions may come true, then further evidence of the primary role of the SIM in solar variability is established.     

Historical Space Climate Data from Finland: Compilation and Analysis

We have compiled archived geomagnetic observations from the Helsinki magnetic observatory as well as visual sightings of auroral occurrence in Finland. The magnetic database comprises about 2 000 000 observations of H- and D-components measured during 1844–1909 with time resolution of 10 min to 1 h. In addition, magnetic observations carried out in the First and Second Polar Years in Finland have been recompiled. Magnetic activity indices (three-hour K-and daily Ak-figures) have been derived from the magnetic observations. Comparisons between the Finnish indices and simultaneous global aa-index (starting in 1868) show a good mutual correlation. The Helsinki activity index series can be used as a (pseudo) extension of the aa-index series for about two solar cycles 1844d –1868. On the annual level the correlation coefficient is about 0.9 during the overlapped time interval 1868–1897. The auroral database consists of about 20 000 single observations observed in Finland since the year 1748. The database of visual auroras has been completed by auroral occurrence (AO) index data derived from the Finnish all-sky camera recordings during 1973 –1997 at several sites in Lapland. The AO-index reveals both spatial and temporal variations of auroras from diurnal to solar cycle time scales in different space weather conditions.     

The 27-Day and 22-Year Cycles in Solar and Geomagnetic Activity

We study the evolution of the longitudinal asymmetry in solar activity through the wave packet technique applied to the period domain of 25 – 31 days (centered at the 27-day solar rotation period) for the sunspot number and geomagnetic aa index. We observe the occurrence of alternating smaller and larger amplitudes of the 11-year cycle, resulting in a 22-year periodicity in the 27-day signal. The evolution of the 22-year cycle shows a change of regime around the year 1912 when the 22-year period disappears from the sunspot number series and appears in the aa index. Other changes, such as a change in the correlation between solar and geomagnetic activity, took place at the same time. Splitting the 27-day frequency domain of aa index shows an 11-year cycle for higher frequencies and a pure22-year cycle for lower frequencies, which we attribute to higher latitude coronal holes. This evidence is particularly clear after 1940, which is another benchmark in the evolution of the aa index. We discuss briefly the mechanisms that could account for the observed features of the 22-year cycle evolution.     

Global solar activity on long time scales

We report the results of the application of our approach to study the behavior of solar activity in the past, where:

When reconstructing the variations of solar activity, geomagnetic parameters, and the interplanetary magnetic field in the past we select a sequence of increasing time scales, which can be naturally represented by the potentials of available observational data. We select a total of four time scales: 150–200 years, 400 years, 1000 years, and 10000 years.

When constructing the series of each successive (in terms of length) time scale we use the data of the previous time scale as reference data.

We abandon, where possible, the series of traditional statistical parameters in favor of the series of physical parameters.

When deriving the relations between any parameters of solar activity, geomagnetic disturbance, and the interplanetary magnetic field, we take into account the differential nature of relations on different time scales. To this end, we use the earlier proposed MSR and DPS methods.

To verify the resulting reconstructions, we use the “principle of witnesses”, which uses independent (in some cases, indirect) information as initial data.

     

Wavelet Analysis on Solar Wind Parameters and Geomagnetic Indices

The geomagnetic activity is the result of the solar wind–magnetosphere interaction. It varies following the basic 11-year solar cycle; yet shorter time-scale variations appear intermittently. We study the quasi-periodic behavior of the characteristics of solar wind (speed, temperature, pressure, density) and the interplanetary magnetic field (B _x , B _y , B _z , β, Alfvén Mach number) and the variations of the geomagnetic activity indices (D _ST, AE, A _p and K _p). In the analysis of the corresponding 14 time series, which span four solar cycles (1966?–?2010), we use both a wavelet expansion and the Lomb/Scargle periodograms. Our results verify intermittent periodicities in our time-series data, which correspond to already known solar activity variations on timescales shorter than the sunspot cycle; some of these are shared between the solar wind parameters and geomagnetic indices.     

Rotation cycles of the sector structure of the solar magnetic field and its activity

We study the rotation of the sector structure of the solar magnetic field by using Stanford magnetographic observations from 1975 until 2000 and magnetic synoptic Hα-maps obtained from 1904 until 2000. The two independent series of observations yielded the same rotation periods of the two-sector (26.86 days) and four-sector (13.64 days) structures. We introduce a new index of the solar rotation, SSPM(t). The spectral power density of the sector structure of the magnetic field is shown to exhibit a 22-year cyclicity. The two-and four-sector structures of the magnetic field rotate faster at the maxima of even 11-year sunspot cycles. This phenomenon may be called the Gnevyshev-Ohl rule for the solar rotation. The 11-year sector-structure activity cycles are shown to lead the 11-year sunspot cycles (Wolf numbers) by 5.5 years. A 55-year component with the slowest rotation in the 18th cycle (1945–1955) was distinguished in the sector-structure rotation.     

Solar cycle dependence of periodic variations in geomagnetic Kp-index

The geomagnetic K_p-index data for the 1932–1969 period have been investigated by means of a modified power spectrum technique on the basis of overlapping 2-yr intervals. The observed 27-, and 13.5-day periodicities show an obvious solar cycle dependence through the whole period concerned. Also, periodicities in the range of 9?4 days have been observed through years of minimum and decreasing phases of solar activity. The periodicities observed are found to be related to the existence of variations in the interplanetary medium structure which modulates the geomagnetic activity.     

Evolution of Solar and Geomagnetic Activity Indices, and Their Relationship: 1960?�C?2001

We employ annually averaged solar and geomagnetic activity indices for the period 1960??C?2001 to analyze the relationship between different measures of solar activity as well as the relationship between solar activity and various aspects of geomagnetic activity. In particular, to quantify the solar activity we use the sunspot number R _s, group sunspot number R _g, cumulative sunspot area Cum, solar radio flux F10.7, and interplanetary magnetic field strength IMF. For the geomagnetic activity we employ global indices Ap, Dst and Dcx, as well as the regional geomagnetic index RES, specifically estimated for the European region. In the paper we present the relative evolution of these indices and quantify the correlations between them. Variations have been found in: i) time lag between the solar and geomagnetic indices; ii) relative amplitude of the geomagnetic and solar activity peaks; iii) dual-peak distribution in some of solar and geomagnetic indices. The behavior of geomagnetic indices is correlated the best with IMF variations. Interestingly, among geomagnetic indices, RES shows the highest degree of correlation with solar indices.     

Large-Scale Structure of the Sunspot Activity and the Background Magnetic Field Formation

Large-scale distribution of the sunspot activity of the Sun has been analyzed by using a technique worked out previously (Erofeev, 1997) to study long-lived, non-axisymmetric magnetic structures with different periods of rotation. Results of the analysis have been compared with those obtained by analyzing both the solar large-scale magnetic field and large-scale magnetic field simulated by means of the well-known flux transport equation using the sunspot groups as a sole source of new magnetic flux in the photosphere. A 21-year period (1964–1985) has been examined.The rotation spectra calculated for the total time interval of two 11-year cycles indicate that sunspot activity consists of a series of discrete components (modes) with different periods of rotation. The largest-scale component of the sunspot activity reveals modes with 27-day and 28-day periods of rotation situated, correspondingly, in the northern and southern hemispheres of the Sun, and two modes with rotation periods of about 29.7 days situated in both hemispheres. Such a modal structure of the sunspot activity agrees well with that of the large-scale solar magnetic field. Moreover, the magnetic field distribution simulated with the flux transport equation also reveals the same modal structure. However, such an agreement between the large-scale solar magnetic field and both the sunspot activity and simulated magnetic field is unstable in time; so, it is absent in the northern hemisphere of the Sun during solar cycle No. 20. Thus the sources of magnetic flux responsible for formation of the large-scale, rigidly rotating magnetic patterns appear to be closely connected, but are not identical with the discrete modes of the sunspot activity.     

Long-Term Correlation Between the Nao and Solar Activity

We extend the correlation analysis of solar signals and the North Atlantic Oscillation (NAO) back in time by using the aa index (since 1868) and the PC index (since 1948) as a proxy of the solar wind energy imparted to the magnetosphere. Prior to the 1940s the records of the NAO and the aa index were not closely connected, while after the 1940s their rhythms matched. We compare two distinctive periods with recent results on the long-scale reconstruction of solar activity. The shift in the NAO–aa interconnection can provide the explanation of a significant increase of solar activity after the 1940s. A strengthening of the interplanetary magnetic field leads to more intensive variations of the high-latitude ionospheric electric field that influences the atmospheric circulation.     

Does the solar magnetic field increase?

We consider measurements of the general magnetic field (GMF) of the Sun as a star at four world observatories from 1968 until 1999. We show that, within the error limits, the mean strength of the photospheric magnetic field H (of its longitudinal component, in magnitude) has not changed over the last 32 years. This is in conflict with the recent conclusion by Lockwood et al. (1999) that the solar coronal magnetic field increased by 40% from 1964 until 1996 and has almost doubled in the last 100 years. The causes of discrepancies in the results are discussed. At the same time, the GMF exhibits a natural 11-year variation associated with the solar cycle. The strength of the photospheric longitudinal magnetic field (in absolute value) averaged over 32 years is 0.46 G (at an rms GMF strength of 0.57 G). The mean GMF for all years of measurements had a south polarity: $\bar H = - 0.030 \pm 0.018 G$ . The difference from zero is statistically significant at 1.7σ (90%) and may be directly related to the outstanding problem of the solar magnetic “monopole.”     

Large-Scale Magnetic Field of the Sun and Evolution of Sunspot Activity

The evolution of the large-scale magnetic field of the Sun has been studied using an algorithm of tomographic inversion. By analyzing line-of-sight magnetograms, we mapped the radial and toroidal components of the Sun??s large-scale magnetic field. The evolution of the radial and toroidal magnetic field components in the 11-year solar cycle has been studied in a time?Clatitude aspect. It is shown that the toroidal magnetic field of the Sun is causally related to sunspot activity; i.e., the sunspot formation zones drift in latitude and follow the toroidal magnetic fields. The results of our analysis support the idea that the high-latitude toroidal magnetic fields can serve as precursors of sunspot activity. The toroidal fields in the current cycle are anomalously weak and also show a barely noticeable equatorward drift. This behavior of the toroidal magnetic field suggests low activity levels in the current cycle and in the foreseeable future.     

A study of the geomagnetic indices asymmetry based on the interplanetary magnetic field polarities

Data of geomagnetic indices (aa, Kp, Ap, and Dst) recorded near 1 AU over the period 1967–2016, have been studied based on the asymmetry between the interplanetary magnetic field (IMF) directions above and below of the heliospheric current sheet (HCS). Our results led to the following conclusions: (i) Throughout the considered period, 31 random years (62%) showed apparent asymmetries between Toward (\(\mathbf{T}\)) and Away (\(\mathbf{A}\)) polarity days and 19 years (38%) exhibited nearly a symmetrical behavior. The days of \(\mathbf{A}\) polarity predominated over the \(\mathbf{T}\) polarity days by 4.3% during the positive magnetic polarity epoch (1991–1999). While the days of \(\mathbf{T}\) polarity exceeded the days of \(\mathbf{A}\) polarity by 5.8% during the negative magnetic polarity epoch (2001–2012). (ii) Considerable yearly North–South (N–S) asymmetries of geomagnetic indices observed throughout the considered period. (iii) The largest toward dominant peaks for \(aa\) and \(Ap\) indices occurred in 1995 near to minimum of solar activity. Moreover, the most substantial away dominant peaks for \(aa\) and \(Ap\) indices occurred in 2003 (during the descending phase of the solar cycle 23) and in 1991 (near the maximum of solar activity cycle) respectively. (iv) The N–S asymmetry of \(Kp\) index indicated a most significant away dominant peak occurred in 2003. (v) Four of the away dominant peaks of Dst index occurred at the maxima of solar activity in the years 1980, 1990, 2000, and 2013. The largest toward dominant peak occurred in 1991 (at the reversal of IMF polarity). (vi) The geomagnetic indices (aa, Ap, and \(Kp\)) all have northern dominance during positive magnetic polarity epoch (1971–1979), while the asymmetries shifts to the southern solar hemisphere during negative magnetic polarity epoch (2001–2012).     

Reconstruction of Wolf Sunspot Numbers on the Basis of Spectral Characteristics and Estimates of Associated Radio Flux and Solar Wind Parameters for the Last Millennium

A reconstruction of sunspot numbers for the last 1000 years was obtained using a sum of sine waves derived from spectral analysis of the time series of sunspot number R _z for the period 1700–1999. The time series was decomposed in frequency levels using the wavelet transform, and an iterative regression model (ARIST) was used to identify the amplitude and phase of the main periodicities. The 1000-year reconstructed sunspot number reproduces well the great maximums and minimums in solar activity, identified in cosmonuclides variation records, and, specifically, the epochs of the Oort, Wolf, Spörer, Maunder, and Dalton Minimums as well the Medieval and Modern Maximums. The average sunspot number activity in each anomalous period was used in linear equations to obtain estimates of the solar radio flux F _10.7, solar wind velocity, and the southward component of the interplanetary magnetic field.     

The Gnevyshev-Ohl rule for physical parameters of the solar magnetic field: The 400-year interval

We consider a number of questions pertaining to the famous Gnevyshev-Ohl rule. We discuss various formulations of the rule and show that it is not violated in its exact formulation in the last pair of 11-year cycles 22 and 23. The rule has been found to hold not only for statistical indices of solar activity but also in the context of physical parameters of the solar magnetic field: the sunspot magnetic flux and the open magnetic flux. We have established that the hypothesis by Usoskin et al. (2001) about the “loss“ of one cycle at the end of the 18th century allows the Gnevyshev-Ohl rule, which regulates the behavior of physical parameters of the solar magnetic field, to be made universal, without any exceptions, at least in the last 400 years. Thus, in fact, we can talk about the Gnevyshev-Ohl law of the long-term dynamics of the solar magnetic field, a law that holds at both normal and extreme levels of solar activity.     

Cyclic Reversal of Magnetic Cloud Poloidal Field

Coronal mass ejections (CMEs) carry magnetic structure from the low corona into the heliosphere. The interplanetary CMEs (ICMEs) that exhibit the topology of helical magnetic fluxropes are traditionally called magnetic clouds (MCs). MC fluxropes with axis of low (high) inclination with respect to the ecliptic plane have been referred to as bipolar (unipolar) MCs. The poloidal field of bipolar MCs has a solar cycle dependence. We report a cyclic reversal of the poloidal field of low inclination MC fluxropes during 1976 to 2009. The MC poloidal field cyclic reversal on the same time scale of the solar magnetic cycle is evident over three sunspot cycles. Approximately 48% of ICMEs are MCs, and 40% of IMCs are bipolar MCs during solar cycle 23. The speed of the bipolar MCs has essentially the same distribution as all ICMEs, which implies that they are not from any special type of CMEs in terms of the solar origin. Although CME fluxropes may undergo a number of complications during the eruption and propagation, a significant group of MCs retains sufficient similarity to the source region magnetic field to posses the same cyclic periodicity in polarity reversal. The poloidal field of bipolar MCs gives the out-of-ecliptic-plane field or B _z component in the IMF time series. MCs with southward B _z field are particularly effective in causing geomagnetic disturbances. During the solar minima, the B _z field IMF sequence within MCs at the leading portion of a bipolar MC is the same with the solar global dipole field. Our finding shows that MCs preferentially remove the like polarity of the solar dipole field, and it supports the participation of CMEs in the solar magnetic cycle.     

Temporal variations in the large-scale magnetic field of the solar atmosphere at heights from the photosphere to the source surface

Calculations of the magnetic field in the potential approximation (using Bd technology (Rudenko, 2001)) were used to study the time variations of several parameters of the large-scale magnetic field in the solar atmosphere during the last four cycles. Synoptic maps (SMs) for the radial component Br of the calculated magnetic field were plotted at 10 heights between the solar surface (R = R _⊙) and the source (R = 2.5R _⊙). On these SMs, we marked the 10-degree latitudinal areas. The following (averaged within the zone) characteristics of the magnetic field were determined corresponding to these zones: Sp, Sm; S _+fields , where Sp is the positive value of Br, Sm is the averaged modulus of the negative Br; S _+fields is the percentage of latitudinal zones with positive Br. The analysis of temporal variations in the magnitude of S points to different origins of the large-scale magnetic field in the near-equatorial and polar regions of the solar atmosphere. The analysis of temporal variations of S _+fields showed that there were almost no periods with a mixed polarity at R = 2.5R _⊙ during the 21st and 22nd solar cycles and in an ascending phase of the 23rd cycle. However, beginning from the maximum of the 23rd cycle, a mixed polarity in the equatorial region was observed until the end of the long minimum of activity. We hypothesized that this could be a precursor for a long minimum between the 23rd and 24th solar cycles. It was shown that during the maximum phase of the 24th solar cycle the magnetic field at R = R _⊙ is much less than that during the maximum phase of the 23rd cycle, and in the region from 55° to 75°, this difference reaches an order of magnitude.     

Does the Babcock-Leighton mechanism operate on the Sun?

The contribution of the Babcock-Leighton mechanism to the generation of the Sun’s poloidal magnetic field is estimated from sunspot data for three solar cycles. Comparison of the derived quantities with the A-index of the large-scale magnetic field suggests a positive answer to the question posed in the title of this paper.     

Predicting maximum sunspot number in solar cycle 24

A few prediction methods have been developed based on the precursor technique which is found to be successful for forecasting the solar activity. Considering the geomagnetic activity aa indices during the descending phase of the preceding solar cycle as the precursor, we predict the maximum amplitude of annual mean sunspot number in cycle 24 to be 111 ± 21. This suggests that the maximum amplitude of the upcoming cycle 24 will be less than cycles 21–22. Further, we have estimated the annual mean geomagnetic activity aa index for the solar maximum year in cycle 24 to be 20.6 ± 4.7 and the average of the annual mean sunspot number during the descending phase of cycle 24 is estimated to be 48 ± 16.8.