The sunspot number (SSN), the total solar irradiance (TSI), a TSI reconstruction, and the solar flare index (SFI), are analyzed for long-range persistence (LRP). Standard Hurst analysis yields $H \approx 0.9$, which suggests strong LRP. However, solar activity time series are non-stationary due to the almost periodic 11 year smooth component, and the analysis does not give the correct $H$ for the stochastic component. Better estimates are obtained by detrended fluctuations analysis (DFA), but estimates are biased and errors are large due to the short time records. These time series can be modeled as a stochastic process of the form $x(t)=y(t)+σ\sqrt{y(t)}\, w_H(t)$, where $y(t)$ is the smooth component, and $w_H(t) $ is a stationary fractional noise with Hurst exponent $H$. From ensembles of numerical solutions to the stochastic model, and application of Bayes' theorem, we can obtain bias and error bars on $H$ and also a test of the hypothesis that a process is uncorrelated ($H=1/2$). The conclusions from the present data sets are that SSN, TSI and TSI reconstruction almost certainly are long-range persistent, but with most probable value $H\approx 0.7$. The SFI process, however, is either very weakly persistent ($H<0.6$) or completely uncorrelated. Some differences between stochastic properties of the TSI and its reconstruction indicate some error in the reconstruction scheme.
The Sun exhibits a well-observed modulation in the number of spots on its disk over a period of about 11 years. From the dawn of modern observational astronomy sunspots have presented a challenge to understanding -- their quasi-periodic variation in number, first noted 175 years ago, stimulates community-wide interest to this day. A large number of techniques are able to explain the temporal landmarks, (geometric) shape, and amplitude of sunspot "cycles," however forecasting these features accurately in advance remains elusive. Recent observationally-motivated studies have illustrated a relati…
Recent studies of radioisotopes in tree rings or ice cores suggest that extreme space weather events occurred in the pre-telescope age. Observational records of naked-eye sunspots and low-latitude auroras in historical documents in pre-telescopic age can provide useful information on past solar activity. In this paper, we present the results of a comprehensive survey of records of sunspots and auroras in Chinese official histories from the 6th century to the 10th century, in the period of Suí, Táng, the Five Dynasties and Ten Kingdoms. These official histories contain records of continuous obs…
Five new correlations between sunspot activity and orbiting position of the Jovian planets are detected. In order to explain these correlations it is suggested that the resonance of the outer planets destabilizes the orbit of Kuiper Belt Objects and generates a cyclical impact frequency on the Sun. The vaporization of the object initiates a shock way disrupting the upwelling of the plasma resulting in a sunspot formation. The proposed model is able to explain the length of the cycle, the latitude distribution of the sunspots and the extremely long term stability of the cycles. Calculating the …
I study the sunspot area fluctuations over the epoch of 12 solar cycles (12-23). Lately, I found three significant quasi-periodicities at 10, 17 and 23 solar rotations, but two longer periods could be treated as subharmonics of the 10-rotation period. Thus, I search this period during the low- and the high-activity periods of each solar cycles. Because of the N-S asymmetry I consider each solar hemisphere separately. The skewness of each fluctuation probability distribution suggests that the positive and the negative fluctuations could be are examined separately. To avoid the problem when a fe…
The average geomagnetic activity during sunspot minimum has been continuously decreasing in the last four cycles. The geomagnetic activity is caused by both interplanetary disturbances - coronal mass ejections and high speed solar wind streams, and the background solar wind over which these disturbances ride. We show that the geomagnetic activity in cycle minimum does not depend on the number and parameters of coronal mass ejections or high speed solar wind streams, but on the background solar wind. The background solar wind has two components: slower and faster. The source of the slower compo…
The dynamic activity of the Sun -- sustained by a magnetohydrodynamic dynamo mechanism working in its interior -- modulates the electromagnetic, particulate and radiative environment in space. While solar activity variations on short timescale create space weather, slow long-term modulation forms the basis of space climate. Space weather impacts diverse space-reliant technologies while space climate influences planetary atmospheres and climate. Having prior knowledge of the Sun's activity is important in these contexts. However, forecasting solar-stellar magnetic activity has remained an outst…
Records of observations of sunspots and auroras in pre-telescopic historical documents provide useful information about past solar activity both in long-term trends and short-term space weather events. In this study, we present the results of a comprehensive survey of the records of sunspots and aurora candidates in the Yuánshǐ and Míngshǐ, Chinese Official Histories spanning 1261-1368 and 1368-1644, based on continuous observations with well-formatted reportds conducted by contemporary professional astronomers. We then provide a brief comparison of these data with Total Solar Irradiance (TSI)…
In addition to regular Schwabe cycles (~ 11 years), solar activity also shows longer periods of enhanced or reduced activity. Of these, reconstructions of the Dalton Minimum provide controversial sunspot group numbers and limited sunspot positions, partially due to limited source record accessibility. We analysed Stephan Prantner's sunspot observations from 1804--1844, the values of which had only been known through estimates despite their notable chronological coverage during the Dalton Minimum. We identified his original manuscript in Stiftsarchiv Wilten, near Innsbruck, Austria. We reviewed…
Sunspot numbers are important tracers of historical solar activity. They are important in the prediction of oncoming solar maximum, in the design of lifetimes of space assets, and in assessing the extent of solar-radiation impact on the space environment. Sunspot numbers were obtained visually from sunspot drawings. The availability of digital images from the US Air Force Improved Solar Optical Observing Network (ISOON) prototype telescope concurrent to observer-dependent sunspot numbers recorded at the National Solar Observatory (NSO) has provided a basis for comparing sunspot numbers determi…
Geomagnetic activity in each phase of the solar cycle consists of 3 parts: (1) a floor below which the geomagnetic activity cannot fall even in the absence of sunspots, related to moderate graduate commencement storms; (2) sunspot-related activity due to sudden commencement storms caused by coronal mass ejections; (3) graduate commencement storms due to high speed solar wind from solar coronal holes. We find that the changes in the floor depend on the global magnetic moment of the Sun, and on the other side, from the height of the floor we can judge about the amplitude of the sunspot cycle.
A striking feature of the solar cycle is that at the beginning, sunspots appear around mid-latitudes, and over time the latitudes of emergences migrate towards the equator.The maximum level of activity (e.g., sunspot number) varies from cycle to cycle.For strong cycles, the activity begins early and at higher latitudes with wider sunspot distributions than for weak cycles. The activity and the width of sunspot belts increase rapidly and begin to decline when the belts are still at high latitudes. Surprisingly, it has been reported that in the late stages of the cycle the level of activity (sun…
Records of sunspots and aurora observations in pre-telescopic historical documents can provide useful information about solar activity in the past. This is also true for extreme space weather events, as they may have been recorded as large sunspots observed by the naked eye or as low-latitude auroras. In this paper, we present the results of a comprehensive survey of records of sunspots and auroras in the Songshi, a Chinese formal chronicle spanning the tenth to the thirteenth century. This chronicle contains a record of continuous observations with well-formatted reports conducted as a policy…
Observations of long-term north-south asymmetry in solar activity demand the equator-symmetric (quadrupolar) mode be present in the solar magnetic field in line with the dominant antisymmetric (dipolar) mode. This paper proposes treating the sunspot area as a proxy for subsurface toroidal magnetic flux to infer the quadrupolar mode of the solar dynamo from sunspot data. Toroidal pseudo-fluxes (PF) in the northern and southern hemispheres are defined as a signed sunspot area with plus or minus sign prescribed to them in accord with the Hale's sunspot polarity rules. Statistical correlation anal…
The long term solar activity dependencies of ionospheric F$_1$ and F$_2$ regions' critical frequencies ($f_0F_1$ and $f_0F_2$) are analyzed for the last four solar cycles (1976--2015). We show that the ionospheric F$_1$ and F$_2$ regions have different solar activity dependencies in terms of the sunspot group (SG) numbers: F$_1$ region critical frequency ($f_0F_1$) peaks at the same time with the small SG numbers, while the $f_0F_2$ reaches its maximum at the same time with the large SG numbers, especially during the solar cycle 23. The observed differences in the sensitivity of ionospheric cr…
On the basis of morphological analysis of yearly values of the maximum CME (coronal mass ejection) speed index, the sunspot number and total sunspot area, sunspot magnetic field, and solar flare index, the solar wind speed and interplanetary magnetic field strength, and the geomagnetic Ap and Dst indices, we point out the particularities of solar and geomagnetic activity during the last cycle 23, the long minimum which followed it and the ascending branch of cycle 24. We also analyze temporal offset between the maximum CME speed index and the above-mentioned solar, geomagnetic, and interplanet…
Solar magnetic activity is expressed via variations of sunspots and active regions varying on different timescales. The most accepted is an 11-year period supposedly induced by the electromagnetic solar dynamo mechanism. There are also some shorter or longer timescales detected: the biennial cycle (2-2.7 years), Gleisberg cycle (80-100 years), and Hallstatt's cycle (2100-2300 years). Recently, using Principal Component Analysis (PCA) of the observed solar background magnetic field (SBMF), another period of 330-380 years, or Grand Solar Cycle (GSC), was derived from the summary curve of two eig…
The correlation scale and the Taylor scale are evaluated for interplanetary magnetic field fluctuations from two-point, single time correlation function using the Advanced Composition Explorer (ACE), Wind, and Cluster spacecraft data during the time period from 2001 to 2017, which covers over an entire solar cycle. The correlation scale and the Taylor scale are respectively compared with the sunspot number to investigate the effects of solar activity on the structure of the plasma turbulence. Our studies show that the Taylor scale increases with the increasing sunspot number, which indicates t…
We consider the statistical relationship between the growth rate of activity in the early phase of a solar cycle with its subsequent amplitude on the basis of four datasets of global activity indices (Wolf sunspot number, group sunspot number, sunspot area, and 10.7-cm radio flux). In all cases, a significant correlation is found: stronger cycles tend to rise faster. Owing to the overlapping of sunspot cycles, this correlation leads to an amplitude-dependent shift of the solar minimum epoch. We show that this effect explains the correlations underlying various so-called precursor methods for t…
