Longitudinal Distribution of Solar Magnetic Fields and Activity During the Ending and Starting Periods of Activity Cycles

Studying the appearance of active regions during periods of solar activity minima, we observed that the magnetic fields of active regions belonging to the old and new cycle were mutually related. This was the reason we decided to investigate the relation of the old and new cycle activity during the two last minima in more detail. We examined the distribution of both activities in heliographic longitude, because the patterns of such distribution change substantially during the time of the minimum, and we studied their relation to the distribution and development of the global (background) magnetic field. We observed that the active regions of the old and new cycles tended to concentrate in the same active longitudes. The sources of their magnetic fluxes seem to have the same heliographic longitude. The beginning of the new cycle activity, occurring at the very beginning to a very weak degree in the equatorial zone, and then proceeding to higher latitudes, occurs in the magnetic field remnants of the old cycle activity. During the transition phase, a relatively large number of small active regions is produced by both cycles.     

Cyclic variation of the global magnetic field indices

The energetical aspect of solar phenomena of different spatial and time scales has been studied with special attention to global magnetic fields. Cyclic regularities in the heliosphere are determined by energetics of global magnetic fields. The energy variation of global fields consists of a number of maxima and minima coinciding with reference points of the sunspot cycle. The correlations of a number of well-known indices in the heliosphere with Wolf numbers and with indices of energetics of the global magnetic field have been investigated. The results can be used to identify more exactly the reference points of the cycle.     

Spatial Structure of Regular and Chaotic Orbits in Self-Consistent Models of Galactic Satellites

In several previous papers we had investigated the orbits of the stars that make up galactic satellites, finding that many of them were chaotic. Most of the models studied in those works were not self-consistent, the single exception being the Heggie and Ramamani (1995) models; nevertheless, these ones are built from a distribution function that depends on the energy (actually, the Jacobi integral) only, what makes them rather special. Here we built up two self-consistent models of galactic satellites, freezed theirs potential in order to have smooth and stationary fields, and investigated the spatial structure of orbits whose initial positions and velocities were those of the bodies in the self-consistent models. We distinguished between partially chaotic (only one non-zero Lyapunov exponent) and fully chaotic (two non-zero Lyapunov exponents) orbits and showed that, as could be expected from the fact that the former obey an additional local isolating integral, besides the global Jacobi integral, they have different spatial distributions. Moreover, since Lyapunov exponents are computed over finite time intervals, their values reflect the properties of the part of the chaotic sea they are navigating during those intervals and, as a result, when the chaotic orbits are separated in groups of low- and high-valued exponents, significant differences can also be recognized between their spatial distributions. The structure of the satellites can, therefore, be understood as a superposition of several separate subsystems, with different degrees of concentration and trixiality, that can be recognized from the analysis of the Lyapunov exponents of their orbits.     

Evidence of Solar Variation in Tree-Ring-Based Climate Reconstructions

Analyses of the summer temperature anomalies in northern Fennoscandia for A.D. –1991 and mean annual temperature in the northern hemisphere for A.D. 1000–1990 (both reconstructed by means of dendrochronological methods) are performed using Fourier and wavelet approaches. It is revealed that the century-type (65–140 yr) periodicity is present in both series during most of the full time range. A comparison of the northern Fennoscandian temperature record with a variety of indicators of solar activity (direct measurements and proxies) shows that this century-scale periodicity most probably was forced by a centennial cycle of solar activity (Gleissberg cycle). Despite the fact that the connection between the centennial variation of global northern hemispheric temperature and that of the Sun's activity is weaker, a link between the two can also not be excluded. The results obtained give us new evidence of the reality of the solar–climate link over a record long-time scale (at least during the last millennium). Variable length of the century-long temperature periodicity may reflect the corresponding changes in the length of the Gleissberg solar cycle. The effects, which can obscure the Sun's influence on the global hemispheric climate, are discussed.     

Period and phase of the 88-year solar cycle and the Maunder minimum: Evidence for a chaotic sun

The problem of whether the solar dynamo is quasi-periodic or chaotic is addressed by examining 1500 years of sunspot, geomagnetic and auroral activity cycles. We find sub-harmonics of the fundamental solar cycle period during the years preceding the Maunder minimum and loss of phase of the subharmonic on emergence from it. These phenomena are indicative of chaos. They indicate that the solar dynamo is chaotic and is operating in a region close to the transition between period doubling and chaos. Since Maunder type minima reoccur irregularly for millennia, it appears that the Sun remains close to this transition to and from chaos. We postulate this as a universal characteristic of solar type stars caused by feedback in the dynamo number.     

Long-term cyclic variations of prominences, green and red coronae over solar cycles

Long-term cyclic variations in the distribution of prominences and intensities of green (530.3 nm) and red (637.4 nm) coronal emission lines over solar cycles 18–23 are presented. Polar prominence branches will reach the poles at different epochs in cycle 23: the north branch at the beginning in 2002 and the south branch a year later (2003), respectively. The local maxima of intensities in the green line show both poleward- and equatorward-migrating branches. The poleward branches will reach the poles around cycle maxima like prominences, while the equatorward branches show a duration of 18 years and will end in cycle minima (2007). The red corona shows mostly equatorward branches. The possibility that these branches begin to develop at high latitudes in the preceding cycles cannot be excluded.     

Identification of Gleissberg Cycles and a Rising Trend in a 315-Year-Long Series of Sunspot Numbers

We show in this short note that the method of singular spectrum analysis (SSA) is able to clearly extract a strong, clean, and clear component from the longest available sunspot (International Sunspot Number, ISN) time series (1700?–?2015) that cannot be an artifact of the method and that can be safely identified as the Gleissberg cycle. This is not a small component, as it accounts for 13% of the total variance of the total original signal. Almost three and a half clear Gleissberg cycles are identified in the sunspot number series. Four extended solar minima (XSM) are determined by SSA, the latest around 2000 (Cycle 23/24 minimum). Several authors have argued in favor of a double-peaked structure for the Gleissberg cycle, with one peak between 55 and 59 years and another between 88 and 97 years. We find no evidence of the former: solar activity contains an important component that has undergone clear oscillations of \(\approx90\) years over the past three centuries, with some small but systematic longer-term evolution of “instantaneous” period and amplitude. Half of the variance of solar activity on these time scales can be satisfactorily reproduced as the sum of a monotonous multi-secular increase, a \(\approx90\)-year Gleissberg cycle, and a double-peaked (\(\approx10.0\) and 11.0 years) Schwabe cycle (the sum amounts to 46% of the total variance of the signal). The Gleissberg-cycle component definitely needs to be addressed when attempting to build dynamo models of solar activity. The first SSA component offers evidence of an increasing long-term trend in sunspot numbers, which is compatible with the existence of the modern grand maximum.     

Some properties of a two-body system under the influence of the Galactic tidal field

In this paper the effect of the Galactic tidal field on a Sun–comet pair will be considered when the comet is situated in the Oort cloud and planetary perturbations can be neglected. First, two averaged models were created, one of which can be solved analytically in terms of Jacobi elliptic functions. In the latter system, switching between libration and circulation of the argument of perihelion is prohibited. The non-averaged equations of motion are integrated numerically in order to determine the regions of the ( e ,  i ) phase space in which chaotic orbits can be found, and an effort is made to explain why the chaotic orbits manifest in these regions only. It is evident that for moderate values of semimajor axis, a ∼50 000 au , chaotic orbits are found for ( e <0.15 , 40°≤ i ≤140°) as determined by integrating the evolution of the comet over a period of 10⁴ orbits. These regions of chaos increase in size with increasing semimajor axis. The typical e-folding times for these orbits range from around 600 Myr to 1 Gyr and thus are of little practical interest, as the time-scales for chaos arising from passing stars are much shorter. As a result of Galactic rotation, the chaotic regions in ( e ,  i ) phase space are not symmetric for prograde and retrograde orbits.     

Spatial inhomogeneity of the martian subsurface water distribution: implication from a global water cycle model

In an effort to test and to understand the global hydrogen distribution in the shallow subsurface of Mars retrieved by the Mars Odyssey gamma-ray spectrometer, the present state and movement of water are investigated by a coupled global subsurface-atmosphere water cycle model. It was found that the observed global subsurface hydrogen distribution is largely consistent with the modeled global water cycle, so a large fraction of hydrogen is likely to exist as water, at low and mid latitudes in the form of adsorbed water. Under the present climate the water content in the shallow subsurface becomes higher in the northern hemisphere than in the southern hemisphere as a result of global water cycle, regardless of the initial water distribution in the soil or adsorptive capacity. The higher annual maximum soil temperature in the south, stronger net northward transport of atmospheric water vapor, and the emission of vapor from the northern residual polar cap in northern summer contribute to this hemispheric asymmetry. The generally higher adsorptive capacity of clay minerals in the northern plains may further increase this bias. The longitudinal inhomogeneity is caused by several factors, such as thermal inertia, adsorptive capacity, and atmospheric surface pressure. The water abundance is locally high in low thermal inertia regions (e.g., Arabia Terra) and at deep places where the surface pressure is high (e.g., Hellas); it is low in soil with a low adsorptive capacity (e.g., Tharsis) and high thermal inertia regions (e.g., Solis Planum). Most of the soil humidity near the surface at low and mid latitudes may originate from the atmosphere. The model implies that the upper soil layer should be largely ice-free because otherwise an excessive sublimation and vapor emission into the atmosphere in warm seasons would violate the observational constraints. Moreover, the more uniform latitudinal variation of the observed hydrogen abundance near the surface compared to that of deeper layers is indicative of the presence of adsorbed water instead of ground ice because the adsorbed water content does not as steeply depend on latitude as the ground ice stability. Concerning the regolith mineralogy, montmorillonite can much better account for the observed water cycle than palagonite. While the presence of permanent ground ice appears likely in the polar region below a thin layer, large seasonal cycle of phase change between pore ice and adsorbed water may be possible. Regolith adsorption/desorption is neither negligible nor crucial for the seasonal atmospheric water cycle, but the surface-atmosphere coupling is a major prerequisite for the long-term evolution of subsurface water distribution.     

Phase Mixing in Unperturbed and Perturbed Hamiltonian Systems

This paper summarises a numerical investigation of phase mixing in time-independent Hamiltonian systems that admit a coexistence of regular and chaotic phase space regions, allowing also for low amplitude perturbations idealised as periodic driving, friction, and/or white and coloured noise. The evolution of initially localised ensembles of orbits was probed through lower order moments and coarse-grained distribution functions. In the absence of time-dependent perturbations, regular ensembles disperse initially as a power law in time and only exhibit a coarse-grained approach towards an invariant equilibrium over comparatively long times. Chaotic ensembles generally diverge exponentially fast on a time scale related to a typical finite time Lyapunov exponent, but can exhibit complex behaviour if they are impacted by the effects of cantori or the Arnold web. Viewed over somewhat longer times, chaotic ensembles typical converge exponentially towards an invariant or near-invariant equilibrium. This, however, need not correspond to a true equilibrium, which may only be approached over very long time scales. Time-dependent perturbations can dramatically increase the efficiency of phase mixing, both by accelerating the approach towards a near-equilibrium and by facilitating diffusion through cantori or along the Arnold web so as to accelerate the approach towards a true equilibrium. The efficacy of such perturbations typically scales logarithmically in amplitude, but is comparatively insensitive to most other details, a conclusion which reinforces the interpretation that the perturbations act via a resonant coupling.     

Maximum and minimum temperatures at armagh observatory, 1844–1992, and the length of the sunspot cycle

The question of whether or not the Earth's climate is influenced by solar activity has received considerable attention since the mid-nineteenth century. Most investigations have adopted the sunspot number as the parameter of solar activity. Recently, however, it has been shown by Friis-Christensen and Lassen (1991) that the mean northern hemisphere temperature, from 1861–1990, follows a strikingly similar trend to thelength of the sunspot cycle, suggesting that the recent global warming could, at least in part, arise from changes in solar activity. In view of the importance of this result, we have examined a set of continuous meteorological records, maintained at Armagh Observatory since 1844, to assess, first, whether data from a single site can give meaningful information on global trends, and second, whether the data from this particular site for the period 1844–1866 can be used to extend the baseline of the comparison with solar activity. We find that both are indeed the case and that there is a strong correlation between the solar cycle length and the mean temperature at Armagh over the past 149 years.     

Determination of the Coronal and Interplanetary Magnetic Field Strength and Radial Profiles from Large-Scale Photospheric Magnetic Fields

We propose a new model for the magnetic field at different distances from the Sun during different phases of the solar cycle. The model depends on the observed large-scale non-polar (\({\pm}\, 55^{\circ }\)) photospheric magnetic field and on the magnetic field measured at polar regions from \(55^{\circ }\) N to \(90^{\circ }\) N and from \(55^{\circ }\) S to \(90^{\circ }\) S, which are the visible manifestations of cyclic changes in the toroidal and poloidal components of the global magnetic field of the Sun. The modeled magnetic field is determined as the superposition of the non-polar and polar photospheric magnetic field and considers cycle variations. The agreement between the model predictions and magnetic fields derived from direct in situ measurements at different distances from the Sun, obtained with different methods and at different solar activity phases, is quite satisfactory. From a comparison of the magnetic fields as observed and calculated from the model at 1 AU, we conclude that the model magnetic field variations adequately explain the main features of the interplanetary magnetic field (IMF) radial, \(B_{\mathrm{x}}\), component cycle evolution at Earth’s orbit. The modeled magnetic field averaged over a Carrington rotation (CR) correlates with the IMF \(B_{\mathrm{x}}\) component also averaged over a CR at Earth’s orbit with a coefficient of 0.691, while for seven CR-averaged data, the correlation reaches 0.81. The radial profiles of the modeled magnetic field are compared with those of already existing models. In contrast to existing models, ours provides realistic magnetic-field radial distributions over a wide range of heliospheric distances at different cycle phases, taking into account the cycle variations of the solar toroidal and poloidal magnetic fields. The model is a good approximation of the cycle behavior of the magnetic field in the heliosphere. In addition, the decrease in the non-polar and polar photospheric magnetic fields is shown. Furthermore, the magnetic field during solar cycle maxima and minima decreased from Cycle 21 to Cycle 24. This implies that both the toroidal and poloidal components, and therefore the solar global magnetic field, decreased from Cycle 21 to Cycle 24.     

Long term evolution and chaotic diffusion of the insolation quantities of Mars

As the obliquity of Mars is strongly chaotic, it is not possible to give a solution for its evolution over more than a few million years. Using the most recent data for the rotational state of Mars, and a new numerical integration of the Solar System, we provide here a precise solution for the evolution of Mars' spin over 10 to 20 Myr. Over 250 Myr, we present a statistical study of its possible evolution, when considering the uncertainties in the present rotational state. Over much longer time span, reaching 5 Gyr, chaotic diffusion prevails, and we have performed an extensive statistical analysis of the orbital and rotational evolution of Mars, relying on Laskar's secular solution of the Solar System, based on more than 600 orbital and 200,000 obliquity solutions over 5 Gyr. The density functions of the eccentricity and obliquity are specified with simple analytical formulas. We found an averaged eccentricity of Mars over 5 Gyr of 0.0690 with standard deviation 0.0299, while the averaged value of the obliquity is 37.62° with a standard deviation of 13.82°, and a maximal value of 82.035°. We find that the probability for Mars' obliquity to have reached more than 60° in the past 1 Gyr is 63.0%, and 89.3% in 3 Gyr. Over 4 Gyr, the position of Mars' axis is given by a uniform distribution on a spherical cap limited by the obliquity 58.62°, with the addition of a random noise allowing a slow diffusion beyond this limit. We can also define a standard model of Mars' insolation parameters over 4 Gyr with the most probable values 0.068 for the eccentricity and 41.80° for the obliquity.     

Cosmological variations in the space-time distribution of absorption systems in quasar spectra

Based on the catalog of Junkkarinen et al. (1991), we analyze the space-time distribution of absorption systems in quasar spectra at cosmological redshifts z=0–3.7. The z distribution of absorbing matter is shown to have a pattern of alternating maxima (peaks) and minima (dips). Within statistical uncertainty, the positions of such peaks and dips do not depend on the direction of observation. We have found a periodicity in the distribution of absorption systems in the functions ln(1+z) and (1+z)^?1/2. We show that the derived sequence of maxima and minima in the space-time distribution of absorbing matter is not a manifestation of the spatial large-scale structure alone, but it is more likely temporal in nature. The most probable source of the putative structure could be an alternation (in the course of cosmological evolution) of pronounced and depressed epochs with a characteristic time interval of 520±160 Myr, depending on the cosmological model chosen.     

The Gleissberg Cycle of Minima

In this short article we show that the sunspot cycle minima exhibit a long cycle (Gleissberg) in addition to the 11-yr cycle. From 1750 onwards, three periods of the Gleissberg cycle can be detected.     

Modeling of Local Magnetic Field Enhancements within Solar Flux Ropes

To model and study local magnetic-field enhancements in a solar flux rope we consider the magnetic field in its interior as a superposition of two linear (constant α) force-free magnetic-field distributions, viz. a global one, which is locally similar to a part of the cylinder, and a local torus-shaped magnetic distribution. The newly derived solution for a toroid with an aspect ratio close to unity is applied. The symmetry axis of the toroid and that of the cylinder may or may not coincide. Both the large and small radii of the toroid are set equal to the cylinder’s radius. The total magnetic field distribution yields a flux tube which has a variable diameter with local minima and maxima. In principle, this approach can be used for the interpretation and analysis of solar-limb observations of coronal loops.     

Angular velocity during the cycle deduced using the sunspot group age selection methodology

We have used the “age selection methodology” (ASM) (Zappalá and Zuccarello 1991) to study the variability of the sunspot groups angular velocity during the activity cycle. The ASM allows us to separate the contribution of Young Sunspot Groups (YSG) from that of Recurrent ones (RSG) in the Ω(θ) determination and therefore to evaluate whether the increase in angular velocity during minima (reported in literature using all sunspot groups as tracers), is due to a greater statistical weight of YSG on RSG or whether it reflects a global characteristic of the Sun. The results obtained from the analysis of sunspot groups data collected during the period 1874‐1981 (Greenwich Photoheliographic Results) indicate that during minima, besides the fact that the percentage of RSG drops to ≤ 5%, both YSG and RSG show the same increase in angular velocity, i.e. 0.16 degrees/day. Comparing our results with those reported in literature and taking into account the internal angular velocity as deduced by p‐mode oscillations, it is possible to conclude that the observed higher angular velocity of the Sun during minima concerns several layers of the Sun.     

Spectral features of burst radio emission over the solar cycle

We have investigated common burst spectral features for the 20th cycle of solar activity. The maximum daily radio fluxes in 8 frequency ranges are analysed. For every year the classification of these daily spectra is obtained by cluster analysis methods. There are two spectral minima for average spectra of clusters (in frequency ranges 4–3 and 0.5–0.25 GHz). As a rule their positions do not change during the solar cycle.Every annual spectrum of weak bursts has three minima (in frequency ranges 4–3, 2–1, and 0.5–0.25 GHz). The positions of these minima remain invariable during the solar cycle. But anuual spectra of strong bursts depend essentially on the phase of solar activity.The basic features of most burst spectra can be explained by gyrosynchrotron radiation of thermal and nonthermal electrons and plasma radiation at the plasma frequency and its second harmonic.     

Areas of Polar Coronal Holes from 1996 Through 2010

Polar coronal holes (PCHs) trace the magnetic variability of the Sun throughout the solar cycle. Their size and evolution have been studied as proxies for the global magnetic field. We present measurements of the PCH areas from 1996 through 2010, derived from an updated perimeter-tracing method and two synoptic-map methods. The perimeter-tracing method detects PCH boundaries along the solar limb, using full-disk images from the SOlar and Heliospheric Observatory/Extreme ultraviolet Imaging Telescope (SOHO/EIT). One synoptic-map method uses the line-of-sight magnetic field from the SOHO/Michelson Doppler Imager (MDI) to determine the unipolarity boundaries near the poles. The other method applies thresholding techniques to synoptic maps created from EUV image data from EIT. The results from all three methods suggest that the solar maxima and minima of the two hemispheres are out of phase. The maximum PCH area, averaged over the methods in each hemisphere, is approximately 6 % during both solar minima spanned by the data (between Solar Cycles 22/23 and 23/24). The northern PCH area began a declining trend in 2010, suggesting a downturn toward the maximum of Solar Cycle 24 in that hemisphere, while the southern hole remained large throughout 2010.     

Influence of the Solar Global Magnetic-Field Structure Evolution on CMEs

We consider the influence of the solar global magnetic-field structure (GMFS) cycle evolution on the occurrence rate and parameters of coronal mass ejections (CMEs) in Solar Cycles 23?–?24. It has been shown that, over solar cycles, CMEs are not distributed randomly, but they are regulated by evolutionary changes in the GMFS. It is proposed that the generation of magnetic Rossby waves in the solar tachocline results in the GMFS cycle changes. Each Rossby wave period favors a particular GMFS. It is proposed that the changes in wave periods result in GMFS reorganization and consequently in CME location, occurrence rate, and parameter changes. The CME rate and parameters depend on the sharpness of the GMFS changes, the strength of the global magnetic field, and the phase of a cycle.