Relativistic time scales in the solar system

This paper deals with a self-consistent relativistic theory of time scales in the Solar system based on the construction of the hierarchy of dynamically non-rotating harmonic reference systems for a four-dimensional space-time of general relativity. In our approach barycentric (TB) and terrestrial (TT) times are regarded as the coordinate times of barycentric (BRS) and geocentric (GRS) reference systems, respectively, with an appropriate choice of the units of measurement. This enables us to avoid some of the inconsistencies and ambiguities of the definitions of these scales as these are currently applied. International atomic time (TAI) is shown to be the physical realization of TT on the surface of the Earth. This realization is achieved by a specific procedure to average the readings of atomic clocks distributed over the terrestrial surface, all of them synchronized with respect to TT. Extending TAI beyond the Earth's surface may be performed along a three-dimensional hypersurface TT = const. The unit of measurement of TAI coincides with TB and TT units and is equal to the SI second on the surface of the geoid in rotation. Due to the specific choice of the units of measurement the TB scale differs from the TT (TAI) scale only by relativistic nonlinear and periodic terms resulting from the planetary and lunar theories of motion. The proper time ₀ of any terrestrial observer coincides with the coordinate time of the corresponding topocentric reference system (TRS) evaluated at its origin. ₀ is reacted to TT (TAI) by the relativistic transformation involving the GRS velocity of the observer, its height above the geoid and the quadrupole tidal gravitational potential of the external masses. The impact of introducing TB and TT on the units of measurement of length and the basic astronomical constants is discussed.     

Global magnetic activity in 22-year solar cycles

Properties of even and odd 11-year solar cycles as part of the 22-year magnetic cycle have been studied on the basis of the data on the zonal structure of the large-scale magnetic field, of polar faculae activity cycles, duration of 11-year cycles, high-latitude prominence areas, inclinations of the coronal streamers, velocity of magnetic neutral line migration, and peculiarities of the polar magnetic field reversal. It is shown that the properties of the odd cycle depend on those of the preceding even cycle. The 22-year magnetic cycle, consisting of an even and odd cycle, is a unified dynamic process. The new data obtained show that the poloidal magnetic fieldB(p) of ‘+’ and ‘−’ polarity for the new 22-year magnetic cycle is formed simultaneously, possibly in deep layers of the Sun in the form of a certain magnetic configuration, containing alternating ‘+’ and ‘−’ polarities of the field.     

Maunder convection mode on the Sun and long solar activity minima

A model of velocity field oscillations in the solar convective zone is suggested. The system of convective equations is investigated for a thin rotating spherical envelope when the rotation velocity is depended on the coordinates. It is shown that two different structures of convective cells (longitudinal, or latitudinal) can exist in the envelope depending on gradients values of the rotation velocity and Prandtl number. It is supposed that two different regimes of convection (stationary and autofluctuating) are possible in the envelope when the angular velocity gradients are determined by the convection itself. In the case of autofluctuating regime the alternation of longitudinal and latitudinal structure of convection is realized. If one assumes that on the Sun there exists an autooscillating convection regime, then the periods of the existence of latitudinal convection structure may be associated with long periods of activity minima since according to Cowling's theorem, the action of the axisymmetric magnetic field generation mechanism is impossible under conditions of axisymmetric velocity structures.     

Spatial structure of solar wind at a time of minimum solar activity

Interplanetary scintillation measurements of the solar wind speed in 1976 show the expected trend that higher speeds are found at higher heliographic latitudes or larger angular distances from the interplanetary current sheet deduced from coronal observations. A careful examination of variations in the speed where the current sheet departs from the equator reveals that the wind speed is not symmetrically distributed about the equator, and the minimum speed occurs at the current sheet. The variation of the speed u with the angular distance from the current sheet, λ, during 1976 is

$\text{u(λ) = 800}\text{sin}{}^{\mathrm{?2\lambda }}\text{+ 350}\text{km/s}\text{,|λ| ?35° = 600}\text{km/s}\text{, |λ| > 35°}$

.     

Discrete cellular scales of solar convection

The theoretical power spectrum of velocity fields and flux fluctuations at the solar photosphere is calculated using a quasi-nonlinear framework of superposition of unstable convective eigenmodes excited in the solar convection zone. It is demonstrated that this power spectrum exhibits at least three distinct peaks corresponding to granulation, mesogranulation and supergranulation. The vertical velocity and the brightness fluctuation at the solar surface are found to be correlated. The theoretical framework can be adopted for application to other types of stars in order to predict the dominant length scales in the power spectrum of convection in these stars.     

Structure of the solar photospheric convection on subgranulation scales

We investigate the structure of convective flows in the solar photosphere on subgranulation scales. The solar granulation pattern is reproduced by solving the inverse problem of nonequilibrium radiation transfer on the basis of the profiles of the neutral iron line λ 523.42 nm. The wave motions are excluded by the k-ω filtration. The line-of-sight velocity has an asymmetric distribution inside the convective flows in large granules (1.5″ and larger) in the lower photosphere and at the bottom of the middle photosphere. This asymmetry is weaker in the upper photosphere. For smaller flows the distribution is more symmetric at all heights. The asymmetry of the temperature distribution is less pronounced. Large convective flows were found to have a fine structure: they are fragmentized into several smaller flows. The fine structure of large flows and spatial smearing are responsible for the observed asymmetry of the convection velocity distribution inside flows.     

Hysteresis,time lag,and relation between solar activity and cosmic rays during solar cycle 24

We study galactic cosmic ray (GCR) modulation during solar cycle 24. For this study we utilize neutron monitor data together with sunspot number (SSN) and 10.7 cm solar radio flux (SRF) data. We plot hysteresis curve between the GCR intensity and SSN, and GCR intensity and SRF. We performed time-lag correlation analysis to determine the time lag between GCR intensity and solar activity parameters. The time lag is determined not only for the whole solar cycle, but also during the two polarity states of the heliosphere (A<0 and A>0) in solar cycle 24. We notice differences in time lags during two polarity epochs of the solar cycle. We discuss these differences in the light of existing modulation models. We compare the results of this very weak solar activity cycle with the corresponding results reported for the previous comparatively more active solar cycles.     

Solar and geomagnetic activity on a long time scale: Reconstructions and possibilities for predictions

Using two mathematical methods based on the wavelet transform and nonlinear dynamics, we reconstructed the behavior of the aa-index of geomagnetic activity in the past. Two versions of the series are provided: for the last 400 years and on an almost 1000-year time scale. We consider typical values of the aa-index at grandiose extrema of solar activity. The same high level of geomagnetic activity as that observed in the last 50 years is shown to have also taken place in the early 12th and late 14th centuries. We suggest an extended time series of A-indices of the large-scale solar magnetic field. On the 400-year time scale, we confirmed that the large-scale magnetic field develops earlier than the magnetic fields of active regions. Ohl’s prediction method was verified on the same time scale.     

Spatial distribution of the N-S asymmetry of solar activity and its time variations

The 1943–2001 data on the brightness of the coronal green λ530.3 nm line are used to investigate the surface distribution of the north-south (N-S) asymmetry index A. Synoptic maps of the asymmetry index in 784 successive Carrington rotations have been constructed. The results are presented in the form of a movie that visualizes the time variation in the spatial distribution of the asymmetry. Examination of a series of synoptic maps shows that the time variation in the general distribution of the A index over the solar surface has a number of peculiar features. In particular, the latitude-longitude regions with the dominance of the green line brightness in one of the hemispheres are replaced by similar (in shape) regions with its dominance in the other hemisphere after 14–18 rotations-in other words, the map, as it were, turns into its negative. This may be a manifestation of the quasi-biennial oscillations in the N-S asymmetry. The synodic rotation period of the asymmetry “structures” has been determined. It has turned out to be equal to the period of the fast coronal rotation mode found previously from the large-scale brightness distribution of the coronal green line, i.e., this is 27 days on the equator and slightly more than 28 days at high latitudes. The N-S asymmetry and its characteristics should be taken into account when considering the dynamo mechanism.     

Soft solar X-rays and solar activity

Soft X-radiation between 8–12 Å was found to be emitted from the Sun at the time of four optically-identified major systems of loop prominences. The peak emission rates and time-integrated X-ray energies are very similar for three of the events while the fourth appeared to emit X-rays only weakly. The data are not consistent with a compression-condensation model for the loops, and support the fast-proton injection model. Proton injection may take place on a long time scale.     

Soft solar X-rays and solar activity

Soft solar X-rays in the wavelength interval 8–12 Å were observed from OSO III. The totality of the observations that were made between 9 March, 1967, and 18 May, 1968, is summarized graphically and compared to the course of solar activity as observed at other wavelengths, with particular emphasis upon visible activity.     

On time variations of the solar differential rotation law and asymmetry of the global distribution of the solar activity

The relation between the systematic time variations of the solar differential rotation at middle latitudes and the asymmetry of global distribution of the solar activity is discussed in connection with the study of the maintenance of the solar differential rotation. The systematic variations at middle latitudes are inferred from a peculiar correlation in the time variations of the solar differential rotation which is shown in this paper to be implied in the data of Howard and Harvey (1970) of spectroscopic measurements of rotational velocities. If we adopt the working hypothesis of the solar equatorial acceleration maintained by the angular momentum transport due to the very large scale convection, the two phenomena are related through the concurrent presence of the neighboring modes with the presumed dominant mode of the very large scale convection.     

On experimental evidence of chaotic dynamics over short time scales in solar wind and cometary data using nonlinear prediction techniques

Strong indications of chaotic dynamics underlying in the interplanetary and cometary magnetic field fluctuations over short time scales are identified using HEOS-2 spacecraft (at 1 AU), Pioneer 10 (at 4.8 AU), Pioneer 11 (at 20 AU) and ICE (Giacobini-Zinner cometary environment) high-resolution measurements. Other non-chaotic candidate processes, such as linear deterministic models, fractal Brownian motion, and linear gaussian stochastic models are rejected at a high confidence level using nonlinear prediction methods. Experimental proofs of phase correlations are obtained. Assuming chaotic dynamics, estimations of the Kolmogorov-Sinai entropy are provided.     

Global isothermal oscillations in the solar photosphere

Observational data on solar irradiance oscillations from the VIRGO (SOHO) and DIFOS-F (CORONAS-F) experiments are used to obtain stratifications of perturbed hydrogen concentrations that produce isothermal oscillations in the solar photosphere. The study reveals the nodes and antinodes of the oscillations in the solar photosphere. A simulation of long-period isothermal oscillations from the DIFOS data shows that the nodes and antinodes of Δn/n tend to shift towards lower photosphere layers with a decrease in the oscillation frequency.     

Global modes constituting the solar magnetic cycle

The sunspot occurrence probability defined in Paper I is used to determine the Legendre-Fourier (LF) terms in the rate of emergence of toroidal magnetic flux,Q(, t), above the photosphere per unit latitude interval, per unit time. Assuming that the magnetic flux tubes whose emergence yields solar activity are produced by interference of global MHD waves in the Sun, we determine how the amplitudes and phases of the LF terms in the toroidal magnetic fieldB , representing the waves, will be related to those of the LF terms inQ(, t). The set of LF terms in Q that represents the set of waves whose interference produces most of the observed sunspot activity is {l = 1, 3, , 13;v =nv _*,n = 1, 3, 5}, wherev _* = 1/21.4 yr^–1. However, among the shapes of sunspot cycles modeled using various sets of the computed LF terms the best agreement with the observed shape, for each cycle, is given by the set {l = 3 orl = 3, 5; andn = 1, 3 orn = 1, 3, 5}. The sets of terms: {l = 1, 3, 5, 7;n = 1}, {l = 1, 3, 5, 7;n = 3}, {l = 9, 11, 13, 15;n = 1} and {l = 9, 11, 13, 15;n = 3} seem to represent four modes of global MHD oscillation. Correlations between the amplitudes (and phases) of LF terms in different modes suggest possible existence of cascade of energy from constituent MHD waves of lowerl andn to those of higherl andn. The spectrum of the MHD waves trapped in the Sun may be maintained by the combined effect of this energy cascade and the loss of energy in the form of the emerging flux tubes. The primary energy input into the spectrum may be occurring in the mode {l = 1, 3, 5, 7;n = 1). As expected from the above phenomenological model, the size of a sunspot cycle and its excess over the previous cycle are well correlated (e.g., 90%) to the phase-changes of the two most dominant oscillation modes during the previous one or two cycles. These correlations may provide a physical basis to forecast the cycle sizes.     

Global modes constituting the solar magnetic cycle

The spherical-harmonic-Fourier analysis of the Sun's magnetic field inferred from the Greenwich sunspot data is refined and extended to include the full length (1874–1976) of the data on the magnetic tape provided by H. Balthasar. Perspective plots and grey level diagrams of the SHF power spectra for the odd and the even degree axisymmetric modes are presented. Comparing these with spectra obtained from two simulated data sets with random redistribution within the wings in the butterfly diagrams, we conclude that there is no clear evidence for the existence of any relation between the harmonic degree and the temporal frequency of the power concentrations of the inferred field. Apart from the power ridge in the narrow frequency band at 1/21.4 y ^–1, and low ridges at odd multiples of this frequency, there are no other spectral features. This strongly suggests that the solar magnetic cycle consists of some global oscillations of the Sun forced at a frequency 1/21.4 y ^–1 and, perhaps, weak resonances at its odd harmonics. The band width of the forcing frequency seems to be much less than 1/107 y ^–1. In case the global oscillations are torsional MHD, the significance of their parity and power peak is pointed out.     

Global modes constituting the solar magnetic cycle

We show that the axisymmetric odd degree SHF modes of 21.4-yr periodicity and degrees l 29 in the solar magnetic field (as inferred from sunspot data during 1874–1976), are at least approximately stationary. Among the sine and cosine components of these SHF modes we find four groups, each defining the geometry of a coherent global oscillation characterized by a distinct power hump and its own level of variation. The first two of these geometrical eigenmodes (viz., B ₁ and B ₂), define the large-scale structure of the butterfly diagrams. Remaining SHF modes define the orderliness of the field distribution even within the wings of the butterflies down to scales l 29. These include the geometrical eigenmodes B ₃ and B ₄, which are not present in simulated data sets in which the latitudes of the sunspot groups are randomly redistributed within the wings of the butterflies.Superposition of B ₁, B ₂, B ₃, and B ₄ is necessary and sufficient to reproduce important observed properties of the latitude-time distribution of the real field, not only in the sunspot zone, but also in the middle (35°–75°) and the high (75°) latitudes, with appropriate relative orders of magnitude and phases. Thus, B ₁, B ₂, B ₃, and B ₄ seem to represent really existing global oscillations in the Sun's internal magnetic field. The geometrical form of B ₁ may also be the form of the forcing oscillation.