The solar dynamo and integrated irradiance variations in the course of the 11-year cycle

Abstractthe effect of the large-scale magnetic fields generated by the solar dynamo on the radiation flux issuing from the convection zone is studied. A governing equation describing convective heat transfer is obtained in the framework of mean-field magnetohydrodynamics, with account for the influence of magnetic fields and differential rotation on the energy budget of the convection zone. The principal effects are illustrated using a one-dimensional numerical model. Calculations indicate that the influence of large-scale magnetic fields can modulate the solar irradiance with a relative amplitude of ～0.07%.     

Magnetohydrodynamic model of the solar tachocline

The tachocline is a thin layer providing the transition from differential to uniform rotation in the upper region of the solar radiative zone, which can be explained as an effect of the magnetic field if the magnetic field lines are closed inside the radiative zone. It is shown that the confined field structure that is necessary for the tachocline formation can arise due to the penetration of meridional flow from the convective envelope to the radiative zone. The time for the distortion of the magnetic field by the penetrating flow is short compared to the time for diffusion to the penetration depth. The most long-lived mode of the poloidal field has a confined geometry, and the Ohmic lifetime of this mode exceeds the age of the Sun. The calculated distribution of the angular velocity in the radiative zone taking into account such a field shows a thin tachocline.     

Form of the latitude distribution of sunspot activity

The spatial (latitude) distribution of sunspots is studied, including its dependence on solar activity. It is shown that the latitude distributions of sunspots for a given year can be approximately described by the normal law, with its variance being a linear function of the current level of solar activity. Thus, an increase in activity is accompanied by an expansion of the zone of solar activity, in good agreement with earlier results. As the solar activity increases, the width of the zone of sunspot generation and the latitude maximum of the sunspot density grow somewhat more slowly than the number of sunspots, in agreement with observations. The results obtained can be used to reconstruct the spatial distributions of sunspots in the past, interpret the magnetic activity of stars, and address the requirements of the dynamo theory in the form of constraints imposed on models of cyclicity.     

Large-scale solar magnetic field: Latitudinal dependence

Large-scale solar magnetic fields in the latitude range 50° S–50° N are analyzed in detail for a long time interval (1915–1990). We are primarily concerned with the two types of large-scale fields forming the two-and four-sector patterns on the Sun. The rotation parameters of these structures are obtained for all latitudes considered. The contribution of the two-sector structure grows and that of the four-sector structure decreases toward high latitudes. The magnetic field is activated simultaneously over a wide latitude range. Since both magnetic-field systems exhibit quasi-rigid rotation, their current systems must either be concentrated in a narrow latitude range or be situated beneath the convection zone, where rotation is only weakly differential. A period of about three years is manifest in the difference between the rotation periods for the two types of magnetic field. Physically, this may imply that these oscillations are external with respect to any level, and there is some phase delay due to their propagation from one level to another. We can conclude with a fair degree of certainty that as the activity level rises, the rotation speed decreases, and vice versa.     

Long and short term relationships between solar wind velocity and geomagnetic field at low latitudes

Solar wind velocity control of low latitude geomagnetic field both on long and short term basis is studied. It is shown that semiannual averages of the low latitude field is inversely related to solar wind velocity and that there is a dominant local time dependence of the relationship. Strongest correlation are confined to the local afternoon hours. It is also shown that for a duration when the solar wind velocity exhibits significant recurrent pattern the low latitude geomagnetic field also depicts strong solar synodic rotation periodicity of 27 days with significant coherence with velocity. The low latitude field on a short term basis is influenced by variable solar wind velocity with a delay of about 1–2 days. During the period of systematic recurrent pattern in solar wind velocity even the quiet-time night field at equatorial and low latitudes show a strong dependence on velocity indicative of the solar wind control of the quiet-time proton belt encompassing the earth.     

Cyclic variations in the differential rotation of the solar corona

The rotation of the solar corona is analyzed using the original database on the brightness of the FeXIV 530.3 nm coronal green line covering six recent activity cycles. The rate of the differential rotation of the corona depends on the cycle phase. In decay phases, there are only small differences in the rotation, which are similar to that of a rigid body. The differences are more significant (though less pronounced than in the photosphere) during rise phases, just before maxima, and sometimes at maxima. The total rate of the coronal rotation is represented as a superposition of two, i.e., fast and slow modes. The synodic period of the fast mode is approximately 27 days at the equator and varies slightly with time. This mode displays weak differences in rotation and is most pronounced in the middle of decay phases. The slow mode is manifested only at high latitudes during the rise phases of activity, and displays a mean period of 31 days. The relative contribution of each mode to the total rotational rate is determined as a function of time and heliographic latitude. These results indicate that the structure of the velocity field in the convective zone must also vary with time. This conclusion can be verified by helioseismology measurements in the near future.     

Generation of solar magnetic fields by the αδΘ dynamo

We consider a solar dynamo mechanism that generates large-scale magnetic fields due to the combined action of cyclonic flows (the α effect), differential rotation (the Θ effect), and the non-uniformity of large-scale magnetic fields (the Θ × J effect). Our results are based on numerical model which takes into account currently available data on the differential rotation of the convection zone and the intensity of convective flows in the solar interior. A reasonable choice of parameters characterizing the intensity of magnetic-field generation by the α and Θ × J mechanisms can account for an oscillatory dynamo regime with properties similar to the 22-year magnetic-activity cycle of the Sun. We analyze the nonlinear saturation of the generation effects in the large-scale magnetic field, due to either magnetic stresses or the conservation of magnetic helicity. Allowance for the helicity of the small-scale magnetic fields is of crucial importance in limiting the energy of the generated large-scale magnetic field.     

Magnetic fields in the radiative-transport zone and the solar cycle

It is shown that a hypothetical relict magnetic field in the solar radiative-transport zone that penetrates into the convective zone would affect the solar dynamo, resulting in radical changes in the butterfly diagrams. This would transform the traveling waves of activity into standing waves. A comparison of our results with the well-known butterfly diagrams for the Sun gives an upper limit of the order of some tens G for the value of relict magnetic field penetrating into the solar convective zone. At the same time, it is not ruled out that such relict magnetic fields in other solar-type stars are strong enough to make the activity waves become standing waves.     

Near-polar starspots and polar dynamo waves

A possible mechanism for the formation of near-polar magnetic spots on some stars with convective envelopes is proposed. The mechanism is based on the idea that the maximum of the dynamo waves that are excited in thin convective shells by the dynamo mechanism is shifted appreciably from the maximum of the magnetic-field sources in the direction of motion of the dynamo wave. If there is no region of super-rotation near the equator for some reason (as a consequence of disruption due to tidal interaction with a companion in a binary system, for example) and the wave of stellar activity propagates toward the poles rather than toward the equator, this maximum will be in the near-polar regions.     

Parity fluctuations in stellar dynamos

Observations of the solar butterfly diagram from sunspot records suggest persistent fluctuations in parity, away from the overall, approximately dipolar pattern. A simple mean-field dynamo model is used with a solar-like rotation law and perturbed α effect. The parity of the magnetic field relative to the rotational equator can demonstrate can be described as resonance behavior, while the magnetic energy behaves in a more or less expected way. Possible applications of this effect are discussed in the context of various deviations of the solar magnetic field from dipolar symmetry, as reported from analyses of archival sunspot data. The model produces fluctuations in field parity, and hence in the butterfly diagram, that are consistent with observed fluctuaions in solar behavior.     

Helioseismic models of the sun with a low heavy element abundance

Helioseismology and neutrino experiments probing the internal structure of the Sun have yieldedmuch information, such as the adiabatic elasticity index, density, and sound speed in the convective and radiative zones, the depth of the convective zone, and the flux of neutrinos from the core. The standard model of the Sun does not adequately reproduce these characteristics, with models with low heavy element contents (mass fraction of metals Z = 0.013 in the convective zone) deviating from the helioseismic data appreciably more strongly than models with high heavy element contents (Z = 0.018). However, a spectroscopic low Z value is supported by studies reconstructing the Γ ₁ profile in the adiabatic part of the convective zone based on the oscillation frequencies. Models of the convective zone show a good agreement precisely for low Z values. This study attempts to construct a model for the Sun with low Z that satisfies the helioseismic constraints. This model requires changes in the p + p reaction cross section and the opacities in the radiative zone. In our view, the helioseismic result for the mass concentrated in the convective zone testifies that the p + p reaction cross section or the electron-screening coefficient in the solar core must be increased by several percent over the current values. This requires a comparatively small correction to the opacities (by less than 5%), in order to obtain a solar model with low Z that is in agreement with the results of helioseismology and the observed solar neutrino fluxes.     

Two modes of the differential rotation of the solar corona

The differential rotation of the solar corona is studied using the brightness of the Fe XIV 530.3 nm green coronal line collected over 5.5 solar-activity cycles. The total observed velocity of the coronal rotation is analyzed as a superposition of two modes—fast and slow. A technique for separating two data series composing the initial data set and corresponding to the two differential-rotation modes of the solar corona is proposed. The first series is obtained by averaging the initial data set over six successive Carrington rotations; this series corresponds to long-lived, large-scale coronal regions. The second series is the difference between the initial data and the averaged series, and corresponds to relatively quickly varying coronal component. The coronal rotation derived from the first series coincides with the fast mode detected earlier using the initial data set; i.e., the synodic period of this mode is 27 days at the equator, then weakly increases with latitude, slightly exceeding 28 days at high latitudes. The second series describes a slow rotation displaying a synodic period of about 34 days. This coincides with the period of rotation of the high-latitude corona derived by M. Waldmeier for polar faculae. We expect that coronal objects corresponding to the fast mode are associated with magnetic fields on the scales typical for large activity complexes. The slow mode may be associated with weak fields on small scales.     

Double Diffusion-Driven Convective Instability of Three-Dimensional Fluid-Saturated Geological Fault Zones Heated from Below

We conduct a theoretical analysis to investigate the double diffusion-driven convective instability of three-dimensional fluid-saturated geological fault zones when they are heated uniformly from below. The fault zone is assumed to be more permeable than its surrounding rocks. In particular, we have derived exact analytical solutions to the total critical Rayleigh numbers of the double diffusion-driven convective flow. Using the corresponding total critical Rayleigh numbers, the double diffusion-driven convective instability of a fluid-saturated three-dimensional geological fault zone system has been investigated. The related theoretical analysis demonstrates that: (1) The relative higher concentration of the chemical species at the top of the three-dimensional geological fault zone system can destabilize the convective flow of the system, while the relative lower concentration of the chemical species at the top of the three-dimensional geological fault zone system can stabilize the convective flow of the system. (2) The double diffusion-driven convective flow modes of the three-dimensional geological fault zone system are very close each other and therefore, the system may have the similar chance to pick up different double diffusion-driven convective flow modes, especially in the case of the fault thickness to height ratio approaching 0. (3) The significant influence of the chemical species diffusion on the convective instability of the three-dimensional geological fault zone system implies that the seawater intrusion into the surface of the Earth is a potential mechanism to trigger the convective flow in the shallow three-dimensional geological fault zone system.     

The coalescence of two rotating sunspots during the emergence of an active region

The rare phenomenon of the coalescence of two rotating sunspots of the same magnetic polarity during the emergence of the active region NOAA 11117 is investigated using data from the SDO space observatory. The coalescing spots rotated in opposite directions. The leading spot which formed from this process rotated counterclockwise with an angular velocity of 4°/h. A possible explanation is presented, based on a model of the emerging, twisted magnetic Ω flux tube that interacts with convective flows as it crosses the convective zone.     

Movement of lithospheric plates relative to subduction zones: Formation of marginal seas and active continental margins

Subduction zones with deep seismicity are believed to be associated with the descending branches of convective flows in the mantle and are subordinated to them. Therefore, the position of subduction zones can be considered as relatively fixed with respect to the steady-state system of convective flows. The lithospheric plate overhanging a subduction zone (as a rule of continental type) may:

1. (1) either move away from the subduction zone; or

2. (2) move onto it. In the first case extensional conditions originate behind the subduction zone and the new oceanic crust of back-arc basins forms. In the second case active Andean-type continental margins with thickening of the crust and lithosphere are observed.

Behind the majority of volcanic island-arcs, along the boundary with marginal-sea basins, independent shallow seismicity belts can be traced. They are parallel to the main seismicity belts coinciding with the Benioff zones. The seismicity belts frame island-arc microplates. Island-arc microplates are assumed to be a frame of reference to calculate relative movements of the consuming and overhanging plates. Using slip vector azimuths for shallow seismicity belts in the frontal parts of the Kurile, Japan, Izu-Bonin, Mariana and Tonga—Kermadec arcs, the position of the pole of rotation of the Pacific plate with respect to the western Pacific island-arc microplates was computed. Its coordinates are 66.1°N, 119.2°W. From the global closure of plate movements it has been determined that for the past 10 m.y. the Eurasian and Indian plates have been moving away from the Western Pacific island-arc system, both rotating clockwise, around poles at 31.1°N, 164.2°W and 1.3°S, 157.5°W, respectively. This provides for the opening of the back-arc basins. At the same time South America is moving onto the subduction zone at the rate of 4 cm/yr. Some “hot spots”, such as Hawaiian, Tibesti, and those of the South Atlantic, are moving relative to the island-arc system at a very low rate, viz. 0.5–0.7 cm/yr. Presumably, the western Pacific subduction zone and “hot spots” form a single frame of reference which can generally be used for the analysis of absolute motions.     

Meridional drift of large-scale solar magnetic fields

It is shown that the meridional drift of large-scale fields starts in the equatorial zone and continues over 15–16 yrs (16–17 according to another estimate), i.e., during three fourths of the 22-year cycle. There is an abrupt retardation of the drift at latitudes of 30°–50°, and a stagnation region where the drift rate does not exceed several meters per second arises. The drift becomes rapid again at higher latitudes. The stagnation region coincides with the area in which the radial gradient of the rotational velocity is close to zero in the convective zone. This drift is compared with helio-seismological data on the rotation in the convective zone. A model taking into account some elements of dynamo theory is proposed.     

Stability of toroidal magnetic fields in the radiation zone of a star

The stability of a toroidal magnetic field in the rotating radiation zone of a star is analyzed to estimate the maximum possible magnitude of relic fields. Equations for small perturbations are obtained taking into account the finite diffusivity and the stabilizing effect of the subadiabatic stratification. The numerical solution of the eigenvalue problem indicates that the threshold field strength for the onset of instability in the radiation zone of the Sun is about 600 G. This figure sets an upper bound for the strength of the relic field. The assumption that magnetic instabilities are present in the solar radiation zone disagrees with the observed abundance of lithium. Our analysis of joint stability of toroidal field and nonuniform rotation shows that two-dimensional MHD solutions for the solar tachocline are stable against three-dimensional perturbations.     

Structure and evolution of the Cauvery Shear Zone system, Southern Granulite Terrain, India: Evidence from deep seismic and other geophysical studies

The Southern Granulite Terrain with exposed Archean lower crustal rocks is studied using various geophysical tools. The crustal structure derived from seismic reflection and refraction/wide-angle reflection studies is used to understand the tectonic evolution of the region. Deep seismic reflection section along the Kolattur–Palani segment shows an oppositely dipping reflection fabric near the Moyar–Bhavani shear zone, which is interpreted as a signature of collision between the Dharwar craton and another crustal block in the south. The thickened crust due to collision was delaminated during the orogenic collapse and modified the central part, covering the Cauvery Shear Zone system, located between the Moyar–Bhavani and Karur–Oddanchatram shear zones. The delaminated lower crust is altered by magmatic underplating as evidenced by the high velocity layer just above the Moho. The velocity model of the region indicates crustal thickening at the boundary of the Dharwar craton and Moyar–Bhavani shear zone and thinning further south. Back-scattered seismic wave field with negative moveout and the Moho-offset indicate the spatial location and strike-slip nature of the shear zones. Present study suggests that the late Archean collision and suturing of the Dharwar craton with the southern crustal block at the Moyar–Bhavani shear zone may be responsible for the evolution of late Archean granulites. Late Neoproterozoic rifting is observed along the paleo-fault zones. The seismic studies constrained by gravity, magnetic and magnetotelluric data suggest that the Moyar–Bhavani and Karur–Oddanchatram shear zones of the Cauvery Shear Zone system mark terrane boundaries/suture zones.     

Oceanic circulation as an element in palaeogeographical reconstructions: the Arenig (early Ordovician) as an example

A new conceptual palaeo-oceanographical model is outlined in this paper. The model differs from previous models by using shifts in Hadley circulation caused by orbital variations, and the rotation rate of the Earth, to locate the position of the planetary oceanic low-and high-pressure systems, around which the planetary ocean surface currents flow. Adapting the model to the Arenig (early Ordovician) the temperate low pressure zones were found to be located at 50° latitude and the subtropical high pressure zones at 25° latitude.
Traditionally, most Palaeozoic palaeogeographical recon-structions are reconstructed using palaeomagnetic data supplemented with data from climate-sensitive lithofacies and palaeo-biogeographical distributions. However, as a new approach in palaeogeographical reconstructions, the con-ceptual palaeo-oceanographical model is combined with palaeobiogeographical data for the Arenig series, comple-menting the palaeomagnetic data, and resulting in a new, refined palaeogeographical reconstruction.     

The evolution of solar-like activity of low-mass stars

An analysis of data on chromospheric activity obtained in the framework of exoplanet-search programs is presented. Observations of 1334 stars showing that the chromospheric activity of the Sun is clearly higher than for the vast majority of stars in the solar vicinity are used. A comparison of chromospheric and coronal activity led to the identification of a significant group of stars with a low level of chromospheric activity, whose coronal radiation spans wide ranges. There are reasons to believe that the chromospheric and coronal activities of one group of stars decrease simultaneously as the rotation decelerates, while, in stars of the other group, the chromospheric activity diminishes, but their coronas remain stronger than that of the Sun. Features of cyclic activity of the Sun are discussed. This enables us to associate differences in the behavior of the activity with different depths of the convective zones of stars of spectral classes earlier and later than G6. Arguments in favor of a two-layer dynamo and different roles of the large-scale and small-scale magnetic fields in the formation and evolution of activity are formulated. Age estimations based on activity levels (gyrochronology) must be carried out differently for these different groups of stars.