Oppositely directed waves of stellar activity in simple dynamo models

Excitations of two oppositely directed waves of stellar activity generated by two dynamo-active layers located in a single stellar hemisphere are examined using simple dynamo models. The domains of model parameters corresponding to various types and directions of the activity waves are found. It is shown that oppositely directed waves of activity are generated if the dynamo numbers have the same order of magnitude, ~10⁵?10⁶, but opposite signs. How frequently this case can be observed among real stars remains open to question. The report of oppositely directed waves of stellar activity in the literature is especially valuable in this connection.     

A dynamo wave near the solar equator

The structure of a dynamo wave near the solar equator is considered in the Parker approximation. The results show that the principal dynamo wave, which travels in the northern hemisphere from middle latitudes toward the equator, penetrates slightly into the southern hemisphere. The wave that propagates in the southern hemisphere exhibits similar behavior. The angular distance the wave is able to penetrate into the neighboring hemisphere can reach about ten degrees of latitude. Possible observational manifestations of this effect are discussed. The growth rate of the dipolar magnetic-field configuration exceeds that of the quadrupolar configuration, and the difference between these growth rates is computed. A possible relation of this quantity to the time characteristics of the Maunder minimum is discussed.     

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%.     

The effect of meridional circulation on dynamo waves approaching the solar poles

Dynamo waves approaching the solar poles are analyzed in the Parker approximation taking into account meridional circulation. Asymptotic solutions of the equations describing the generation of the magnetic field are constructed. It is shown in which cases the effect of meridional circulation results in traveling dynamo waves both incident on and reflected from the pole, or in a superposition of standing dynamo waves.     

Variations in the solar luminosity,radius, and quadrupole moment as effects of a large-scale dynamo in the solar convection zone

Astronomy Reports - The effect of large-scale magnetic fields generated by the solar dynamo on the irradiance of the Sun and stratification of the solar convection zone is studied using a numerical...     

The structure of the global solar magnetic field excited by the turbulent dynamo mechanism

A mixing-length approximation is used to calculate Kλ for a Parker dynamo wave excited by the dynamo mechanism near the base of the solar convection zone (K is the wave number of the dynamo wave and λ the extent of the dynamo region). In a turbulent-dynamo model, this number characterizes the modes of the global magnetic field generated by a mechanism based on the joint action of the mean helical turbulence and solar differential rotation. Estimates are obtained for the helicity and radial angular-velocity gradient using the most recent helioseismological measurements at the growth phase of solar cycle 23. These estimates indicate that the dynamo mechanism most efficiently excites the fundamental antisymmetric (odd), dipole, mode of the poloidal field (Kλ≈?7) at low latitudes, while the conditions at latitudes above 50° are more favorable for the excitation of the lowest symmetric (even), quadrupole, mode (Kλ≈+8). The resulting north-south asymmetry of the poloidal field can explain the magnetic anomaly (“monopole” structure) of the polar fields observed near solar-cycle maxima. The effect of α quenching increases the calculated period of the dynamo-wave propagation from middle latitudes to the equator to about seven years, in rough agreement with the observed duration of the solar cycle.     

Effects of various types of solar meridional circulation on the propagation of dynamo waves

We examine the effects of solar meridional circulation on the propagation of dynamo waves depending on the type of matter motion in a Parker approximation. The meridional circulation can lengthen the solar-activity cycle, with the dynamo-wave behavior depending on the latitude variations in the velocity of the moving material. The results obtained can qualitatively explain the Maunder minimum.     

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.     

Current helicity and the small-scale dynamo

The small-scale dynamo inherent to mirror-asymmetric turbulence can generate a magnetic field characterized by substantial mirror asymmetry of the associated electric currents. In general, the corresponding helicity should be taken into account in calculations of the helicity balance, which is now used as a basis for models describing the suppression of the large-scale dynamo. However, the mirror asymmetry of the fluctuating magnetic fields is concentrated on scales much shorter than the magnetic-loop diameter. Therefore, the unaccounted-for contribution to the helicity balance is, in fact, not important.     

Cosmological magnetic dynamo in the early Universe

We study the behavior of large-scale magnetic fields in the early Universe influenced by an instability associated with breaking of mirror symmetry in weak interactions. It is shown that the magnetic field, whose present scale reaches about 500 m, which is negligible for galactic sizes, increases considerably if we correctly take into account the dynamics of the Universe. We conclude that this magnetic field is unlikely to provide the seed field for galactic dynamos, nearly independent of the particular instability considered.     

Magnetic flux in an active solar region and its correlation with flares

The correlation between the magnetic flux in an active solar region and associated powerful solar flares is studied. The behavior of the active regions AR 10486 and AR 10365 is considered. These regions produced a series of class X flares as they crossed the solar disk. The flares appeared when the magnetic flux exceeded 10²² Mx. The magnetic flux remained constant during all the flares except for one. During this flare, the flux decreased by about 10%; this impulsive decrease of the flux was also recorded in the absence of flares. No energy flux from the photosphere to the corona at the time of the flare was observed. The behavior of the photospheric field in AR 10486 and AR 10365 is consistent with a slow accumulation of energy in the corona and the explosive release of energy stored in the magnetic field of a current sheet above an active region during the flare.     

A simple procedure to improve the explicit integration of Cam-Clay models

A simple procedure is proposed to reduce the error in the calculation of the stresses when simulating stress paths applying explicit stress integration schemes in Cam-Clay models with an associated flow rule. The procedure consists of defining the value of the preconsolidation stress (the hardening parameter of a Cam-Clay model) so that the drift of the yield surface is zero at each calculation step. The results demonstrate the efficiency of the proposed procedure, especially along softening paths. The method can easily be implemented in existing explicit integration modules, which facilitates its practical application.     

Magnetic field models for HD 116458 and HD 126515

We have modeled the magnetic fields of the slowly rotating stars HD 116458 and HD 126515 using the “magnetic charge” technique. HD 116458 has a small angle between its rotation axis and dipole axis (β = 12°), whereas this angle is large for HD 126515 (β = 86°). Both stars can be described with a decentered-dipole model, with the respective displacements being r = 0.07 and r = 0.24 in units of the stellar radius. The decentered-dipole model is able to satisfactorily explain the phase relations for the effective field, B_e(P), and the mean surface field, B_s(P), for both stars, along with the fact that the B_e(P) phase relation for HD 126515 is anharmonic. We discuss the role of systematic measurement errors possibly resulting from instrumental or methodical effects in one or both of the phase relations. The displacement of the dipole probably reflects real asymmetry of the stellar field structure, and is not due to measurement errors. Using both phase relations, B_e(P) and B_s(P), in the modeling considerably reduces the influence of the nonuniform distribution of chemical elements on the stellar surface.     

Quantitative models of very high fluid pressure: the possible role of lateral stresses

Because of the occurrence of very large observed overpressure in a well located in SE Asia, numerical modelling has been undertaken to evaluate evolution of the sediments. The intensity of the excess pressure, close to lithostatic pressure, and the likely relation to induced, open-fracture anomalies, as well as evidence of large fluid transfers, all lead to the suggestion that the tectonic regime is related to the generation of high excess pressure. To verify this hypothesis, a 2D fluid-flow/compaction model (GEOPETTI) was used to test whether high excess pressure could be obtained without considering the effect of lateral stresses. While high excess pressures are possible, even if undercompaction is the only process considered, the distribution of fluid pressure with depth does not correspond to that observed, and the migration of fluids cannot be reproduced because of the extremely low permeability of the sediments. Accordingly, the model has been modified so that the effect of lateral stresses can be investigated through: (1) the value of the fracturing coefficient which controls the maximum overpressure that it is possible to generate; (2) the sensitivity of the system to a possible compressive event, which could squeeze the sediments laterally so that the rate of fluid expulsion would be greater than if the fluids were driven only by the mechanical load of sediments. Finally, the role of faulting or fracturing is discussed as a possible mechanism responsible for the upward transfer of fluid which can lead to an increase of excess pressure at depths shallower than the depth where excess pressure was first generated, a mechanism also leading to high excess pressure. Moreover, this mechanism allows for a good reproduction of observed excess pressure distributions.     

A simple procedure to simulate a smooth elastic-plastic transition in Cam-Clay models

A simple procedure is proposed to simulate a smooth transition from elastic to elastoplastic behaviour in Cam-Clay models. The procedure consists of the definition of an external constitutive surface where full yield is assumed, and an internal one that allows the definition of the position in which plastic strains start to appear before the external yield surface is reached. The comparison of the model results with different laboratory tests shows the validity of the procedure. The method considers one additional parameter with regard to a “standard” critical state model, and it can easily be implemented in existing integration modules.     

A low-mode dynamo with meridional circulation and dipolar symmetry of the magnetic field

A dynamic system for the Parker dynamo including meridional circulation that is applicable to astrophysical objects is constructed. The meridional circulation is able to control the regimes for the generation of magnetic fields. If the meridional flows are weak, regimes with steady oscillations, dynamo bursts, fluctuations, and chaotic components are possible. When the meridional circulation is strengthened, the range of dynamo numbers required for fluctuations and dynamo bursts is reduced, and gradually vanishes; at the same time, the range required for oscillations is increased and raised to higher dynamo numbers. The latitude-time distributions of the toroidal and poloidal magnetic fields for steady oscillations are presented.     

Numerical simulations of simple shear with non‐coaxial soil models

This paper investigates the effects of a non‐coaxial model on simulated stress–strain behaviour of granular materials subject to simple shearing under various initial conditions. In most cases, a significant difference of predictions between coaxial and non‐coaxial modelling is found during the early stage in shearing. With the increase in shearing, non‐coaxial simulations approach and tend to coincide with coaxial simulations. It is also found that the roles of non‐coaxial modelling in simulating simple shear behaviour are considerably influenced by hardening rules, flow rules, initial static lateral pressure coefficients. In some cases, the non‐coaxial modelling gives a similar simulation as the coaxial modelling. In other cases, the non‐coaxial modelling decreases the hardening response or softening response of materials, compared with the coaxial modelling. Under certain conditions, the predicted peak strength of materials with non‐coaxial modelling is larger than that for coaxial modelling. Some of these observations can be attributed to the amount of principal stress rotation in various cases analysed. Others can be attributed to the difference between the directions of the non‐coaxial plastic flow and those for coaxial plastic flow. Copyright © 2005 John Wiley & Sons, Ltd.     

A dynamical system for the parker dynamo in the case of quadrupole symmetry of the magnetic field

Adynamical systemin the case of quadrupolar symmetry of the toroidal field is constructed. The system obtained reproduces the regimes of oscillations, vacillations, dynamo bursts, and a configuration with monotonically growing magnetic fields reaching stationary regimes. The ranges of dynamo numbers corresponding to these regimes are found. Butterfly diagrams for the steady-oscillation regime are constructed for both the poloidal and toroidal components of the magnetic field.     

Levels of coronal and chromospheric activity in late-type stars and various types of dynamo waves

We analyze the X-ray emission and chromospheric activity of late-type F, G, and K stars studied in the framework of the HK project. More powerful coronas are possessed by stars displaying irregular variations of their chromospheric emission, while stars with cyclic activity are characterized by comparatively modest X-ray luminosities and ratios of the X-ray to bolometric luminosity L _X/L _bol. This indicates that the nature of processes associated with magnetic-field amplification in the convective envelope changes appreciably in the transition from small to large dynamo numbers, directly affecting the character of the (α-Ω) dynamo. Due to the strong dependence of both the dynamo number and the Rossby number on the speed of axial rotation, earlier correlations found between various activity parameters and the Rossby number are consistent with our conclusions. Our analysis makes it possible to draw the first firm conclusions about the place of solar activity among analogous processes developing in active late-type stars.     

Global solar magnetology and reference points of the solar cycle

The solar cycle can be described as a complex interaction of large-scale/global and local magnetic fields. In general, this approach agrees with the traditional dynamo scheme, although there are numerous discrepancies in the details. Integrated magnetic indices introduced earlier are studied over long time intervals, and the epochs of the main reference points of the solar cycles are refined. A hypothesis proposed earlier concerning global magnetometry and the natural scale of the cycles is verified. Variations of the heliospheric magnetic field are determined by both the integrated photospheric i(B _r )_ph and source surface i(B _r )_ss indices, however, their roles are different. Local fields contribute significantly to the photospheric index determining the total increase in the heliospheric magnetic field. The i(B _r )_ss index (especially the partial index ZO, which is related to the quasi-dipolar field) determines narrow extrema. These integrated indices supply us with a “passport” for reference points, making it possible to identify them precisely. A prominent dip in the integrated indices is clearly visible at the cycle maximum, resulting in the typical double-peak form (the Gnevyshev dip), with the succeeding maximum always being higher than the preceding maximum. At the source surface, this secondary maximum significantly exceeds the primary maximum. Using these index data, we can estimate the progression expected for the 23rd cycle and predict the dates of the ends of the 23rd and 24th cycles (the middle of 2007 and December 2018, respectively).