arXiv subjects

L. L. Kitchatinov

Publications and source records attributed to L. L. Kitchatinov.

46 records · Page 3Linked to original sources

arXiv2007

Sunspot models with bright rings

A theoretical sunspot model is provided including magnetic suppression of the diffusivities and also a strong stratification of density and temperature. Heat diffusion alone with given magnetic field and zero mean flow only produces (after a very long relaxation time) dark spots without any bright ring. Models with full dynamics of both field and flow, however, provide rings and also the observed correlation of ring temperature excess and the spot size. The rings are formed as the result of heat transport by the resulting flow system and increased thermal diffusivity due to reduced magnetic quenching around spots.

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arXiv2007

Stability of Toroidal Magnetic Fields in Rotating Stellar Radiation Zones

The questions of how strong magnetic fields can be stored in rotating stellar radiative zones without being subjected to pinch-type instabilities and how much radial mixing is produced if the fields are unstable are addressed. Linear equations are derived for weak disturbances of magnetic and velocity fields which are global in horizontal dimensions but short--scaled in radius. The equations are solved to evaluate the stability of toroidal field patterns with one or two latitudinal belts under the influence of a rigid basic rotation. Hydrodynamic stability of latitudinal differential rotation is also considered. The magnetic instability is essentially three--dimensional. It does not exist in a 2D formulation with strictly horizontal disturbances on decoupled spherical shells. Only stable (magnetically modified) r-modes are found in this case. The instability recovers in 3D. The most rapidly growing modes for the Sun have radial scales smaller than 1 Mm. The finite thermal conductivity makes a strong destabilizing effect. The marginal field strength for the onset of the instability in the upper part of the solar radiative zone is about 600 G. The toroidal field can only slightly exceed this critical value for otherwise the radial mixing produced by the instability would be too strong to be compatible with the observed lithium abundance. Also the threshold for hydrodynamic instability of differential rotation which exists in 2D is lowered in 3D. When radial displacements are included, the value of 28% for critical shear is reduced to 21%.

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arXiv2007

Structure and stability of the magnetic solar tachocline

Rather weak fossil magnetic fields in the radiative core can produce the solar tachocline if the field is poloidal and almost horizontal in the tachocline region, i.e. if the field is confined within the core. This particular field geometry is shown to result from a shallow (<~1Mm) penetration of the meridional flow existing in the convection zone into the radiative core. I.e., two conditions are crucial for a magnetic tachocline theory: (i) the presence of meridional flow of a few meters per second at the base of the convection zone, and (ii) a magnetic diffusivity inside the tachocline smaller than 10^8 cm^2s^-1. Numerical solutions for both confined poloidal fields and the resulting tachocline structures are presented. We find that the tachocline thickness runs as B _p^-1/2 with the poloidal field amplitude falling below 5% of the solar radius for B ^p > 5 mG. The resulting toroidal field amplitude inside the tachocline of about 100 G does not depend on the B ^p. The hydromagnetic stability of the tachocline is only briefly discussed. For the hydrodynamic stability of latitudinal differential rotation we found that the critical 29% of the 2D theory of Watson (1981) are reduced to only 21% in 3D for marginal modes of about 6 Mm radial scale.

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arXiv2006

Do mean-field dynamos in nonrotating turbulent shear-flows exist?

A plane-shear flow in a fluid with forced turbulence is considered. If the fluid is electrically-conducting then a mean electromotive force (EMF) results even without basic rotation and the magnetic diffusivity becomes a highly anisotropic tensor. It is checked whether in this case self-excitation of a large-scale magnetic field is possible (so-called WxJ-dynamo) and the answer is NO. The calculations reveal the cross-stream components of the EMF perpendicular to the mean current having the wrong signs, at least for small magnetic Prandtl numbers. After our results numerical simulations with magnetic Prandtl number of about unity have only a restricted meaning as the Prandtl number dependence of the diffusivity tensor is rather strong. If, on the other hand, the turbulence field is stratified in the vertical direction then a dynamo active alpha-effect is produced. The critical magnetic Reynolds number for such a self-excitation in a simple shear flow is slightly above 10 like for the other - but much more complicated - flow patterns used in existing dynamo experiments with liquid sodium or gallium.

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arXiv2006

Magnetic field confinement by meridional flow and the solar tachocline

We show that the MHD theory that explains the solar tachocline by an effect of the magnetic field can work with the decay modes of a fossil field in the solar interior if the meridional flow of the convection zone penetrates slightly the radiative zone beneath. An equatorward flow of about 10 m/s penetrating to a maximum depth of 1000 km below the convection zone is able to generate almost horizontal field lines in the tachocline region so that the internal field is almost totally confined to the radiative zone. The theory of differential solar rotation indeed provides meridional flows of about 10 m/s and a penetration depth of < 1000 km for viscosity values that are characteristic of a stable tachocline.

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arXiv2005

Differential rotation and meridional flow in the solar convection zone and beneath

The influence of the basic rotation on anisotropic and inhomogeneous turbulence is discussed in the context of differential rotation theory. An improved representation for the original turbulence leads to a $\Lam$-effect which complies with the results of 3D numerical simulations. The resulting rotation law and meridional flow agree well with both the surface observations ($\partial\Om/\partial r<0$ and meridional flow towards the poles) and with the findings of helioseismology. The computed equatorward flow at the bottom of convection zone has an amplitude of about 10 m/s and may be significant for the solar dynamo. The depth of the meridional flow penetration into the radiative zone is proportional to $ν^{0.5}_\mathrm{core}$, where $ν_\mathrm{core}$ is the viscosity beneath the convection zone. The penetration is very small if the tachocline is laminar.

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arXiv2005

Anti-solar differential rotation

The differential rotation of anti-solar type detected by observations for several stars may result from a fast meridional flow. The sufficiently intensive meridional circulation may be caused by large-scale thermal inhomogeneities or, perhaps, by tidal forcing from a companion star. First results of simulations of the anti-solar rotation of a giant star with magnetically induced thermal inhomogeneities are presented. Perspectives for observational check of the theory are discussed.

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arXiv2005

The influence of the Hall effect on the global stability of cool protostellar disks

The influence of the Hall effect on the global stability of cool Kepler disks under the influence of an axial magnetic field is considered. For sufficiently large magnetic Reynolds numbers Rm the magnetorotational instability (MRI) exists in a finite interval of magnetic field amplitudes, $B$_{min} < $B$ < $B$_{max}. For Kepler disks the pure MRI needs both rather high Rm (representing the needed electrical conductivity) as well as $B$_{min} of order 0.1 G. The magnetic field pattern resulting from our global and linear calculations is of quadrupolar parity. For magnetic fields $antiparallel$ to the rotation axis the Hall effect reduces the minimum magnetic Reynolds number by about one order of magnitude. The $B$_{min}, however, is even (sightly) increased (see Fig. 6). For magnetic fields $parallel$ to the rotation axis the Hall effect drives its own instability without the action of the Lorentz force. The corresponding critical magnetic Reynolds number proves to be larger with Hall effect (Rm ~ 10) than without Hall effect (Rm ~ 7) so that the Hall effect for parallel fields even disturbs the formation of MHD-instability in cool protoplanetary disks. If the disk is supercritical then the main result of the Hall effect for positive fields is the strong reduction of the minimum magnetic field amplitude which is necessary to start the instability. Observations must show whether in star-forming regions the rotation axis and the magnetic field orientation are correlated or are anticorrelated. If the magnetic fields are high enough then our model predicts the dominance of fields antiparallel to the rotation axis.

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arXiv2004

The eddy heat-flux in rotating turbulent convection

The three components of the heat-flux vector $F =ρC_p are numerically computed for a stratified rotating turbulent convection using the NIRVANA code in a flat box. The latitudinal component $F_θ$ proves to be negative (positive) in the northern (southern) hemisphere so that the heat always flows towards the poles. As a surprise, the radial heat-flux $F_r$ peaks at the equator rather than at the poles (Taylor numbers O(10^6)). The same behavior is observed for the radial turbulence intensity $ $ which for \emph{free} turbulence is also believed to peak at the poles (see Eq. (19) below). As we can show, however, the consequences of this unexpected result (also obtained by Kaepylae, Korpi and Tuominen 2004) for the theory of differential rotation are small as mainly the $F_θ$ is responsible to solve the `Taylor number puzzle'. In all our simulations the azimuthal component $F_ϕ$ proves to be negative so that the rotating turbulence produces an westwards directed azimuthal heat-flux which should be observable. Fluctuations with higher temperature are expected to be anticorrelated with their own angular velocity fluctuations. We find this rotation-induced result as understandable as the $F_ϕ$ is closely related to the radial Λ-effect which is known to be also negative in stratified and rapidly rotating convection zones.

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arXiv2004

Seed fields for galactic dynamos by the magnetorotational instabilities

A linear but global numerical model for the magnetorotational instability (MRI) in disk geometry is considered to estimate the instability parameters for galaxies. Similarity rules suggested by a local analysis are applied to reveal a universal behavior approached by the results of global calculations for large magnetic Prandtl numbers. The findings are used to estimate the MRI characteristics for galaxies with their very large magnetic Prandtl numbers which cannot be attained in any numerical simulations. The resulting minimum field for the instability, Bmin 10-25 G, is small compared to any seed fields currently discussed. The growth times of MRI are estimated to be on the order of the rotation period of the inner rigidly-rotating core, i.e. ~100 Myr. Global MRI excites preferentially the magnetic field modes of quadrupolar symmetry.

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