arXiv subjects

L. L. Kitchatinov

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

At least 37 records · Page 2Linked to original sources

arXiv2012

Differential rotation of main-sequence dwarfs: predicting the dependence on surface temperature and rotation rate

Gyrochronology and recent theoretical findings are used to reduce the number of input parameters of differential rotation models. This eventually leads to a theoretical prediction for the surface differential rotation as a function of only two stellar parameters - surface temperature and rotation period - that can be defined observationally. An analytical approximation for this function is suggested. The tendency for the differential rotation to increase with temperature is confirmed. The increase is much steeper for late F-stars compared to G- and K-dwarfs. Slow and fast rotation regimes for internal stellar rotation are identified. A star attains its maximum differential rotation at rotation rates intermediate between these two regimes. The amplitude of the meridional flow increases with surface temperature and rotation rate. The structure of the flow changes considerably between cases of slow and fast rotation. The flow in rapid rotators is concentrated in the boundary layers near the top and bottom of the convection zone with very weak circulation in between.

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arXiv2012

Transport of angular momentum and chemical species by anisotropic mixing in stellar radiative interiors

Small levels of turbulence can be present in stellar radiative interiors due to, e.g., instability of rotational shear. In this paper we estimate turbulent transport coefficients for stably stratified rotating stellar radiation zones. Stable stratification induces strong anisotropy with a very small ratio of radial-to-horizontal turbulence intensities. Angular momentum is transported mainly due to the correlation between azimuthal and radial turbulent motions induced by the Coriolis force. This non-diffusive transport known as the Lambda-effect has outward direction in radius and is much more efficient compared to the effect of radial eddy viscosity. Chemical species are transported by small radial diffusion only. This result is confirmed using direct numerical simulations combined with the test-scalar method. As a consequence of the non-diffusive transport of angular momentum, the estimated characteristic time of rotational coupling (< 100 Myr) between radiative core and convective envelope in young solar-type stars is much shorter compared to the time-scale of Lithium depletion (~1 Gyr).

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arXiv2012

Suppression of the large-scale Lorentz force by turbulence

The components of the total stress tensor (Reynolds stress plus Maxwell stress) are computed within the quasilinear approximation for a driven turbulence influenced by a large-scale magnetic background field. The conducting fluid has an arbitrary magnetic Prandtl number and the turbulence without the background field is assumed as homogeneous and isotropic with a free Strouhal number St. The total large-scale magnetic tension is always reduced by the turbulence with the possibility of a `catastrophic quenching' for large magnetic Reynolds number Rm so that even its sign is reversed. The total magnetic pressure is enhanced by turbulence with short correlation time (`white noise') but it is reduced by turbulence with long correlation time. Also in this case the sign of the total pressure may reverse but only for special turbulences with sufficiently large St> 1. The turbulence-induced terms of the stress tensor are suppressed by strong magnetic fields. For the tension term this quenching grows with the square of the Hartmann number of the magnetic field. For microscopic (i.e. small) diffusivity values the magnetic tension term becomes thus highly quenched even for field amplitudes much smaller than their equipartition value. In the opposite case of large-eddy simulations the magnetic quenching is only mild but then also the turbulence-induced Maxwell tensor components for weak fields remain rather small.

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arXiv2011

Solar differential rotation: origin, models, and implications for dynamo

Helioseismology shows that the regions occupied by convection and differential rotation inside the sun almost coincide. This supports the leading theoretical concept for the origin of differential rotation as a result of interaction between convection and rotation. This talk outlines the current state of the differential rotation theory. Numerical models based on the theory reproduce the observed solar rotation quite closely. The models also compute meridional flow and predict that the flow at the bottom of the convection zone is not small compared to the surface. Theoretical predictions for stellar differential rotation as a function of the stellar mass and rotation rate are discussed and compared with observations. The implications of the differential rotation models for solar and stellar dynamos are briefly discussed.

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arXiv2011

Does the Babcock--Leighton Mechanism Operate on the Sun?

The contribution of the Babcock-Leighton mechanism to the generation of the Sun's poloidal magnetic field is estimated from sunspot data for three solar cycles. Comparison of the derived quantities with the A-index of the large-scale magnetic field suggests a positive answer to the question posed in the title of this paper.

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arXiv2011

Solar Dynamo Model with Diamagnetic Pumping and Nonlocal Alpha-Effect

A combination of diamagnetic pumping and a nonlocal alpha-effect of the Babcock-Leighton type in a solar dynamo model helps to reproduce observations of solar magnetic activity. The period of the solar cycle can be reproduced without reducing magnetic diffusivity in the bulk of the convection zone below the standard mixing-length value of $10^{13}$ cm$^2$s$^{-1}$. The simulated global fields are antisymmetric about the equator and the toroidal-to-poloidal field ratio is about a thousand. The time-latitude diagrams of magnetic fields in the model without meridional flow, however, differ from observations. Only when the meridional flow is included and the alpha-effect profile peaking at mid latitudes is applied, can the observational butterfly diagrams be reproduced.

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arXiv2011

Helicity and dynamo action in magnetized stellar radiation zones

Helicity and αeffect driven by the nonaxisymmetric Tayler instability of toroidal magnetic fields in stellar radiation zones are computed. In the linear approximation a purely toroidal field always excites pairs of modes with identical growth rates but with opposite helicity so that the net helicity vanishes. If the magnetic background field has a helical structure by an extra (weak) poloidal component then one of the modes dominates producing a net kinetic helicity anticorrelated to the current helicity of the background field. The mean electromotive force is computed with the result that the αeffect by the most rapidly growing mode has the same sign as the current helicity of the background field. The αeffect is found as too small to drive an α^{2} dynamo but the excitation conditions for an αΩdynamo can be fulfilled for weak poloidal fields. Moreover, if the dynamo produces its own αeffect by the magnetic instability then problems with its sign do not arise. For all cases, however, the αeffect shows an extremely strong concentration to the poles so that a possible αΩdynamo might only work at the polar regions. Hence, the results of our linear theory lead to a new topological problem for the existence of large-scale dynamos in stellar radiation zones on the basis of the current-driven instability of toroidal fields.

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arXiv2011

Solar dynamo model with nonlocal alpha-effect

The first results of the solar dynamo model that allows for the diamagnetic effect of inhomogeneous turbulence and the nonlocal alpha-effect due to the rise of magnetic loops are discussed. The nonlocal alpha-effect is not subject to the catastrophic quenching related to the conservation of magnetic helicity. Given the diamagnetic pumping, the magnetic fields are concentrated near the base of the convection zone, although the distributed-type model covers the entire thickness of the convection zone. The magnetic cycle period, the equatorial symmetry of the field, its meridional drift, and the polar-to-toroidal field ratio obtained in the model are in agreement with observations. There is also some disagreement with observations pointing the ways of improving the model.

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arXiv2011

The differential rotation of G dwarfs

A series of stellar models of spectral type G is computed to study the rotation laws resulting from mean-field equations. The rotation laws of the slowly rotating Sun, the fast rotating MOST stars epsilon Eri and kappa1 Cet and the rapid rotators R58 and LQ Lup can easily be reproduced. We also find that differences in the depth of the convection zone cause large differences in the surface rotation law and that the extreme surface shear of HD 171488 can only be explained with a artificially shallow convection layer. We also check the thermal wind equilibrium in fast-rotating G dwarfs and find that the polar subrotation (dOmega/dz<0) is due to the barocline effect and that the equatorial superrotation (dOmega/dr>0) is due to the Lambda effect as part of the Reynolds stresses. In the bulk of the convection zones where the meridional flow is slow and smooth the thermal wind equilibrium actually holds between the centrifugal and the pressure forces. It does not hold, however, in the bounding shear layers including the equatorial region where the Reynolds stresses dominate.

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arXiv2011

Alleviation of catastrophic quenching in solar dynamo model with nonlocal alpha-effect

The nonlocal alpha-effect of Babcock-Leighton type is not prone to the catastrophic quenching due to conservation of magnetic helicity. This is shown with a dynamo model, which jointly applies the nonlocal alpha-effect, the diamagnetic pumping, and dynamical equation for the magnetic alpha-effect. The same model shows catastrophic quenching when the alpha-effect is changed to its local formulation. The nonlocal model shows the preferred excitation of magnetic fields of dipolar symmetry, which oscillate with a period of about ten years and have a toroidal-to-polar fields ratio of about a thousand.

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arXiv2010

Cross helicity and turbulent magnetic diffusivity in the solar convection zone

In a density-stratified turbulent medium the cross helicity is considered as a result of the interaction of the velocity fluctuations and a large-scale magnetic field. By means of a quasilinear theory and by numerical simulations we find the cross helicity and the mean vertical magnetic field anti-correlated. In the high-conductivity limit the ratio of the helicity and the mean magnetic field equals the ratio of the magnetic eddy diffusivity and the (known) density scale height. The result can be used to predict that the cross helicity at the solar surface exceeds the value of 1 Gauss km/s. Its sign is anti-correlated with that of the radial mean magnetic field. Alternatively, we can use our result to determine the value of the turbulent magnetic diffusivity from observations of the cross helicity.

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arXiv2010

Differential rotation of main-sequence dwarfs and its dynamo-efficiency

A new version of a numerical model of stellar differential rotation based on mean-field hydrodynamics is presented and tested by computing the differential rotation of the Sun. The model is then applied to four individual stars including two moderate and two fast rotators to reproduce their observed differential rotation quite closely. A series of models for rapidly rotating ($P_{rot} = 1$ day) stars of different masses and compositions is generated. The effective temperature is found convenient to parameterize the differential rotation: variations with metallicity, that are quite pronounced when the differential rotation is considered as a function of the stellar mass, almost disappear in the dependence of differential rotation on temperature. The differential rotation increases steadily with surface temperature to exceed the largest differential rotation observed to date for the hottest F-stars we considered. This strong differential rotation is, however, found not to be efficient for dynamos when the efficiency is estimated with the standard $C_Ω$-parameter of dynamo models. On the contrary, the small differential rotation of M-stars is the most dynamo-efficient. The meridional flow near the bottom of the convection zone is not small compared to the flow at the top in all our computations. The flow is distributed over the entire convection zone in slow rotators but retreats to the convection zone boundaries with increasing rotation rate, to consist of two near-boundary jets in rapid rotators. The implications of the change of the flow structure for stellar dynamos are briefly discussed.

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arXiv2009

The kink-type instability of toroidal stellar magnetic fields with thermal diffusion

The stability of toroidal magnetic fields in rotating radiative stellar zones is studied for realistic values of both the Prandtl numbers. The two considered models for the magnetic geometry represent fields with odd and even symmetry with respect to the equator. In the linear theory in Boussinesq approximation the resulting complex eigenfrequency (including growth rate and drift rate) are calculated for a given radial wavenumber of a nonaxisymmetric perturbation with m=1. The ratio of the Alfven frequency, Ω_A, to the rate of the basic rotation, Ω, controls the eigenfrequency of the solution. For strong fields with Ω_A > Ωthe solutions do not feel the thermal diffusion. The growth rate runs with Ω_A and the drift rate is close to -Ωso that the magnetic pattern will rest in the laboratory system. For weaker fields with Ω_A < Ωthe growth rate strongly depends on the thermal conductivity. For fields with dipolar parity and for typical values of the heat conductivity the resulting very small growth rates are almost identical with those for vanishing gravity. For fields with dipolar symmetry the differential rotation of any stellar radiative zone (like the solar tachocline) is shown as basically stabilizing the instability independent of the sign of the shear. Finally, the current-driven kink-type instability of a toroidal background field is proposed as a model for the magnetism of Ap stars. The recent observation of a lower magnetic field treshold of about 300 Gauss for Ap stars is understood as corresponding to the minimum magnetic field producing the instability.

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arXiv2009

Dissipative and nonaxisymmetric standard-MRI in Kepler disks

Deviations from axial symmetry are necessary to maintain self-sustained MRI-turbulence. We define the parameters region where nonaxisymmetric MRI is excited and study dependence of the unstable modes structure and growth rates on the relevant parameters. We solve numerically the linear eigenvalue problem for global axisymmetric and nonaxisymmetric modes of standard-MRI in Keplerian disks with finite diffusion. For small magnetic Prandtl number the microscopic viscosity completely drops out from the analysis so that the stability maps and the growth rates expressed in terms of the magnetic Reynolds number Rm and the Lundquist number S do not depend on the magnetic Prandtl number Pm. The minimum magnetic field for onset of nonaxisymmetric MRI grows with Rm. For given S all nonaxisymmetric modes disappear for sufficiently high Rm. This behavior is a consequence of the radial fine-structure of the nonaxisymmetric modes resulting from the winding effect of differential rotation. It is this fine-structure which presents severe resolution problems for the numerical simulation of MRI at large Rm. For weak supercritical magnetic fields only axisymmetric modes are unstable. Nonaxisymmetric modes need stronger fields and not too fast rotation. If Pm is small its real value does not play any role in MRI.

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arXiv2009

Stability of latitudinal differential rotation in stars

The question is addressed whether stellar differentially rotating radiative zones (like the solar tachocline) excite nonaxisymmetric r-modes which can be observed. To this end the hydrodynamical stability of latitudinal differential rotation is studied. The amount of rotational shear required for the instability is estimated in dependence of the character of radial stratification and the flow patterns excited by the instability are found. The eigenvalue equations for the nonaxisymmetric disturbances are formulated in 3D and then solved numerically. Radial displacements and entropy disturbances are included. The equations contain the 2D approximation of strictly horizontal displacements as a special limit. The critical magnitude of the latitudinal differential rotation for onset of the instability is considerably reduced in the 3D theory compared to the 2D approximation. The instability requires a subadiabatic stratification. It does not exist in the bulk of convection zone with almost adiabatic stratification but may switch on near its base in the region of penetrative convection. Growth rates and symmetry types of the modes are computed in dependence on the rotation law parameters. The S1 mode with its transequatorial toroidal vortices is predicted as the dominating instability mode. The vortices show longitudinal drift rates retrograde to the basic rotation which are close to that of the observed weak r-mode signatures at the solar surface.

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arXiv2009

Magnetic pinch-type instability in stellar radiative zones

The solar tachocline is shown as hydrodynamically stable against nonaxisymmetric disturbances if it is true that no cos^{4}θterm exists in its rotation law. We also show that the toroidal field of 200 Gauss amplitude which produces the tachocline in the magnetic theory of Ruediger & Kitchatinov (1997) is stable against nonaxisymmetric MHD disturbances -- but it becomes unstable for rotation periods slightly slower than 25 days. The instability of such weak fields lives from the high thermal diffusivity of stellar radiation zones compared with the magnetic diffusivity. The growth times, however, result as very long (of order of 10\^5 rotation times). With estimations of the chemical mixing we find the maximal possible field amplitude to be ~500 Gauss in order to explain the observed lithium abundance of the Sun. Dynamos with such low field amplitudes should not be relevant for the solar activity cycle. With nonlinear simulations of MHD Taylor-Couette flows it is shown that for the rotation-dominated magnetic instability the resulting eddy viscosity is only of the order of the molecular viscosity. The Schmidt number as the ratio of viscosity and chemical diffusion grows to values of ~20. For the majority of the stellar physics applications, the magnetic-dominated Tayler instability will be quenched by the stellar rotation.

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arXiv2008

Diamagnetic pumping near the base of a stellar convection zone

The property of inhomogeneous turbulence in conducting fluids to expel large-scale magnetic fields in the direction of decreasing turbulence intensity is shown as important for the magnetic field dynamics near the base of a stellar convection zone. The downward diamagnetic pumping confines a fossil internal magnetic field in the radiative core so that the field geometry is appropriate for formation of the solar tachocline. For the stars of solar age, the diamagnetic confinement is efficient only if the ratio of turbulent magnetic diffusivity of the convection zone to the (microscopic or turbulent) diffusivity of the radiative interiour is larger than 10^5. Confinement in younger stars require still larger diffusivity ratio. The observation of persistent magnetic structures on young solar-type stars can thus provide evidences for the nonexistence of tachoclines in stellar interiors and on the level of turbulence in radiative cores.

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arXiv2007

Stability of toroidal magnetic fields in the solar tachocline and beneath

Stability of toroidal magnetic field in a stellar radiation zone is considered for the cases of uniform and differential rotation. In the rigidly rotating radiative core shortly below the tachocline, the critical magnetic field for instability is about 600 G. The unstable disturbances for slightly supercritical fields have short radial scales ~1 Mm. Radial mixing produced by the instability is estimated to conclude that the internal field of the sun can exceed the critical value of 600 G only marginally. Otherwise, the mixing is too strong and not compatible with the observed lithium abundance. Analysis of joint instability of differential rotation and toroidal field leads to the conclusion that axisymmetric models of the laminar solar tachocline are stable to nonaxisymmetric disturbances. The question of whether sun-like stars can posses tachoclines is addressed with positive answer for stars with rotation periods shorter than about two months.

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