arXiv subjects

Leonid Kitchatinov

Publications and source records attributed to Leonid Kitchatinov.

At least 19 recordsLinked to original sources

arXiv2026

Small-Scale Dynamo for Full Spectrum of Hydrodynamic Turbulence in Kazantsev Model

A method is proposed for computing coefficients in the Kazantsev equation of small-scale dynamo for the full spectrum of hydromagnetic turbulence comprising the inertial range together with the range of viscous dissipation. The dynamo equation with so-defined coefficients is solved numerically for magnetic (Rm) and hydrodynamic (Re) Reynolds numbers from $10^2$ to $10^8$. The threshold value ${\rm Rm}_c$ for onset of dynamo increases initially with Re but then saturates at a constant value of ${\rm Rm}_c \simeq 300$ for ${\rm Re}\geq 10^5$. In the case of small Prandtl number Pm = Rm/Re << 1, the field growth rate is also small and depends logarithmically on Rm. In this case, the magnetic energy spectrum peaks around the scale of Ohmic dissipation, which decreases with increasing Pm. The decrease stops at the scale of viscous dissipation while the growth rate increases sharply when Pm approaches the value of one. The increase in the growth rate proceeds to ${\rm Pm} > 1$ but slows down and then saturates at a value somewhat below the inverse lifetime of most short-living eddies. An explanation of the results is proposed.

physics.flu-dyn↗

arXiv2024

Modeling effects of starspots on stellar magnetic cycles

Observations show that faster-rotating stars tend to have stronger magnetic activity and shorter magnetic cycles. The cyclical magnetic activity of the Sun and stars is believed to be driven by the dynamo process. The success of the Babcock-Leighton (BL) dynamo in understanding the solar cycle suggests an important role that starspots could play in stellar magnetic cycles. We aim at extending the BL mechanism to solar-mass stars with various rotation rates and explore the effects of emergence properties of starspots in latitudes and tilt angles on stellar magnetic cycles. We adopt a kinematic BL-type dynamo model operating in the bulk of the convection zone. The profiles of the large-scale flow fields are from the mean-field hydrodynamical model for various rotators. The BL source term in the model is constructed based on the rotation dependence of starspots emergence. That is, faster rotators have starspots at higher latitudes with larger tilt angles.Faster rotators have poloidal flux appearing closer to about $\pm55^\circ$ latitudes, where the toroidal field generation efficiency is the strongest because of the strongest latitudinal differential rotation there. It takes a shorter time for faster rotators to transport the surface poloidal field from their emergence latitude to the $\pm 55^\circ$ latitudes of efficient $Ω$-effect thus shortening their magnetic cycles. The faster rotators operate in a more supercritical regime due to a stronger BL $α$-effect relating to the tilt angles, which leads to stronger saturated magnetic fields and a coupling of the poloidal field between two hemispheres more difficult. Thus the magnetic field parity shifts from the hemispherically asymmetric mixed mode to quadrupole, and further to dipole when a star spins down. The emergence of starspots plays an essential role in the large-scale stellar dynamo.

astro-ph.SR↗

arXiv2024

Origin of the Near-Surface Shear Layer of Solar Rotation

Helioseismology has revealed an increase in the rotation rate with depth in a thin ($\sim$30 Mm) near-surface layer. The normalized rotational shear in this layer is independent of latitude. This rotational state is shown to be a consequence of the short characteristic time of near-surface convection compared to the rotation period, and the radial anisotropy of the convective turbulence. Analytical derivations within mean-field hydrodynamics reproduce the observed normalized rotational shear and are in agreement with numerical experiments on the radiative hydrodynamics of solar convection. The near-surface shear layer is the source of the global meridional flow important for the solar dynamo.

astro-ph.SR↗

arXiv2023

Near-surface shear layer of solar rotation: origin and significance

Helioseismology has discovered a thin layer beneath the solar surface where the rotation rate increases rapidly with depth. The normalized rotational shear in the upper 10 Mm of the layer is constant with latitude. Differential rotation theory explains such a rotational state by a radial-type anisotropy of the near-surface convection and a short correlation time of convective turbulence compared to the rotation period. The shear layer is the main driver of the global meridional circulation.

astro-ph.SR↗

arXiv2023

The Dependence of Stellar Activity Cycles on Effective Temperature

This paper proposes the idea that the observed dependence of stellar activity cycles on rotation rate can be a manifestation of a stronger dependence on the effective temperature. Observational evidence is recalled and theoretical arguments are given for the presence of cyclic activity in the case of sufficiently slow rotation only. Slow rotation means proximity to the observed upper bound on the rotation period of solar-type stars. This maximum rotation period depends on temperature and shortens for hotter stars. The maximum rotation period is interpreted as the minimum rotation rate for operation of a large-scale dynamo. A combined model for differential rotation and the dynamo is applied to stars of different mass rotating with a rate slightly above the threshold rate for the dynamo. Computations show shorter dynamo cycles for hotter stars. As the hotter stars rotate faster, the computed cycles are also shorter for faster rotation. The observed smaller upper bound for rotation period of hotter stars can be explained by the larger threshold amplitude of the $α$-effect for onset of their dynamos: a larger $α$ demands faster rotation. The amplitude of the (cycling) magnetic energy in the computations is proportional to the difference between the rotation period and its upper bound for the dynamo. Stars with moderately different rotation rates can differ significantly in super-criticality of their dynamos and therefore in their magnetic activity, as observed.

astro-ph.SR↗

arXiv2023

Dynamo modelling for cycle variability and occurrence of grand minima in Sun-like stars: Rotation rate dependence

Like the solar cycle, stellar activity cycles are also irregular. Observations reveal that rapidly rotating (young) Sun-like stars exhibit a high level of activity with no Maunder-like grand minima and rarely display smooth regular activity cycles. On the other hand, slowly rotating old stars like the Sun have low activity levels and smooth cycles with occasional grand minima. We, for the first time, try to model these observational trends using flux transport dynamo models. Following previous works, we build kinematic dynamo models of one solar mass star with different rotation rates. Differential rotation and meridional circulation are specified with a mean-field hydrodynamic model. We include stochastic fluctuations in the Babcock-Leighton source of the poloidal field to capture the inherent fluctuations in the stellar convection. Based on extensive simulations, we find that rapidly rotating stars produce highly irregular cycles with strong magnetic fields and rarely produce Maunder-like grand minima, whereas the slowly-rotating stars (with a rotation period of 10 days and longer) produce smooth cycles of weaker strength, long-term modulation in the amplitude, and occasional extended grand minima. The average duration and the frequency of grand minima increase with decreasing rotation rate. These results can be understood as the tendency of less supercritical dynamo in slower rotating stars to be more prone to produce extended grand minima

astro-ph.SR↗

arXiv2023

Mean field models of flux transport dynamo and meridional circulation in the Sun and stars

The most widely accepted model of the solar cycle is the flux transport dynamo model. This model evolved out of the traditional $αΩ$ dynamo model which was first developed at a time when the existence of the Sun's meridional circulation was not known. In these models, the toroidal magnetic field (which gives rise to sunspots) is generated by the stretching of the poloidal field by solar differential rotation. The primary source of the poloidal field in the flux transport models is attributed to the Babcock--Leighton mechanism, in contrast to the mean-field $α$-effect used in earlier models. With the realization that the Sun has a meridional circulation, which is poleward at the surface and is expected to be equatorward at the bottom of the convection zone, its importance for transporting the magnetic fields in the dynamo process was recognized. Much of our understanding about the physics of both the meridional circulation and the flux transport dynamo has come from the mean field theory obtained by averaging the equations of MHD over turbulent fluctuations. The mean field theory of meridional circulation makes clear how it arises out of an interplay between the centrifugal and thermal wind terms. We provide a broad review of mean field theories for solar magnetic fields and flows, the flux transport dynamo modeling paradigm and highlight some of their applications to solar and stellar magnetic cycles. We also discuss how the dynamo-generated magnetic field acts on the meridional circulation of the Sun and how the fluctuations in the meridional circulation, in turn, affect the solar dynamo. We conclude with some remarks on how the synergy of mean field theories, flux transport dynamo models, and direct numerical simulations can inspire the future of this field.

astro-ph.SR↗

arXiv2022

Inferring Quadrupolar Dynamo Mode from Sunspot Statistics

Observations of long-term north-south asymmetry in solar activity demand the equator-symmetric (quadrupolar) mode be present in the solar magnetic field in line with the dominant antisymmetric (dipolar) mode. This paper proposes treating the sunspot area as a proxy for subsurface toroidal magnetic flux to infer the quadrupolar mode of the solar dynamo from sunspot data. Toroidal pseudo-fluxes (PF) in the northern and southern hemispheres are defined as a signed sunspot area with plus or minus sign prescribed to them in accord with the Hale's sunspot polarity rules. Statistical correlation analysis and wavelet analysis of so-defined PFs reveal quadrupolar oscillations with a period of about 16 yr and amplitude of about 0.17 relative to the amplitude of the dominant 22-yr dipolar mode.

astro-ph.SR↗

arXiv2021

Dynamo Model for North-South Asymmetry of Solar Activity

Observations reveal a relatively small but statistically significant North-South (NS) asymmetry in sunspot activity varying on a time scale of several solar cycles. This paper proposes a dynamo model for the phenomenon of long-term NS asymmetry. The model separates dynamo equations for magnetic fields of dipolar and quadrupolar equatorial parity. The NS asymmetry results from the superposition of dipolar and quadrupolar fields. Model computations confirm the formerly proposed excitation of the quadrupolar dynamo mode by a dominant dipolar mode mediated by the equator-symmetric fluctuations in the $α$-effect as a mechanism for the long-term NS asymmetry. An analytically solvable example of oscillations excited by short-term random forcing is given to justify the numerical result of NS asymmetry coherent on a time scale of several (about 6 in the present model) solar cycles resulting from random variations in the $α$-effect on a time scale of one solar rotation. The model computations show the phase locking phenomenon of dipolar and quadrupolar fields oscillating predominantly in phase (northern type asymmetry) or in antiphase (southern type asymmetry) with relatively short irregular transitions between these two states. Large asymmetry in the simulated Grand minima is found and explained by weak magnetic quenching of the $α$-effect during the minima. The possibility of polar field asymmetry in activity minima as a precursor of sunspot asymmetry in the following activity cycles is discussed based on the dynamo model and observations.

astro-ph.SR↗

arXiv2021

Subcritical dynamo and hysteresis in a Babcock-Leighton type kinematic dynamo model

In Sun and sun-like stars, it is believed that the cycles of the large-scale magnetic field are produced due to the existence of differential rotation and helicity in the plasma flows in their convection zones (CZs). Hence, it is expected that for each star, there is a critical dynamo number for the operation of a large-scale dynamo. As a star slows down, it is expected that the large-scale dynamo ceases to operate above a critical rotation period. In our study, we explore the possibility of the operation of the dynamo in the subcritical region using the Babcock--Leighton type kinematic dynamo model. In some parameter regimes, we find that the dynamo shows hysteresis behavior, i.e., two dynamo solutions are possible depending on the initial parameters -- decaying solution if started with weak field and strong oscillatory solution (subcritical dynamo) when started with a strong field. However, under large fluctuations in the dynamo parameter, the subcritical dynamo mode is unstable in some parameter regimes. Therefore, our study supports the possible existence of subcritical dynamo in some stars which was previously shown in a mean-field dynamo model with distributed $α$ and MHD turbulent dynamo simulations.

astro-ph.SR↗

arXiv2021

Hall instability: origin, properties, and asymptotic theory for its tearing mode

Hall instability in electron magnetohydrodynamics is interpreted as the shear-Hall instability driven jointly by helicoidal oscillations and shear in the electron current velocity. This explanation suggests an antiparallel orientation of the background magnetic field and vorticity of the current velocity as the necessary condition for Hall instability. The condition is tested and generally confirmed by numerical computations in plane slab geometry. Unstable eigenmodes are localized in the spatial regions of the antiparallel field and vorticity. Computations of the tearing-type mode of the instability are complemented by (and generally agree with) asymptotic analytical estimations for large Hall numbers. The stabilizing effect of perfect conductor boundary conditions is found and explained. For large Hall numbers, the growth rates approach the power law dependence $σ\propto B^αη^{1-α}$ on the magnetic field ($B$) and diffusivity ($η$). Almost all computations give the power index $α= 3/4$ with one exception of the tearing-type mode with vacuum boundary conditions for which case $α= 2/3$.

physics.plasm-ph↗

arXiv2020

Flux-tubes forming instability near the base of the rotating convection zone: A possible explanation for low latitudes of sunspots

The rise of flux-tubes with intense magnetic fields from the base of the convection zone to the solar surface has been substantiated as a probable mechanism for sunspot formation. The origin of flux-tubes of sufficient strength (~10^5 G) is however uncertain. This paper considers the instability of a large-scale toroidal magnetic field caused by the magnetic suppression of convective heat transport as a candidate for the flux tube forming mechanism. The consideration employs the analytical dependence of the eddy diffusion on the magnetic field supplied by mean-field magnetohydrodynamics. The instability tends to produce regions of increased field strength with spatial scales of an order of 100 Mm at the base of the convection zone. Characteristic growth times of the instability are short compared to the 11-year cycle. The threshold field strength for the onset of the instability increases from several hundred Gauss in the vicinity of the equator to some kilo-Gauss at middle latitudes. Growth rates of unstable disturbances decrease with latitude. These latitudinal trends can be the reason for the observed confinement of sunspot activity to a near-equatorial belt.

astro-ph.SR↗

arXiv2019

Modelling differential rotation of red giants: the case of the evolved sun

Asteroseismology has revealed that cores of red giants rotate about one order of magnitude faster than their convective envelopes. This paper attempts an explanation for this rotational state in terms of the theory of angular momentum transport in stellar convection zones. A differential rotation model based on the theory is applied to a sequence of evolutionary states of a red giant of one solar mass. The model computations show a rotation of about ten times faster in the cores compared to the stellar surface. This rotational state is caused by the non-diffusive downward convective transport of angular momentum. The contrast in rotational rates between core and envelope increases with the radius (age) of the star. Seismologically detected scaling for the spindown of the giants' cores is also reproduced.

astro-ph.SR↗

arXiv2019

Exploring cycle period and parity of stellar magnetic activity with dynamo modeling

Observations of chromospheric and coronal emissions from various solar-type stars show that the stellar magnetic activity varies with the rotation rates of the stars. The faster the star rotates, its magnetic activity gets stronger but activity cycle period does not show a straightforward variation with the rotation rate. For slowly rotating stars, the cycle period decreases with the increase of rotation rate, while for the fast rotators dependency of cycle period on rotation is presently quite complicated. We aim to provide an explanation of these observational trends of stellar magnetic activity using a dynamo model. We construct a theoretical dynamo model for stars of mass 1 $M_\odot$ based on the kinematic flux transport dynamo model including radial pumping near the surface of the stars. The inclusion of this near surface downward radial pumping is found to be necessary to match the observed surface magnetic field in case of the Sun. The main ingredients of our dynamo model, meridional circulation and differential rotation for stars are obtained from a mean-field hydrodynamic model. Our model shows a decrease of cycle period with increasing rotation rate in the slowly rotating regime and a slight increase of cycle period with rotation rate for the rapid rotators. The strength of the magnetic field is found to be increasing as the rotation rate of the star increases. We also find that the parity of the stellar magnetic field changes with rotation. According to our model, the parity flips to quadrupolar from dipolar if the rotation period of the star is less than 17 days.

astro-ph.SR↗

arXiv2019

Stability of a force-free Hall equilibrium and release of magnetic energy

Conservation of magnetic helicity by the Hall drift does not prevent Hall instability of helical fields. This conclusion follows from stability analysis of a force-free spatially-periodic Hall equilibrium. The growth rates of the instability scale as $σ\propto B^{3/4}η^{1/4}$ with the field strength $B$ and magnetic diffusivity $η$ and can be large compared to the rate of resistive decay of the background field. The instability deviates the magnetic field from the force-free configuration. The unstable eigenmodes include a fine spatial structure which evolves into current sheets at the nonlinear stage of the instability. The instability catalyses the resistive release of magnetic energy. The energy is released in a sequence of spikes, every spike emits several percent of the total energy. A numerically defined scaling for the energy released in a single spike permits an extrapolation to astrophysically relevant values of the Hall number. The instability can be relevant to magnetic energy release in a neutron star crust and, possibly, in stellar coronae.

astro-ph.SR↗

arXiv2019

Can the long-term hemispheric asymmetry of solar activity result from fluctuations in dynamo parameters?

The hemispheric asymmetry of sunspot activity observed possesses a regular component varying on a time scale of several solar cycles whose origin and properties are currently debated. This paper addresses the question of whether the long-term hemispheric asymmetry can result from random variations of solar dynamo parameters in time and latitude. Scatter in the observed tilt angles of sunspot groups is estimated to infer constraints on fluctuations in the dynamo mechanism for poloidal field regeneration. A dynamo model with fluctuations in the Babcock-Leighton type $α$-effect is designed in accordance with these constraints and then used to compute a large number of magnetic cycles for statistical analyses of their hemispheric asymmetry. Hemispheric asymmetry in the simulated dynamo results from the presence of an equator-symmetric part in the oscillating magnetic field. The subdominant quadrupolar oscillations are stochastically forced by dominant dipolar oscillations via the equator-symmetric part of the fluctuating $α$-effect. The amplitude and sense of the asymmetry of individual cycles varies on a time scale of the order of four dynamo-cycle periods. The variations are irregular, i.e. not periodic. The model suggests that asymmetry in the polar magnetic fields in the solar minima can be used as a precursor for asymmetry of sunspot activity in the following solar cycle.

astro-ph.SR↗

arXiv2018

Solar cycle asymmetry as a consequence of fluctuations in dynamo parameters

The duration of activity growths in solar cycles is on average shorter than the duration of its declines. This asymmetry can result from fluctuations in dynamo parameters. A solar dynamo model with fluctuations in the $α$-effect shows the statistical asymmetry which increases with both fluctuation amplitude and coherence time. An interpretation for the asymmetry origin is suggested, which predicts a correlation between the asymmetry measure and delay of the polar field reversals relative to the activity maxima. Data on the twelve latest solar cycles confirm such a correlation.

astro-ph.SR↗

arXiv2017

How supercritical are stellar dynamos, or why do old main-sequence dwarfs not obey gyrochronology?

Asteroseismological determinations of stellar ages have shown that old main-sequence dwarfs do not obey gyrochronology. Their rotation is slow compared to young stars but faster than gyrochronology predicts. This can be explained by the presence of a maximum rotation period beyond which the large-scale dynamo switches off and stops providing global magnetic fields necessary for stellar spindown. Assuming this explanation, the excess of stellar dynamo parameters over their marginal values can be estimated for given spectral type and rotation rate. The estimation gives the dynamo number for the Sun about 10% above its critical value. The corresponding dynamo model provides - though with some further tuning - reasonable results for the Sun. Following the same approach, the differential rotation and marginal dynamo modes are computed for stars between 0.7 and 1.2 solar masses. With increasing stellar mass, the differential rotation and the ratio of toroidal-to-poloidal field are predicted to increase while the field topology changes from dipolar to mixed quadrupolar-dipolar parity.

astro-ph.SR↗