arXiv subjects

P. J. Käpylä

Publications and source records attributed to P. J. Käpylä.

At least 19 recordsLinked to original sources

arXiv2026

Grand minima and intermittency in near-critical convection-driven dynamos

Context: Solar magnetism exhibits long-term variations on timescales of decades to centuries. Aims: The main aim is to study how the supercriticality of the dynamo affects the variability of magnetic fields on timescales relevant to the Sun. Methods: Three-dimensional rotating magnetohydrodynamic simulations in a spherical wedge geometry are used to produce self-consistent convection-driven dynamos. The supercriticality of the dynamo is controlled by varying the magnetic diffusivity. Results: The main result is that long-term variability of the dynamo increases with decreasing supercriticality of the dynamo and that cases nearest to the onset of dynamo action show extended grand minima-like periods of low activity. The simulations fall in three classes where the least supercritical cases show the largest variations of magnetic activity and where the flow including differential rotation is almost unaffected by the magnetic field. In the cases with the highest supercriticality the magnetic field is permanently strong and differential rotation permanently quenched, both having relatively little temporal variation. In an intermediate regime both the magnetic fields and differential rotation exhibit strong anticorrelated fluctuations. Conclusions: The occurrence of grand minima in the Sun has been conjectured to be due to a weakly supercritical dynamo. The current results support this idea and suggest that the absence of grand minima in earlier global dynamo simulations is because their large-scale dynamos were too supercritical. Furthermore, the current results suggest that the effect of the magnetic field on differential rotation is negligible if the average rms-field is less than about 2~kG.

astro-ph.SR↗

arXiv2026

$Λ$ effect in rotating hydrodynamic convection

Context: Rotating anisotropic convection generates differential rotation in stellar convection zones. Aims: The main aim is to compute the non-diffusive contribution ($Λ$ effect) to angular momentum transport, described by Reynolds stress, from rotating turbulent convection. Methods: Rotating hydrodynamic convection is simulated in Cartesian geometry at different latitudes and rotation rates. Large-scale flows are suppressed such that the Reynolds stress is due to non-diffusive effects. Results: The radial angular momentum flux is downward (outward) for slow (fast) rotation. This is in contrast in prevailing theories in mean-field hydrodynamics where the radial transport is always downward. The outward transport at rapid rotation is due to thermal Rossby waves that manifest as elongated large-scale convection cells near the equator. The horizontal angular momentum flux is always equatorward, with increasing concentration toward the equator as in earlier Cartesian studies. The magnitudes of the $Λ$ effect coefficients are roughly an order of magnitude lower than in the case of anisotropically forced turbulence or in analytic theories. Conclusions: The current results highlight the tension between numerical simulations, widely used mean-field models, and solar observations. The mean-fields models have been remarkably successful in reproducing solar differential rotation but underlying assumptions regarding turbulence in these models seem to be at odds with 3D simulations. The current simulation results for the vertical (radial) angular momentum transport are in accordance with spherical shell simulations, where thermal Rossby waves are responsible for the generation of equatorial acceleration or solar-like differential rotation. Thermal Rossby waves are absent in the turbulence models of current mean-field theories and they have not been unambiguously detected in the Sun.

astro-ph.SR↗

arXiv2025

Shaping core dynamos in A-type stars: The role of dipolar fossil fields

Large-scale magnetic fields of Ap/Bp stars are stable over long timescales and have typically simple dipolar geometries, leading to the idea of a fossil origin. These stars are also expected to have convective cores that can host strong dynamo action. We aim to study the interaction between the magnetic fields generated by the convective core dynamo of the star, and a dipolar fossil field reminiscent of observed magnetic topologies of Ap/Bp stars. We use numerical 3D star-in-a-box simulations of a $2.2M_\odot$ A-type star, where the core encompasses $20\%$ of the stellar radius. As an initial condition, we impose two purely poloidal configurations, both with a surface dipolar strength of 6 kG, and we explore different obliquity angles $β$ (the angle between the magnetic and rotational axes), ranging from $0^\circ$ to $90^\circ$. The inclusion of a poloidal field where none of the magnetic field lines are closed inside the star, does not affect the core dynamo in a significant way. Dipolar configurations where all the field lines are closed inside the star can enhance the dynamo, producing a superequipartition quasi-stationary solution, where the magnetic energy is 5 times stronger than the kinetic energy. The enhanced core dynamos have typical magnetic field strengths between 105 and 172 kG, where the strength has an inverse relation with $β$. The strong magnetic fields produce an almost rigid rotation in the radiative envelope, and change the differential rotation of the core from solar-like to anti-solar. The only cases where the imposed dipoles are unstable and decay are those with $β= 90^\circ$. In the rest of cases, the core dynamos are enhanced and the surface magnetic field survives keeping simple topologies like in the observations.

astro-ph.SR↗

arXiv2025

Simulations of entropy rain-driven convection

Context: The paradigm of convection in solar-like stars is questioned based on recent solar observations. Aims: The primary aim is to study the effects of surface-driven entropy rain on convection zone structure and flows. Methods: Simulations of compressible convection in Cartesian geometry with non-uniform surface cooling are used. The cooling profile includes localized cool patches that drive deeply penetrating plumes. Results are compared with cases with uniform cooling. Results: Sufficiently strong surface driving leads to strong non-locality and a largely subadiabatic convectively mixed layer. In such cases the net convective energy transport is done almost solely by the downflows. The spatial scale of flows decreases with increasing number of cooling patches for the vertical flows whereas the horizontal flows still peak at large scales. Conclusions: To reach the plume-dominated regime with a predominantly subadiabatic bulk of the convection zone requires significantly more efficient entropy rain than what is realized in simulations with uniform cooling. It is plausible that this regime is realized in the Sun but that it occurs on scales smaller than those resolved currently. Current results show that entropy rain can lead to largely mildly subadiabatic convection zone, whereas its effects for the scale of convection are more subtle.

astro-ph.SR↗

arXiv2024

Magnetohydrodynamic simulations of A-type stars: Long-term evolution of core dynamo cycles

Early-type stars have convective cores due to a steep temperature gradient produced by the CNO cycle. These cores can host dynamos, and the generated magnetic fields can be relevant to explain the magnetism observed in Ap/Bp stars. Our main objective is to characterise the convective core dynamos and differential rotation, and to do the first quantitative analysis of the relation between magnetic activity cycle and rotation period. We use numerical 3D star-in-a-box simulations of a $2.2~M_\odot$ A-type star with a convective core of roughly $20\%$ of the stellar radius surrounded by a radiative envelope. Rotation rates from 8 to 20 days are explored. We use two models of the entire star, and an additional zoom set, where $50\%$ of the radius is retained. The simulations produce hemispheric core dynamos with cycles and typical magnetic field strengths around 60 kG. However, only a very small fraction of the magnetic energy is able to reach the surface. The cores have solar-like differential rotation, and a substantial part of the radiative envelope has quasi-rigid rotation. In the most rapidly rotating cases the magnetic energy in the core is roughly 40\% of the kinetic energy. Finally, we find that the magnetic cycle period $P_\mathrm{cyc}$ increases with decreasing the rotation period $P_\mathrm{rot}$ which is also observed in many simulations of solar-type stars. Our simulations indicate that a strong hemispherical core dynamo arises routinely, but that it is not enough the explain the surface magnetism of Ap/Bp stars. Nevertheless, as the core dynamo produces dynamically relevant magnetic fields it should not be neglected when other mechanisms are explored.

astro-ph.SR↗

arXiv2023

Simulations of dynamo action in slowly rotating M dwarfs: Dependence on dimensionless parameters

The aim of this study is to explore the magnetic and flow properties of fully convective M dwarfs as a function of rotation period Prot and magnetic Reynolds ReM and Prandlt numbers PrM. We performed three-dimensional simulations of fully convective stars using a star-in-a-box setup. This setup allows global dynamo simulations in a sphere embedded in a Cartesian cube. The equations of non-ideal magnetohydrodynamics were solved with the Pencil Code. We used the stellar parameters of an M5 dwarf with 0.21M_odot at three rotation rates corresponding to rotation periods (Prot): 43, 61 and 90 days, and varied the magnetic Prandtl number in the range from 0.1 to 10. We found systematic differences in the behaviour of the large-scale magnetic field as functions of rotation and PrM. For the simulations with Prot = 43 days and PrM <= 2, we found cyclic large-scale magnetic fields. For PrM > 2 the cycles vanish and field shows irregular reversals. In simulations with Prot = 61 days for PrM <= 2 the cycles are less clear and the reversal are less periodic. In the higher-PrM cases, the axisymmetric mean field shows irregular variations. For the slowest rotation case with Prot = 90 days, the field has an important dipolar component for PrM <= 5. For the highest PrM the large-scale magnetic field is predominantly irregular at mid-latitudes, with quasi-stationary fields near the poles. For the simulations with cycles, the cycle period length slightly increases with increasing ReM.

astro-ph.SR↗

arXiv2023

Origin of magnetism in early-type stars

According to our understanding of stellar evolution, early-type stars have radiative envelopes and convective cores due to a steep temperature gradient produced by the CNO cycle. Some of these stars (mainly, the subclasses Ap and Bp) have strong magnetic fields, enough to be directly observed using the Zeeman effect. Here, we present 3D magnetohydrodynamic simulations of an $2 ~M_{\odot}$ A-type star using the star-in-a-box model. Our goal is to explore if the modeled star is able to maintain a magnetic field as strong as the observed ones, via a dynamo driven by its convective core, or via maintaining a stable fossil field configuration coming from its early evolutionary stages, using different rotation rates. We created two models, a partially radiative and a fully radiative one, which are determined by the value of the heat conductivity. Our model is able to explore both scenarios, including convection-driven dynamos.

astro-ph.SR↗

arXiv2022

Magnetism, rotation, and nonthermal emission in cool stars -- Average magnetic field measurements in 292 M dwarfs

Stellar dynamos generate magnetic fields that are of fundamental importance to the variability and evolution of Sun-like and low-mass stars, and for the development of their planetary systems. We report measurements of surface-average magnetic fields in 292 M dwarfs from a comparison with radiative transfer calculations; for 260 of them, this is the first measurement of this kind. Our data were obtained from more than 15,000 high-resolution spectra taken during the CARMENES project. They reveal a relation between average field strength, , and Rossby number, $Ro$, resembling the well-studied rotation-activity relation. Among the slowly rotating stars, we find that magnetic flux, $Φ_\textrm{B}$, is proportional to rotation period, $P$, and among the rapidly rotating stars that average surface fields do not grow significantly beyond the level set by the available kinetic energy. Furthermore, we find close relations between nonthermal coronal X-ray emission, chromospheric H$α$ and Ca H&K emission, and magnetic flux. Taken together, these relations demonstrate empirically that the rotation-activity relation can be traced back to a dependence of the magnetic dynamo on rotation. We advocate the picture that the magnetic dynamo generates magnetic flux on the stellar surface proportional to rotation rate with a saturation limit set by the available kinetic energy, and we provide relations for average field strengths and nonthermal emission that are independent of the choice of the convective turnover time. We also find that Ca H&K emission saturates at average field strengths of $\langle B \rangle \approx 800$ G while H$α$ and X-ray emission grow further with stronger fields in the more rapidly rotating stars. This is in conflict with the coronal stripping scenario predicting that in the most rapidly rotating stars coronal plasma would be cooled to chromospheric temperatures.

astro-ph.SR↗

arXiv2020

Generation of mean flows in rotating anisotropic turbulence: The case of solar near-surface shear layer

The radial gradient of the rotation rate in the near-surface shear layer (NSSL) of the Sun is independent of latitude and radius. Theoretical mean-field models have been successful in explaining this property of the solar NSSL, while global direct convection models have been unsuccessful. We investigate reason for this discrepancy by measuring the mean flows, Reynolds stress, and turbulent transport coefficients under NSSL conditions. Simulations have minimal ingredients. These ingredients are inhomogeneity due to boundaries, anisotropic turbulence, and rotation. Parameters of the simulations are chosen such they match the weakly rotationally constrained NSSL. The simulations probe locally Cartesian patches of the star at a given depth and latitude. The depth of the patch is varied by changing the rotation rate such that the resulting Coriolis numbers<1. We measure the turbulent transport coefficient relevant for the non-diffusive and diffusive parts of the Reynolds stress and compare them with predictions of current mean-field theories. A negative radial gradient of mean flow similar to the solar NSSL is generated only at the equator where meridional flows are absent. At other latitudes the meridional flow is comparable to the mean flow corresponding to differential rotation. We also find that meridional components of the Reynolds stress cannot be ignored. Additionally, we find that the turbulent viscosity is quenched by rotation by about 50\% from the surface to the bottom of the NSSL. Our local simulations do not validate the explanation for the generation of the NSSL from mean-field theory where meridional stresses are neglected. However, the rotational dependence of turbulent viscosity in our simulations is in good agreement with theoretical prediction. Our results are in qualitative agreement with global convection simulations in that a NSSL obtained near the equator.

astro-ph.SR↗

arXiv2020

The Pencil Code, a modular MPI code for partial differential equations and particles: multipurpose and multiuser-maintained

The Pencil Code is a highly modular physics-oriented simulation code that can be adapted to a wide range of applications. It is primarily designed to solve partial differential equations (PDEs) of compressible hydrodynamics and has lots of add-ons ranging from astrophysical magnetohydrodynamics (MHD) to meteorological cloud microphysics and engineering applications in combustion. Nevertheless, the framework is general and can also be applied to situations not related to hydrodynamics or even PDEs, for example when just the message passing interface or input/output strategies of the code are to be used. The code can also evolve Lagrangian (inertial and noninertial) particles, their coagulation and condensation, as well as their interaction with the fluid.

astro-ph.IM↗

arXiv2020

Electrodynamics of turbulent fluids with fluctuating electric conductivity

The influence of fluctuating conductivity on the coefficients known from the mean-field electrodynamics is considered. If the conductivity fluctuations are assumed as uncorrelated with the turbulent velocity field then only the effective magnetic diffusivity of the fluid is reduced and the decay time of a large-scale magnetic field is increased. If the fluctuations of conductivity and flow are correlated in a certain direction then an additional diamagnetic pumping effect results transporting magnetic field in opposite direction to the resistivity flux vector $\langle η'\vec{u}'\rangle$. Even for homogeneous turbulence fields in the presence of rotation an alpha effect appears. With the characteristic values of the outer core of the Earth or the solar convection zone, however, the dynamo number of the alpha effect never reaches supercritical values to operate as an $α^2$-dynamo.

physics.plasm-ph↗

arXiv2019

Stellar dynamos in the transition regime: multiple dynamo modes and anti-solar differential rotation

Global and semi-global convective dynamo simulations of solar-like stars are known to show a transition from an anti-solar (fast poles, slow equator) to solar-like (fast equator, slow poles) differential rotation (DR) for increasing rotation rate. The dynamo solutions in the latter regime can exhibit regular cyclic modes, whereas in the former one, only stationary or temporally irregular solutions have been obtained so far. In this paper we present a semi-global dynamo simulation in the transition region, exhibiting two coexisting dynamo modes, a cyclic and a stationary one, both being dynamically significant. We seek to understand how such a dynamo is driven by analyzing the large-scale flow properties (DR and meridional circulation) together with the turbulent transport coefficients obtained with the test-field method. Neither an $αΩ$ dynamo wave nor an advection-dominated dynamo are able to explain the cycle period and the propagation direction of the mean magnetic field. Furthermore, we find that the $α$ effect is comparable or even larger than the $Ω$ effect in generating the toroidal magnetic field, and therefore, the dynamo seems to be $α^2Ω$ or $α^2$ type. We further find that the effective large-scale flows are significantly altered by turbulent pumping.

astro-ph.SR↗

arXiv2018

Large-scale dynamos in rapidly rotating plane layer convection

Context: Convectively-driven flows play a crucial role in the dynamo processes that are responsible for producing magnetic activity in stars and planets. It is still not fully understood why many astrophysical magnetic fields have a significant large-scale component. Aims: Our aim is to investigate the dynamo properties of compressible convection in a rapidly rotating Cartesian domain, focusing upon a parameter regime in which the underlying hydrodynamic flow is known to be unstable to a large-scale vortex instability. Methods: The governing equations of three-dimensional nonlinear magnetohydrodynamics (MHD) are solved numerically. Different numerical schemes are compared and we propose a possible benchmark case for other similar codes. Results: In keeping with previous related studies, we find that convection in this parameter regime can drive a large-scale dynamo. The components of the mean horizontal magnetic field oscillate, leading to a continuous overall rotation of the mean field. Whilst the large-scale vortex instability dominates the early evolution of the system, it is suppressed by the magnetic field and makes a negligible contribution to the mean electromotive force that is responsible for driving the large-scale dynamo. The cycle period of the dynamo is comparable to the ohmic decay time, with longer cycles for dynamos in convective systems that are closer to onset. In these particular simulations, large-scale dynamo action is found only when vertical magnetic field boundary conditions are adopted at the upper and lower boundaries. Strongly modulated large-scale dynamos are found at higher Rayleigh numbers, with periods of reduced activity ("grand minima"-like events) occurring during transient phases in which the large-scale vortex temporarily re-establishes itself, before being suppressed again by the magnetic field.

astro-ph.SR↗

arXiv2016

Convection-driven spherical shell dynamos at varying Prandtl numbers

(abidged) Context: Stellar convection zones are characterized by vigorous high-Reynolds number turbulence at low Prandtl numbers. Aims: We study the dynamo and differential rotation regimes at varying levels of viscous, thermal, and magnetic diffusion. Methods: We perform three-dimensional simulations of stratified fully compressible magnetohydrodynamic convection in rotating spherical wedges at various thermal and magnetic Prandtl numbers (from 0.25 to 2 and 5, respectively). Results: We find that the rotation profiles for high thermal diffusivity show a monotonically increasing angular velocity from the bottom of the convection zone to the top and from the poles toward the equator. For sufficiently rapid rotation, a region of negative radial shear develops at mid-latitudes as the thermal diffusivity is decreased. This coincides with a change in the dynamo mode from poleward propagating activity belts to equatorward propagating ones. Furthermore, the cyclic solutions disappear at the highest magnetic Reynolds numbers. The total magnetic energy increases with the magnetic Reynolds number in the range studied here ($5-151$), but the energies of the mean magnetic fields level off at high magnetic Reynolds numbers. The differential rotation is strongly affected by the magnetic fields and almost vanishes at the highest magnetic Reynolds numbers. In some of our most turbulent cases we find that two regimes are possible where either differential rotation is strong and mean magnetic fields relatively weak or vice versa. Conclusions: Our simulations indicate a strong non-linear feedback of magnetic fields on differential rotation, leading to qualitative changes in the behaviors of large-scale dynamos at high magnetic Reynolds numbers. Furthermore, we do not find indications of the simulations approaching an asymptotic regime where the results would be independent of diffusion coefficients.

astro-ph.SR↗

arXiv2016

Robustness of oscillatory $α^2$ dynamos in spherical wedges

We study the connection between spherical wedge and full spherical shell geometries using simple mean-field $α^2$ dynamos. We solve the equations for a one-dimensional time-dependent mean-field dynamo to examine the effects of varying the polar angle $θ_0$ between the latitudinal boundaries and the poles in spherical coordinates. We investigate the effects of turbulent magnetic diffusivity and $α$ effect profiles as well as different latitudinal boundary conditions to isolate parameter regimes where oscillatory solutions are found. Finally, we add shear along with a damping term mimicking radial gradients to study the resulting dynamo regimes. We find that the commonly used perfect conductor boundary condition leads to oscillatory $α^2$ dynamo solutions only if the wedge boundary is at least one degree away from the poles. Other boundary conditions always produce stationary solutions. By varying the profile of the turbulent magnetic diffusivity alone, oscillatory solutions are achieved with models extending to the poles, but the magnetic field is strongly concentrated near the poles and the oscillation period is very long. By introducing radial shear and a damping term mimicking radial gradients, we again see oscillatory dynamos, and the direction of drift follows the Parker--Yoshimura rule. Oscillatory solutions in the weak shear regime are found only in the wedge case with $θ_0 = 1^\circ$ and perfect conductor boundaries. A reduced $α$ effect near the poles with a turbulent diffusivity concentrated toward the equator yields oscillatory dynamos with equatorward migration and reproduces best the solutions in spherical wedges.

astro-ph.SR↗

arXiv2015

Magnetic flux concentrations from turbulent stratified convection

(abridged) Context: The mechanisms that cause the formation of sunspots are still unclear. Aims: We study the self-organisation of initially uniform sub-equipartition magnetic fields by highly stratified turbulent convection. Methods: We perform simulations of magnetoconvection in Cartesian domains that are $8.5$-$24$ Mm deep and $34$-$96$ Mm wide. We impose either a vertical or a horizontal uniform magnetic field in a convection-driven turbulent flow. Results: We find that super-equipartition magnetic flux concentrations are formed near the surface with domain depths of $12.5$ and $24$ Mm. The size of the concentrations increases as the box size increases and the largest structures ($20$ Mm horizontally) are obtained in the 24 Mm deep models. The field strength in the concentrations is in the range of $3$-$5$ kG. The concentrations grow approximately linearly in time. The effective magnetic pressure measured in the simulations is positive near the surface and negative in the bulk of the convection zone. Its derivative with respect to the mean magnetic field, however, is positive in the majority of the domain, which is unfavourable for the negative effective magnetic pressure instability (NEMPI). Furthermore, we find that magnetic flux is concentrated in regions of converging flow corresponding to large-scale supergranulation convection pattern. Conclusions: The linear growth of large-scale flux concentrations implies that their dominant formation process is tangling of the large-scale field rather than an instability. One plausible mechanism explaining both the linear growth and the concentrate on of the flux in the regions of converging flow pattern is flux expulsion. Possible reasons for the absence of NEMPI are that the derivative of the effective magnetic pressure with respect to the mean magnetic field has an unfavourable sign and that there may not be sufficient scale separation.

astro-ph.SR↗

arXiv2014

Dynamical quenching with non-local alpha and downward pumping

In light of new results, the one-dimensional mean-field dynamo model of Brandenburg & Kapyla (2007) with dynamical quenching and a nonlocal Babcock-Leighton alpha effect is re-examined for the solar dynamo. We extend the one-dimensional model to include the effects of turbulent downward pumping (Kitchatinov & Olemskoy 2011), and to combine dynamical quenching with shear. We use both the conventional dynamical quenching model of Kleeorin & Ruzmaikin (1982) and the alternate one of Hubbard & Brandenburg (2011), and confirm that with varying levels of non-locality in the alpha effect, and possibly shear as well, the saturation field strength can be independent of the magnetic Reynolds number.

astro-ph.SR↗

arXiv2014

Confirmation of bistable stellar differential rotation profiles

(abridged) Context: Solar-like differential rotation is characterized by a rapidly rotating equator and slower poles. However, theoretical models and numerical simulations can result in a slower equator and faster poles when the rotation is slow. Aims: We study the critical rotational influence under which differential rotation flips from solar-like (fast equator, slow poles) to an anti-solar one (slow equator, fast poles). We estimate the non-diffusive ($Λ$ effect) and diffusive (turbulent viscosity) contributions to the Reynolds stress. Methods: We present the results of three-dimensional numerical simulations of mildly turbulent convection in spherical wedge geometry. Here we apply a fully compressible setup which would suffer from a prohibitive time step constraint if the real solar luminosity was used. We regulate the convective velocities by varying the amount of heat transported by thermal conduction, turbulent diffusion, and resolved convection. Results: Increasing the efficiency of resolved convection leads to a reduction of the rotational influence on the flow and a sharp transition from solar-like to anti-solar differential rotation for Coriolis numbers around 1.3. We confirm the recent finding of a large-scale flow bistability: contrasted with running the models from an initial condition with unprescribed differential rotation, the initialization of the model with certain kind of rotation profile sustains the solution over a wider parameter range. Conclusions: Our results may have implications for real stars that start their lives as rapid rotators implying solar-like rotation in the early main-sequence evolution. As they slow down, they might be able to retain solar-like rotation for lower Coriolis numbers before switching to anti-solar rotation. This could partially explain the puzzling findings of anti-solar rotation profiles for models in the solar parameter regime.

astro-ph.SR↗