arXiv subjects

Petri J. Käpylä

Publications and source records attributed to Petri J. Käpylä.

At least 19 recordsLinked to original sources

arXiv2026

Mean-field interpretation of star-in-a-box simulations of red giants

Context: The origin of magnetic fields and the dynamo mechanism in red giants are still not fully understood. Aims: We aim to interpret the dynamo behaviour of global 3D simulations of red giants using mean-field dynamo models. Methods: We use mean-field models constrained by the differential rotation profile extracted from 3D simulations. We perform $α^2$, $αΩ$, and $α^2Ω$ mean-field dynamo simulations, varying the strength of the $α$ effect and the differential rotation. Results: The mean-field models can reproduce the growth rate of several 3D runs. The morphology of the large-scale magnetic field is better reproduced for the slowly rotating 3D cases than for the rapidly rotating ones. Faster rotation enhances dynamo action and it also modifies the dominant mode of the dynamo. Rapidly rotating 3D runs produce predominantly non-axisymmetric equatorial dipoles instead of axisymmetric fields at slower rotation. Mean-field models are supercritical even in the absence of differential rotation, indicating $α^2$ dynamo action. By contrast, models using the $αΩ$ approximation require sufficiently strong differential rotation to become supercritical. Conclusions: Our results suggest that the magnetic field in red giants requires dynamo action. In our mean-field runs, differential rotation speeds up the magnetic decay, disfavouring the idea of a persistent fossil magnetic field in red giants.

astro-ph.SR↗

arXiv2026

Eclipsing time variations in close binaries produced by azimuthal dynamo waves

The nature of eclipsing time variations (ETVs) in post-common-envelope binaries (PCEBs) is still unknown. Circumbinary planets routinely fail the test of time and the Applegate mechanism has energetic constraints and problems in reproducing observations. Based on recent analytic models of magnetically-induced ETVs and stellar dynamo simulations, we aim at explaining ETVs via non-axisymmetric magnetic fields that drift in the azimuthal direction of the star, know as azimuthal dynamo waves (ADWs). We implement a time-varying non-axisymmetric quadrupole moment ($Q$) in a binary system. We solve for the dynamics of the system, compute the resulting eclipsing times, and construct O-C, diagrams. We perform several simulations with different amplitudes of $Q$, periods, stellar masses and binary separations. ADWs naturally give rise to characteristic shapes in the O-C diagram that resemble observations. Depending on how fast $Q$ changes, the solutions can have a sharp decrease in O-C producing amplitudes such as the one obtained in QS Vir, or sinusoidal-like shapes such as in V471 Tau or NN Ser. We also find that the amplitude of the eclipsing times varies from tens to hundreds of seconds. ADWs offer a self-consistent explanation for ETVs as they are expected in dynamo theory. They can explain a variety of features in the observed O-C diagrams. As suggested by dynamo simulations, ADWs are easily excited in rapidly rotating stars, alleviating energetic constrains required in the context of the Applegate mechanism. They produce non-axis $Q$ that in turn produce ETVs that can account for the long-term variation of the O-C, diagrams. We expect in this case that the resulting O-C diagrams are not strictly periodic, unlike explanations based on a third body that would imply a strict periodicity unless additional mechanisms are being invoked.

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arXiv2025

Magnetorotational instability in a solar near-surface mean-field dynamo

We address the question whether the magnetorotational instability (MRI) can operate in the near-surface shear layer (NSSL) of the Sun and how it affects the interaction with the dynamo process. Using hydromagnetic mean-field simulations of $αΩ$-type dynamos in rotating shearing-periodic boxes, we show that for negative shear, the MRI can operate above a certain critical shear parameter. This parameter scales inversely with the equipartition magnetic field strength above which $α$ quenching set in. Like the usual $Ω$ effect, the MRI produces toroidal magnetic field when the field is sufficiently strong. The work done by the Lorentz force is positive, so the magnetic field drives kinetic energy and not the other way around, as in a turbulent dynamo. This results in strong kinetic energy production and dissipation, which occurs at the expense of the magnetic energy. In view of the application to the solar NSSL, we conclude that the turbulent magnetic diffusivity may be too large for the MRI to be excited and that therefore only the standard $Ω$ effect is expected to operate.

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arXiv2025

Connecting mean-field theory with dynamo simulations

Mean-field dynamo theory, describing the evolution of large-scale magnetic fields, has been the mainstay of theoretical interpretation of magnetism in astrophysical objects such as the Sun for several decades. More recently, three-dimensional magnetohydrodynamic simulations have reached a level of fidelity where they capture dynamo action self-consistently on local and global scales without resorting to parametrization of unresolved scales. Recent global simulations also capture many of the observed characteristics of solar and stellar large-scale magnetic fields and cycles. Successful explanation of the results of such simulations with corresponding mean-field models is a crucial validation step for mean-field dynamo theory. Here the connections between mean-field theory and current dynamo simulations are reviewed. These connections range from the numerical computation of turbulent transport coefficients to mean-field models of simulations, and their relevance to the solar dynamo. Finally, the most notable successes and current challenges in mean-field theoretical interpretations of simulations are summarized.

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arXiv2025

Helicity effect on turbulent passive and active scalar diffusivities

Turbulent flows are known to produce enhanced effective magnetic and passive scalar diffusivities, which can fairly accurately be determined with numerical methods. It is now known that, if the flow is also helical, the effective magnetic diffusivity is reduced relative to the nonhelical value. Neither the usual second-order correlation approximation nor the various $τ$ approaches have been able to capture this. Here we show that the helicity effect on the turbulent passive scalar diffusivity works in the opposite sense and leads to an enhancement. We have also demonstrated that the correlation time of the turbulent velocity field increases with the kinetic helicity. This is a key point in the theoretical interpretation of the obtained numerical results. Simulations in which helicity is being produced self-consistently by stratified rotating turbulence resulted in a turbulent passive scalar diffusivity that was found to be decreasing with increasing rotation rate.

physics.flu-dyn↗

arXiv2023

Effects of rotation and surface forcing on deep stellar convection zones

The canonical undestanding of stellar convection has recently been put under doubt due to helioseismic results and global 3D convection simulations. This "convective conundrum" is manifested by much higher velocity amplitudes in simulations at large scales in comparison to helioseismic results, and the difficulty in reproducing the solar differential rotation and dynamo with global 3D simulations. Here some aspects of this conundrum are discussed from the viewpoint of hydrodynamic Cartesian 3D simulations targeted at testing the rotational influence and surface forcing on deep convection. More specifically, the dominant scale of convection and the depths of the convection zone and the weakly subadiabatic -- yet convecting -- Deardorff zone are discussed in detail.

astro-ph.SR↗

arXiv2023

Convective scale and subadiabatic layers in simulations of rotating compressible convection

(abridged) Context: Rotation is thought to influence the size of convective eddies and the efficiency of convective energy transport in the deep convection zones of stars. Rotationally constrained convection has been invoked to explain the lack of large-scale power in observations of solar flows. Aims: The main aims are to quantify the effects of rotation on the scale of convective eddies and velocity, the depths of convective overshoot, and the subadiabatic Deardorff layers. Methods: Three-dimensional hydrodynamic simulations of rotating convection in Cartesian domains were run. The results were compared with theoretical scaling results that assume a balance between Coriolis, inertial, and buoyancy (Archemedean) forces (CIA balance). Results: The scale of convective eddies decreases as rotation increases, and ultimately reaches a rotationally constrained regime consistent with the CIA balance. Using a new measure of the rotational influence on the system, it is shown that even the deep parts of the solar convection zone are not in the rotationally constrained regime. The simulations capture the slowly and rapidly rotating scaling laws predicted by theory, and the Sun appears to be in between these two regimes. Both, the overshooting depth and the extent of the Deardorff layer, decrease as rotation becomes more rapid. For sufficiently rapid rotation the Deardorff layer is absent. Conclusions: Relating the simulations with the Sun suggests that the convective scale even in the deep parts of the Sun is only mildly affected by rotation and that some other mechanism is needed to explain the lack of strong large-scale flows in the Sun. Taking the current results at face value, the overshoot and Deardorff layers are estimated to span roughly five per cent of the pressure scale height at the base of the convection zone in the Sun.

astro-ph.SR↗

arXiv2023

Effects of the centrifugal force in stellar dynamo simulations

The centrifugal force is often omitted from simulations of stellar convection either for numerical reasons or because it is assumed to be weak compared to the gravitational force. However, it might be an important factor in rapidly rotating stars, such as solar analogs, due to its $Ω^2$ scaling, where $Ω$ is the rotation rate of the star. We study the effects of the centrifugal force in a set of 21 semi-global stellar dynamo simulations with varying rotation rates. Included in the set are three control runs aimed at distinguishing the effects of the centrifugal force from the nonlinear evolution of the solutions. We decomposed the magnetic field into spherical harmonics and studied the migration of azimuthal dynamo waves (ADWs), the energy of different large-scale magnetic modes, and differential rotation. In the regime with the lowest rotation rates, $Ω= 5-10Ω_\odot$, where $Ω_\odot$ is the rotation rate of the Sun, we see no marked changes in either the differential rotation or the magnetic field properties. For intermediate rotation, $Ω= 20-25Ω_\odot$, we identify an increase in the differential rotation as a function of centrifugal force. The axisymmetric magnetic energy tends to decrease with centrifugal force, while the non-axisymmetric one increases. The ADWs are also affected, especially in the propagation direction. In the most rapidly rotating set with $Ω=30Ω_\odot$, these changes are more pronounced, and in one case the propagation direction of the ADW changes from prograde to retrograde. The control runs suggest that the results are a consequence of the centrifugal force and not due to the details of the initial conditions or the history of the run. We find that the differential rotation and the ADWs only change as a function of the centrifugal force when rotation is rapid enough.

astro-ph.SR↗

arXiv2023

Simulations of solar and stellar dynamos and their theoretical interpretation

We review the state of the art of three dimensional numerical simulations of solar and stellar dynamos. We summarize fundamental constraints of numerical modelling and the techniques to alleviate these restrictions. Brief summary of the relevant observations that the simulations seek to capture is given. We survey the current progress of simulations of solar convection and the resulting large-scale dynamo. We continue to studies that model the Sun at different ages and to studies of stars of different masses and evolutionary stages. Both simulations and observations indicate that rotation, measured by the Rossby number which is the ratio of rotation period and convective turnover time, is a key ingredient in setting the overall level and characteristics of magnetic activity. Finally, efforts to understand global 3D simulations in terms of mean-field dynamo theory are discussed.

astro-ph.SR↗

arXiv2022

Origin of eclipsing time variations in Post-Common-Envelope binaries: role of the centrifugal force

Eclipsing time variations (ETVs) in post-common-envelope binaries (PCEBs) were proposed to be due to the time-varying component of the stellar gravitational quadrupole moment. This is suggested to be produced by changes in the stellar structure due to an internal redistribution of angular momentum and the effect of the centrifugal force. We examined this hypothesis and present 3D simulations of compressible magnetohydrodynamics (MHD) performed with the {\sc Pencil Code}. We modeled the stellar dynamo for a solar-mass star with angular velocities of 20 and 30 times solar. We included and varied the strength of the centrifugal force and compared the results with reference simulations without the centrifugal force and with a simulation in which its effect is enhanced. The centrifugal force causes perturbations in the evolution of the numerical model, so that the outcome in the details becomes different as a result of nonlinear evolution. While the average density profile is unaffected by the centrifugal force, a relative change in the density difference between high latitudes and the equator of $\sim10^{-4}$ is found. The power spectrum of the convective velocity is found to be more sensitive to the angular velocity than to the strength of the centrifugal force. The quadrupole moment of the stars includes a fluctuating and a time-independent component, which vary with the rotation rate. As very similar behavior is produced in absence of the centrifugal force, we conclude that it is not the main ingredient for producing the time-averaged and fluctuating quadrupole moment of the star. In a real physical system, we thus expect contributions from both components, that is, from the time-dependent gravitational force from the variation in the quadrupole term and from the spin-orbit coupling that is due to the persistent part of the quadrupole.

astro-ph.SR↗

arXiv2022

Turbulent Prandtl number from isotropically forced turbulence

Turbulent motions enhance the diffusion of large-scale flows and temperature gradients. Such diffusion is often parameterized by coefficients of turbulent viscosity ($ν_{\rm t}$) and turbulent thermal diffusivity ($χ_{\rm t}$) that are analogous to their microscopic counterparts. We compute the turbulent diffusion coefficients by imposing large-scale velocity and temperature gradients on a turbulent flow and measuring the response of the system. We also confirm our results using experiments where the imposed gradients are allowed to decay. To achieve this, we use weakly compressible three-dimensional hydrodynamic simulations of isotropically forced homogeneous turbulence. We find that the turbulent viscosity and thermal diffusion, as well as their ratio the turbulent Prandtl number, ${\rm Pr}_{\rm t} = ν_{\rm t}/χ_{\rm t}$, approach asymptotic values at sufficiently high Reynolds and Peclét numbers. We also do not find a significant dependence of ${\rm Pr}_{\rm t}$ on the microscopic Prandtl number ${\rm Pr} = ν/χ$. These findings are in stark contrast to results from the $k-ε$ model which suggests that ${\rm Pr}_{\rm t}$ increases monotonically with decreasing ${\rm Pr}$. The current results are relevant for the ongoing debate of, for example, the nature of the turbulent flows in the very low ${\rm Pr}$ regimes of stellar convection zones.

physics.flu-dyn↗

arXiv2022

Transition from anti-solar to solar-like differential rotation: Dependence on Prandtl number

(abridged) Context: Late-type stars such as the Sun rotate differentially due to the interaction of turbulent convection and rotation. Aims: The aim of the study is to investigate the effects of the thermal Prandtl number on the transition from anti-solar (slow equator, fast poles) to solar-like (fast equator, slow poles) differential rotation. Methods: Three-dimensional hydrodynamic and magnetohydrodynamic simulations in semi-global spherical wedge geometry are used to model convection zones of solar-like stars. Results: The overall convective velocity amplitude increases as the Prandtl number decreases in accordance with earlier studies. The transition from anti-solar to solar-like differential rotation is insensitive to the Prandtl number for Prandtl numbers below unity but for Prandtl numbers greater than unity, solar-like differential rotation becomes significantly harder to excite. Magnetic fields and more turbulent regimes with higher fluid and magnetic Reynolds numbers help in achieving solar-like differential rotation in near-transition cases. Solar-like differential rotation occurs only in cases with radially outward angular momentum transport at the equator. The dominant contribution to such outward transport near the equator is due to prograde propagating thermal Rossby waves. Conclusions: The differential rotation is sensitive to the Prandtl number only for large Prandtl numbers in the parameter regime explored in the current study. Magnetic fields have a greater effect on the differential rotation, although the inferred presence of a small-scale dynamo does not lead to drastically different results in the present study. The dominance of the thermal Rossby waves in the simulations is puzzling given the non-detection in the Sun. The current simulations are shown to be incompatible with the currently prevailing mean-field theory of differential rotation.

astro-ph.SR↗

arXiv2022

Simulations of fully convective M dwarfs: dynamo action with varying magnetic Prandtl numbers

M dwarfs are low-mass main-sequence stars, the most numerous type of stars in the solar neighbourhood, which are known to have significant magnetic activity. The aim of this work is to explore the dynamo solutions and magnetic fields of fully convective M dwarfs with varying magnetic Prandtl numbers ${\rm Pr_M}$, and a rotation period (${\rm P_{rot}}$) of 43 days. ${\rm Pr_M}$ is known to play an important role in the dynamo action; dynamos for low-$\rm Pr_M$ and large-$\rm Pr_M$ have very different properties. We performed three-dimensional magnetohydrodynamical (MHD) numerical simulations with the ``star-in-a-box'' model using stellar parameters for an M5 dwarf with $0.21 M_{\odot}$. We found that the dynamo solutions are sensitive to ${\rm Pr_M}$. The simulations at this rotation period present periodic cycles of the large-scale magnetic field up to ${\rm Pr_M} \leq 2$; for higher values the cycles disappear and irregular solutions to arise. Our results are consistent with previous studies and suggest that the dynamos operating in fully convective stars behave similarly as those in partially convective stars.

astro-ph.SR↗

arXiv2022

Origin of eclipsing time variations: Contributions of different modes of the dynamo-generated magnetic field

The possibility to detect circumbinary planets and to study stellar magnetic fields through eclipsing time variations (ETVs) in binary stars has sparked an increase of interest in this area of research. We revisit the connection between stellar magnetic fields and the gravitational quadrupole moment $Q_{xx}$ and compare different dynamo-generated ETV models with our simulations. We present magnetohydrodynamical simulations of solar mass stars with rotation periods of 8.3, 1.2, and 0.8 days and perform a detailed analysis of the magnetic and quadrupole moment using spherical harmonic decomposition. The extrema of $Q_{xx}$ are associated with changes in the magnetic field structure. This is evident in the simulation with a rotation period of 1.2 days. Its magnetic field has a more complex behavior than in the other models, as the large-scale nonaxisymmetric field dominates throughout the simulation and the axisymmetric component is predominantly hemispheric. This triggers variations in the density field that follow the magnetic field asymmetry with respect to the equator, affecting the $zz$ component of the inertia tensor, and thus modulating $Q_{xx}$. The magnetic field of the two other runs are less variable in time and more symmetric with respect to the equator, such that the variations in the density are weaker, and therefore only small variations in $Q_{xx}$ are seen. If interpreted via the classical Applegate mechanism (tidal locking), the quadrupole moment variations obtained in the current simulations are about two orders of magnitude below those deduced from observations of post-common-envelope binaries. However, if no tidal locking is assumed, our results are compatible with the observed ETVs.

astro-ph.SR↗

arXiv2022

Solar-like dynamos and rotational scaling of cycles from star-in-a-box simulations

Magnetohydrodynamic star-in-a-box simulations of convection and dynamos in a solar-like star with different rotation rates are presented. These simulations produce solar-like differential rotation with a fast equator and slow poles, and magnetic activity that resembles that of the Sun with equatorward migrating activity at the surface. Furthermore, the ratio of rotation to cycle period is almost constant as the rotation period decreases in the limited sample considered here. This is reminiscent of the suggested inactive branch of stars from observations and differs from most earlier simulation results from spherical shell models. While the exact excitation mechanism of the dynamos in the current simulations is not yet clear, it is plausible that the greater freedom that the magnetic field has due to the inclusion of the radiative core and regions exterior to the star are important in shaping the dynamo.

astro-ph.SR↗

arXiv2021

Prandtl number dependence of compressible convection: Flow statistics and convective energy transport

(abridged) Context: The ratio of kinematic viscosity to thermal diffusivity, the Prandtl number, is much smaller than unity in stellar convection zones. Aims: To study the statistics of convective flows and energy transport as functions of the Prandtl number. Methods: Three-dimensional numerical simulations convection in Cartesian geometry are used. The convection zone (CZ) is embedded between two stably stratified layers. Statistics and transport properties of up- and downflows are studied separately. Results: The rms velocity increases with decreasing Prandtl number. At the same time the filling factor of downflows decreases and leads to stronger downflows at lower Prandtl numbers, and to a strong dependence of overshooting on the Prandtl number. Velocity power spectra do not show marked changes as a function of Prandtl number. At the highest Reynolds numbers the velocity power spectra are compatible with the Bolgiano-Obukhov $k^{-11/5}$ scaling. The horizontally averaged convected energy flux ($\overline{F}_{\rm conv}$) is independent of the Prandtl number within the CZ. However, the upflows (downflows) are the dominant contribution to the convected flux at low (high) Prandtl number. These results are similar to those from Rayleigh-Benárd convection in the low Prandtl number regime where convection is vigorously turbulent but inefficient at transporting energy. Conclusions: The current results indicate a strong dependence of convective overshooting and energy flux on the Prandtl number. Numerical simulations of astrophysical convection often use Prandtl number of unity. The current results suggest that this can lead to misleading results and that the astrophysically relevant low Prandtl number regime is qualitatively different from the parameters regimes explored in typical simulations.

astro-ph.SR↗

arXiv2021

Star-in-a-box simulations of fully convective stars

(abridged) Context: Main-sequence late-type stars with masses less than $0.35 M_\odot$ are fully convective. Aims: The goal is to study convection, differential rotation, and dynamos as functions of rotation in fully convective stars. Methods: Three-dimensional hydrodynamic and magnetohydrodynamic numerical simulations with a star-in-a-box model, where a spherical star is immersed inside of a Cartesian cube, are used. The model corresponds to a $0.2M_\odot$ M5 dwarf. Rotation periods ($P_{\rm rot}$) between 4.3 and 430 days are explored. Results: The slowly rotating model with $P_{\rm rot}=430$ days produces anti-solar differential rotation with a slow equator and fast poles, along with predominantly axisymmetric quasi-steady large-scale magnetic fields. For intermediate rotation ($P_{\rm rot}=144$ and $43$ days) differential rotation is solar-like (fast equator, slow poles) and large-scale magnetic fields are mostly axisymmetric and either quasi-stationary or cyclic. The latter occurs in a similar parameter regime as in other numerical studies in spherical shells, and the cycle period is similar to observed cycles in fully convective stars with comparable $P_{\rm rot}$. In the rapid rotation regime the differential rotation is weak and the large-scale magnetic fields are increasingly non-axisymmetric with a dominating $m=1$ mode. This large-scale non-axisymmetric field also exhibits azimuthal dynamo waves. Conclusions: The results of the star-in-a-box models agree with simulations of partially convective late-type stars in spherical shells in that the transitions in differential rotation and dynamo regimes occur at similar rotational regimes in terms of the Coriolis (inverse Rossby) number. This similarity between partially and fully convective stars suggests that the processes generating differential rotation and large-scale magnetism are insensitive to the geometry of the star.

astro-ph.SR↗

arXiv2020

Common dynamo scaling in slowly rotating young and evolved stars

One interpretation of the activity and magnetism of late-type stars is that these both intensify with decreasing Rossby number up to a saturation level, suggesting that stellar dynamos depend on both rotation and convective turbulence. Some studies have claimed, however, that rotation alone suffices to parametrise this scaling adequately. Here, we tackle the question of the relevance of turbulence to stellar dynamos by including evolved, post main sequence stars in the analysis of the rotation-activity relation. These stars rotate very slowly compared with main sequence stars, but exhibit similar activity levels. We show that the two evolutionary stages fall together in the rotation-activity diagram and form a single sequence in the unsaturated regime in relation only to Rossby numbers derived from stellar models, confirming earlier preliminary results that relied on a more simplistic parametrisation of the convective turnover time. This mirrors recent results of fully convective M dwarfs, which likewise fall on the same rotation-activity sequence as partially convective solar-type stars. Our results demonstrate that turbulence plays a crucial role in driving stellar dynamos and suggest that there is a common turbulence-related dynamo mechanism explaining the magnetic activity of all late-type stars.

astro-ph.SR↗