Keywords

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.

The existence of partially conserved enstrophy-like quantities is conjectured to cause inverse energy transfers to develop embedded in magnetohydrodynamical (MHD) turbulence, in analogy to the influence of enstrophy in two-dimensional nonconducting turbulence. By decomposing the velocity and magnetic fields in spectral space onto helical modes, we identify subsets of three-wave (triad) interactions conserving two new enstrophy-like quantities that can be mapped to triad interactions recently identified with facilitating large-scale α-type dynamo action and the inverse transfer of magnetic helicity. Due to their dependence on interaction scale locality, invariants suggest that the inverse transfer of magnetic helicity might be facilitated by both local- and nonlocal-scale interactions, and is a process more local than the α-dynamo. We test the predicted embedded (partial) energy fluxes by constructing a shell model (reduced wave-space model) of the minimal set of triad interactions (MTI) required to conserve the ideal MHD invariants. Numerically simulated MTIs demonstrate that, for a range of forcing configurations, the partial invariants are, with some exceptions, indeed useful for understanding the embedded contributions to the total spectral energy flux. Furthermore, we demonstrate that strictly inverse energy transfers may develop if enstrophy-like conserving interactions are favored, a mechanism recently attributed to the energy cascade reversals found in nonconducting three-dimensional turbulence subject to strong rotation or confinement. The presented results have implications for the understanding of the physical mechanisms behind large-scale dynamo action and the inverse transfer of magnetic helicity, processes thought to be central to large-scale magnetic structure formation.

Global and semi-global convective dynamo simulations of solar-like stars are known to show a transition from an antisolar (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 of α²Ω or α² type. We further find that the effective large-scale flows are significantly altered by turbulent pumping.

If the α effect plays a role in the generation of the Sun's magnetic field, the field should show evidence of magnetic helicity of opposite signs at large and small length scales. Measuring this faces two challenges: (i) in weak-field regions, horizontal field measurements are unreliable because of the π ambiguity, and (ii) one needs a truly global approach to computing helicity spectra in the case where one expects a sign reversal across the equator at all wavenumbers. Here we develop such a method using spin-2 spherical harmonics to decompose the linear polarization in terms of the parity-even and parity-odd E and B polarizations, respectively. Using simple one- and two-dimensional models, we show that the product of the spectral decompositions of E and B, taken at spherical harmonic degrees that are shifted by one, can act as a proxy of the global magnetic helicity with a sign that represents that in the northern hemisphere. We then apply this method to the analysis of solar synoptic vector magnetograms, from which we extract a pseudo-polarization corresponding to a "π-ambiguated" magnetic field, i.e., a magnetic field vector that has no arrow. We find a negative sign of the global EB helicity proxy at spherical harmonic degrees of around 6. This could indicate a positive magnetic helicity at large length scales, but the spectrum fails to capture clear evidence of the well-known negative magnetic helicity at smaller scales. This method might also be applicable to stellar and Galactic polarization data.

Weak magnetic fields have recently been detected in a number of A-type stars, including Vega and Sirius. At the same time, space photometry observations of A and late B-type stars from Kepler and TESS have highlighted the existence of rotational modulation of surface features akin to stellar spots. Here we explore the possibility that surface magnetic spots might be caused by the presence of small envelope convective layers at or just below the stellar surface, caused by recombination of H and He. Using 1D stellar evolution calculations and assuming an equipartition dynamo, we make simple estimates of field strength at the photosphere. For most models, the largest effects are caused by a convective layer driven by second helium ionization. While it is difficult to predict the geometry of the magnetic field, we conclude that the majority of intermediate-mass stars should have dynamo-generated magnetic fields of order a few Gauss at the surface. These magnetic fields can appear at the surface as bright spots and cause photometric variability via rotational modulation, which could also be widespread in A-stars. The amplitude of surface magnetic fields and their associated photometric variability are expected to decrease with increasing stellar mass and surface temperature, so that magnetic spots and their observational effects should be much harder to detect in late B-type stars.

We compute magnetic helicity and energy spectra from about 2485 patches of about 100 Mm side length on the solar surface using data from Hinode during 2006–2017. An extensive database is assembled where we list the magnetic energy and helicity, large- and small-scale magnetic helicity, mean current helicity density, fractional magnetic helicity, and correlation length along with the Hinode map identification number (MapID), as well as the Carrington latitude and longitude for each MapID. While there are departures from the hemispheric sign rule for magnetic and current helicities, the weak trend reported here is in agreement with the previous results. This is argued to be a physical effect associated with the dominance of individual active regions that contribute more strongly in the better-resolved Hinode maps. In comparison with earlier work, the typical correlation length is found to be 6–$8\,\mathrm{Mm}$, while the length scale relating the magnetic and current helicities to each other is around $1.4\,\mathrm{Mm}$.

The Tayler instability (TI) is a non-axisymmetric linear instability of an axisymmetric toroidal magnetic field in magnetohydrostatic equilibrium (MHSE). In a differentially rotating radiative region of a star, the TI could drive the Tayler–Spruit dynamo, which generates magnetic fields that can significantly impact stellar structure and evolution. Heuristic prescriptions disagree on the efficacy of the dynamo, and numerical simulations have yet to definitively agree upon its existence. The criteria for the TI to develop were derived using fully compressible magnetohydrodynamics, while numerical simulations of dynamical processes in stars frequently use an anelastic approximation. This motivates us to derive new anelastic Tayler instability criteria. We find that some MHSE configurations are unstable in the fully compressible case but become stable in the anelastic case. We find and characterize the unstable modes of a simple family of cylindrical MHSE configurations using numerical calculations, and we discuss the implications for fully nonlinear anelastic simulations.

Two fundamental properties of stellar magnetic fields have been determined by observations for solar-like stars with different Rossby numbers (${\rm{Ro}}$), namely, the magnetic field strength and the magnetic cycle period. The field strength exhibits two regimes: (1) for fast rotation, it is independent of ${\rm{Ro}}$, and (2) for slow rotation, it decays with ${\rm{Ro}}$ following a power law. For the magnetic cycle period, two regimes of activity, the active and inactive branches, have also been identified. For both of them, the longer the rotation period, the longer the activity cycle. Using global dynamo simulations of solar-like stars with Rossby numbers between ∼0.4 and ∼2, this paper explores the relevance of rotational shear layers in determining these observational properties. Our results, consistent with nonlinear ${\alpha }^{2}{\rm{\Omega }}$ dynamos, show that the total magnetic field strength is independent of the rotation period. Yet at surface levels, the origin of the magnetic field is determined by ${\rm{Ro}}$. While for ${\rm{Ro}}\lesssim 1$, it is generated in the convection zone, for ${\rm{Ro}}\gtrsim 1$, strong toroidal fields are generated at the tachocline and rapidly emerge toward the surface. In agreement with the observations, the magnetic cycle period increases with the rotational period. However, a bifurcation is observed for ${\rm{Ro}}\sim 1$, separating a regime where oscillatory dynamos operate mainly in the convection zone from the regime where the tachocline has a predominant role. In the latter, the cycles are believed to result from the periodic energy exchange between the dynamo and the magneto-shear instabilities developing in the tachocline and the radiative interior.

We show that at large magnetic Prandtl numbers, the Lorentz force does work on the flow at small scales and drives fluid motions, whose energy is dissipated viscously. This situation is the opposite of that in a normal dynamo, where the flow does work against the Lorentz force. We compute the spectral conversion rates between kinetic and magnetic energies for several magnetic Prandtl numbers and show that normal (forward) dynamo action occurs on large scales over a progressively narrower range of wavenumbers as the magnetic Prandtl number is increased. At higher wavenumbers, reversed dynamo action occurs, i.e., magnetic energy is converted back into kinetic energy at small scales. We demonstrate this in both direct numerical simulations forced by volume stirring and in large eddy simulations (LESs) of solar convectively driven small-scale dynamos. Low-density plasmas such as stellar coronae tend to have large magnetic Prandtl numbers, i.e., the viscosity is large compared with the magnetic diffusivity. The regime in which viscous dissipation dominates over resistive dissipation for large magnetic Prandtl numbers was also previously found in LESs of the solar corona, i.e., our findings are a more fundamental property of MHD that is not just restricted to dynamos. Viscous energy dissipation is a consequence of positive Lorentz force work, which may partly correspond to particle acceleration in close-to-collisionless plasmas. This is, however, not modeled in the MHD approximation employed. By contrast, resistive energy dissipation on current sheets is expected to be unimportant in stellar coronae.

The presence of magnetic field is crucial in the transport of energy through the solar atmosphere. Recent ground-based and space-borne observations of the quiet Sun have revealed that magnetic field accumulates at photospheric heights, via a local dynamo or from small-scale flux emergence events. However, most of this small-scale magnetic field may not expand into the chromosphere due to the entropy drop with height at the photosphere. Here we present a study that uses a high-resolution 3D radiative MHD simulation of the solar atmosphere with non-gray and non-LTE radiative transfer and thermal conduction along the magnetic field to reveal that (1) the net magnetic flux from the simulated quiet photosphere is not sufficient to maintain a chromospheric magnetic field (on average), (2) processes in the lower chromosphere, in the region dominated by magnetoacoustic shocks, are able to convert kinetic energy into magnetic energy, (3) the magnetic energy in the chromosphere increases linearly in time until the rms of the magnetic field strength saturates at roughly 4–30 G (horizontal average) due to conversion from kinetic energy, (4) and that the magnetic features formed in the chromosphere are localized to this region.