Observations of differential rotation within the solar convection zone have revealed a cyclic pattern of zonal shear flows. Given that the 11‐yr periodicity of this flow pattern is approximately half that of the 22‐yr solar activity cycle, it is likely that these flows are magnetically driven. In this paper, these zonal shear flows are investigated in the context of a parametrized mean‐field solar dynamo model which incorporates the feedback of the large‐scale magnetic fields upon an imposed differential rotation profile. This ‘interface‐like’ model produces dynamo action and a pattern of zonal flows that is qualitatively consistent with solar observations. One of the key parameters in this model is the magnetic Prandtl number – when this parameter is small, it is possible to find time‐dependent solutions that are characterized by prolonged phases of significantly reduced magnetic activity (so‐called ‘grand minima’). Despite the presence of grand minima, it is still possible to find a solar‐like pattern of zonal shear flows in this highly modulated, low magnetic Prandtl number regime.

The propagation of charged particles, including cosmic rays, in a partially ordered magnetic field is characterized by a diffusion tensor whose components depend on the particle's Larmor radius R L and the degree of order in the magnetic field. Most studies of the particle diffusion presuppose a scale separation between the mean and random magnetic fields (e.g., there being a pronounced minimum in the magnetic power spectrum at intermediate scales). Scale separation is often a good approximation in laboratory plasmas, but not in most astrophysical environments such as the interstellar medium (ISM). Modern simulations of the ISM have numerical resolution of order 1 pc, so the Larmor radius of the cosmic rays that dominate in energy density is at least 10 6 times smaller than the resolved scales. Large-scale simulations of cosmic ray propagation in the ISM thus rely on oversimplified forms of the diffusion tensor. We take the first steps towards a more realistic description of cosmic ray diffusion for such simulations, obtaining direct estimates of the diffusion tensor from test particle simulations in random magnetic fields (with the Larmor radius scale being fully resolved), for a range of particle energies corresponding to 10 −2 R L /l c 10 3 , where l c is the magnetic correlation length. We obtain explicit expressions for the cosmic ray diffusion tensor for R L /l c ≪ 1, that might be used in a sub-grid model of cosmic ray diffusion. The diffusion coefficients obtained are closely connected with existing transport theories that include the random walk of magnetic lines.

We examine the evolution of the Parker instability in galactic disks using 3D numerical simulations. We consider a local Cartesian box section of a galactic disk, where gas, magnetic fields, and cosmic rays are all initially in a magnetohydrostatic equilibrium. This is done for different choices of initial cosmic-ray density and magnetic field. The growth rates and characteristic scales obtained from the models, as well as their dependences on the density of cosmic rays and magnetic fields, are in broad agreement with previous (linearized, ideal) analytical work. However, this nonideal instability develops a multimodal 3D structure, which cannot be quantitatively predicted from the earlier linearized studies. This 3D signature of the instability will be of importance in interpreting observations. As a preliminary step toward such interpretations, we calculate synthetic polarized intensity and Faraday rotation measure (RM) maps, and the associated structure functions of the latter, from our simulations; these suggest that the correlation scales inferred from RM maps are a possible probe for the cosmic-ray content of a given galaxy. Our calculations highlight the importance of cosmic rays in these measures, making them an essential ingredient of realistic models of the interstellar medium.

Westward winds have now been inferred for two hot Jupiters (HJs): HAT-P-7b and CoRoT-2b. Such observations could be the result of a number of physical phenomena such as cloud asymmetries, asynchronous rotation, or magnetic fields. For the hotter HJs magnetic fields are an obvious candidate, though the actual mechanism remains poorly understood. Here we show that a strong toroidal magnetic field causes the planetary-scale equatorial magneto-Kelvin wave to structurally shear as it travels, resulting in westward tilting eddies, which drive a reversal of the equatorial winds from their eastward hydrodynamic counterparts. Using our simplified model we estimate that the equatorial winds of HAT-P-7b would reverse for a planetary dipole field strength B dip,HAT-P-7b 6 G, a result that is consistent with three-dimensional magnetohydrodynamic simulations and lies below typical surface dipole estimates of inflated HJs. The same analysis suggests the minimum dipole field strength required to reverse the winds of CoRoT-2b is B dip, 3 kG, which considerably exceeds estimates of the maximum surface dipole strength for HJs. We hence conclude that our magnetic wave-driven mechanism provides an explanation for wind reversals on HAT-P-7b; however, other physical phenomena provide more plausible explanations for wind reversals on CoRoT-2b.

We discuss the difficulties of predicting the solar cycle using mean-field models. Here we argue that these difficulties arise owing to the significant modulation of the solar activity cycle, and that this modulation arises owing to either stochastic or deterministic processes. We analyse the implications for predictability in both of these situations by considering two separate solar dynamo models. The first model represents a stochastically-perturbed flux transport dynamo. Here even very weak stochastic perturbations can give rise to significant modulation in the activity cycle. This modulation leads to a loss of predictability. In the second model, we neglect stochastic effects and assume that generation of magnetic field in the Sun can be described by a fully deterministic nonlinear mean-field model -this is a best case scenario for prediction. We designate the output from this deterministic model (with parameters chosen to produce chaotically modulated cycles) as a target timeseries that subsequent deterministic meanfield models are required to predict. Long-term prediction is impossible even if a model that is correct in all details is utilised in the prediction. Furthermore, we show that even short-term prediction is impossible if there is a small discrepancy in the input parameters from the fiducial model. This is the case even if the predicting model has been tuned to reproduce the output of previous cycles. Given the inherent uncertainties in determining the transport coefficients and nonlinear responses for mean-field models, we argue that this makes predicting the solar cycle using the output from such models impossible.

The presence of magnetic fields in many astrophysical objects is due to dynamo action, whereby a part of the kinetic energy is converted into magnetic energy. A turbulent dynamo that produces magnetic field structures on the same scale as the turbulent flow is known as the fluctuation dynamo. We use numerical simulations to explore the nonlinear, statistically steady state of the fluctuation dynamo in driven turbulence. We demonstrate that as the magnetic field growth saturates, its amplification and diffusion are both affected by the back-reaction of the Lorentz force upon the flow. The amplification of the magnetic field is reduced due to stronger alignment between the velocity field, magnetic field, and electric current density. Furthermore, we confirm that the amplification decreases due to a weaker stretching of the magnetic field lines. The enhancement in diffusion relative to the field line stretching is quantified by a decrease in the computed local value of the magnetic Reynolds number. Using the Minkowski functionals, we quantify the shape of the magnetic structures produced by the dynamo as magnetic filaments and ribbons in both kinematic and saturated dynamos and derive the scalings of the typical length, width, and thickness of the magnetic structures with the magnetic Reynolds number. We show that all three of these magnetic length scales increase as the dynamo saturates. The magnetic intermittency, strong in the kinematic dynamo (where the magnetic field strength grows exponentially) persists in the statistically steady state, but intense magnetic filaments and ribbons are more volume-filling.

We explore the effects of the multi-phase structure of the interstellar medium (ISM) on galactic magnetic fields. Basing our analysis on compressible magnetohydrodynamic (MHD) simulations of supernova-driven turbulence in the ISM, we investigate the properties of both the mean and fluctuating components of the magnetic field. We find that the mean magnetic field preferentially resides in the warm phase and is generally absent from the hot phase. The fluctuating magnetic field does not show such pronounced sensitivity to the multi-phase structure.

Synchrotron radiation from cosmic rays is a key observational probe of the galactic magnetic field. Interpreting synchrotron emission data requires knowledge of the cosmic ray number density, which is often assumed to be in energy equipartition (or otherwise tightly correlated) with the magnetic field energy. However, there is no compelling observational or theoretical reason to expect such tight correlation to hold across all scales. We use test particle simulations, tracing the propagation of charged particles (protons) through a random magnetic field, to study the cosmic ray distribution at scales comparable to the correlation scale of the turbulent flow in the interstellar medium ( 100 pc in spiral galaxies). In these simulations, we find that there is no spatial correlation between the cosmic ray number density and the magnetic field energy density. In fact, their distributions are approximately statistically independent. We find that low-energy cosmic rays can become trapped between magnetic mirrors, whose location depends more on the structure of the field lines than on the field strength.