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The details of the dynamo process that is responsible for driving the solar magnetic activity cycle are still not fully understood. In particular, whilst differential rotation provides a plausible mechanism for the regeneration of the toroidal (azimuthal) component of the large-scale magnetic field, there is ongoing debate regarding the process that is responsible for regenerating the Sun's large-scale poloidal field. Our aim is to demonstrate that magnetic buoyancy, in the presence of rotation, is capable of producing the necessary regenerative effect. Building upon our previous work, we carry out numerical simulations of a local Cartesian model of the tachocline, consisting of a rotating, fully compressible, electrically conducting fluid with a forced shear flow. An initially weak, vertical magnetic field is sheared into a strong, horizontal magnetic layer that becomes subject to magnetic buoyancy instability. By increasing the Prandtl number we lessen the back reaction of the Lorentz force onto the shear flow, maintaining stronger shear and a more intense magnetic layer. This in turn leads to a more vigorous instability and a much stronger mean electromotive force, which has the potential to significantly influence the evolution of the mean magnetic field. These results are only weakly dependent upon the inclination of the rotation vector, i.e. the latitude of the local Cartesian model. Although further work is needed to confirm this, these results suggest that magnetic buoyancy in the tachocline is a viable poloidal field regeneration mechanism for the solar dynamo., Comment: Accepted for publication in MNRAS, 13 pages, 11 figures, 1 table

Resistive tearing instabilities are common in fluids that are highly electrically conductive and carry strong currents. We determine the effect of stable stratification on the tearing instability under the Boussinesq approximation. Our results generalise previous work that considered only specific parameter regimes, and we show that the length scale of the fastest growing mode depends non-monotonically on the stratification strength. We confirm our analytical results by solving the linearised equations numerically, and we discuss whether the instability could operate in the solar tachocline.

The leading theoretical paradigm for the Sun's magnetic cycle is an $\alpha\omega$-dynamo process, in which a combination of differential rotation and turbulent, helical flows produces a large-scale magnetic field that reverses every 11 years. Most $\alpha\omega$ solar dynamo models rely on differential rotation in the solar tachocline to generate a strong toroidal field. The most problematic part of such models is then the production of the large-scale poloidal field, via a process known as the $\alpha$-effect. Whilst this is usually attributed to small-scale convective motions under the influence of rotation, the efficiency of this regenerative process has been called into question by some numerical simulations. Motivated by likely conditions within the tachocline, the aim of this paper is to investigate an alternative mechanism for the poloidal field regeneration, namely the magnetic buoyancy instability in a shear-generated, rotating magnetic layer. We use a local, fully compressible model in which an imposed vertical shear winds up an initially vertical magnetic field. The field ultimately becomes buoyantly unstable, and we measure the resulting mean electromotive force (EMF). For sufficiently rapid rotation, we find that a significant component of the mean EMF is aligned with the direction of the mean magnetic field, which is the characteristic feature of the classical $\alpha\omega$-dynamo model. Our results therefore suggest that magnetic buoyancy could contribute directly to the generation of large-scale poloidal field in the Sun., Comment: Accepted for publication in MNRAS, 16 pages, 12 figures, 3 tables

The presence of acoustic waves in models of compressible flows can present complications for analytical and numerical analysis. Therefore, several methods have been developed to filter out these waves, leading to various "sound-proof" models, including the Boussinesq, anelastic and pseudo-incompressible models. We assess the validity of each of these approximate models for describing magnetic buoyancy in the context of the solar interior. A general sound-proof model is introduced and compared to the fully compressible system in a number of asymptotic regimes, including both non-rotating and rotating cases. We obtain specific constraints that must be satisfied in order that the model captures the leading-order behaviour of the fully compressible system. We then discuss which of the existing sound-proof models satisfy these constraints, and in what parameter regimes. We also present a variational derivation of the pseudo-incompressible MHD model, demonstrating its underlying Hamiltonian structure.

We use results of shallow-water magnetohydrodynamics (SWMHD) to place estimates on the minimum magnetic field strengths required to cause atmospheric wind variations (and therefore westward venturing hotspots) for a dataset of hot Jupiters (HJs), including HAT-P-7b, CoRoT-2b, Kepler-76, WASP-12b, and WASP-33b, on which westward hotspots have been observationally inferred. For HAT-P-7b and CoRoT-2b our estimates agree with past results; for Kepler-76b we find that the critical dipolar magnetic field strength, over which the observed wind variations can be explained by magnetism, lies between $4\mbox{ G}$ and $19\mbox{ G}$; for WASP-12b and WASP-33b westward hotspots can be explained by $1\mbox{ G}$ and $2\mbox{ G}$ dipolar fields respectively. Additionally, to guide future observational missions, we identify $61$ further HJs that are likely to exhibit magnetically-driven atmospheric wind variations and predict these variations are highly-likely in $\sim 40$ of the hottest HJs., Comment: 10 pages, 3 figures, 2 tables

Magnetically-driven hotspot variations (which are tied to atmospheric wind variations) in hot Jupiters are studied using non-linear numerical simulations of a shallow-water magnetohydrodynamic (SWMHD) system and a linear analysis of equatorial SWMHD waves. In hydrodynamic models, mid-to-high latitude geostrophic circulations are known to cause a net west-to-east equatorial thermal energy transfer, which drives hotspot offsets eastward. We find that a strong toroidal magnetic field can obstruct these energy transporting circulations. This results in winds aligning with the magnetic field and generates westward Lorentz force accelerations in hotspot regions, ultimately causing westward hotspot offsets. In the subsequent linear analysis we find that this reversal mechanism has an equatorial wave analogy in terms of the planetary scale equatorial magneto-Rossby waves. We compare our findings to three-dimensional MHD simulations, both quantitively and qualitatively, identifying the link between the mechanics of magnetically-driven hotspot and wind reversals. We use the developed theory to identify physically-motivated reversal criteria, which can be used to place constraints on the magnetic fields of ultra-hot Jupiters with observed westward hotspots., Comment: 30 pages, 9 figures, 3 tables

We study dynamo action using numerical simulations of planar Boussinesq convection at rapid rotation (low Ekman numbers, Ek), focusing on subcritical dynamo action in which the dynamo is sustained for Rayleigh numbers, Ra, below the critical Rayleigh number for the onset of nonmagnetic convection, Ra$_c$. These solutions are found by first investigating the supercritical regime, in which the dynamo is able to generate a large-scale magnetic field that significantly influences the convective motions, with an associated Elsasser number of order Ek$^{1/3}$. Subcritical solutions are then found by tracking this solution branch into the subcritical regime, taking a supercritical solution and then gradually lowering the corresponding Rayleigh number. We show that decreasing the Ekman number leads to an extension of the subcritical range of Ra/Ra$_c$, down to an optimal value of Ek$=10^{-5}$. For magnetic Prandtl numbers of order unity, subcriticality is then hampered by the emergence of a large-scale mode at lower Ekman numbers when the dynamo driven by the smaller scale convection generates relatively stronger large-scale magnetic field. The inability of the large-scale mode to sustain dynamo action leads to an intermittent behaviour that appears to inhibit subcriticality. The subcritical solutions are also sensitive to the value of the magnetic Reynolds number (or equivalently, the magnetic Prandtl number, Pm), as values of the magnetic Reynolds number greater than 70 are required to produce dynamo action, but large values lead to fluctuations that are able to push the system too far from the subcritical branch and towards the trivial conducting state., Comment: Accepted for publication in Phys. Rev. Fluids

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., Comment: 17 pages, 19 figures, accepted for publication in Physical Review Fluids

We explore the effect of magnetic fields on the vertical distribution and multiphase structure of the supernova-driven interstellar medium (ISM) in simulations that admit dynamo action. As the magnetic field is amplified to become dynamically significant, gas becomes cooler and its distribution in the disc becomes more homogeneous. We attribute this to magnetic quenching of vertical velocity, which leads to a decrease in the cooling length of hot gas. A non-monotonic vertical distribution of the large-scale magnetic field strength, with the maximum at |z| $\approx$ 300 pc causes a downward pressure gradient below the maximum which acts against outflow driven by SN explosions, while it provides pressure support above the maximum., Comment: 10 pages, 10 figures

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_{\text{dip},\text{HAT-P-7b}} \gtrsim 6 \, \mathrm{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 $B_{\text{dip},\text{CoRoT-2b}} \gtrsim 3 \, \mathrm{kG}$, 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.

Interpretations of synchrotron observations often assume a tight correlation between magnetic and cosmic ray energy densities. We examine this assumption using both test-particle simulations of cosmic rays and MHD simulations which include cosmic rays as a diffusive fluid. We find no spatial correlation between the cosmic rays and magnetic field energy densities at turbulent scales. Moreover, the cosmic ray number density and magnetic field energy density are statistically independent. Nevertheless, the cosmic ray spatial distribution is highly inhomogeneous, especially at low energies because the particles are trapped between random magnetic mirrors. These results can significantly change the interpretation of synchrotron observations and thus our understanding of the strength and structure of magnetic fields in the Milky Way and nearby spiral galaxies., Comment: 4 pages, 2 figures, Proceedings of Focus Meeting FM8: New Insights in Extragalactic Magnetic Fields, XXXth IAU General Assembly, Vienna, August 29-31, 2018

The role of magnetic fields in the multi-phase interstellar medium (ISM) is explored using magnetohydrodynamic (MHD) simulations that include energy injection by supernova (SN) explosions and allow for dynamo action. Apart from providing additional pressure support of the gas layer, magnetic fields reduce the density contrast between the warm and hot gas phases and quench galactic outflows. A dynamo-generated, self-consistent large-scale magnetic field affects the ISM differently from an artificially imposed, unidirectional magnetic field., Comment: 2 pages, Proceedings of FM8 "New Insights in Extragalactic Magnetic Fields", XXXth General Assembly of the IAU, Vienna, August 20-31, 2018

A convenient representation of the structure of the large-scale galactic magnetic field is required for the interpretation of polarization data in the sub-mm and radio ranges, in both the Milky Way and external galaxies. We develop a simple and flexible approach to construct parametrised models of the large-scale magnetic field of the Milky Way and other disc galaxies, based on physically justifiable models of magnetic field structure. The resulting models are designed to be optimised against available observational data. Representations for the large-scale magnetic fields in the flared disc and spherical halo of a disc galaxy were obtained in the form of series expansions whose coefficients can be calculated from observable or theoretically known galactic properties. The functional basis for the expansions is derived as eigenfunctions of the mean-field dynamo equation or of the vectorial magnetic diffusion equation. The solutions presented are axially symmetric but the approach can be extended straightforwardly to non-axisymmetric cases. The magnetic fields are solenoidal by construction, can be helical, and are parametrised in terms of observable properties of the host object, such as the rotation curve and the shape of the gaseous disc. The magnetic field in the disc can have a prescribed number of field reversals at any specified radii. Both the disc and halo magnetic fields can separately have either dipolar or quadrupolar symmetry. The model is implemented as a publicly available software package GalMag which allows, in particular, the computation of the synchrotron emission and Faraday rotation produced by the model's magnetic field. The model can be used in interpretations of observations of magnetic fields in the Milky Way and other spiral galaxies, in particular as a prior in Bayesian analyses. (Abridged.), Comment: 20 pages, 14 figures. Accepted for publication in A&A

The Hall-Petch effect has been described for the past sixty years as a dependence of the strength of polycrystalline metals on the inverse square-root of grain size d. The value of the coefficient of the dependence has been the subject of discussion throughout. Here, we find what factors in the experiments determine its values. A meta-analysis using maximum-likelihood methods is reported of the literature values of the coefficient in sixty-one datasets. Weak dependence is found on composition and bulk strength. Clear dependence is found on the elastic anisotropy of the different metals and on their stacking fault energies. Surprisingly, no dependence is found on plastic strain, and the strongest dependence is found on the average grain size of each study. Combining these effects accounts for the reported values of about 80% of the sixty-one coefficients. The grain-size dependence and the bulk strength dependence indicate that the Hall-Petch coefficient is an artefact arising from incorrect fitting of the data. Moreover, the grain-size dependence implies a minimum strength described by a simple inverse 1/d or a lnd/d function, which arises theoretically from considerations of dislocation curvature., Comment: 19 pages, 5 Figures, 3 Tables

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., Comment: 16 pages, 16 figures, to appear in Astronomy & Astrophysics. The material in the Appendix could form the basis for a possible benchmarking exercise; we would encourage anyone who might be interested in participating in such an exercise to contact the authors

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 ($\simeq 100\,{\rm pc}$ 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., Comment: 14 pages, 15 figures, 1 table, Accepted for publication in MNRAS, Video showing trajectory of a cosmic ray particle in a magnetic trap- https://youtu.be/EzabLlio3FE

The cellular automaton model of Piegari, Di Maio, Scandone and Milano, J. Volc. Geoth. Res., 202, 22-28 (2011) is extended to include magma-induced stress (i.e. a local magma-related augmentation of the stress field). This constitutes a nonlinear coupling between the magma and stress fields considered by this model, which affects the statistical distributions of eruptions obtained. The extended model retains a power law relation between eruption size and frequency for most events, as expected from the self organised criticality inspiring this model; but the power law now applies for a reduced range of size, and there are new peaks of relatively more frequent eruptions of intermediate and large size. The cumulative frequency of repose time between events remains well modelled by a stretched exponential function of repose time (approaching a pure exponential distribution only for the longest repose times), but the time scales of this behaviour are slightly longer, reflecting the increased preference for larger events. The eruptions are relatively more likely to have high volatile (water) content, so would generally be more explosive. The new model also naturally favours a central `axial' transport conduit, as found in many volcano systems, but which otherwise must be artificially imposed within such models., Comment: 12 pages, 9 figures, accepted by Journal of Volcanology and Geothermal Research

We determine the asymptotic conditions under which the Boussinesq approximation is valid for oscillatory convection in a rapidly rotating fluid. In the astrophysically relevant parameter regime of small Prandtl number, we show that the Boussinesq prediction for the onset of convection is valid only under much more restrictive conditions than those that are usually assumed. In the case of an ideal gas, we recover the Boussinesq results only if the ratio of the domain height to a typical scale height is much smaller than the Prandtl number. This requires an extremely shallow domain in the astrophysical parameter regime. Other commonly-used "sound-proof" approximations generally perform no better than the Boussinesq approximation. The exception is a particular implementation of the pseudo-incompressible approximation, which predicts the correct instability threshold beyond the range of validity of the Boussinesq approximation., Comment: 13 pages, 1 figure, accepted for publication in JFM

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 non-ideal instability develops a multi-modal 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 towards such interpretations, we calculate synthetic polarized intensity and Faraday rotation measure maps, and the associated structure functions of the latter, from our simulations; these suggest that the correlation scales inferred from rotation measure 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., Comment: 15 pages, 16 figures. Accepted for publication in ApJ

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 $10^{-2}\lesssim R_L/l_c \lesssim 10^{3}$, where $l_c$ is the magnetic correlation length. We obtain explicit expressions for the cosmic ray diffusion tensor for $R_L/l_c \ll 1$, 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., Comment: 13 pages, 12 figures, accepted for publication in MNRAS

The experimental evidence for the Hall-Petch dependence of strength on the inverse square-root of grain size is reviewed critically. Both the classic data and more recent results are considered. While the data can be fitted to the inverse square-root dependence excellently (but using two free fitting parameters for each dataset), it is also consistent with a dependence on the simple inverse of grain size (with one free fitting parameter for each dataset). There have been difficulties, recognised for half-a-century, in explaining the inverse square-root expression. A Bayesian analysis shows that the data strongly supports the simple inverse expression proposed. Since this expression derives from underlying theory, it is also more readily explicable. It is concluded that the Hall-Petch effect is not to be explained by the variety of theories found in the literature, but is a manifestation of, or underlain by, the general size effect observed throughout micromechanics, due to the inverse relationship between the stress required and the space available for dislocation sources to operate., Comment: Paper presented at Plasticity 2014, The Bahamas

We estimate the energy input into the solar corona from photospheric footpoint motions, using observations of a plage region by the Hinode Solar Optical Telescope. Assuming a perfectly ideal coronal evolution, two alternative lower bounds for the Poynting flux are computed based on field line footpoint trajectories, without requiring horizontal magnetic field data. When applied to the observed velocities, a bound based solely on displacements between the two footpoints of each field line is tighter than a bound based on relative twist between field lines. Depending on the assumed length of coronal magnetic field lines, the higher bound is found to be reasonably tight compared with a Poynting flux estimate using an available vector magnetogram. It is also close to the energy input required to explain conductive and radiative losses in the active region corona. Based on similar analysis of a numerical convection simulation, we suggest that observations with higher spatial resolution are likely to bring the bound based on relative twist closer to the first bound, but not to increase the first bound substantially. Finally, we put an approximate upper bound on the magnetic energy by constructing a hypothetical ``unrelaxed'' magnetic field with the correct field line connectivity., Comment: 10 pages, 11 figures, accepted in Astronomy & Astrophysics

Regions of quiet Sun generally exhibit a complex distribution of small-scale magnetic field structures, which interact with the near-surface turbulent convective motions. Furthermore, it is probable that some of these magnetic fields are generated locally by a convective dynamo mechanism. In addition to the well-known granular and supergranular convective scales, various observations have indicated that there is an intermediate scale of convection, known as mesogranulation, with vertical magnetic flux concentrations accumulating preferentially at mesogranular boundaries. Our aim is to investigate the small-scale dynamo properties of a convective flow that exhibits both granulation and mesogranulation, comparing our findings with solar observations. Adopting an idealised model for a localised region of quiet Sun, we use numerical simulations of compressible magnetohydrodynamics, in a 3D Cartesian domain, to investigate the parametric dependence of this system (focusing particularly upon the effects of varying the aspect ratio and the Reynolds number). In purely hydrodynamic convection, we find that mesogranulation is a robust feature of this system provided that the domain is wide enough to accommodate these large-scale motions. The mesogranular peak in the kinetic energy spectrum is more pronounced in the higher Reynolds number simulations. We investigate the dynamo properties of this system in both the kinematic and the nonlinear regimes and we find that the dynamo is always more efficient in larger domains, when mesogranulation is present. Furthermore, we use a filtering technique in Fourier space to demonstrate that it is indeed the larger scales of motion that are primarily responsible for driving the dynamo. In the nonlinear regime, the magnetic field distribution compares very favourably to observations, both in terms of the spatial distribution and the measured field strengths., Comment: 12 pages, 11 figures, accepted for publication in Astronomy & Astrophysics

Mean-field dynamo theory suggests that turbulent convection in a rotating layer of electrically-conducting fluid produces a significant alpha-effect, which is one of the key ingredients in any mean-field dynamo model. Provided that this alpha-effect operates more efficiently than (turbulent) magnetic diffusion, such a system should be capable of sustaining a large-scale dynamo. However, in the Boussinesq model that was considered by Cattaneo&Hughes (2006) the dynamo produced small-scale, intermittent magnetic fields with no significant large-scale component. In this paper, we consider the compressible analogue of the rotating convective layer that was considered by Cattaneo&Hughes (2006). Varying the horizontal scale of the computational domain, we investigate the dependence of the dynamo upon the rotation rate. Our simulations indicate that these turbulent compressible flows can drive a small-scale dynamo but, even when the layer is rotating very rapidly (with a mid-layer Taylor number of Ta=10^8), we find no evidence for the generation of a significant large-scale component of the magnetic field on a dynamical timescale. Like Cattaneo&Hughes(2006), we measure a negligible (time-averaged) alpha-effect when a uniform horizontal magnetic field is imposed across the computational domain. Although the total horizontal magnetic flux is a conserved quantity in these simulations, the (depth-dependent) horizontally-averaged magnetic field always exhibits strong fluctuations. If these fluctuations are artificially suppressed within the code, we measure a significant mean electromotive force that is comparable to that found in related calculations in which the alpha-effect is measured using the test-field method, even though we observe no large-scale dynamo action., Comment: 25 pages, 10 figures, to appear in J. Fluid Mech

Localised states are found in many pattern forming systems. The aim of this paper is to investigate the occurrence of oscillatory localised states in two-dimensional Boussinesq magnetoconvection. Initially considering an idealised model, in which the vertical structure of the system has been simplified by a projection onto a small number of Fourier modes, we find that these states are restricted to the low $\zeta$ regime (where $\zeta$ represents the ratio of the magnetic to thermal diffusivities). These states always exhibit bistability with another non-trivial solution branch, in other words they show no evidence of subcritical behaviour. This is due to the weak flux expulsion that is exhibited by these time-dependent solutions. Using the results of this parameter survey, we locate corresponding states in a fully-resolved two-dimensional system, although the mode of oscillation is more complex in this case. This is the first time that a localised oscillatory state, of this kind, has been found in a fully-resolved magnetoconvection simulation., Comment: 12 pages, 14 figures, 2 tables

[Abridged] Bipolar magnetic regions are formed when loops of magnetic flux emerge at the solar photosphere. Our aim is to investigate the flux emergence process in a simulation of granular convection. In particular we aim to determine the circumstances under which magnetic buoyancy enhances the flux emergence rate (which is otherwise driven solely by the convective upflows). We use three-dimensional numerical simulations, solving the equations of compressible magnetohydrodynamics in a horizontally-periodic Cartesian domain. A horizontal magnetic flux tube is inserted into fully developed hydrodynamic convection. We systematically vary the initial field strength, the tube thickness, the initial entropy distribution along the tube axis and the magnetic Reynolds number. Focusing upon the low magnetic Prandtl number regime (Pm<1) at moderate magnetic Reynolds number, we find that the flux tube is always susceptible to convective disruption to some extent. However, stronger flux tubes tend to maintain their structure more effectively than weaker ones. Magnetic buoyancy does enhance the flux emergence rates in the strongest initial field cases, and this enhancement becomes more pronounced when we increase the width of the flux tube. This is also the case at higher magnetic Reynolds numbers, although the flux emergence rates are generally lower in these less dissipative simulations because the convective disruption of the flux tube is much more effective in these cases. These simulations seem to be relatively insensitive to the precise choice of initial conditions: for a given flow, the evolution of the flux tube is determined primarily by the initial magnetic field distribution and the magnetic Reynolds number., Comment: 12 pages, 15 figures, 2 tables. Accepted for publication in Astronomy and Astrophysics

We study dynamo action in a convective layer of electrically-conducting, compressible fluid, rotating about the vertical axis. At the upper and lower bounding surfaces, perfectly-conducting boundary conditions are adopted for the magnetic field. Two different levels of thermal stratification are considered. If the magnetic diffusivity is sufficiently small, the convection acts as a small-scale dynamo. Using a definition for the magnetic Reynolds number $R_M$ that is based upon the horizontal integral scale and the horizontally-averaged velocity at the mid-layer of the domain, we find that rotation tends to reduce the critical value of $R_M$ above which dynamo action is observed. Increasing the level of thermal stratification within the layer does not significantly alter the critical value of $R_M$ in the rotating calculations, but it does lead to a reduction in this critical value in the non-rotating cases. At the highest computationally-accessible values of the magnetic Reynolds number, the saturation levels of the dynamo are similar in all cases, with the mean magnetic energy density somewhere between 4 and 9% of the mean kinetic energy density. To gain further insights into the differences between rotating and non-rotating convection, we quantify the stretching properties of each flow by measuring Lyapunov exponents. Away from the boundaries, the rate of stretching due to the flow is much less dependent upon depth in the rotating cases than it is in the corresponding non-rotating calculations. It is also shown that the effects of rotation significantly reduce the magnetic energy dissipation in the lower part of the layer. We also investigate certain aspects of the saturation mechanism of the dynamo., Comment: 23 pages, 12 figures

Within the umbrae of sunspots, convection is generally inhibited by the presence of strong vertical magnetic fields. However, convection is not completely suppressed in these regions: bright features, known as umbral dots, are probably associated with weak, isolated convective plumes. Motivated by observations of umbral dots, we carry out numerical simulations of three-dimensional, compressible magnetoconvection. By following solution branches into the subcritical parameter regime (a region of parameter space in which the static solution is linearly stable to convective perturbations), we find that it is possible to generate a solution which is characterised by a single, isolated convective plume. This solution is analogous to the steady magnetohydrodynamic convectons that have previously been found in two-dimensional calculations. These results can be related, in a qualitative sense, to observations of umbral dots., Comment: submitted to MNRAS

Small-scale mechanical behaviour shows significant departures from classical elastic-plastic theory. In a remarkable number of instances, the strength of a material appears to scale as the reciprocal square root of the smallest length scale. There are several recent experimental and modeling results in the literature that show an interaction between dimensional (extrinsic) size and microstructural (intrinsic) size effects. In this paper, we present a mechanical model that naturally produces the inverse square root strengthening and derive an expression for the effective length when both the extrinsic and intrinsic size effects are significant. The theory fits well to data from a wide range of deformation geometries and includes the interaction between the microstructural and dimensional size effects. Furthermore, this approach is able to predict the size effect under uniform deformation without strain gradient.

Motivated by the interface model for the solar dynamo, this paper explores the complex magnetohydrodynamic interactions between convective flows and shear-driven instabilities. Initially, we consider the dynamics of a forced shear flow across a convectively-stable polytropic layer, in the presence of a vertical magnetic field. When the imposed magnetic field is weak, the dynamics are dominated by a shear flow (Kelvin-Helmholtz type) instability. For stronger fields, a magnetic buoyancy instability is preferred. If this stably stratified shear layer lies below a convectively unstable region, these two regions can interact. Once again, when the imposed field is very weak, the dynamical effects of the magnetic field are negligible and the interactions between the shear layer and the convective layer are relatively minor. However, if the magnetic field is strong enough to favour magnetic buoyancy instabilities in the shear layer, extended magnetic flux concentrations form and rise into the convective layer. These magnetic structures have a highly disruptive effect upon the convective motions in the upper layer., Comment: 11 pages, 10 figures, accepted for publication in MNRAS

Kilogauss-strength magnetic fields are often observed in intergranular lanes at the photosphere in the quiet Sun. Such fields are stronger than the equipartition field $B_e$, corresponding to a magnetic energy density that matches the kinetic energy density of photospheric convection, and comparable with the field $B_p$ that exerts a magnetic pressure equal to the ambient gas pressure. We present an idealised numerical model of three-dimensional compressible magnetoconvection at the photosphere, for a range of values of the magnetic Reynolds number. In the absence of a magnetic field, the convection is highly supercritical and is characterised by a pattern of vigorous, time-dependent, ``granular'' motions. When a weak magnetic field is imposed upon the convection, magnetic flux is swept into the convective downflows where it forms localised concentrations. Unless this process is significantly inhibited by magnetic diffusion, the resulting fields are often much greater than $B_e$, and the high magnetic pressure in these flux elements leads to their being partially evacuated. Some of these flux elements contain ultra-intense magnetic fields that are significantly greater than $B_p$. Such fields are contained by a combination of the thermal pressure of the gas and the dynamic pressure of the convective motion, and they are constantly evolving. These ultra-intense fields develop owing to nonlinear interactions between magnetic fields and convection; they cannot be explained in terms of ``convective collapse'' within a thin flux tube that remains in overall pressure equilibrium with its surroundings., Comment: 10 pages, 6 figures, 1 table, Accepted for publication in Monthly Notices of the Royal Astronomical Society

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 mean-field 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., Comment: 22 Pages, 5 Figures, Preprint accepted for publication in ApJ