A physical approach to modelling large-scale galactic magnetic fields

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&

Localised plumes in three-dimensional compressible magnetoconvection

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 MNRA

Estimating the Rate of Field Line Braiding in the Solar Corona by Photospheric Flows

In this paper, we seek to understand the timescale in which the photospheric motions on the Sun braid coronal magnetic field lines. This is a crucial ingredient for determining the viability of the braiding mechanism for explaining the high temperatures observed in the corona. We study the topological complexity induced in the coronal magnetic field, primarily using plasma motions extracted from magneto-convection simulations. This topological complexity is quantified using the field line winding, finite time topological entropy (FTTE), and passive scalar mixing. With these measures, we contrast mixing efficiencies of the magneto-convection simulation, a benchmark flow known as a "blinking vortex", and finally photospheric flows inferred from sequences of observed magnetograms using local correlation tracking. While the highly resolved magneto-convection simulations induce a strong degree of field line winding and FTTE, the values obtained from the observations from the plage region are around an order of magnitude smaller. This behavior is carried over to the FTTE. Nevertheless, the results suggest that the photospheric motions induce complex tangling of the coronal field on a timescale of hours

Convective intensification of magnetic fields in the quiet Sun

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

On Predicting the Solar Cycle using Mean-Field Models

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 Ap