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We review the surface flux transport model for the evolution of magnetic flux patterns on the Sun's surface. Our underlying motivation is to understand the model's prediction of the polar field (or axial dipole) strength at the end of the solar cycle. The main focus is on the "classical" model: namely, steady axisymmetric profiles for differential rotation and meridional flow, and uniform supergranular diffusion. Nevertheless, the review concentrates on recent advances, notably in understanding the roles of transport parameters and – in particular – the source term. We also discuss the physical justification for the surface flux transport model, along with efforts to incorporate radial diffusion, and conclude by summarizing the main directions where researchers have moved beyond the classical model. [ABSTRACT FROM AUTHOR]

We describe a new automated technique for active region emergence in coronal magnetic field models, based on the inversion of the electric field locally from a single line-of-sight magnetogram for each region. The technique preserves the arbitrary shapes of magnetic field distribution associated with individual active regions and incorporates emerging magnetic helicity (twist) in a parametrized manner through a noninductive electric field component. We test the technique with global magnetofrictional simulations of the coronal magnetic field during Solar Cycle 24 Maximum from 2011 June 1 to 2011 December 31. The active regions are determined in a fully automated and objective way using Spaceweather HMI Active Region Patch (SHARP) data. Our primary aim is to constrain two free parameters in the emergence algorithm: the duration of emergence and the twist parameter for each individual active region. While the duration has a limited effect on the resulting coronal magnetic field, changing the sign and amplitude of the twist parameters profoundly influences the amount of nonpotentiality generated in the global coronal magnetic field. We explore the possibility of constraining both the magnitude and sign of the twist parameter using estimates of the current helicity derived from vector magnetograms and supplied in the SHARP metadata for each region. Using the observed sign of twist for each region reduces the overall nonpotentiality in the corona, highlighting the importance of scatter in the emerging active region helicities. [ABSTRACT FROM AUTHOR]

An important element of 3D data-driven simulations of solar magnetic fields is the determination of the horizontal electric field at the solar photosphere. This electric field is used to drive the 3D simulations and inject energy and helicity into the solar corona. One outstanding problem is the localisation of the horizontal electric field such that it is consistent with Ohm's law. Yeates (Astrophys. J.836(1), 131, 2017) put forward a new "sparse" technique for computing the horizontal electric field from normal-component magnetograms that minimises the number of non-zero values. This aims to produce a better representation of Ohm's law compared to previously used "non-sparse" techniques. To test this new approach we apply it to active region (AR) 10977, along with the previously developed non-sparse technique of Mackay, Green, and van Ballegooijen (Astrophys. J.729(2), 97, 2011). A detailed comparison of the two techniques with coronal observations is used to determine which is the most successful. Results show that the non-sparse technique of Mackay, Green, and van Ballegooijen (2011) produces the best representation for the formation and structure of the sigmoid above AR 10977. In contrast, the Yeates (2017) approach injects strong horizontal fields between spatially separated, evolving magnetic polarities. This injection produces highly twisted unphysical field lines with significantly higher magnetic energy and helicity. It is also demonstrated that the Yeates (2017) approach produces significantly different results that can be inconsistent with the observations depending on whether the horizontal electric field is solved directly or indirectly through the magnetic vector potential. In contrast, the Mackay, Green, and van Ballegooijen (2011) method produces consistent results using either approach. The sparse technique of Yeates (2017) has significant pitfalls when applied to spatially resolved solar data, where future studies need to investigate why these problems arise. [ABSTRACT FROM AUTHOR]

We study coherent structures in solar photospheric flows in a plage in the vicinity of the active region AR 10930 using the horizontal velocity data derived from Hinode/Solar Optical Telescope magnetograms. Eulerian and Lagrangian coherent structures (LCSs) are detected by computing the Q-criterion and the finite-time Lyapunov exponents of the velocity field, respectively. Our analysis indicates that, on average, the deformation Eulerian coherent structures dominate over the vortical Eulerian coherent structures in the plage region. We demonstrate the correspondence of the network of high magnetic flux concentration to the attracting Lagrangian coherent structures (aLCSs) in the photospheric velocity based on both observations and numerical simulations. In addition, the computation of aLCS provides a measure of the local rate of contraction/expansion of the flow. [ABSTRACT FROM AUTHOR]

In this review, our present day understanding of the Sun's global photospheric and coronal magnetic fields is discussed from both observational and theoretical viewpoints. Firstly, the large-scale properties of photospheric magnetic fields are described, along with recent advances in photospheric magnetic flux transport models. Following this, the wide variety of theoretical models used to simulate global coronal magnetic fields are described. From this, the combined application of both magnetic flux transport simulations and coronal modeling techniques to describe the phenomena of coronal holes, the Sun's open magnetic flux and the hemispheric pattern of solar filaments is discussed. Finally, recent advances in non-eruptive global MHD models are described. While the review focuses mainly on solar magnetic fields, recent advances in measuring and modeling stellar magnetic fields are described where appropriate. In the final section key areas of future research are identified. [ABSTRACT FROM AUTHOR]