We study the influence of the spatial resolution on scales of $5deg$ and smaller of solar surface magnetic field maps on global magnetohydrodynamic solar wind models, and on a model of coronal heating and X-ray emission. We compare the solutions driv
en by a low-resolution Wilcox Solar Observatory magnetic map, the same map with spatial resolution artificially increased by a refinement algorithm, and a high-resolution Solar and Heliospheric Observatory Michelson Doppler Imager map. We find that both the wind structure and the X-ray morphology are affected by the fine-scale surface magnetic structure. Moreover, the X-ray morphology is dominated by the closed loop structure between mixed polarities on smaller scales and shows significant changes between high and low resolution maps. We conclude that three-dimensional modeling of coronal X-ray emission has greater surface magnetic field spatial resolution requirements than wind modeling, and can be unreliable unless the dominant mixed polarity magnetic flux is properly resolved.
Junction conditions for vacuum solutions in five-dimensional Einstein-Gauss-Bonnet gravity are studied. We focus on those cases where two spherically symmetric regions of space-time are joined in such a way that the induced stress tensor on the junct
ion surface vanishes. So a spherical vacuum shell, containing no matter, arises as a boundary between two regions of the space-time. A general analysis is given of solutions that can be constructed by this method of geometric surgery. Such solutions are a generalized kind of spherically symmetric empty space solutions, described by metric functions of the class $C^0$. New global structures arise with surprising features. In particular, we show that vacuum spherically symmetric wormholes do exist in this theory. These can be regarded as gravitational solitons, which connect two asymptotically (Anti) de-Sitter spaces with different masses and/or different effective cosmological constants. We prove the existence of both static and dynamical solutions and discuss their (in)stability under perturbations that preserve the symmetry. This leads us to discuss a new type of instability that arises in five-dimensional Lovelock theory of gravity for certain values of the coupling of the Gauss-Bonnet term. The issues of existence and uniqueness of solutions and determinism in the dynamical evolution are also discussed.
