Physical viscosity in smoothed particle hydrodynamics simulations of galaxy clusters

Most hydrodynamical simulations of galaxy cluster formation carried out to date have tried to model the cosmic gas as an ideal, inviscid fluid, where only a small amount of (unwanted) numerical viscosity is present, arising from practical limitations of the numerical method employed, and with a strength that depends on numerical resolution. However, the physical viscosity of the gas in hot galaxy clusters may in fact not be negligible, suggesting that a self-consistent treatment that accounts for the internal gas friction would be more appropriate. To allow such simulations using the smoothed particle hydrodynamics (SPH) method, we derive a novel SPH formulation of the Navier-Stokes and general heat transfer equations and implement them in the GADGET-2 code. We include both shear and bulk viscosity stress tensors, as well as saturation criteria that limit viscous stress transport where appropriate. Adopting Braginskii's parameterization for the shear viscosity of hot gaseous plasmas, we then study the influence of viscosity on the interplay between AGN-inflated bubbles and the surrounding intracluster medium (ICM). We find that certain bubble properties like morphology, maximum clustercentric radius reached, or survival time depend quite sensitively on the assumed level of viscosity. Interestingly, the sound waves launched into the ICM by the bubble injection are damped by physical viscosity, establishing a non-local heating process. Finally, we carry out cosmological simulations of galaxy cluster formation with a viscous intracluster medium. Viscosity modifies the dynamics of mergers and the motion of substructures through the cluster atmosphere. Substructures are generally more efficiently stripped of their gas, leading to prominent long gaseous tails behind infalling massive halos. (Abridged)Comment: 24 pages, 13 figures, minor revisions, MNRAS accepte

The Importance of Equity Finance for R&D Activity – Are There Differences Between Young and Old Companies?

This paper analyzes the importance of equity finance for the R&D activity of small and medium-sized enterprises. We use information on almost 6000 German SMEs from a company survey. Using the intensity of banking competition at the district level as instrument to control for endogeneity, we find that a higher equity ratio is conducive to more R&D for young but not for old companies. Equity may be a constraining factor for young companies which have to rely on the original equity investment of their owners since they have not yet accumulated retained earnings and can relay less on outside financing. The positive influence is found for R&D intensity but not for the decision whether to perform R&D. Equity financing is therefore especially important for the most innovative, young companies