Observations of Cool-Star Magnetic Fields

Cool stars like the Sun harbor convection zones capable of producing substantial surface magnetic fields leading to stellar magnetic activity. The influence of stellar parameters like rotation, radius, and age on cool-star magnetism, and the importance of the shear layer between a radiative core and the convective envelope for the generation of magnetic fields are keys for our understanding of low-mass stellar dynamos, the solar dynamo, and also for other large-scale and planetary dynamos. Our observational picture of cool-star magnetic fields has improved tremendously over the last years. Sophisticated methods were developed to search for the subtle effects of magnetism, which are difficult to detect particularly in cool stars. With an emphasis on the assumptions and capabilities of modern methods used to measure magnetism in cool stars, I review the different techniques available for magnetic field measurements. I collect the analyses on cool-star magnetic fields and try to compare results from different methods, and I review empirical evidence that led to our current picture of magnetic fields and their generation in cool stars and brown dwarfs.Comment: Published version at http://www.livingreviews.org/lrsp-2012-

Rotation- and temperature-dependence of stellar latitudinal differential rotation

More than 600 high resolution spectra of stars with spectral type F and later were obtained in order to search for signatures of differential rotation in line profiles. In 147 stars, the rotation law could be measured, 28 of them are found to be differentially rotating. Comparison to rotation laws in stars of spectral type A reveals that differential rotation sets in at the convection boundary in the HR-diagram; no star that is significantly hotter than the convection boundary exhibits the signatures of differential rotation. Four late A-/early F-type stars close to the convection boundary and at vsini~100 km/s show extraordinarily strong absolute shear at short rotation periods around one day. It is suggested that this is due to their small convection zone depth and that it is connected to a narrow range in surface velocity. Detection frequencies of differential rotation were analyzed in stars with varying temperature and rotation velocity. Measurable differential rotation is more frequent in late-type stars and slow rotators. The strength of absolute shear and differential rotation are examined as functions of the stellar effective temperature and rotation period. The strongest shear is found at rotation periods between two and three days. In slower rotators, the strongest shear at a given rotation rate is given approximately by DOmega_max ~ P^{-1}. In faster rotators, alpha_max and DOmega_max diminish less rapidly. A comparison with differential rotation measurements in stars of later spectral type shows that F-stars exhibit stronger shear than cooler stars do, the upper boundary in absolute shear DOmega with temperature is consistent with the temperature scaling law found in Doppler Imaging measurements.Comment: 15 pages, accepted for publication in A&A, typos correcte

Cross-diffusion systems with entropy structure

Some results on cross-diffusion systems with entropy structure are reviewed. The focus is on local-in-time existence results for general systems with normally elliptic diffusion operators, due to Amann, and global-in-time existence theorems by Lepoutre, Moussa, and co-workers for cross-diffusion systems with an additional Laplace structure. The boundedness-by-entropy method allows for global bounded weak solutions to certain diffusion systems. Furthermore, a partial result on the uniqueness of weak solutions is recalled, and some open problems are presented