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Understanding stars, their magnetic activity phenomena and the underlying dynamo action is the foundation for understanding 'life, the universe and everything' - as stellar magnetic fields play a fundamental role for star and planet formation and for the terrestrial atmosphere and climate. Starspots are the fingerprints of magnetic field lines and thereby the most important sign of activity in a star's photosphere. However, they cannot be observed directly, as it is not (yet) possible to spacially resolve the surfaces of even the nearest neighbouring stars. Therefore, an indirect approach called 'Doppler imaging' is applied, which allows to reconstruct the surface spot distribution on rapidly rotating, active stars. In this work, data from 11 years of continuous spectroscopic observations of the active binary star EI Eridani are reduced and analysed. 34 Doppler maps are obtained and the problem of how to parameterise the information content of Doppler maps is discussed. Three approaches for parameter extraction are introduced and applied to all maps: average temperature, separated for several latitude bands; fractional spottedness; and, for the analysis of structural temperature distribution, longitudinal and latitudinal spot-occurrence functions. The resulting values do not show a distinct correlation with the proposed activity cycle as seen from photometric long-term observations, thereby suggesting that the photometric activity cycle is not accompanied by a spot cycle as seen on the Sun. The general morphology of the spot pattern on EI Eri remains persistent for the whole period of 11 years. In addition, a detailed parameter study is performed. Improved orbital parameters suggest that EI Eri might be complemented by a third star in a wide orbit of about 19 years. Preliminary differential rotation measurements are carried out, indicating an anti-solar orientation.
Understanding the formation of stars in galaxies is central to much of modern astrophysics. For several decades it has been thought that the star formation process is primarily controlled by the interplay between gravity and magnetostatic support, modulated by neutral-ion drift. Recently, however, both observational and numerical work has begun to suggest that supersonic interstellar turbulence rather than magnetic fields controls star formation. This review begins with a historical overview of the successes and problems of both the classical dynamical theory of star formation, and the standard theory of magnetostatic support from both observational and theoretical perspectives. We then present the outline of a new paradigm of star formation based on the interplay between supersonic turbulence and self-gravity. Supersonic turbulence can provide support against gravitational collapse on global scales, while at the same time it produces localized density enhancements that allow for collapse on small scales. The efficiency and timescale of stellar birth in Galactic gas clouds strongly depend on the properties of the interstellar turbulent velocity field, with slow, inefficient, isolated star formation being a hallmark of turbulent support, and fast, efficient, clustered star formation occurring in its absence. After discussing in detail various theoretical aspects of supersonic turbulence in compressible self-gravitating gaseous media relevant for star forming interstellar clouds, we explore the consequences of the new theory for both local star formation and galactic scale star formation. The theory predicts that individual star-forming cores are likely not quasi-static objects, but dynamically evolving. Accretion onto these objects will vary with time and depend on the properties of the surrounding turbulent flow. This has important consequences for the resulting stellar mass function. Star formation on scales of galaxies as a whole is expected to be controlled by the balance between gravity and turbulence, just like star formation on scales of individual interstellar gas clouds, but may be modulated by additional effects like cooling and differential rotation. The dominant mechanism for driving interstellar turbulence in star-forming regions of galactic disks appears to be supernovae explosions. In the outer disk of our Milky Way or in low-surface brightness galaxies the coupling of rotation to the gas through magnetic fields or gravity may become important.