Propagation of a dome-shaped, large-scale extreme-ultraviolet wave in the solar corona

Context. The first observation of a dome-shaped extreme-ultraviolet (EUV) wave was recorded by the EUVI instrument on board the STEREO-B spacecraft on January 17, 2010. This observation has allowed us to study the three-dimensional propagation of a largescale EUV wave in the solar corona, which is considered to be a manifestation of a large-amplitude magnetohydrodynamic (MHD) wave. Aims. These unique observations by EUVI o ffer the opportunity to compare the theory of large-amplitude MHD waves with observations. Methods. Nonlinear MHD equations were employed for describing large-amplitude fast magnetosonic waves in terms of so-called simple waves. Results. Measuring the velocity of the EUV wave across the solar surface allows us to determine the quiet Sun's magnetic field to be approximate to 3.2 G. This magnetic field can be extrapolated to the corona by means of magnetic flux conservation. Then, the height dependence of the Alfven velocity can be calculated, adopting an isothermal, gravitationally stratified density model with a temperature of 1.4MK for the quiet corona. The Alfven velocity has a local maximum of approximate to 680 km s(-1) at a height of approximate to 1030Mm above the photosphere. The observations show that the EUV wave initially steepens and subsequently decays during its further evolution along the solar surface. This behavior can be aptly explained in terms of simple MHD waves. Initially, the wave front steepens due to nonlinear e ffects. Since the EUV waves are circularly or spherically propagating waves in the corona, their amplitudes are decreasing during the evolution. Hence, the wave steepening vanishes at the final state of the evolution of the EUV wave, which is consistent with the observations. In reality, the nature of the considered EUV wave is a combination of that of a circular and a spherical wave in the corona. Conclusions. The propagation of this dome-shaped EUV wave can be well described by the theory of large amplitude (simple) MHD waves.