A model of the Alfvén speed in the solar corona

Abstract

We present an analytic model of the Alfvén speed v_A in the solar corona. The coronal magnetic field is modeled by a radial component representing the global field and by a dipole representing an active region. The free parameters of the model are constrained by actual observations of solar magnetic fields and coronal electron densities. The coronal magnetic field strength in the quiet Sun is determined by coronal seismology, using EIT waves as proxies for the fast magnetosonic speed v_ms, and thus for the magnetic field strength. Depending on the orientation of the dipole, we find local minima of v_A (and v_ms) at the coronal base at distances of 0.2-0.3 solar radii from the center of the modelled active region (AR), as well as above the AR at comparable heights. For all dipole orientations, a global maximum is found at 3.5 solar radii. We apply our model to the study of the formation and propagation of coronal shock waves which are observed as flare waves and as type II radio bursts, using a sample of eight solar events. We find that flare waves are initially highly supermagnetosonic (with magnetosonic Mach numbers of M_ms ≈ 2-3). During their propagation, they decelerate until M_ms=1 is reached. This behavior can be explained by a strong shock or large-amplitude simple wave that decays to an ordinary fast magnetosonic wave. The observed starting frequencies and Mach numbers of the associated type II bursts are consistent with the predictions of the model.