Apparent cross-field superslow propagation of magnetohydrodynamic waves in solar plasmas

In this paper we show that the phase mixing of continuum Alfvén waves
and/or continuum slow waves in magnetic structures of the solar atmosphere
as, e.g., coronal arcades, can create the illusion of wave propagation across the
magnetic eld. This phenomenon could be erroneously interpreted as fast mag-
netosonic waves. The cross-field propagation due to phase mixing of continuum
waves is apparent because there is no real propagation of energy across the magnetic surfaces. We investigate the continuous Alfvén and slow spectra in 2D
Cartesian equilibrium models with a purely poloidal magnetic field. We show
that apparent superslow propagation across the magnetic surfaces in solar coronal structures is a consequence of the existence of continuum Alfvén waves and continuum slow waves that naturally live on those structures and phase mix as time evolves. The apparent cross-field phase velocity is related to the spatial variation of the local Alfvén/slow frequency across the magnetic surfaces and is slower than the Alfvén/sound velocities for typical coronal conditions. Understanding the nature of the apparent cross-field propagation is important for the correct analysis of numerical simulations and the correct interpretation of observations.