X-ray emitting MHD accretion shocks in classical T Tauri stars. Case for moderate to high plasma-β values

AIMS. We investigate the stability and dynamics of accretion shocks in CTTSs, considering the case of beta >= 1 in the post-shock region. In these cases the 1D approximation is not valid and a multi-dimensional MHD approach is necessary. METHODS. We model an accretion stream propagating through the atmosphere of a CTTS and impacting onto its chromosphere, by performing 2D axisymmetric MHD simulations. The model takes into account the stellar magnetic field, the gravity, the radiative cooling, and the thermal conduction (including the effects of heat flux saturation). RESULTS. The dynamics and stability of the accretion shock strongly depends on the plasma beta. In the case of shocks with beta > 10, violent outflows of shock-heated material (and possibly MHD waves) are generated at the base of the accretion column and strongly perturb the surrounding stellar atmosphere and the accretion column itself (modifying, therefore, the dynamics of the shock). In shocks with beta ~ 1, the post-shock region is efficiently confined by the magnetic field. The shock oscillations induced by cooling instability are strongly influenced by beta: for beta > 10, the oscillations may be rapidly dumped by the magnetic field, approaching a quasi-stationary state, or may be chaotic with no obvious periodicity due to perturbation of the stream induced by the post-shock plasma itself; for beta ~ 1 the oscillations are quasi-periodic, although their amplitude is smaller and the frequency higher than those predicted by 1D models.