  Classical T Tauri stars (CTTSs) are variable in different time-scales. One
type of variability is possibly connected with the accretion of matter through
the Rayleigh-Taylor instability that occurs at the interface between an
accretion disc and a stellar magnetosphere. In this regime, matter accretes in
several temporarily formed accretion streams or `tongues' which appear in
random locations, and produce stochastic photometric and line variability. We
use the results of global three-dimensional magnetohydrodynamic simulations of
matter flows in both stable and unstable accretion regimes to calculate
time-dependent hydrogen line profiles and study their variability behaviours.
In the stable regime, some hydrogen lines (e.g. H-beta, H-gamma, H-delta,
Pa-beta and Br-gamma) show a redshifted absorption component only during a
fraction of a stellar rotation period, and its occurrence is periodic. However,
in the unstable regime, the redshifted absorption component is present rather
persistently during a whole stellar rotation cycle, and its strength varies
non-periodically. In the stable regime, an ordered accretion funnel stream
passes across the line of sight to an observer only once per stellar rotation
period while in the unstable regime, several accreting streams/tongues, which
are formed randomly, pass across the line of sight to an observer. The latter
results in the quasi-stationarity appearance of the redshifted absorption
despite the strongly unstable nature of the accretion. In the unstable regime,
multiple hot spots form on the surface of the star, producing the stochastic
light curve with several peaks per rotation period. This study suggests a CTTS
that exhibits a stochastic light curve and a stochastic line variability, with
a rather persistent redshifted absorption component, may be accreting in the
unstable accretion regime.
