摘要：Context. Accretion discs are ubiquitous in the Universe, and it is
crucial to understand how angular momentum and mass are radially transported in these
objects.
Aims. Here, we study the role played by non-linear spiral patterns
within hydrodynamical and non-self-gravitating accretion discs assuming that external
disturbances such as infall onto the disc may trigger them.
Methods. To do so, we computed self-similar solutions that describe
discs in which a spiral wave propagates. These solutions present shocks and critical sonic
points that were analyzed.
Results. We calculated the wave structure for all allowed temperatures
and for several spiral shocks. In particular, we inferred the angle of the spiral pattern,
the stress it exerts on the disc, and the associated flux of mass and angular momentum as
a function of temperature. We quantified the rate of angular momentum transport by means
of the dimensionless α parameter. For the thickest disc we considered
(corresponding to h/r values of
about one-third), we found values of α as high as 0.1 that scaled with the temperature
T such that
α ∝ T3
/ 2 ∝
(h/r)3.
The spiral angle scales with the temperature as arctan(r/h).
Conclusions. These solutions suggests that perturbations occurring at
disc outer boundaries, such as perturbations due to infall motions, can propagate deep
inside the disc and therefore should not be ignored, even when considering small radii.
