Accretion onto moving object
Depending on the approach, this mode of accretion is commonly called Bondi-Hoyle
or Bondi-Hoyle-Lyttleton accretion. We will follow the simplest possible one which
is based on motion of incoherent particles. Hydrodynamics in this model is implemented
by an assumption that particles collide beyond the moving object (a star) at the
symmetry axis, losing the tangential component of momentum while keeping the radial one.
The relevant part of the textbook by Vladimir Karas is
Section 4.2. Some derivations, radial velocity of the particle on the axis in particular,
can be found in my hand-notes.
A few comments:
strictly speaking, the disjunct areas I, II and III are well defined only in the case of
non-interacting particles that feel solely gravity of the massive body. Boundary between
regions I and II is given by the same dust particles trajectories that determine boundary
between the regions II and III
the model of accretion assumes that particles passing through the symmetry axis beyond
the massive body interact with their symmetric counterparts which leads to cancellation
of their momentum perpendicular to the axis, while the parallel component remains unchanged.
Depending on whether the parallel component is smaller or larger than escape velocity from
the massive body, they either accrete onoto it or leave to infinity