*Astron. Astrophys. 358, 299-309 (2000)*
## 3. Ballistic orbits for the case of an explosive event
We consider the motions of a group of test particles, which have
been ejected simultaneously a time
ago from a point E located in the galactic plane in the direction of
galactic longitude , at a distance
from the Sun. We assume that: i) an
energetic explosive event within a dense and massive molecular cloud
produced an expanding shell; ii) the braking forces due to the
accretion of gas acted drastically in the very initial stages of the
event disrupting the cloud and reducing the expansion velocity of a
given test particle to an equivalent initial velocity
; iii) the distances *r* of the
test particles are always small as compared with the distances to the
galactic center C; iv) the *z*-motions can be decoupled from the
motions parallel to the galactic plane. These assumptions appear to be
adequate for studying the gas at
since mostly, we avoid the motions near to the galactic plane.
The motions are refered to a system of coordinates
, with its origin at E, which is
rotating about C with the angular velocity
=
25 km
kp. The
-axis points in the direction
, the
-axis in the direction
, and the z-axis in the direction
. Under the assumptions stated above
the equations of motion as functions of the time *t* are
well-known (e.g. Olano 1982). If the explosive event is characterized
by an isotropic ejection of particles with velocity
at
, the initial conditions will be
where (azimuth, measured
clockwise from the -axis) and
(altitude, measured northwards from
the galactic plane) refer to the direction of ejection.
In this Section we consider that the components
,
and of any interaction force
between the ejected test particle and the surrounding medium can be
neglected (ballistic orbits). Therefore, Chandrasekhar's (1942)
analytical solution can be adopted for the
- and
-motions, whereas the
*z*-motions can be approximated by small oscillations about the
galactic plane with a period *T*. The latter could become an
oversimplification, since the proportionality between the galactic
gravitational force per unit mass
and the altitude *z* breaks down at about 350 pc above the plane
(cf. Dickey 1993). Nevertheless, small oscillations appear as an
acceptable insight into most of the z-motions occurring in our model.
We refer to Olano (1982) for further details. In order to allow a
comparison with the observations of the CNM, the computed results are
referred to an inertial system
which we identify with the LSR. If the position and the velocity of
the observer are , and
respectively, and the observer
measures , and *V*, we
have:
The computations of *r* can be checked independently of the
21-cm observations in all those cases where identifications of the
clouds are possible and the distances are known. Furthermore, in our
computations we considered also an initial altitude
of E above the galactic plane (cf.
Paper I), a velocity of the
observer, as well as an altitude of
the Sun above the galactic plane.
© European Southern Observatory (ESO) 2000
Online publication: June 26, 2000
helpdesk.link@springer.de |