## Appendix A: a model for the SiO jetHere we present a simple model to reproduce the maximum and minimum velocities of the SiO line emission observed along the jet axis. An estimate of the line intensity goes beyond the purpose of the present treatment. The goal is to determine the kinematical and geometrical parameters of the jet by fitting the shape of the position-velocity plot of Fig. 3 bottom. We assume that the gas traced by the SiO line is ejected inside a
cone with aperture angle (see
Fig. A1), up to a maximum distance
from the centre. The gas is moving along straight lines passing
through the apex of the cone into two opposite directions, with
velocity proportional to the angular distance from the apex, where is the maximum velocity reached by the ejected gas.
In the following we define a coordinate system with where is the maximum velocity and the minimum for , and vice versa for . In the First of all, we know that the outflow intersects the plane of the sky, i.e. : therefore, can be directly measured in the map as the maximum distance along the axis of the flow between the centre and the farthest point from the centre where SiO emission is detected. This gives 12" to a very good approximation (see e.g. Fig. 12 bottom). The other three parameters can be obtained by fixing the values of the minimum and maximum velocities for (or, equivalently, for ). For , for example, these are reached respectively for and , and are given by the following expressions: After some algebra, these take the form where we have posed . We need a third condition to determine , , and . This is given by the expression relating the aperture angle of the cone, , to the projection of it on the plane of the sky (), which can be written as The three Eqs. (A6), (A7), and (A8) can be solved to determine
, ,
and . For this we need an estimate
for ,
, and
. The first two parameters can be
measured from Fig. 12 bottom, whereas
can be estimated from the map of
the SiO jet (see Fig. 3 right). Plausible values are
=32.5-44 km s We thus conclude that the three unknowns are constrained in the
following ranges: =2:O8-11:O6,
=8:O5-22 © European Southern Observatory (ESO) 1999 Online publication: April 28, 1999 |