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Subsections

Appendix A: Description of the bow-shock models

A.1. Hartigan-Dutrey model

In model 1 the bow shock shape is simply assumed to be parabolic, i.e. that the constant B in Eq. (1) in Dutrey et al. (1997) is zero. Dutrey et al. (1997) assumed that the ambient material consists of a low-velocity molecular outflow. The ratio of the ambient and shock velocities ($V_{\rm amb}/V_{\rm shock}$) is described by the parameter $\gamma$, which in the example spectrum is set to 0.2. This situation represents the case where the ambient medium into which the jet is penetrating moves at a relatively low velocity with respect to the exciting source. Accordingly the peak emission is slightly shifted from the ambient cloud velocity at small viewing angles. As in Dutrey et al. (1997) the density distribution is supposed to be gaussian as a function of the distance from the apex. This distribution is characterized by the density dispersion $\sigma_n$. This quantity as well as other quantities which have the dimension of distance are expressed in the units of the parameter p of a parabola (one half of the distance between the focus and the apex). The observed line of sight velocity of a certain element on the surface of the shock (in the units of the shock velocity) is
\begin{displaymath}
\frac{v_{\rm rad}}{v_{\rm shock}} = (1-\gamma) \frac{\rho}{1...
 ...2} 
[\rho \cos{\phi} + \sin{\phi} \cos{\psi}] - \cos{\phi} \, ,\end{displaymath} (A1)
where $\rho$ is the radial distance of the element from the bow-shock axis, chosen as the z-axis, in the units of the parameter p:
\begin{displaymath}
\rho = \frac{\sqrt{x^2+y^2}}{p}; \quad \frac{z}{p} = \frac{1}{2} \rho^2 \, ,\end{displaymath} (A2)
and $\psi$ is its angle from the direction determined be the line of sight and z axes (chosen as the x-axis, see Fig. 1 in Hartigan et al. 1987). The assumed density weighting function wn is


\begin{displaymath}
w_n = {\rm e}^{-\frac{1}{2 \sigma_n^2} \rho^2 \left(1 + \frac{\rho^2}{4}\right)} \, .\end{displaymath} (A3)
The spectrum from the assumed material distribution is obtained by summing up the contributions of all surface elements weighted by their area and surface density.

A.2. Wilkin model

In the model of Wilkin (1996) (model 2), analytical formulae for the shape of the bow shock, tangential velocity and surface density are given as functions of the angular distance $\theta$ from the apex (Eqs. 9-12). The observed radial velocity for an element in the units of the central star velocity is
\begin{displaymath}
\frac{v_{\rm rad}}{v_\star} = \frac{1}{c}[a \cos{\phi} - b \sin{\phi}
\cos{\psi}] - \cos{\phi} \, ,\end{displaymath} (A4)
where
\begin{eqnarray}
a &=& \varpi^2 - \sin^2{\theta} \nonumber \\ b &=& \theta-\cos{...
 ...theta} \\ c &=& 2\alpha (1-\cos{\theta}) + \varpi^2 \; .\nonumber \end{eqnarray}
(A5)
$\varpi$ is the cylindrical radius in the units of the standoff distance R0, which is determined by Eq. (1) in Wilkin (1996). The dependence of $\varpi$ on the apex angle $\theta$ is given by Eq. (10) in Wilkin (1996). The parameter $\alpha$ is the ratio of the central star velocity to the stellar wind velocity $V_\star/V_{\rm wind}$. The resulting profiles are very similar to those in the Hartigan-Dutrey model in the case when $\gamma=0$ i.e. when the ambient velocity is zero with respect to the exciting source.

A.3. Raga & Cabrit model

Raga & Cabrit (1993) modeled turbulent wakes behind internal working surfaces of jets and the associated bow shocks. Their purpose was to investigate whether molecular outflows could be interpreted as gas entrained in these wakes. The model is best understood by inspecting their Fig. 1. The parameters of the model are the shape of the wake (determined by the index $\beta$ and the length to width ratio x0/r0), and the ratio M1 between the jet velocity vj and the sound speed c1 in the mixing layer. In the calculation of profiles we have used the set of parameters depicted in Fig. 3b in Raga & Cabrit (1993), namely $\beta=-2$, M1=20 and x0/r0 = 5. In this model, the systematic velocity toward the jet axis (vr) is very small compared with the sound speed c1 in the mixing layer, and is therefore neglected. Consequently, when the wake is seen from the side ($\phi=90^\circ$) the the observed profile is determined by the turbulent motion in the wake. Raga & Cabrit give the distributions of the velocity along the jet axis (vx(x,r)), the density n(x,r) and temperature T(x,r) in their Eqs. (16), (21) and (22), respectively. The line of sight velocity distribution can be obtained by a multiplication by the cosine of the viewing angle $\phi$. According to the assumption of optically thin emission the spectrum has been calculated by adding all volume elements weighted by a function of

density n and temperature T. The weighting function used is


\begin{displaymath}
w = n \, \frac{{\rm e}^{-E_{\rm u}/T}}{T} \, ,\end{displaymath} (A6)
where $E_{\rm u}$ is the energy of the upper transition level. This function comes from the local absorption coefficient by assuming thermal equilibrium. A further assumption made here is that the background radiation is negligible in the antenna equation. On the basis of the above determination of the excitation temperatures these assumptions are not justified. However, we feel that for the purpose of obtaining a qualitative picture of the profiles produced by this model, the method of calculation is reasonable.


\begin{table*}
\noindent {\bf Table B.1.} {SEST source catalogue and the observe...
 ...5mm}\\ }
\centerline{
\psfig {file=tabb1.eps,angle=180,width=16cm}
}\end{table*}


\begin{table*}
\noindent {\bf Table B.2.} {Onsala source catalogue and the obser...
 ...5mm}\\ }
\centerline{
\psfig {file=tabb2.eps,angle=180,width=16cm}
}\end{table*}


\begin{figure*}
\centerline{
\psfig {file=h0592f1.eps,width=9.5cm}
}\end{figure*}

\begin{figure*}
\centerline{
\psfig {file=h0592f2.eps,width=9.5cm}
}\end{figure*}

Acknowledgements

We thank the referee, Dr. J. Brand, for a careful reading of the manuscript and for very helpful comments and suggestions. We are grateful to him and Dr. J.G.A. Wouterloot for the program for calculating kinematic distances. We thank also Dr. C.M. Walmsley and Prof. K. Mattila for useful information and discussions. This work by J.H. and K.L. has been supported by the Finnish Academy through grant No. 1011055. The Swedish-ESO Submillimetre Telescope is operated jointly by ESO and the Swedish National Facility for Radio Astronomy, Onsala Space Observatory at Chalmers University of Technology.


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