Astron. Astrophys. 364, 763-768 (2000)

3. The model

We compute a numerical model of a jet with a sinusoidal variable ejection velocity of period  yr, half-amplitude  km s^-1 and mean velocity  km s^-1 (see Eq. 1). The injection velocity has a direction at an angle of from the z-axis, initially lying on the xz-plane, and then precessing around the z-axis with a precession period  yr. We also impose an initial jet radius  cm. These parameters are consistent with the VLA observations of the Serpens triple radio source (see Sect. 2).

We choose an initial jet density of  cm^-3 and a  cm^-3, uniform density for the surrounding environment (this low environmental density being chosen so that the leading working surface of the jet can propagate at a high velocity through the computational grid). We have chosen a jet density consistent with the lower boundary of the density range estimated by Curiel et al. (1993, also see Sect. 2) in order to have as good a resolution of the post-shock cooling regions as possible.

We assume that both the jet and the environment are initially neutral, and that both have an initial temperature of  K (the precise value for this temperature not being important, since the Mach number of the flow is very high and all of the shocks are strong).

The numerical simulation is carried out with the 3D adaptive grid code "yguazú-a", which is described in detail by Raga et al. (2000). In the configuration which has been used for the calculation, the code integrates the 3D gasdynamic equations, an advection equation for a passive scalar (with which different regions of the flow can be labeled), and a rate equation for the ionization of hydrogen. The simple cooling function discussed by Raga et al. (1999) has been included in the energy equation.

The calculation is done on a hierarchical, binary adaptive grid with a maximum resolution of  cm (along the three axes). The maximum resolution is only allowed in the region of space occupied by the material originally coming from the jet, and the region filled by environmental material is resolved at most with a grid of  cm spacing. The resulting grid structure is illustrated in Fig. 2.

Fig. 2. Column density (left, factor of contours), pressure stratification on the central, plane of the outflow (centre, factor of 2 contours) and the points on this plane chosen by the adaptive grid algorithm (right), for the flow obtained after a 60 yr time-integration. The thick contour in the pressure plot (centre) delineates the contact discontinuity separating the jet from the environmental material. The axes are labeled in cm.

The flow stratification obtained after a  yr time-integration is shown in Fig. 2, where we display the column density (integrated along the y-axis), and the pressure stratification on the xz-plane. The grid points on this plane (chosen by the adaptive grid algorithm) are also shown. In this figure, one can clearly see four separate working surfaces. The leading working surface has a complex structure which results from the merger of a number of knots that catch up with the leading bow shock of the jet.

Fig. 3 and Fig. 4 show the 3.6 cm, free-free continuum maps predicted from the numerical jet model for different integration times. The maps have been computed assuming that the xz-plane coincides with the plane of the sky. In Fig. 3, we see the knots which are produced by the ejection velocity variability travelling down the jet flow, and eventually catching up with the leading bow shock. The successive knots travel in different directions, as a result of the precession.

Fig. 3. 3.6 cm radio continuum maps predicted from the numerical jet model for integration times from 10 to 60 years. The greyscales are logarithmic, with the range shown by the wedge (in erg s-1 cm-2 Hz- 1 sterad-1). The axes are labeled in cm. The successive working surfaces formed along the jet flow are labeled A through F, in order to identify the individual knots as they travel down the jet flow.

Fig. 4. 3.6 cm radio continuum maps predicted from the numerical jet model for integration times from 60 to 75 years (also see Fig. 3). The greyscales are logarithmic, with the range shown by the wedge (in erg s-1 cm-2 Hz- 1 sterad-1). The axes are labeled in cm.

It is clear that the knots show a complex time-evolution. In Fig. 4, we see that over a period of 10 years knot F becomes fainter (for  yr). Knot D also fades away, but knot E becomes brighter with increasing time. Knot D, however, had shown a dramatic intensity increase for  yr (see Fig. 3).

These complex changes in radio continuum intensity are illustrated in Fig. 5, where we show the 3.6 cm emission integrated along the x-axis. The resulting intensity vs. position curves show that while at some times the emission of the whole outflow lobe is dominated by a single knot (e.g., at  yr, see Fig. 5), at other times several knots of comparable intensities are observed (e.g., at and 70 yr).

Fig. 5. 3.6 cm radio continuum emission integrated across the width of the outflow in the maps predicted from the numerical jet model (see Fig. 3 and Fig. 4) for integration times from 10 to 70 years. The emission is given in erg s-1 cm- 1 Hz-1 sterad-1.

Given the extreme complexity of the flow, it is hard to understand in detail the light curves obtained for the successive knots. As pointed out by Raga & Noriega-Crespo (1998), the knots produced by a time-dependent ejection velocity have an intensity that first increases, and then decreases as the knots travel away from the source.

In the present simulation, this effect is combined with the precession, which becomes more important at larger distances from the source (Raga et al. 1993). As the knots diverge from each other at larger distances from the source (Raga & Biro 1993), the trailing knots eventually cross the bow shock wings of previously ejected knots. These interactions lead to brightenings of the knots.

A more dramatic effect is seen when the trajectory of one of the knots intersects the leading bow shock of the outflow. This is seen for knot C in the  yr map, and for knot D in the  yr map (see Fig. 3).

A qualitative comparison of these results with the 3.6 cm VLA maps of the Serpens jet is presented in the following section.

© European Southern Observatory (ESO) 2000

Online publication: January 29, 2001
helpdesk.link@springer.de