Free Access
Volume 567, July 2014
Article Number A13
Number of page(s) 15
Section Interstellar and circumstellar matter
Published online 04 July 2014

Online material

Appendix A: The test case

The simulations discussed in Sect. 4 were run in two steps. In the first, stationary phase, the bow-shock sweeps out the ISM that fills the numerical box, up to 300 AU and 1200 AU in radial and longitudinal direction, respectively. Once it has left the numerical domain from the right side of the box, and the solution inside the domain has achieved a quasi-stationary configuration, the next pulsated phase is switched on, and the emissivity properties of the inner region, close to the source, are investigated.

In the present Appendix, the effects of the adopted numerical domain size and cooling model are discussed in some detail. For what concerns the cooling model, in particular, the nonequilibrium SNeq cooling model was used, which takes hydrogen ionization-recombination effects and the corresponding cooling losses into account, under the prescription that temperature does not exceed 75 000 K.

thumbnail Fig. A.1

Selected outputs from a large-scale simulation (TestDG3). Solid lines in the nozzle region represent the area investigated in all simulations listed in Table 2.

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thumbnail Fig. A.2

Density (top) and temperature (bottom) fields: the DG3 case patterns (left) vs. the stationary test case ones (right).

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thumbnail Fig. A.3

Two-dimensional emissivity patterns: the DG4 case (left) vs. the test case (right). The figures show both the stationary configuration (top) and the pulsated one (bottom).

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thumbnail Fig. A.4

Left: synthetic PVDs for the stationary μ = −0.5 test case, that is simulation TestDG3, to be compared with Fig. 8 of case DG3. Right: same for the unsteady simulation of case TestDG4, to be compared with Fig. 10.

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Two questions arise:

  • 1.

    It is well known that bow-shocks (namely, the triple-point Mach-disk region behind them) are suitable to generate recirculating flows of matter that can move in reverse, and that they affect the region close to the nozzle. If so, how can we be sure that expelling the bow-shock from the simulation box at only 1300 AU from the source does not alter dynamical and emitting properties of the region under investigation, the emitting region, extending from the nozzle up to the first ~5 arcsec?

  • 2.

    Though in the emitting region weak shocks are at work, with temperatures of order a few thousands degrees, well below the cooling model limit, it is well known that in the post bow-shock region temperature may achieve values of order 106 K. If so, how can we be sure that miscalculating the cooling losses in the post-bow shock region does not affect the global jet dynamics and the properties of the emitting region as a consequence?

In order to be confident with the results presented in the paper, we run a three-step test-case. In the first step, a stationary jet propagates into a wider, large-scale domain that extends over 870 × 6700 AU in r and z respectively, (1340 × 8060 grid points). Figure A.1 shows density and temperature fields (top and bottom, respectively) in the domain used in this large-scale simulation (to make a comparison, the small-scale domain of the runs of Table 2 is highlighted in the figure with solid lines).

The adopted, simplified tabulated cooling model, in which cooling losses are a function of temperature and assigned (solar) abundances only, allows us to skip the temperature limit of the Sneq model. Thanks to both the larger domain size and the cooling model, the quasistationary solution obtained in this first step, once the bow-shock has left the domain, guarantees a better description of the jet global dynamics, with respect to the simulations of Table 2.

In the second step (simulation TestDG3), the internal portion of the stationary solution of the first step, marked in blue in Fig. A.1, is used to restart a stationary, small-scale simulation in which the precise Sneq cooling model is recovered to properly calculate the emissivity pattern and synthetic PVds. Finally, in the third step (TestDG4) pulsating inflow conditions like those of case DG4 are imposed. Also, for this case, the emissivity field and synthetic PVDs are calculated. The test case results are reported in Figs. A.2A.4.

Figure A.2 shows density and temperature fields (top and bottom, respectively) for the test case (right column) vs. the DG4 case (left column). The patterns are basically the same. Actually, filaments of recirculating matter in the cocoon region, which are still visible in the DG4 case, have disappeared in TestDG3, because of the “older” age of the jet. The panel of Fig. A.3 shows the emissivity patterns in the rz plane for the DG4 case (on the left), and for the test case (on the right), for both the stationary (top) and pulsated (bottom) phase. The already mentioned filaments in the cocoon region do not provide relevant contribution to the jet emissivity, and play no role in PVDs formation, as shown by comparing Fig. A.4 with Figs. 8 and 10.

As a conclusion, the test case confirms that the adopted domain size and cooling model do not affect the bow-shock feedback in the emitting region and the reliabilty of the results.

© ESO, 2014

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