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Astron. Astrophys. 362, 333-341 (2000)

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5. Gravitational collapse

Can we distinguish a collapsing self-gravitating cloud from a turbulent region within which the Jeans mass is not reached? We here take a simulation of driven hydrodynamic turbulence in which self-gravity is switched on after a steady driven state has been reached (Model D2 from Klessen et al. 2000). The particular parameters chosen are shown in the caption to Fig. 9.

[FIGURE] Fig. 9. The distribution of shocks in driven turbulence with gravity. The initial rms speed is 9.9[FORMULA], [FORMULA], wavenumber [FORMULA] and the density is chosen to be 0.125 (total mass of unity in the periodic box). The gravitational constant is set to unity. The gravity is switched on after the driven turbulence is well established at time [FORMULA]. The turbulent Jeans mass is 3.2 (see Klessen et al. 2000).

The number and distribution of shock speeds is not particularly different from the equivalent non-gravity numerical experiment. The power-law section is limited, consistent with other low wavenumber simulations (see Fig. 2).

In stark contrast, the dissipated energy transforms from the typical non-gravity case (upper box of Fig. 10) to one dominated by a few accretion shocks (lower box of Fig. 10). A relatively small number of well-defined shocks generates strong individual signatures. These shocks are of typical cloud speeds but are strongly dissipative because they propagate into very dense regions.

[FIGURE] Fig. 10. The power dissipated by shocks in driven turbulence with gravity at the four indicated times. Gravity is just switched on at the time [FORMULA]. The parameters are as in Fig. 9.

The distribution of the shocks at time t = 6 is displayed in Fig. 11. The elongated cloud at time t = 2 (Fig. 6) has now collapsed into narrow filaments and cores. There is high shock dissipation around the collapsing cores although other strong shocks are still quite widespread. The code does not distinguish between a shock and a collapsing flow. The artificial viscosity prescription treats all converging flow regions as dissipative. Nevertheless, a collapsing flow does physically dissipate its energy as it shocks onto a growing core. Hence the dynamical evolution is correctly modelled. The surface brightness of the shocks is, of course, limited by the grid resolution. The high SPH resolution, however, verifies that the general properties are realistic (Klessen et al. 2000). A new problem arising in the shock analysis is that a single converging flow onto a core may actually be a double shock layer. We would here record this as a single shock in the counting procedure and in Fig. 10. We have not tried to correct for this.

[FIGURE] Fig. 11. Maps of the column and power dissipated in driven turbulence with gravity at the time t = 6. Note the grey scaling allow a direct comparison with Fig. 6. The elongated cloud at time t = 2 has now collapsed into narrow filaments and cores.

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© European Southern Observatory (ESO) 2000

Online publication: October 30, 19100