Astron. Astrophys. 317, 793-814 (1997)

3. Shape of the shock cone

Fig. 2 shows the density distribution of five models towards the end of the simulations, emphasizing the distribution of matter on scales between one and ten accretion radii. The left Figs.  2a,c and e, show models with a small gradient in velocity (3%), while the right Figs. b and d have large gradients (20%). Similarly to 3D models without gradients (see Ruffert 1996, and references therein), these new models do not exhibit the "flip-flop" flow visible in previous 2D simulations. The shape of the shock cones shown in Fig. 2 is fairly constant in time and remains roughly conical, contrary to the 2D flows, whose cones shifted strongly from side to side. One notices the following features when inspecting Fig. 2. The mass is distributed in a hollow shock cone (as has been reported previously) for the models with a small gradient, i.e. the density is maximal just behind the shock, while downstream from the accretor, the density is minimal along the axis. The asymmetry of the velocities in the incoming flow reflects itself in higher density maxima along the cone on the side of the lower velocities. This density asymmetry is so pronounced in the models with strong gradients (Figs. 2) that the "hollow cone" shape can be recognized only with difficulty. The line of minimum density is very irregular and is shifted from the -axis by several accretion radii. Already upstream of the shock a higher density is indicated by the contour of value 0.01 being detached from the shock on the positive y -axis side, while it is very close to the shock on the negative y -axis side. This density difference is easily explicable: on the side of smaller velocities gravity can act relatively more strongly to divert the flow. Thus the effective local accretion radius is larger on the side of smaller velocities and so a larger volume of matter can be gravitationally focused by the accretor. One also notices that the side of the cone with smaller densities is more irregularly shaped than the high-density side. The cavities and lumps produced by the fluctuating flow close to the accretor (at distances closer than roughly one accretion radius) can propagate more easily downstream on the side of the cone with lower densities. Since the velocity enters the accretion radius Eq. (5) via a square, one might wonder, whether the velocity is so small, that the local accretion radius is comparable to the distance of the accretor to the boundary of the computational box which is approximately at 16 . This is not the case, since inserting (from Eq. (4)) into Eq. (5) one obtains 4 , which is a factor of 4 smaller than the distance to the computational boundary.

Fig. 2a-e. Contour plots showing snapshots of the density together with the flow pattern at large distances from the accretor. The contour lines are spaced logarithmically in intervals of 0.1 dex. The bold contour levels are sometimes labeled with their respective values (0.01 and 0.4). The dark shades of gray indicate a high density. The dashed contour delimits supersonic from subsonic regions. The time of the snapshot together with the velocity scale is given in the legend in the upper right hand corner of each panel.

© European Southern Observatory (ESO) 1997

Online publication: July 8, 1998
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