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

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6. Results of models with index 4/3

As a check for the numerics two models were run with the same physical initial and boundary conditions, but differing in resolution of the accretor: model SS used 9 grids, model ST used 10 grids (cf. Table 1 for the other parameters). The two left panels of Fig. 10 show contour plots of the density distribution, while the acretion rates of mass and angular momentum can be found in Fig. 11. Especially the temporal evolution of the accretion rates confirm that also for [FORMULA] using grids to 9 levels deep is sufficient: within the time in which the two models SS and ST overlap, the mass accretion rate and the angular momentum accretion agree to within a few percent.

[FIGURE] Fig. 10a-c. Contour plots showing snapshots of the density together with the flow pattern in a plane containing the center of the accretor for models SS, ST and RL. The contour lines are spaced logarithmically in intervals of 0.1 dex for panels a and c, while panel b shows contours in intervals of 0.02 dex. The bold contour levels are labeled with their respective values. 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.
[FIGURE] Fig. 11a-f. The accretion rates of several quantities are plotted as a function of time for models SS, ST and RL. The left panels contain the mass and angular momentum accretion rates, the right panels the specific angular momentum of the matter that is accreted. In the left panels, the straight horizontal lines show the analytical mass accretion rates: dotted is the Hoyle-Lyttleton rate (Eq. (1) in Ruffert 1994a), solid is the Bondi-Hoyle approximation formula (Eq. (3) in Ruffert 1994a) and half that value. The upper solid bold curve represents the numerically calculated mass accretion rate. The lower three curves of the left panels trace the x (dotted), y (thin solid) and z (bold solid) component of the angular momentum accretion rate. The same components apply to the right panels. The horizontal line in the right Panel of model ST shows the specific angular momentum value as given by Eq. (7). It is outside the range of the plot for models SS and RL.

Models SS and ST (Fig. 11) are equivalent to models IS and IT, (Fig. 4) so a comparison should show what effects are due to the different adiabatic index [FORMULA]. Additionally, model SS can be compared to model CS shown in Fig. 6 of Ruffert (1995). Both the mean and the amplitude of the mass accretion rate of model SS are similar to the ones of model CS, and even the angular momentum accretion fluctuations do not show any striking difference. When comparing model SS to model IS one notices that the mass accretion rate proceeds in a much more unstable way in model SS. The rate of mass accretion as well as the specific angular momentum of the z -component are larger in model SS. So much so, that in a short burst model ST actually reaches the analytically estimated value (middle right panel of Fig. 11) contrary to model IS or IT. Thus we conclude that the models with [FORMULA] accrete in a less stable way than their [FORMULA] equivalents, which is the opposite from what had been observed in the simulations without gradients (Ruffert 1995 and references therein). More [FORMULA] models are necessary before any more systematic statements can be made.

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© European Southern Observatory (ESO) 1997

Online publication: July 8, 1998
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