Marginal Torus - Model E3r

Model E3r is a marginal torus rotating in the retrograde sense around a Kerr black hole with a=-1.0. The torus has an initial maximum density of $\rho_{max_{0}}=0.43$ at r=15.7 M. Figure 10(a) shows that at mode saturation the disk remains largely unperturbed, with an insignificant fractional density decrease of 0.01. Figure 10(b) shows a gray-scale enhanced view of the inner region near the static limit clearly shows that an inflow has developed that contacts the static limit in the upper right quadrant of panel (b); it must be noted that this inflow is extremely weak ( x 100 enhancement) yet it bears some similarity to the other retrograde model, B3r, in that the stream of matter exhibits a change in flow direction near the static limit. The growth of the PPI modes is weak, with the m=1 mode levelling off quickly after a brief initial growth, and the m=2 mode showing little activity, as seen in Figure 10(c). The m=1 mode reaches a very broad, weak maximum at $\sim 20\,T_{orb}$, making a precise determination of t_sat difficult. Unlike the previous models, a noticeable amount of inflow is present from the outset as can be seen in Figure 10(d), which shows the mass influx in the equatorial plane inside the inner edge of the torus. Since this model is marginal, the early onset of an inflow is to be expected. In comparing panels (c) and (d), we see that the inflow is established before any significant mode growth has occured; inflow levels off to a more or less constant value in the first 5 orbits; the mode growth also levels off in this period. This would suggest that early accretion is an effective mechanism for inhibiting mode growth. This observation is strengthened by the last model to be considered, X3p.

Figure 10: E3r Model. (a) (Top left) Equatorial slice through torus at saturation. Density contours linearly spaced between $\rho _{max}$ and 0.0. (b) (Bottom left) Magnified view of flow near static limit at saturation ( x 100 density enhancement). The edge of the central black circle is the static limit. (c) (Top right) Mode growth. (d) (Bottom right) Mass influx at inner edge of disk. (Black hole rotates in counter-clockwise sense.)

2002-06-05