Marginal Torus - Model X3p

Model X3p is a marginal torus rotating in the prograde sense around a Kerr black hole with a=0.5. The torus has an initial maximum density of $\rho_{max_{0}}=1.58$ at r=6.4 M. Figure 11(a) shows that at mode saturation the disk remains largely unperturbed, with an insignificant fractional density decrease of 0.01. Figure 11(b) shows a gray-scale enhanced view of the inner region near the static limit clearly shows that a highly symmetric, weak inflow has developed. The growth of the PPI modes is weak, with both modes tracking one another, as seen in Figure 11(c). Although Table 3 would suggest that these modes have a vigorous growth rate, their maximum amplitude is comparable to that of model E3r, and the outcome is very similar to that model, which is interesting since model X3p is much more closely related, in terms of its structural parameters, to model E3p. The m=1 mode reaches a very broad, weak maximum at $\sim 5.5\,T_{orb}$. As with model E3r, a noticeable amount of inflow is present from the outset as can be seen in Figure 11(d), which shows the mass influx in the equatorial plane inside the inner edge of the torus. As with E3r, this model is marginal, and 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 4 orbits; the mode growth also levels off in this period. As with model E3r, early accretion appears to be an effective mechanism for inhibiting mode growth.

Figure 11: X3p 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 10 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