Marginal Torus - Model E3p

Model E3p 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 $\rho_{max_{0}}=0.86$ at r=6.8 M. Figure 9(a) shows that at mode saturation an elongated planet has formed, with a density maximum at $r\sim6\,M$ and a fractional density decrease of 0.01. A gray-scale view ( x 2 enhancement) 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). Figure 9(c) shows that the m=1 mode undergoes steady growth from the outset, with some variability in the first 10 orbits. The m=2 mode tracks the m=1 mode until $12\, T_{orb}$, where it flattens out until $25\, T_{orb}$, then grows again until the m=1 mode saturates at $33\,T_{orb}$. Perhaps the most striking feature of this model can be seen in the mass influx curve, Figure 9(d), again plotted for a point in the equatorial plane inside the inner edge of the disk. The transition between quiescence and accretion is less sharply defined than in other models, and a strong inflow begins after $\sim 25\,T_{orb}$, roughly corresponding to the point where the m=2 mode begins to grow again. Compared to the other models, the amount of accretion in this model is remarkable; panels (a) and (b) clearly show very prominent in-bound spirals of matter.

Figure 9: E3p 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 2 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.)

 View animation: E3apaa.mpg (rotation sense of animations is reversed)

2002-06-05