Wide Torus - Model B3p

Model B3p is a wide torus rotating in the prograde sense around a Kerr black hole with a=1.0. The torus has an initial maximum density of $\rho_{max_{0}}=0.72$ at r=17.2 M. Although the disk extends to $r \approx90 M$, most of the matter is concentrated inside $r \approx 30 M$. Figure 8(a) shows that at mode saturation a planet has formed, with a density maximum at $r\sim 11\,M$ and a fractional density enhancement of 0.35. The planet has a tightly-wrapped crescent shape with a noticeable outward spiral wave in the upper right quadrant of panel (a). 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 lower right quadrant of panel (b). There is also a hint of frame dragging of the flow near the static limit where dense material appears to smear out into a ring. A weaker inbound spiral of matter in the upper half of panel (b) is also feeding the inner ring of matter. The growth of the PPI modes is strong from the outset, as seen in Figure 8(c). The m=1 and m=2 modes track one another, with the m=1 mode growing a a slightly greater rate. The m=1 mode is also less erratic than the m=2 mode. Both modes exhibit strong linear growth up to saturation at $\sim 13\,T_{orb}$; the saturation peak is very broad, making a precise determination of t_sat difficult. As with the previous two models, inflow is triggered at saturation, as can be seen in Figure 8(d), which shows the mass influx in the equatorial plane inside the inner edge of the torus. The flow of matter is quiescent until 11 T_orb, and reaches a maximum at 13 T_orb, again corresponding with mode saturation.

Figure 8: B3p 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 4 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: B3apaa.mpg (rotation sense of animations is reversed)

2002-06-05