Intermediate Torus - Model A3p

Model A3p is an intermediate torus rotating in the prograde sense around a Kerr black hole with a=1.0. The torus has an initial maximum density of $\rho_{max_{0}}=0.23$ at r=17.2 M. Figure 7(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 0.57. The planet has a narrow crescent shape with an outward spiral wave visible in the upper left quadrant of panel (a). A gray-scale highly enhanced ( x 50) view of the inner region near the static limit clearly shows that a weak inspiral of material is underway at saturation; however, this is by far the weakest of the inflows in the set of planet-forming simulations. The growth of the PPI modes is strong from the outset, as seen in Figure 7(c). The m=1 and m=2 modes track one another, with the m=1 mode growing at 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 10 T_orb. A small amount of inflow is present at saturation, as can be seen in Figure 7(d), which shows the mass influx in the equatorial plane inside the inner edge of the torus. The inflow of matter is quiescent until 8 T_orb, and reaches a maximum at mode saturation. The apparent reversal of the flow after 10 T_orb, combined with the lack of evidence for substantial inflow in panel (b), suggests that the planet is settling down to a new equilibrium state, and that this apparent outward flow of matter is simply indicative of the reorganization of matter within the disk.
 

Figure 7: A3p 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 50 density enhancement, linear gray scale). 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: A3apaa.mpg (rotation sense of animations is reversed)

2002-06-05