Fig. 3.
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Trajectory of the torus angular-momentum vector in the x-y plane when the accretion torque evolves exponentially from zero to τf = −1 for various cases. A torus that is initially precessing with an angular momentum L(0) = − 0.3i approaches the final state of precession about the new equilibrium point, iτf/ωp, slowly or rapidly for a low (ωh = 0.2ωp) or high (ωh = 2ωp) healing frequency, as in the left and middle panels, respectively. The right panel presents the same case as in the left panel (i.e., ωh = 0.2ωp), except that initially the torus has a zero angular momentum projection onto the x-y plane, i.e., L(0) = 0, highlighting that a change in accretion torque can induce precession in a torus. In all three examples, we set ωp = 1 and the phase evolution is represented by both the color and the decreasing thickness of the curve.
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