N-body simulation of clumpy torus

N is number of particles
r₀ is a geometrical parameter of torus
M_c is a central mass
M_torus is a torus mass

Section 2. Keplerian torus

1. The lines of nodes for all particles coincide (N=5, r₀=0.4) [fig.1]
2. The lines of nodes for all particles coincide (N=5, r₀=0.7) [fig.2]
3. The lines of nodes are randomize (N=5, r₀=0.4) [fig.3]
4. Keplerian torus with N=300 particles and r₀=0.4 [fig.4]

Section 3. Trajectories of test particle in the inner potential of homogeneous circular torus and potential of the central mass

M_torus / M_c = 1

1. Change of cross-section of the torus with r₀=0.3 consisting from N=1 500 particles [gif, avi]
2. Average cross-section of the torus with r₀=0.3 consisting from N=1 500 particles [gif]

Section 4. Self-gravitating torus in the gravitational field of the central mass: N-body simulation

Change of torus cross-section due to self-gravitation for M_torus / M_c = 0.02, N = 16 384.
Initial conditions correspond to Keplerian torus with:

1. r₀=0.3 [avi]
2. r₀=0.5 [avi]