Numerical simulations of cold clumps in the hot accretion flows around black holes

Previous numerical simulations have shown that cold clumps can form within hot accretion flows, offering insights into the detailed processes of the state transition in black hole X-ray binaries. However, the evolution of the cold clumps has not been investigated in detail yet. In this paper, we conduct hydrodynamic simulations to investigate the evolution of the cold clumps. In addition to previous result that when the accretion rate is high enough the cold clumps emerge within the hot accretion flow, we found that instead of directly moving toward to the black hole, the clumps moves outward when they initially form. The reason should be the combination of viscous torque and the condensation of hot gas from larger radii, which lead to the slightly super-Keplerian angular momentum of the clumps. After reaching the equilibrium position, the clumps begin to fragment at the inner edge with each fragment moving inward sequentially. Generally, the azimuthal movement of the clumps are quasi-Keplerian, being closer to the outer detached Keplerian cold disk rather than the surrounding sub-Keplerian hot accretion flow, which agrees well with the semi-analytical results for weak coupling case in Wang et al. (2012).