Ultra-luminous X-ray sources (ULXs) have been puzzling us with a debate whether they consist of an intermediate mass black hole or super-Eddington accretion by a stellar mass black hole. Here we suggest that in the presence of large scale strong magnetic fields and non-negligible vertical motion, the luminosity of ULXs, particularly in their hard states, can be explained with sub-Eddington accretion by stellar mass black holes. In this framework of 2.5D magnetized advective accretion flows, magnetic tension plays the role of transporting matter (equivalent to viscous shear via turbulent viscosity) and we neither require to invoke an intermediate mass black hole nor super-Eddington accretion. Our model explains the sources, like, NGC 1365 X1/X2, M82 X42.3+59, M99 X1 etc. which are in their hard power-law dominated states.
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