Abstract The quasi-periodic oscillations (QPOs) in black hole (BH) systems with different scales are interpreted based on the magnetic reconnection of large-scale magnetic fields generated by toroidal electric currents flowing in the inner region of the accretion disk, where the current density is assumed to be proportional to the mass density of the accreting plasma. The magnetic connection (MC) is taken into account in resolving dynamic equations describing the accretion disk, in which the MC between the inner and outer disk regions, between the plunging region and the disk, and between the BH horizon and the disk are involved. It turns out that a single QPO frequency associated with several BH systems with different scales can be fitted by invoking the magnetic reconnection due to the MC between the inner and outer regions of the disk, including the BH binaries XTE J1859+226, XTE J1650¡ 500 and GRS 1915+105 and the massive BHs in NGC 5408 X-1 and RE J1034+396. In addition, the X-ray spectra corresponding to the QPOs for these sources are fitted based on the typical disk-corona model.

Keywords accretion, accretion disks — black hole physics — magnetic fields — stars: individual (XTE J1859+226, XTE J1650¡500, GRS 1915+105) — galaxies: individual (NGC 5408, RE J1034+396)

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