In this work, we construct a sample of black hole X-ray binaries (BH XRBs), low-luminosity active galactic nuclei (LLAGNs), and FR Is with wider distribution of Eddington ratios and re-explore their fundamental plane of BH activities, that is, log L R = X log L X + M log L M BH + c 0. We find that the quiescent BH sources follow a similar fundamental plane (ξ X ∼ 0.6) with sub-Eddington BH sources very well, while the strong radio sources (e.g., FR Is) follow a steeper fundamental plane (ξ X ∼ 1.30). We also find that the radio-X-ray correlation of quiescent BH sources are still on the extension of sub-Eddington BH sources and the strong radio sources follow a steeper correlation (ξ X ∼ 1.30). The results are consistent with recent observations in BH XRBs. It is predicted that the X-ray emissions of both sub-Eddington BH sources and quiescent BH sources originate from radiatively inefficient accretion mode, while the X-ray emissions of strong radio sources dominantly originate from the jet.

One normal outburst and three mini-outbursts have been detected by Rossi X-ray Timing Explorer satellite after 2000 in the well-known black hole X-ray binary XTE J1550-564. In this work, we explore the hysteresis effect of the four outbursts, which is a phenomenon that a similar spectral state transition occurs at different luminosity in an outburst of black hole X-ray binary. A q-like track was found in the hardness-intensity diagram of the normal outburst in 2000 but not in the three mini-outbursts that only occur in the Low/Hard state. The results demonstrate that the hysteresis effect is not apparent in the three mini-outbursts and the X-ray spectra are harder than that of the normal outburst at the same photon count rate. Furthermore, the results of the correlation analysis show that the Γ − F2−10keV correlation of mini-outburst maintain negative in the Low/Hard state with the harder spectra than that of the normal outburst at the same X-ray flux. The X-ray spectral evolution can be well-explained by the state-transition model from the Shakura–Sunyaev disk to the advection-dominated accretion flow, which implies that the three mini-outbursts of XTE J1550-564 might originate from a smaller discrete accretion event.