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tokens: 0.02, respectively. These values are also within the typical range obtained in the study of GRB afterglows (Medvedev 2006 ). We note that different values of ε e and ε B will only change the normalization, but not the slope, of the η jet – relationship (cf. equation 3 below). We then calculate the synchrotron emission from these accelerated electrons. Like any other jet models in literature, our jet model is phenomenological. Besides, we assume that all the jet parameters remain unchanged for different sources and accretion rates, which is certainly a strong assumption. This is partly because we still do not have good constraint on them. To conclude, the only free parameter in our jet model is its mass-loss rate . We note that the L R is found to be a power-law function of (see also Heinz Sunyaev 2003 ). 2.2 Hot accretion flow model Depending on the accretion rate, two types of hot accretion flow exist. They are the advection-dominated accretion flow (ADAF; Narayan Yi 1994 , 1995 ; Abramowicz et al. 1995 ) below certain critical accretion rate and the luminous hot accretion flow (LHAF; Yuan 2001 ) above it (see review by Yuan Narayan 2014 ). LHAF is thermally unstable (Yuan 2003 ). But if accretion rate is relatively low, , the growth time-scale of the thermal instability is larger than the accretion time-scale, so the gas can remain hot throughout the flow. We call it type-I LHAF. Above , the growth time-scale of the thermal instability is shorter than the accretion time-scale thus some cold dense clumps should be formed, embedded in the hot phase medium. We call it type-II LHAF or two-phase accretion flow. We follow the standard approach to calculate the dynamical structure and the emitted spectrum of ADAFs and type-I LHAF (e.g. YCN05 ). The L X at 3–9 keV band is then derived from the spectrum. For the two-phase accretion flow, optical/UV radiation from cold clumps will provide additional (likely dominant) seed photons for the inverse Compton scattering process, to generate the X-ray emission. The whole process is obviously complicated, depending on the detailed dynamics of the two-phases accretion flow such as the filling factor and temperature of clumps and so on. Following Yuan Zdziarski ( 2004 ), we simplify the problem by replacing the electron energy equation with the Compton y -parameter. With the assumption that the electron advection term is zero in the two-phase flow, we can calculate the radiative cooling rate. The bolometric luminosity can then be derived (Xie Yuan 2012 ). In order to derive 3–9 keV L X , we assume the spectrum to be a simple power law with exponential cutoffs at both the high and low ends, i.e. F E ∼ E 1−Γ exp (− E min / E )exp (− E / E max ), where the photon index Γ is constrained by the Compton y -parameter. E min is set arbitrarily to be 0.02 keV. E max is numerically determined by the electron temperature, i.e. E max = kT e , at the location where most of the radiation comes out (Yuan Zdziarski 2004 ).