The dominant paradigms for jet production are outlined in the works of Blandford & Znajek (1977; BZ model) and Blandford & Payne (1982; BP model). In both of the models, the large-scale ordered magnetic fields threading the accretion flow or spinning black hole are required. It is suggested that the large-scale magnetic fields may diffuse outward rapidly if the half-thickness of the accretion disk H is significantly less than the radius r (Lubow et al. 1994; Heyvaerts et al. 1996; Guan & Gammie 2009). Then, the jet discussed in our paper should be produced in a geometrically thick disk (Maccarone et al. 2003; Sikora et al. 2007; Coriat et al. 2011; Russell et al. 2011), such as the ADAF or the slim disk (Abramowicz et al. 1988). Our work focuses on the jet produced in the ADAF, for which the accretion rate is relatively low. The jet power (





) in the BP and BZ models is associated with the strength of the large-scale ordered poloidal magnetic field 





. In the BP model, the jet power can be described as (e.g., Livio et al. 1999; Cao 2002; Li & Cao 2012)
3





where 





 is the angular velocity of the disk, 





 is the torque applied on the disk, and 





 is introduced to describe the contribution of different radius to the jet power. In the BP model, the energy of the jet is mainly from the inner region of the disk. Then, μ should be larger than or equal to 0, i.e.,
4





The strength of the large-scale poloidal magnetic field remains uncertain, but is believed to be associated with the accreting process (e.g., Moderski & Sikora 1996; Ghosh & Abramowicz 1997; Livio et al. 1999; Meier 2001; Nemmen et al. 2007). In addition, the strength of the small-scale magnetic field (





) in the magnetohydrodynamic turbulence of the disk is usually used to estimate the strength of 





, i.e., 





 in the ADAF (Livio et al. 1999; Meier 2001; Wu & Cao 2008). In the accretion flow, 





 may be radius dependent. In order to model this behavior, we adopt (Livio et al. 1999; Meier 2001; Wu & Cao 2008; Li & Cao 2012)
5





where 





 is the stress in the magnetohydrodynamic accretion flow. If the parameter s in Equation (5) is larger than 0, 





 in the outer region will suppress the magnetorotational instability (Velikhov 1959; Chandrasekhar 1960; Balbus & Hawley 1991, 1998), which is responsible for the angular momentum transport. Then, s should be larger than or equal to 0, i.e.,
6





Based on the above discussion, Equation (3) becomes
7





where 





 and 





 are taken and ζ is a constant. In the BZ model, the variability of jet power, which is induced by the fluctuations of the magnetic field in the vicinity of black hole, does not present a significant difference to Equation (7). Then, we use Equation (7) to describe the jet power. This equation reveals that the power of the jet depends linearly on the accretion rate in the ADAF, which has been used in a number of works (e.g., Meier 2001; Nemmen et al. 2007; Martínez-Sansigre & Rawlings 2011). Equation (7) is similar to Equation (1) but with 





 and 





. It was discussed previously that the variabilities based on Equation (2) (or Equation (7)) with varying γ (





) do not show significant difference. Then, the variability of jet power based on Equation (7) would follow that of the accretion rate or LX except for the amplitude of the variability, which has been found in the observation of GX 339–4 (Casella et al. 2010). This fact implies that Equation (7) is applicable to describing the jet power. In our work, we take 





 (please see the discussion in Section 3.2). In this situation, we take 





, which corresponds to the case in which 10% of the gravitational energy released in the accretion process enters the jet.
Citation: Li & Cao 2012
Citation function: Uses; Uses
Citation: Li & Cao 2012
Citation function: Uses; Uses