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tokens: 0.9 R ⊙ , see Section 2 ). The sound speed at the outer edge of the disc is usually in the regime dominated by the bound-free opacities and gas pressure. The mid-plane temperature could be estimated from the standard disc structure, as, e.g. in equation 5.49 of Frank et al. ( 2002 ), which yields T d ∼ 10 4 K. However, the disc in Cyg X-3 is embedded in the strong blackbody radiation of the donor, with T * ≈ 10 5 K. Thus, T d ∼ T * is likely. The sound speed is where Γ ≈ 5/3 is the adiabatic index, μ is the mean molecular weight, which is within μ ≈ 4/3 for fully ionized He and 4 for neutral He (which is most likely the main element of the WR star in Cyg X-3), and m p is the proton mass. At 10 5 K, He will be predominantly fully ionized, which yields H / R d ≈ 0.03. The field advection time-scale in the presence of magnetic outflows, equation ( 9 ), then becomes On the other hand, the standard viscous time-scale (i.e. in the absence of outflows), equation ( 10 ), is We see that the latter time-scale estimate is of the order of the average ∼50-d radio lag observed in Cyg X-3 . It may also be consistent with it for lower values of R d / R L and some plausible combinations of the parameters. Equation ( 6 ) estimates the value of the minimum strength of the magnetic field at R d required for the appearance of magnetic outflows. Using our estimates of the parameters of Cyg X-3 , it can be written as Current constraints give the average soft-state bolometric flux of erg cm −2 s −1 , as we discuss in Section 2 . Likely values of are then in the range of ≈100–200 G. Note that the dependence on the uncertain BH mass is weak. 3.3 The nature of the hard state In the low/hard state, a geometrically thick and hot inner accretion flow surrounded by an outer thin disc is present (e.g. see Yuan Narayan 2014 and the references therein). The hot accretion flow may be advection dominated (hereafter abbreviated as ADAF) though the degree of the flow advection at high Eddington ratios is uncertain. Also, the flow is likely to contain some condensed cold clumps. Still, for notational simplicity, we will use the term ADAF hereafter, but without implying a specific physics of the flow. Variations of the mass accretion rate trigger then state transitions. A hard-to-soft state transition occurs when the accretion rate increases above the critical value, . Then the ADAF cools efficiently and collapses to a thin accretion disc, which is accompanied by disappearance of jets. Steady jets are universally observed in the hard state of BH XRBs, which implies the presence of strong vertical/poloidal magnetic fields near the BH. The origin of such strong fields is unclear. If the ADAF extended all the way to the outer edge of the disc in this state, any outer field could be efficiently advected on the viscous time scale (Cao 2011 ). Equation ( 10 ) then yields ≈0.3 d for an ADAF extending to R d for typical values of H / R d = 0.5 and α = 0.1. In principle, this could also