The high-mass accreting binary Cyg X-3 is distinctly different from low-mass X-ray binaries (LMXBs) in having powerful radio and $gamma$-ray emitting jets in its soft spectral state. However, the transition from the hard state to the soft one is first associated with quenching of the hard-state radio emission, as in LMXBs. The powerful soft-state jets in Cyg X-3 form, on average, $sim$50 d later. We interpret the initial jet quenching as due to the hard-state vertical magnetic field quickly diffusing away in the thin disc extending to the innermost stable circular orbit in the soft state, or, if that field is produced in situ, also cessation of its generation. The subsequent formation of the powerful jets occurs due to advection of the magnetic field from the donor. We find this happens only above certain threshold accretion rate associated with appearance of magnetically driven outflows. The $sim$50 d lag is of the order of the viscous timescale in the outer disc, while the field advection is much faster. This process does not happen in LMXBs due to the magnetic fluxes available from their donors being lower than that for the wind accretion from the Wolf-Rayet donor of Cyg X-3. In our model, the vertical magnetic field in the hard state, required to form the jets both in Cyg X-3 and LMXBs, is formed in situ rather than advected from the donor. Our results provide a unified scenario of the soft and hard states in both Cyg X-3 and LMXBs.
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