Magnetic field upper limits for jet formation

Context.Very high magnetic fields at the surface of neutron stars or in the accretion disk of black holes inhibit the production of jets. Aims.We quantify here the magnetic field strength for jet formation. Methods.By using the Alfvén Radius, RA, we study what we call the basic condition, $R_{\rm A}/ R_* = 1$ or $R_{\rm A}/ R_{\rm LSO} = 1$ (LSO, last stable orbit), in its dependency on the magnetic field strength and the mass accretion rate, and we analyse these results in 3-D and 2-D plots in the case of neutron star and black hole accretor systems, respectively. For this purpose, we did a systematic search of all available observational data for magnetic field strength and the mass accretion rate. Results.The association of a classical X-ray pulsar (i.e. $B \sim 10^{12}$ G) with jets is excluded even if accreting at the Eddington critical rate. Z-sources may develop jets for $B \la 10^{8.2}$ G, whereas Atoll-sources are potential sources of jets if $B \la 10^{7.7}$ G. It is not ruled out that a millisecond X-ray pulsar could develop jets, at least for those sources where $B \la 10^{7.5}$ G. In this case the millisecond X-ray pulsar could switch to a microquasar phase during its maximum accretion rate. For stellar-mass black hole X-ray binaries, the condition is that $B \la 1.35 \times 10^8$ G and $B \la 5 \times 10^8$ G at the last stable orbit for a Schwarzschild and a Kerr black hole, respectively. For active galactic nuclei (AGNs), it reaches $B \la 10^{5.9}$ G for each kind of black hole. These theoretical results are in complete agreement with available observational data