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The observed correlation between the radio and X-ray fluxes in the hard stateof black-hole X-ray binaries (BHXRBs) has been around for more than twodecades. It is currently accepted that the hard X-rays in BHXRBs come fromComptonization in the corona and the radio emission from the relativistic jet(Lorentz $\gamma >> 1$), which is a narrow structure of a few $R_g=GM/c^2$ atits base. The relativistic jet and the corona, however, are separate entitieswith hardly any communication between them, apart from the fact that both arefed from the accreting matter. It is also widely accepted that the accretionflow around black holes in BHXRBs consists of an outer thin disk and an innerhot flow. From this hot inner flow, an outflow emanates in the hard andhard-intermediate states of the source. By considering Compton up-scattering ofsoft disk photons in the outflow (i.e., in the outflowing corona, which is awider structure, tens to hundreds of $R_g$ at its base, with low Lorentz gamma)as the mechanism that produces the hard X-ray spectrum, we have been able toexplain quantitatively a number of observed correlations. Here, we demonstratethat this outflowing corona can also explain quantitatively the observed radio- X-ray correlation. In addition, we make the following theoretical predictionsfor GX 339-4: 1) the radio flux in the hard and hard-intermediate states shouldbe a bell-shaped curve as a function of the photon-number spectral index Gamma,2) the radio - X-ray correlation should break down when the source moves fromthe hard to the hard-intermediate state and instead the radio flux should firstincrease sharply in the hard-intermediate state and then decrease also sharply,in a very narrow range of the X-ray flux, and 3) the X-ray polarization will beparallel to the outflow in the hard state and perpendicular to it in thehard-intermediate one.

A quantitative explanation of the radio--X-ray correlation in black-hole X-ray binaries