The role of outflows in black-hole X-ray binaries

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The hot inner flow in black-hole X-ray binaries is not just a static corona rotating around the black hole: it must be partially outflowing. It is therefore a mildly relativistic ``outflowing corona.'' We have developed a model in which Comptonization takes place in this outflowing corona. In all of our previous work, we assumed a rather high outflow speed of $0.8c$. Here, we investigate whether an outflow with a significantly lower speed can also reproduce the observations. Thus, in this work we consider an outflow speed of $0.1c$ or less. As in all of our previous work, we used a Monte Carlo code to compute not only the emergent X-ray spectra, but also the time lags that are introduced to the higher-energy photons with respect to the lower-energy ones via multiple scatterings. We also record the angle (with respect to the symmetry axis of the outflow) and the height at which photons escape. Our results are very similar to those of our previous work, with some small quantitative differences that can be easily explained. We are again able to quantitatively reproduce five observed correlations: (a) the time lag as a function of Fourier frequency, (b) the time lag as a function of photon energy, (c) the time lag as a function of Gamma , (d) the time lag as a function of the cutoff energy in the spectrum, and (e) the long-standing radio--X-ray correlation -- and all of them with only two parameters, which vary in the same ranges for all the correlations. Our model does not require a compact, narrow relativistic jet, although its presence does not affect the results. The essential ingredient of our model is the parabolic shape of the Comptonizing corona. The outflow speed plays a minor role. Furthermore, the bottom of the outflow, in the hard state, looks like a ``slab'' to the incoming soft photons from the disk, and this can explain the observed X-ray polarization, which is along the outflow. In the hard-intermediate state, we predict that the polarization of GX 339-4 will be perpendicular to the outflow.