A Model for Emission from Jets in X-ray Binaries: Consequences of a Single Acceleration Episode

There are strong evidence for powerful jets in the low/hard state of black-hole X-ray binaries (BHXRBs). Here, we present a model in which electrons are accelerated once at the base of the jet, and are cooled by synchrotron emission and possible adiabatic energy losses. The accelerated electrons assume a Maxwellian distribution at low energies and possible energetic power law tail. These assumptions yield to a wealth of spectra, which we study in details. We identify critical values of the magnetic field, and five transition frequencies in the spectra. In particular, we show that: (I) the decay of the magnetic field along the jet enables, for wide jets, production of flat radio spectra without the need for electrons re-acceleration along the jet. (II) An increase of the magnetic field above a critical value of ~10^5 G leads to a sharp decrease in the flux at the radio band, while the flux at higher frequencies saturates to a constant value. (III) For strong magnetic field, the flux decays in the optical/UV band as F_nu ~ nu^{-1/2}, irrespective of the electrons initial distribution. (IV) For B_0 ~ 10^4 G, the X-ray flux gradually steepens. (V) With adiabatic energy losses, flat spectrum can be obtained only at a limited frequency range, and under certain conditions (VI) For narrow jets, r(x) ~ x^{alpha} with alpha < 1/2, flat radio spectrum cannot be obtained. We provide full description of the spectrum in the different scenarios, and show that our model is consistent with the key observed properties of BHXRBs.