A model for emission from jets in x-ray binaries: Consequences of a single acceleration episode

There is 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 a wealth of spectra, which we study in detail. We identify critical values of the magnetic field, and five transition frequencies in the spectra. In particular, we show that (1) for wide jets, the decay of the magnetic field along the jet enables the production of flat radio spectra without the need for electron re-acceleration along the jet; (2) an increase in the magnetic field above a critical value of 10⁵ G leads to a sharp decrease in the flux at the radio band, while the flux at higher frequencies saturates to a constant value; (3) for a strong magnetic field, the flux decays in the optical/UV band as F _ν ν^-1/2, irrespective of the electrons' initial distribution; (4) for B ₀ 10⁴ G, the X-ray flux gradually steepens; (5) with adiabatic energy losses, flat spectrum can be obtained only at a limited frequency range, and under certain conditions; and (6) for narrow jets, r(x) x ^α with α < 1/2, flat radio spectrum cannot be obtained. We provide a full description of the spectrum in different scenarios, and show that our model is consistent with the key observed properties of BHXRBs.