Spectra and time variability of black-hole binaries in the low/hard state

We propose a jet model for the low/hard state of galactic black-hole X-ray sources which explains the energy spectra from radio to X-rays and a number of timing properties in the X-ray domain such as the time lag spectra, the hardening of the power density spectra and the narrowing of the autocorrelation function with increasing photon energy. The model assumes that (i) there is a magnetic field along the axis of the jet, (ii) the electron density in the jet drops inversely proportional to distance, (iii) the jet is “hotter” near its center than at its periphery, and (iv) the electrons in the jet follow a power-law distribution function. We have performed Monte Carlo simulations of Compton upscattering of soft photons from the accretion disk and have found power-law high-energy spectra with photon-number index in the range 1.5–2 and cutoff at a few hundred keV, power-law time lags versus Fourier frequency with index 0.8, and an increase of the rms amplitude of variability and a narrowing of the autocorrelation function with increasing photon energy as they have been observed in Cygnus X-1. The spectrum at long wavelengths (radio, infrared, optical) is modeled to come from synchrotron radiation of the energetic electrons in the jet. We find flat to inverted radio spectra that extend from the radio up to about the optical band. For magnetic field strengths of the order 10⁵–10⁶ G at the base of the jet, the calculated spectra agree well in slope and flux with the observations.