Jet models for the high-energy emission of Galactic X-ray binary sources haveregained significant interest with detailed spectral and timing studies of theX-ray emission from microquasars, the recent detection by the HESScollaboration of very-high-energy gamma-rays from the microquasar LS~5039, andthe earlier suggestion of jet models for ultraluminous X-ray sources observedin many nearby galaxies. Here we study the synchrotron and Compton signaturesof time-dependent electron injection and acceleration, adiabatic and radiativecooling, and different jet geometries in the jets of Galactic microquasars.Synchrotron, synchrotron-self-Compton, and external-Compton radiation processeswith soft photons provided by the companion star and the accretion disk aretreated. An analytical solution is presented to the electron kinetic equationfor general power-law geometries of the jets for Compton scattering in theThomson regime. We pay particular attention to predictions concerning the rapidflux and spectral variability signatures expected in a variety of scenarios,making specific predictions concerning possible spectral hysteresis, similar towhat has been observed in several TeV blazars. Such predictions should betestable with dedicated monitoring observations of Galactic microquasars andultraluminous X-ray sources using Chandra and/or XMM-Newton.
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