Wang, JM (reprint author), Chinese Acad Sci, Inst High Energy Phys, High Energy Astrophys Lab, Beijing 10039, Peoples R China.
It has been argued that blobs ejected from advection-dominated accretion flow through the accretion-ejection instability undergo expansion because of their high internal energy density. The expanding blobs interact with their surroundings and form a strong shock, which accelerates a group of electrons to be relativistic. Then flares are formed. This model has advances in two aspects: shock acceleration and self-consistent injection. We derive an analytical formula of the injection function of relativistic electrons based on Sedov's law. We calculate the time-dependent spectrum of relativistic electrons in such an expanding blob. The light-travel effect, the evolution of the electron spectrum due to energy loss, and the escape of relativistic electrons from the radiating region are considered, as well as the expansion (at subrelativistic speed) of the coasting blob. A large number of light curves spanning a wide range of parameters have been given in this paper. Regarding the symmetry, relative amplitude, duration of a flare, and the time lag between peak fluxes, we find four basic kinds of light curves for the nonexpanding blob and seven basic kinds of light curves for the expanding blob. The expansion weakens the magnetic field as well as enlarging the size of the blob. The predicted light curves thus show very complicated properties that are composed of the basic light curves, because the physical conditions are changing in the expanding blob. For the rapid decays of magnetic field (for example, B proportional to r(-n)), we find that the falling profile is a power law of time as nuF(nu) proportional to t((1-alpha)n/5), where alpha is the power-law index of injected electrons. This decline is controlled by the decay of magnetic field rather than the energy losses of relativistic electrons. We also calculate the evolution of the photon spectrum from both nonexpanding and expanding blobs, Different shapes in the phase of decreasing luminosity are then obtained for different parameter values. The photon index alpha(ph) stays constant for nonexpanding blobs when luminosity decreases, whereas alpha(ph) continues to decrease after the luminosity reaches its maximum for expanding blobs. It is expected that we can extract the information on ejected blobs from the observed light curves based on the present model.