Evolution of the X-ray spectrum in the flare model of Active Galactic   Nuclei
  Nayakshin & Kazanas (2002) have considered the time-dependent illumination of an accretion disc in Active Galactic Nuclei, in the lamppost model. We extend their study to the flare model, which postulates the release of a large X-ray flux above a small region of the accretion disc. A fundamental difference with the lamppost model is that the region of the disc below the flare is not illuminated before the onset of the flare.   A few test models show that the spectrum which follows immediately the increase in continuum flux should display the characteristics of a highly illuminated but dense gas, i.e. very intense X-ray emission lines and ionization edges in the soft X-ray range. The behaviour of the iron line is different in the case of a "moderate" and a ``strong'' flare: for a moderate flare, the spectrum displays a neutral component of the Fe K$\alpha$ line at 6.4 keV, gradually leading to more highly ionized lines. For a strong flare, the lines are already emitted by FeXXV (around 6.7 keV) after the onset, and have an equivalent width of several hundreds of eV. We find that the observed correlations between $R$, $\Gamma$, and the X-ray flux, are well accounted by a combination of flares having not achieved pressure equilibrium, strongly suggesting that the observed spectrum is dominated by regions in non-pressure equilibrium, typical of the onset of the flares. Finally a flare being confined to a small region of the disc, the spectral lines should be narrow (except for a weak Compton broadening), Doppler shifted, and moving. 
S. Collin, S. Coup\'e, A-M. Dumont (Observatoire Paris-Meudon,   France), P-O. Petrucci (LAOG, Grenoble, France), A. R\'o\.z...