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, where it is assumed that an X-ray source illuminates the whole inner-disc region in a relatively steady way. 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 to the lamppost model is that the region of the disc below the flare is not illuminated before the onset of the flare. After the onset, the temperature and the ionization state of the irradiated skin respond immediately to the increase of the continuum, but pressure equilibrium is achieved later. A few typical test models show that the reflected spectrum that follows immediately the increase in continuum flux should always 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 however different in the case of a "moderate" and a "strong" flare: for a moderate flare, the spectrum displays a neutral component of the Fe Kalpha 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 are very intense, with an equivalent width of several hundreds eV. A strong flare is also characterized by a steep soft X-ray spectrum. The variation timescale in the flare model is likely smaller than in the lamppost model, due to the smaller dimension of the emission region, so the timescale for pressure equilibrium is long compared to the duration of a flare. It is therefore highly probable that several flares contribute at the same time to the luminosity. We find that the observed correlations between R, Gamma, and the X-ray flux are well accounted for by a combination of flares having not achieved pressure equilibrium, also strongly suggesting that the observed spectrum is always 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) and Doppler shifted, as stressed by Nayakshin & Kazanas (2001). All these features should constitute specific variable signatures of the flare model, distinguishing it from the lamppost model. It is however difficult, on the basis of the present observations and models, to conclude in favor of one of the hypothese.