Minimum X-ray source size for a lamp-post corona in light-bending models for AGN

The lamppost model is often used to describe the X-ray source geometry in AGN, where an infinitesimal point source is located on the black hole spin axis. This is especially invoked for Narrow Line Seyfert 1 (NLS1) galaxies, where an extremely broad iron line seen in episodes of low X-ray flux can both be explained by extremely strong relativistic effects as the source approaches the black hole horizon. The most extreme spectrum seen from the NLS1 1H0707-495 requires that the source is less than 1Rg above the event horizon in this geometry. However, the source must also be large enough to intercept sufficient seed photons from the disk to make the hard X-ray Compton continuum which produces the observed iron line/reflected spectrum. We use a fully relativistic ray tracing code to show that this implies that the source must be substantially larger than 1Rg in 1H0707-495 if the disk is the source of seed photons. Hence the source cannot fit as close as 1Rg to the horizon, so the observed spectrum and variability are not formed purely by effects of strong gravity but probably also by changes in corona and inner accretion flow geometry.

An XSPEC model to explore spectral features from black-hole sources - II. The relativistic iron line in the lamp-post geometry

In X-ray spectra of several active galactic nuclei and Galactic black hole binaries a broad relativistically smeared iron line is observed. This feature arises by fluorescence when the accretion disc is illuminated by hot corona above it. Due to central location of the corona the illumination and thus also the line emission decrease with radius. It was reported in the literature that this decrease is very steep in some of the sources, suggesting a highly compact corona. We revisit the lamp-post setup in which the corona is positioned on the axis above the rotating black hole and investigate to what extent the steep emissivity can be explained by this scenario. We show the contributions of the relativistic effects to the disc illumination by the primary source - energy shift, light bending and aberration. The lamp-post radial illumination pattern is compared to the widely used radial broken power-law emissivity profile. We find that very steep emissivities require the primary illuminating source to be positioned very near the black hole horizon and/or the spectral power-law index of the primary emission to be very high. The broken power-law approximation of the illumination can be safely used when the primary source is located at larger heights. However, for low heights the lamp-post illumination considerably differs from this approximation. We also show the variations of the iron line local flux over the disc due to the flux dependence on incident and emission angles. The former depends mainly on the height of the primary source while the latter depends on the inclination angle of the observer. Thus the strength of the line varies substantially across the disc. This effect may contribute to the observed steeper emissivity.