A&A 454, 741-752 (2006)
DOI: 10.1051/0004-6361:20054344

The structure and X-ray radiation spectra of illuminated accretion disks in AGN

III. Modeling fractional variability

R. W. Goosmann^{1, 2}, B. Czerny^{2, 3}, M. Mouchet^{2, 4}, G. Ponti^{5, 6, 7}, M. Dovciak¹, V. Karas¹, A. Rózanska^{2, 3} and A.-M. Dumont<sup>2

1</sup>  Astronomical Institute, Academy of Sciences of the Czech Republic, Bocni II 1401, 14131 Prague, Czech Republic
    e-mail: [goosmann;dovciak]@astro.cas.cz; vladimir.karas@cuni.cz
²  Observatoire de Paris, Section de Meudon, LUTH, 5 place Jules Janssen, 92195 Meudon Cedex, France
    e-mail: [martine.mouchet;anne-marie.dumont]@obspm.fr
³  Copernicus Astronomical Center, Bartycka 18, 00-716 Warsaw, Poland
    e-mail: [bcz;agata]@camk.edu.pl
⁴  Laboratoire Astroparticules et Cosmologie, Université Denis Diderot, 2 place Jussieu, 75251 Paris Cedex 05, France
⁵  Dipartimento di Astronomia, Università di Bologna, via Ranzani 1, 40127 Bologna, Italy
    e-mail: ponti@bo.iasf.cnr.it
⁶  INAF - IASF Sezione di Bologna, via Gobetti 101, 40129 Bologna, Italy
⁷  Institute of Astronomy, Madingley Road, Cambridge CB3 0HA, UK

(Received 12 October 2005 / Accepted 18 March 2006 )

Abstract
Context.Random magnetic flares above the accretion disks of Active Galactic Nuclei can account for the production of the primary radiation and for the rapid X-ray variability that have been frequently observed in these objects. The primary component is partly reprocessed in the disk atmosphere, forming a hot spot underneath the flare source and giving rise to distinct spectral features.
Aims.Extending the work of Czerny et al. (2004, A&A, 420, 1), we model the fractional variability amplitude due to distributions of hot spots co-orbiting on the accretion disk around a supermassive black hole. We compare our results to the observed fractional variability spectrum of the Seyfert galaxy MCG-6-30-15.
Methods.According to defined radial distributions, our code samples random positions for the hot spots across the disk. The local spot emission is computed as reprocessed radiation coming from a compact primary source above the disk. The structure of the hot spot and the anisotropy of the re-emission are taken into account. We compute the fractional variability spectra expected from such spot ensembles and investigate dependencies on the parameters describing the radial spot distribution. We consider the fractional variability with respect to the spectral mean and the so-called point-to-point definition . Our method includes relativistic corrections due to the curved space-time in the vicinity of a rotating supermassive black hole at the disk center; the black hole's angular momentum is a free parameter and is subject to the fitting procedure.
Results.We confirm that the rms-variability spectra involve intrinsic randomness at a significant level when the number of flares appearing during the total observation time is too small. Furthermore, the fractional variability expressed by is not always compatible with . In the special case of MCG-6-30-15, we can reproduce the short-timescale variability and model the suppressed variability in the energy range of the K line without any need to postulate reprocessing farther away from the center. The presence of the dip in the variability spectrum requires an increasing rate of energy production by the flares toward the center of the disk. The depth of the feature is well represented only if we assume a fast rotation of the central black hole and allow for considerable suppression of the primary flare emission. The modeled line remains consistent with the measured equivalent width of the iron K line complex. The model can reproduce the frequently observed suppression of the variability in the spectral range around 6.5 keV, thereby setting constraints on the black hole spin and on the disk inclination.

Key words: radiative transfer -- accretion, accretion disks -- galaxies: active -- galaxies: Seyfert -- X-rays: galaxies

© ESO 2006

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