The Central Engine of Active Galactic Nuclei ASP Conference Series, Vol. 000, 2007 L. C. Ho and J.-M. Wang(eds) Modeling the X-ray fractional variability spectrum of Active Galactic Nuclei using multiple flares R. W. Goosmann, M. Dovˇciak, V. Karas Astronomical Institute, Academy of Sciences, Prague, Czech Republic 7 0 B. Czerny 0 2 Copernicus Astronomical Center, Warsaw, Poland n a M. Mouchet J Laboratoire ApC, Universit´e Denis Diderot, Paris, France 7 1 G. Ponti v 4 Dipartimento di Astronomia, Universita` di Bologna, Bologna, Italy 6 1 1 Abstract. Using Monte-Carlosimulations of X-ray flare distributions across 0 the accretion disk of active galactic nuclei (AGN), we obtain modeling results 7 for the energy-dependentfractionalvariability amplitude. Referring to previous 0 results of this model, we illustrate the relation between the shape of the point- / to-point fractional variability spectrum, F , and the time-integrated spectral h pp energy distribution, F . The results confirm that the spectral shape and vari- p E - ability ofthe ironKαline aredominatedby the flaresclosestto the disk center. o r t s Thefractionalvariability spectrumofAGNdescribesthevariability proper- a ties as a function of photon energy (see e.g. Edelson et al. 2002; Vaughan et al. : v 2003). In Goosmann et al. (2006) we present modeling of AGN fractional vari- i ability spectra for distributions of magnetic flares co-rotating with the accretion X disk. Using a Monte-Carlo method, we sample the time evolution of the flare r a distribution for different choices of the global parameters. These determine the radial distribution of the flare number and luminosity across the disk, the indi- vidual flare life times, the average X-ray luminosity of the object, the mass of the black hole, and its spin. By using a ray-tracing method, the computations include general relativistic and Doppler corrections. For this proceedings note we present an extension of our work by empha- sizing the connection between F and F for a given model setup. We consider pp E parameter sets that only differ in the radial distribution of the individual flare luminosity, ruled by the parameter β. All other parameters are set as for our best fit to the F variability spectrum of MCG-6-30-15, which was computed pp froma95ksecXMM-Newtonobservation (fordetails seeGoosmann et al.2006). In Fig. 1 we show results for F and F with β = 3, 4 and 5. The normal- pp E ization (but not the shape) of F can vary for the same parameter set within pp the limits of Monte-Carlo statistics. Therefore, we normalize the F spectra in pp Fig. 1 to the variability level of ∼ 20% as obtained for our best fit to MCG-6- 30-15. Thus, we only investigate the shape of F and not the normalization. pp 1 2 Goosmann et al. 22 10u.] %] 20 b. F[pp 18 β = 3 5 F [arE E 16 14 0 22 10u.] %] 20 b. F[pp 18 β = 4 5 F [arE E 16 14 0 22 10u.] %] 20 b. F[pp 18 β = 5 5 F [arE E 16 14 0 4 6 8 10 4 6 8 10 Energy [kev] Energy [keV] Figure1. Point-to-pointfractionalvariabilityF (left)andthecorrespond- pp ingtime-integratedspectra(right)forflaredistributionswithdifferentβ. The F spectra are all normalized to the same variability level. pp For β = 3, when the radial profile of the X-ray luminosity is roughly pro- portional to the radial profile of the disk luminosity, the variations of F with pp energy are relatively low. For higher values of β the variability is significantly depressed around the iron Kα line, and the iron line profile is more strongly smeared out. Hence, if the X-ray luminosity is due to individual, localized flares, and if their luminosity rises more strongly than the disk luminosity to- ward the center, then we expect not only a broadened iron-line profile, but also a significant depression of the spectral variability across the line. Note that such a strong rise of the disk irradiation toward the center is predicted by the light-bending models (see e.g. Suebsuwong et al. 2006). Acknowledgments. We are grateful to A.-M. Dumont and A. Ro´z˙an´ska for their help with computing the local flare spectra used in this model. References Edelson, R., Turner, T. J., Pounds, K., Vaughan, S., Markowitz, A., Marshall, H., Dobbie, P., & Warwick, R. 2002, ApJ, 568, 610 Goosmann, R. W., Czerny, B., Mouchet, M., Ponti, G., Dovˇciak, M., Karas, V., Ro´z˙an´ska, A., & Dumont, A.-M. 2006,A&A, 454, 741 Suebsuwong, T., Malzac, J., Jourdain, E., & Marcowith, A. 2006,A&A, 453, 773 Vaughan, S., Edelson, R., Warwick, R. S., & Uttley, P. 2003, MNRAS, 345, 1271