Quasar spectral variability from the XMM-Newton serendipitous source catalogue

Context. X-ray spectral variability analyses of active galactic nuclei (AGN) with moderate luminosities and redshifts typically show a softer when brighter behaviour. Such a trend has rarely been investigated for high-luminosity AGNs ($L_{bol}\gtrsim {10}^{44}$ erg/s), nor for a wider redshift range (e.g. $0\lesssim z\lesssim 5$). Aims. We present an analysis of spectral variability based on a large sample of 2,700 quasars, measured at several different epochs, extracted from the fifth release of the XMM-Newton Serendipitous Source Catalogue. Methods. We quantified the spectral variability through the parameter $\beta$ defined as the ratio between the change in the photon index $\mathrm{\Gamma }$ and the corresponding logarithmic flux variation, $\beta =-\mathrm{\Delta }\mathrm{\Gamma }\mathrm{/}\mathrm{\Delta }\log F_X$. Results. Our analysis confirms a softer when brighter behaviour for our sample, extending the previously found general trend to high luminosity and redshift. We estimate an ensemble value of the spectral variability parameter $\beta =-0.69\pm 0.03$. We do not find dependence of $\beta$ on redshift, X-ray luminosity, black hole mass or Eddington ratio. A subsample of radio-loud sources shows a smaller spectral variability parameter. There is also some change with the X-ray flux, with smaller $\beta$ (in absolute value) for brighter sources. We also find significant correlations for a small number of individual sources, indicating more negative values for some sources.