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
$\Gamma$ and the corresponding logarithmic flux variation,
$\beta=-\Delta\Gamma/\Delta\log F_X$. 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 $\beta=-0.69\pm0.03$. 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.
