Correlations between X-ray properties and Black Hole Mass in AGN:
  towards a new method to estimate black hole mass from short exposure X-ray
  observations
  Several investigations of the X-ray variability of active galactic nuclei
(AGN) using the normalised excess variance (${\sigma^2_{\rm NXS}}$) parameter
have shown that variability has a strong anti-correlation with black hole mass
($M_{\rm BH}$) and X-ray luminosity ($L_{\rm X}$). In this study we confirm
these previous correlations and find no evidence of a redshift evolution. Using
observations from XMM-Newton, we determine the ${\sigma^2_{\rm NXS}}$ and
$L_{\rm X}$ for a sample of 1091 AGN drawn from the XMM-Newton Cluster Survey
(XCS) - making this the largest study of X-ray spectral properties of AGNs. We
created light-curves in three time-scales; 10 ks, 20 ks and 40 ks and used
these to derive scaling relations between ${\sigma^2_{\rm NXS}}$, $L_{\rm X}$
(2.0-10 keV range) and literature estimates of $M_{\rm BH}$ from reverberation
mapping. We confirm the anti-correlation between $M_{\rm BH}$ and
${\sigma^2_{\rm NXS}}$ and find a positive correlation between $M_{\rm BH}$ and
$L_{\rm X}$. The use of ${\sigma^2_{\rm NXS}}$ is practical only for pointed
observations where the observation time is tens of kiloseconds. For much
shorter observations one cannot accurately quantify variability to estimate
$M_{\rm BH}$. Here we describe a method to derive $L_{\rm X}$ from short
duration observations and used these results as an estimate for $M_{\rm BH}$.
We find that it is possible to estimate $L_{\rm X}$ from observations of just a
few hundred seconds and that when correlated with $M_{\rm BH}$, the relation is
statistically similar to the relation of $M_{\rm BH}$-$L_{\rm X}$ derived from
a spectroscopic analysis of full XMM observations. This method may be
particularly useful to the eROSITA mission, an all-sky survey, which will
detect $>$10$^{6}$ AGN.
