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

Abstract

Several investigations of the X-ray variability of active galactic nuclei (AGN) using the normalised excess variance ($\ddot{I}{ƒ}_{\mathrm{NXS}}^2$) parameter have shown that variability has a strong anti-correlation with black hole mass ($M_{\mathrm{BH}}$) and X-ray luminosity ($L_{\mathrm{X}}$). In this study we confirm these previous correlations and find no evidence of a redshift evolution. Using observations from XMM-Newton, we determine the $\ddot{I}{ƒ}_{\mathrm{NXS}}^2$ and $L_{\mathrm{X}}$ 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 $\ddot{I}{ƒ}_{\mathrm{NXS}}^2$, $L_{\mathrm{X}}$ (2.0-10 keV range) and literature estimates of $M_{\mathrm{BH}}$ from reverberation mapping. We confirm the anti-correlation between $M_{\mathrm{BH}}$ and $\ddot{I}{ƒ}_{\mathrm{NXS}}^2$ and find a positive correlation between $M_{\mathrm{BH}}$ and $L_{\mathrm{X}}$. The use of $\ddot{I}{ƒ}_{\mathrm{NXS}}^2$ 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 $M_{\mathrm{BH}}$. Here we describe a method to derive $L_{\mathrm{X}}$ from short duration observations and used these results as an estimate for $M_{\mathrm{BH}}$. We find that it is possible to estimate $L_{\mathrm{X}}$ from observations of just a few hundred seconds and that when correlated with $M_{\mathrm{BH}}$, the relation is statistically similar to the relation of $M_{\mathrm{BH}}$-$L_{\mathrm{X}}$ 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.

19 pages, 20 figures