Correlations between X-ray properties and Black Hole Mass in AGN : a potential new method to estimate Black Hole Mass from short exposure X-ray observations

The normalised excess variance (σ NXS) parameter can be used to measure the X-ray variability of active galactic nuclei (AGN). Several investigations have shown that σ NXS has a strong anti-correlation with both X-ray luminosity (LX) and black hole mass (MBH). Therefore, σ 2 NXS can be used to estimate MBH if other measurements are not available. Unfortunately, σ 2 NXS can only be measured from long duration X-ray observations (tens of kiloseconds). By comparison, the typical exposure time during forthcoming eROSITA all-sky survey is only a few hundred seconds. eROSITA will yield large numbers (up to 1 million) of LX values for AGN, but few, if any, σ 2 NXS measurements. In this study, we have investigated the possibility of using eROSITA LX data to estimate MBH. For this, we have used XMM-Newton observations of a sample of AGN drawn from the XMMNewton Cluster Survey (XCS). Using 18 (11) AGN with σ NXS measurements in 10ks (20ks) segments, we reconfirm the strong correlation between σ NXS and LX found by other authors. Using 30 AGN with spectrally determined LX values and reverbation method determined MBH values, we show that these quantities are also correlated. Using 154 AGN with spectrally determined LX measurements, we find that LX values estimated from eROSITA countrates will be robust. We conclude that although it may be possible to use LX measurements from eROSITA to estimate MBH values for large samples (>10) of AGN, further tests of the MBH to LX correlation are needed, especially at higher redshifts.