Predicting the black hole mass and correlations in X-ray reverberating AGNs using neural networks

We develop neural network models to predict the black hole mass using 22 reverberating active galactic nucleus (AGN) samples in the XMM-Newton archive. The model features include the fractional excess variance (F_var) in 2-10 keV band, Fe-K lag amplitude, 2-10 keV photon counts, and redshift. We find that the prediction accuracy of the neural network model is significantly higher than what is obtained from the traditional linear regression method. Our predicted mass can be confined within ±(2-5) per cent of the true value, suggesting that the neural network technique is a promising and independent way to constrain the black hole mass. We also apply the model to 21 non-reverberating AGNs to rule out their possibility to exhibit the lags (some have too small mass and F_var, while some have too large mass and F_var that contradict the F_var-lag-mass relation in reverberating AGNs). We also simulate 3200 reverberating AGN samples using the multifeature parameter space from the neural network model to investigate the global relations if the number of reverberating AGNs increases. We find that the F_var-mass anticorrelation is likely stronger with increasing number of newly discovered reverberating AGNs. Contrarily, to maintain the lag-mass scaling relation, the tight anticorrelation between the lag and F_var must preserve. In an extreme case, the lag-mass correlation coefficient can significantly decrease and, if observed, may suggest the extended corona framework where their observed lags are more driven by the coronal property rather than geometry.