On the Black Hole Mass---X-ray Excess Variance Scaling Relation for Active Galactic Nuclei in the Low-mass Regime

Recent studies of active galactic nuclei (AGN) found a statistical inverse linear scaling between the X-ray normalized excess variance $\sigma_{\rm rms}^2$ (variability amplitude) and the black hole mass spanning over $M_{\rm BH}=10^6- 10^9\ M_{\odot}$. Being suggested to have a small scatter, this scaling relation may provide a novel method to estimate the black hole mass of AGN. However, a question arises as to whether this relation can be extended to the low-mass regime below $\sim10^6\ M_{\odot}$. If confirmed, it would provide an efficient tool to search for AGN with low-mass black holes using X-ray variability. This paper presents a study of the X-ray excess variances for a sample of AGN with black hole masses in the range of $10^5- 10^6\ M_{\odot}$ observed with {\it XMM-Newton} and {\it ROSAT}, including data both from the archives and from newly preformed observations. It is found that the relation is no longer a simple extrapolation of the linear scaling; instead, the relation starts to flatten at $\sim10^6\ M_{\odot}$ toward lower masses. Our result is consistent with the recent finding of \citet{L15}. Such a flattening of the $M_{\rm BH}-\sigma_{\rm rms}^2$ relation is actually expected from the shape of the power spectrum density of AGN, whose break frequency is inversely scaled with the mass of black holes.