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Recent studies of active galactic nuclei (AGN) found a statistical inverselinear scaling between the X-ray normalized excess variance $\sigma_{\rmrms}^2$ (variability amplitude) and the black hole mass spanning over $M_{\rmBH}=10^6- 10^9\ M_{\odot}$. Being suggested to have a small scatter, thisscaling relation may provide a novel method to estimate the black hole mass ofAGN. However, a question arises as to whether this relation can be extended tothe low-mass regime below $\sim10^6\ M_{\odot}$. If confirmed, it would providean efficient tool to search for AGN with low-mass black holes using X-rayvariability. This paper presents a study of the X-ray excess variances for asample 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 thearchives and from newly preformed observations. It is found that the relationis no longer a simple extrapolation of the linear scaling; instead, therelation starts to flatten at $\sim10^6\ M_{\odot}$ toward lower masses. Ourresult is consistent with the recent finding of \citet{L15}. Such a flatteningof the $M_{\rm BH}-\sigma_{\rm rms}^2$ relation is actually expected from theshape of the power spectrum density of AGN, whose break frequency is inverselyscaled with the mass of black holes.

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