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 $M_{rm BH}=10^6- 10^9 M_{odot}$. B
eing 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.
We discuss further observational support of an idea formulated a decade ago by Abramowicz, Klu{z}niak, McClintock and Remillard. They demonstrated that the 3:2 pairs of frequencies of the twin-peak black hole (BH) high-frequency quasi-periodic oscill
ations (QPOs) scale inversely with the BH masses and that the scaling covers the entire range from stellar to supermassive BHs. For this reason, they believed that the QPOs may be used for accurate measurements of masses and spins of BHs.
