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

Abstract

Recent studies of active galactic nuclei (AGNs) found a statistically inverse linear scaling between the X-ray normalized excess variance {σ }_{rms}² (variability amplitude) and the black hole (BH) mass spanning over {M}_{BH}={10}⁶-{10}⁹ {M}_⊙ . Suggested as having a small scatter, this scaling relation may provide a novel method to estimate the BH mass of AGNs. However, a question arises as to whether this relation can be extended to the low-mass regime below ∼ {10}⁶ {M}_⊙ . If confirmed, it would provide an efficient tool to search for AGNs with low-mass BHs using X-ray variability. This paper presents a study of the X-ray excess variances for a sample of AGNs with BH masses in the range of {10}⁵-{10}⁶ {M}_⊙ observed with XMM-Newton and 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 ∼ {10}⁶ {M}_⊙ toward lower masses. Our result is consistent with the recent finding of Ludlam et al. Such a flattening of the {M}_{BH}-{σ }_{rms}² relation is actually expected from the shape of the power spectrum density of AGNs, for which the break frequency is inversely scaled with the mass of BHs.