Abstract:
The scaling relations between the black hole (BH) mass and soft lag properties for both active galactic nuclei (AGNs) and BH
X-ray binaries (BHXRBs) suggest the same underlying physical mechanism at work in accreting BH systems spanning a broad
range of mass. However, the low-mass end of AGNs has never been explored in detail. In this work, we extend the existing scaling
relations to lower mass AGNs, which serve as anchors between the normal-mass AGNs and BHXRBs. For this purpose, we
construct a sample of low-mass AGNs (MBH < 3 × 106 M) from the XMM–Newton archive and measure frequency-resolved
time-delays between the soft (0.3–1 keV) and hard (1–4 keV) X-ray emissions. We report that the soft band lags behind the hard
band emission at high frequencies ∼[1.3−2.6] × 10−3 Hz, which is interpreted as a sign of reverberation from the inner accretion
disc in response to the direct coronal emission. At low frequencies (∼[3−8] × 10−4 Hz), the hard-band lags behind the soft-band
variations, which we explain in the context of the inward propagation of luminosity fluctuations through the corona. Assuming a
lamppost geometry for the corona, we find that the X-ray source of the sample extends at an average height and radius of ∼10rg
and ∼6rg, respectively. Our results confirm that the scaling relations between the BH mass and soft lag amplitude/frequency
derived for higher mass AGNs can safely extrapolate to lower mass AGNs, and the accretion process is indeed independent of
the BH mass
