Discovery of soft and hard X-ray time lags in low-mass AGN.

The scaling relations between the black hole (BH) mass and soft lag properties for both active galactic nuclei (AGN) 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 AGN has never been explored in detail. In this work, we extend the existing scaling relations to lower-mass AGN, which serve as anchors between the normal-mass AGN and BHXRBs. For this purpose, we construct a sample of low-mass AGN ($M_{\rm BH}<3\times 10^{6} M_{\rm \odot}$) 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 emission. We report that the soft band lags behind the hard band emission at high frequencies $\sim[1.3-2.6]\times 10^{-3}$ Hz, which is interpreted as a sign of reverberation from the inner accretion disc in response to the direct coronal emission. At low frequencies ($\sim[3-8]\times 10^{-4}$ 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. We find that the X-ray source for the sample extends at an average radius of around $8r_{\rm g}$ and a median height of around $15r_{\rm g}$ above the disc plane, assuming a lamppost geometry for the corona. Our results confirm that the scaling relations between the BH mass and soft lag amplitude/frequency derived for higher-mass AGN can safely extrapolate to lower-mass AGN, and the accretion process is indeed independent of the BH mass.