Fundamental Plane of Black Hole Activity in Quiescent Regime

A correlation among the radio luminosity ($L_{\rm R}$), X-ray luminosity ($L_{\rm X}$), and black hole mass ($M_{\rm BH}$) in active galactic nuclei (AGNs) and black hole binaries is known to exist and is called the "Fundamental Plane" of black hole activity. Yuan & Cui (2005) predicts that the radio/X-ray correlation index, $\xi_{\rm X}$, changes from $\xi_{\rm X}\approx 0.6$ to $\xi_{\rm X}\approx 1.2-1.3$ when $L_{\rm X}/L_{\rm Edd}$ decreases below a critical value $\sim 10^{-6}$. While many works favor such a change, there are also several works claiming the opposite. In this paper, we gather from literature a largest quiescent AGN (defined as $L_{\rm X}/L_{\rm Edd} < 10^{-6}$) sample to date, consisting of $75$ sources. We find that these quiescent AGNs follow a $\xi_{\rm X}\approx 1.23$ radio/X-ray relationship, in excellent agreement with the Yuan \& Cui prediction. The reason for the discrepancy between the present result and some previous works is that their samples contain not only quiescent sources but also "normal" ones (i.e., $L_{\rm X}/L_{\rm Edd} > 10^{-6}$). In this case, the quiescent sources will mix up with those normal ones in $L_{\rm R}$ and $L_{\rm X}$. The value of $\xi_{\rm X}$ will then be between $0.6$ and $\sim1.3$, with the exact value being determined by the sample composition, i.e., the fraction of the quiescent and normal sources. Based on this result, we propose that a more physical way to study the Fundamental Plane is to replace $L_{\rm R}$ and $L_{\rm X}$ with $L_{\rm R}/L_{\rm Edd}$ and $L_{\rm X}/L_{\rm Edd}$, respectively.