Fundamental Plane of Black Hole Activity in the Quiescent Regime

A correlation among the radio luminosity ($L_R$), X-ray luminosity ($L_X$), and black hole (BH) mass ($M_{BH}$) in active galactic nuclei (AGNs) and BH binaries is known to exist and is called the "fundamental plane" of BH activity. Yuan and Cui predict that the radio/X-ray correlation index, ${\xi }_X$, changes from ${\xi }_X\approx 0.6$ to ${\xi }_X\approx 1.2\text{--}1.3$ when $L_X/L_{Edd}$ decreases below a critical value of $\sim {10}^{-6}$. While many works favor such a change, there are also several works claiming the opposite. In this paper, we gather from the literature the largest quiescent AGN (defined as $L_X/L_{Edd}\lesssim {10}^{-6}$) sample to date, consisting of 75 sources. We find that these quiescent AGNs follow a ${\xi }_X\approx 1.23$ radio/X-ray relationship, in excellent agreement with the Yuan and 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., $L_X/L_{Edd}\gtrsim {10}^{-6}$). In this case, the quiescent sources will mix up with those normal ones in $L_R$ and $L_X$. The value of ${\xi }_X$ will then be between 0.6 and ∼1.3, 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 $L_R$ and $L_X$ with $L_R/L_{Edd}$ and $L_X/L_{Edd}$, respectively.