Fundamental Plane of Black Hole Activity in Quiescent Regime

A correlation among the radio luminosity ($L_{\mathrm{R}}$), X-ray luminosity ($L_{\mathrm{X}}$), and black hole mass ($M_{\mathrm{B}\mathrm{H}}$) 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, ${\xi }_{\mathrm{X}}$, changes from ${\xi }_{\mathrm{X}}\approx 0.6$ to ${\xi }_{\mathrm{X}}\approx 1.2-1.3$ when $L_{\mathrm{X}}\mathrm{/}{L}_{\mathrm{E}\mathrm{d}\mathrm{d}}$ 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 $L_{\rm X}/L_{\rm Edd} < 10^{-6}$)sampletodate,consistingof$75$ sources. We find that these quiescent AGNs follow a ${\xi }_{\mathrm{X}}\approx 1.23$ 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., $L_{\mathrm{X}}\mathrm{/}{L}_{\mathrm{E}\mathrm{d}\mathrm{d}}>{10}^{-6}$). In this case, the quiescent sources will mix up with those normal ones in $L_{\mathrm{R}}$ and $L_{\mathrm{X}}$. The value of ${\xi }_{\mathrm{X}}$ will then be between $0.6$ and $\sim 1.3$, 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 $L_{\mathrm{R}}$ and $L_{\mathrm{X}}$ with $L_{\mathrm{R}}\mathrm{/}{L}_{\mathrm{E}\mathrm{d}\mathrm{d}}$ and $L_{\mathrm{X}}\mathrm{/}{L}_{\mathrm{E}\mathrm{d}\mathrm{d}}$, respectively.