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.
