It is very controversial whether radio–X-ray correlation as defined in low-hard state of X-ray binaries ( XRBs ) can extend to quiescent state ( e.g. , X-ray luminosity less than a critical value of L _ { X,c } \sim 10 ^ { -5.5 } L _ { Edd } ) or not .
In this work , we collect a sample of XRBs and low luminosity active galactic nuclei ( LLAGNs ) with wide distribution of Eddington ratios ( L _ { X } / L _ { Edd } \sim 10 ^ { -9 } -10 ^ { -3 } ) to reexplore the fundamental plane between 5 GHz radio luminosity , L _ { R } , 2-10 keV X-ray luminosity , L _ { X } , and black hole ( BH ) mass , M _ { BH } , namely \log L _ { R } = \xi _ { X } \log L _ { X } + \xi _ { M } \log M _ { BH } + constant .
For the whole sample , we confirm the former fundamental plane of Merloni et al .
and Falcke et al .
that \xi _ { X } \sim 0.6 and \xi _ { M } \sim 0.8 even after including more quiescent BHs .
The quiescent BHs follow the fundamental plane very well , and , however , FR I radio galaxies follow a steeper track comparing other BH sources .
After excluding FR Is , we investigate the fundamental plane for BHs in quiescent state with L _ { X } < L _ { X,c } and sub-Eddington BHs with L _ { X } > L _ { X,c } respectively , and both subsamples have a similar slope , \xi _ { X } \sim 0.6 , which support that quiescent BHs may behave similar to those in low-hard state .
We further select two subsamples of AGNs with BH mass in a narrow range ( FR Is with M _ { BH } = 10 ^ { 8.8 \pm 0.4 } and other LLAGNs with M _ { BH } = 10 ^ { 8.0 \pm 0.4 } ) to simulate the behavior of a single supermassive BH evolving from sub-Eddington to quiescent state .
We find that the highly sub-Eddington sources with L _ { X } / L _ { Edd } \sim 10 ^ { -6 } -10 ^ { -9 } still roughly stay on the extension of radio–X-ray correlation as defined by other sub-Eddington BHs .
Our results are consistent with several recent observations in XRBs that the radio–X-ray correlation as defined in low-hard state can extend to highly sub-Eddington quiescent state .