The fundamental plane of black hole activity for low-luminosity radio active galactic nuclei across 1 < z < 4

The fundamental plane of back hole activity (BHFP) describes the correlation between radio luminosity (L_R), X-ray luminosity (L_X), and black hole mass (M_BH). It reflects a connection between accretion disc and jet. However, the dependence of the BHFP on various physical properties of active galactic nuclei (AGNs) and host galaxies remains unclear, especially for low-luminosity AGNs. From the deep and large multi-wavelength surveys in the GOODS-N, GOODS-S, and COSMOS/UltraVISTA fields, we constructed a large and homogeneous radio AGN sample including 208 objects. We divided this sample into 141 radio-quiet (RQ) AGNs and 67 radio-loud (RL) AGNs according to the radio-loudness defined by the ratio of L_R to L_X. The L_R-to-L_X ratio shows a bimodal distribution that is well described by two single Gaussian models. Their cross point corresponds to a radio-loudness threshold of log (L_R/L_X)=-2.73. The RQ AGNs have larger Eddington ratio (λ_Edd) than the RL AGNs. Our RQ and RL AGNs show different BHFPs that are log L_R=(0.55± 0.05)log L_X+(0.28± 0.06)log M_BH+(13.54± 2.27) and log L_R=(0.82± 0.08)log L_X+(0.07± 0.08)log M_BH+(5.24± 3.33), respectively. For both RQ and RL AGNs, the BHFP does not show a significant dependence on redshift and galaxy star-formation properties, while it shows a significant dependence on λ_Edd. The BHFP sheds important light on the accretion physics of central engines. RQ AGNs at 0.01<λ_Edd<0.1 agree with the advection dominated accretion flow (ADAF) coupled with a synchrotron jet model, while at 0.1<λ_Edd< 1, they mainly follow the jet model. RL AGNs are consistent with a combination of ADAF and jet model at λ_Edd<0.01, and agree with the jet model at 0.01<λ_Edd<0.1, and follow a combination of the standard thin disc and jet model at λ_Edd>0.1.