Revisiting the "Fundamental Plane" of Black Hole Activity at Extremely Low Luminosities

We investigate the origin of the X-ray emission in low-luminosity AGNs (LLAGNs). Yuan & Cui (2005) predicted that the X-ray emission should originate from jets rather than from an advection-dominated accretion flow (ADAF) when the X-ray luminosity $L_{\rm X}$ of the source is below a critical value of $L_{\rm X,crit} \approx 10^{-6}L_{\rm Edd}$. This prediction implies that the X-ray spectrum in such sources should be fitted by jets rather than ADAFs. Furthermore, below $L_{\rm X,crit}$ the correlation between radio ($L_{\rm R}$) and X-ray ($L_{\rm X}$) luminosities and the black hole mass ($M$)–the so-called fundamental plane of black hole activity–should deviate from the general correlation obtained by Merloni, Heinz & Di Matteo (2003) and become steeper. The Merloni et al. correlation is described by ${\rm log}L_{\rm R} =0.6{\rm log}L_{\rm X}+0.78{\rm log}M+7.33$, while the predicted correlation is ${\rm log}L_{\rm R}=1.23{\rm log}L_{\rm X} +0.25{\rm log}M-13.45$. We collect data from the literature to check the validity of these two expectations. We find that among the 16 LLAGNs with good X-ray and radio spectra, 13 are consistent with the Yuan & Cui prediction. For the 22 LLAGNs with $L_{\rm X} < L_{\rm X,crit}$, the fundamental plane correlation is described by ${\rm log}L_{\rm R}=1.22{\rm log}L_{\rm X}+0.23{\rm log}M-12.46 $, also in excellent agreement with the prediction.

💡 Research Summary

The paper revisits the “Fundamental Plane” of black‑hole activity in the regime of extremely low luminosities, focusing on low‑luminosity active galactic nuclei (LLAGNs). The authors test two predictions made by Yuan & Cui (2005). First, when the X‑ray luminosity falls below a critical value of roughly $L_{\rm X,crit}\simeq10^{-6}L_{\rm Edd}$, the X‑ray emission should be dominated by synchrotron or synchrotron‑self‑Compton processes in a relativistic jet rather than by thermal bremsstrahlung from an advection‑dominated accretion flow (ADAF). Second, in this jet‑dominated regime the three‑parameter correlation among radio luminosity ($L_{\rm R}$), X‑ray luminosity ($L_{\rm X}$), and black‑hole mass ($M$) should steepen relative to the “canonical” fundamental plane derived by Merloni, Heinz & Di Matteo (2003). The canonical plane is
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