The fundamental plane of FSRQs based on the black hole spin-mass energy

Previous studies have identified the Fundamental Plane (FP) of Active Galactic Nuclei (AGNs) in recent years. However, these findings relied on total black hole mass, also known as dynamical mass, (Mdyn). Instead the fundamental plane may be governed by BH spin. In this study, we take the black hole spin-mass energy (\(M_{\mathrm{spin}}\)) as a new variable, which is closely related to the supermassive black hole (SMBH). We collected a sample of 62 flat-spectrum radio quasars (FSRQs) with gamma-ray luminosity (\(L_{\gamma }\)), X-ray luminosity (\(L_{\mathrm{X}}\)) and spin-mass energy (\(M_{ \mathrm{spin}}\)) to construct a new fundamental plane of blazars. Our analysis demonstrates that the fundamental plane (\(\log L_{\gamma }={0.662}_{+0.193}^{-0.193}\log L_{ \mathrm{X}}+{0.495}_{+0.154}^{-0.154}\log M_{\mathrm{spin}} +{14.579}_{+7.140}^{-7.140}\) with R-Square = 0.783) has a stronger correlation with spin-mass energy (\(M_{\mathrm{spin}}\)) compared to the black hole mass. Therefore, \(M_{\mathrm{spin}}\) should be considered as an essential variable for the fundamental plane of blazars. Our findings may improve the understanding of the Blandford-Znajek process in FSRQs.