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

We examine the fundamental plane of 91 blazars which include flat-spectrum radio quasars and BL Lacertae objects with known X-ray luminosity (LR), radio luminosity (LX), and black hole mass measurements (M) to reflect the relationship between jet and accretion for blazars. The fundamental plane of blazars are log LR  =  |${0.273}_{+0.059}^{-0.059}\log L_X$|  +  |${0.695}_{+0.191}^{-0.191}\log M$|  +  |${25.457}_{+2.728}^{-2.728}$| and log LR  =  |${0.190}_{+0.049}^{-0.049}\log L_X$|  +  |${0.475}_{+0.157}^{-0.157}\log M$|  +  |${28.568}_{+2.245}^{-2.245}$| after considering the effect of beam factor. Our results suggest that the jet of blazars has connection with accretion. We set the black hole spin energy as a new variable to correct the black hole mass and explore the effect of black hole spin on the fundamental relationship. We find that the fundamental plane of blazars is affected by the black hole spin, which is similar to the previous work for active galactic nuclei. We additionally examine a new fundamental plane which is based on the black hole spin-mass energy (M spin). The new fundamental plane (log LR  =  |${0.332}_{+0.081}^{-0.081}\log L_X$|  +  |${0.502}_{+0.091}^{-0.091}\log M_{spin}$|  +  |${22.606}_{+3.346}^{-3.346}$| with R-Square = 0.575) shows that M spin has a better correlation coefficient compared to the M for fundamental plane of blazars. These results suggest that the black hole spin should be considered as an important factor for the study of fundamental plane for blazars. And these may further our understanding of the Blandford–Znajek process in blazars. [ABSTRACT FROM AUTHOR]