The relation between the optical variability timescale, magnetic field of jets and black hole spin in active galactic nuclei

We investigate the relationship among the jet magnetic field, black hole spin, black hole mass, Eddington ratio, and optical variability timescales in jetted active galactic nuclei (AGNs). By fitting a damped random walk (DRW) model to the g-band light curves, we obtain the characteristic variability timescale ($\tau_{\rm DRW}$) for 41 jetted AGNs with precise supermassive black hole (SMBH) mass measurements. Our main results are as follows: (i) Our analysis reveals a significant correlation between the jet magnetic field ($B_{\rm 1pc}$), black hole spin ($j$) and the characteristic variability timescale within our sample. These findings suggest that the optical variability of jetted AGNs is influenced by the jet magnetic field and black hole spin. Furthermore, the characteristic variability timescale aligns with the electron escape timescale, as evidenced by the relationship between the characteristic variability timescale and jet magnetic field ($\tau_{\rm DRW}\propto B_{\rm 1pc}^{0.76\pm0.22}$). (ii) We confirm a significant correlation between the characteristic variability timescale and SMBH mass, expressed as: $\log \rm \tau_{\rm DRW} = 0.52(\pm0.21)\log M _{\rm BH}/M_{\rm \odot}-3.12(\pm1.90)$, with an intrinsic scatter of 0.08 dex. The slope of this relationship is consistent with that between the thermal timescale and black hole mass. Our results support the hypothesis that magnetorotational instability (MRI) fluctuations drive the intrinsic variability observed in the light curves emitted by the AGNs accretion disk.