Spatial variations of magnetic field along active galactic nuclei jets on sub-pc to Mpc scales

We report the systematic analysis of knots, hotspots, and lobes in 57 active galactic nuclei (AGNs) to investigate the variation of the magnetic field along with the jet from the sub-pc base to the terminus in kpc-to-Mpc scales. Expanding the number of radio/X-ray samples in Kataoka & Stawarz (2005), we analyzed the data in 12 FR I and 30 FR II radio galaxies, 12 quasars, and 3 BL Lacs that contained 76 knots, 42 hotspots, and 29 radio lobes. We first derived the equipartition magnetic fields in the cores and then estimated those in various jet components by assuming $B_{rm est}$ $propto$ $d^{-1}$, where $d$ is the distance from the jet base. On the other hand, the magnetic field in large-scale jets (knots, hotspots, and lobes), $B_{rm eq}$, can be estimated from the observed flux and spatial extent under the equipartition hypothesis. We show that the magnetic field decreases as the distance along the jet increases, but generally gentler than $propto d^{-1}$. The increase in $B_{rm eq}/B_{rm est}$ at a larger $d$ may suggest the deceleration of the jet around the downstream, but there is no difference between FR I and FR II jets. Moreover, the magnetic fields in the hotspots are systematically larger than those of knots and lobes. Finally, we applied the same analysis to knots and lobes in Centaurus A to check whether the above discussion will hold even in a single jet source.