Magnetic field strength constraints on

We present a multi-wavelength study of the flat spectrum radio quasar PKS 1222+216 that analyzes its long-term variability of radio data obtained from 2013 to 2020 from the iMOGABA, MOJAVE, and VLBA-BU-BLAZAR programs, along with γ-ray data from Fermi-LAT. We found that the radio flux densities at 15, 22, 43, and 86 GHz declined exponentially by 37–56% over a year following a γ-ray flare in November 2014. We estimated the jet physical parameters through Gaussian model fitting of VLBA 43 GHz data, and identified ten jet components. The cooling timescales of the jet emission regions, i.e., newly ejected components C9, C10, and C11, range from 43 to 222 days; the estimated jet viewing angles were approximately 8 degrees and the magnetic field strengths were 77–134 mG in the jet emission regions. Additionally, by determining the magnetic field strength at different frequencies, we found that the magnetic field scales as B ∝ r−0.3 ± 0.04, indicating a nonequipartition condition (kr ≳ 1) or a slow decline in magnetic field strength profile (m < 1). By analyzing the component ejection times, we discovered that the γ-ray flare in 2014 coincided with the interaction between the moving component C9 and the stationary feature A1. We estimated that the γ-ray emission region is located at 9.2 ± 1.0 pc from the central engine, beyond the broad-line region (BLR) and dusty torus, suggesting that the seed photons for inverse Compton scattering originate from the jet itself, from external cosmic microwave background (CMB) radiation, or from a surrounding sheath. Our results favor a scenario where γ-ray emission originates farther downstream from the central engine through interactions between moving and stationary components. Additionally, our study presents an alternative method for estimating magnetic field strengths in active galactic nuclei (AGNs) undergoing long-term synchrotron cooling based on the associated timescale.