Magnetic field strength constraints on $γ$-ray flaring regions in the flat spectrum radio quasar PKS 1222+216

Abstract

We present a multi-wavelength study of the Flat Spectrum Radio Quasar PKS 1222+216, analyzing its long-term variability of radio data obtained in 2013-2020 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 jet physical parameters through Gaussian model fitting of VLBA 43 GHz data, identifying 10 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, with the estimated jet viewing angles of approximately 8 degrees and magnetic field strengths of 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 $B\propto r^{-0.3\pm0.04}$, indicating a non-equipartition condition ($k_\text{r}\gtrsim 1$) or a slow decline in magnetic field strength profile ($m<1$). By analyzing 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 $9.2\pm1.0$ pc from the central engine, beyond the BLR and dusty torus, suggesting that the seed photons for inverse Compton scattering originate from the jet itself, external CMB radiation, or a surrounding sheath. Our results favor a scenario where $γ$-ray emission originates further 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 AGNs undergoing long-term synchrotron cooling based on the associated timescale.

Figures (8)

• Figure 1: CLEAN images of PKS 1222+216 obtained by KVN observations at 22, 43, and 86 GHz on January 13, 2016. The radio cores are aligned to the (0,0) position. Color and contours indicate the intensity of each map. The contours start at three times the root mean square (RMS) of the residual map and increase by a factor of 1.4. The RMS levels are 0.012, 0.019, and 0.013 Jy/beam at 22, 43, and 86 GHz, respectively. Synthesized beams are plotted on the lower right side of each map as a gray ellipse.
• Figure 2: CLEAN maps at VLBA 43 GHz from July 2014 to September 2016. The contour starts from three times the RMS noise level and increases by a scale factor of 1.4. The yellow circles indicate the sizes (FWHM) of individual components at each observation. The gray ellipses indicate the synthesized beam sizes for each epoch.
• Figure 3: Light curves of PKS 1222+216 observed from December 2012 to March 2020 (MJD 56265--58914) at 15, 22, 43, and 86 GHz. The total CLEAN flux densities are shown for each frequency. In the third panel, the green circles represent the iMOGABA data, while the olive circles correspond to the BU data. The error bars used typical values of 10% for K and Q, and 20% for W. BU and MOJAVE were applied at 5% jorstad2017kinematics. The bottom panel shows the 0.1--100 GeV $\gamma$-ray light curve from the Fermi-LAT LCR. The upper limit of the flux density is indicated by the gray triangles. The gray vertical dashed line refers to the $\gamma$-ray peak at MJD 56975.5 ezhikode2022long. The gray boxes are the periods that fit the exponential decay profiles at each frequency.
• Figure 4: Radio spectral indices at 22--43 GHz and 43--86 GHz. The top panel represents the values derived from the CLEAN total flux, while the bottom panel corresponds to the active flux. The orange scatters represent the spectral index at 22--43 GHz, while the green ones indicate the spectral index at 43--86 GHz. The horizontal dashed line indicates that the spectral index is zero, and the dotted line of the top panel is the mean value with $\alpha=-0.6$. In the bottom panel, the orange dotted line represents the average active spectral index of $-0.19$ at 22--43 GHz, while the green dotted line represents the average active spectral index of $-0.37$ at 43--86 GHz. The gray box indicates the decreasing period from 57124 to 57636 at 43 GHz.
• Figure 5: Spectral index of PKS 1222+216 in the quiescent state. The black points represent the quiescent-state flux densities at 22, 43, and 86 GHz, with error bars indicating flux uncertainties. The orange slope corresponds to the quiescent spectral index between 22 and 43 GHz ($\alpha_\text{KQ} = -0.81$), while the green slope represents the quiescent spectral index between 43 and 86 GHz ($\alpha_\text{QW} = -0.628$).