Pinpointing the location of the gamma-ray emitting region in the FSRQ 4C+01.28

TL;DR

This study localizes the gamma-ray emitting region in the FSRQ 4C+01.28 by combining long-term 43 GHz VLBA jet kinematics with cross-correlation analyses between Fermi/LAT gamma-ray and multi-frequency radio light curves (ALMA/SMA/OVRO). The data reveal two newly ejected jet components, J4 and J5, with apparent speeds up to β_{app} ≈ 19 and an upper bound on the viewing angle φ ≲ 4°, consistent with a conical, equipartition jet (l ≈ 0.97, s ≈ −3.31, k_r ≈ 1.09). Cross-correlation shows radio variations lagging the gamma-ray emission by roughly 2–8 months across frequencies, enabling a deprojected gamma-ray location of 2.6 pc ≤ d_{γ} ≤ 20 pc from the jet base, well beyond the BLR. Consequently, the results challenge BLR seed-photon inverse-Compton models for gamma-ray production in this source and favor alternative mechanisms such as SSC, EC on IR photons, CMB, or hadronic processes, possibly within a spine-sheath jet structure. Overall, the paper demonstrates how combining parsec-scale kinematics with variability analysis can robustly constrain high-energy emission sites in blazar jets and inform the physics of gamma-ray production in FSRQs.

Abstract

The FSRQ 4C+01.28 is a bright and highly variable radio and $γ$-ray emitter. We aim to pinpoint the location of the $γ$-ray emitting region within its jet in order to derive strong constraints on $γ$-ray emission models for blazar jets. We use radio and $γ$-ray data obtained with ALMA, OVRO, SMA and Fermi/LAT to study the cross-correlation between $γ$-ray and multi-frequency radio light curves. Moreover, we employ VLBA observations at 43 GHz over a period of around nine years to study the parsec-scale jet kinematics. To pinpoint the location of the $γ$-ray emitting region, we use a model in which outbursts shown in the $γ$-ray and radio light curves are produced when moving jet components pass through the $γ$-ray emitting and the radio core regions. We find two bright and compact newly ejected jet components that are likely associated with a high activity period visible in the $γ$-ray and radio light curves. The kinematic analysis of the VLBA observations leads to a maximum apparent jet speed of $β_{app}=19\pm10$ and an upper limit on the viewing angle of $φ$ < 4 deg. We determine the power law indices that are characterizing the jet geometry, brightness temperature distribution, and core shift to be $l=0.974\pm0.098$, $s=-3.31\pm0.31$, and $k_r=1.09\pm0.17$, which are in agreement with a conical jet in equipartition. A cross-correlation analysis shows that the radio light curves follow the $γ$-ray light curve. We pinpoint the location of the $γ$-ray emitting region with respect to the jet base to the range of $2.6\,\mathrm{pc}\leq d_γ\leq20\,\mathrm{pc}$. Our derived observational limits places the location of $γ$-ray production in 4C+01.28 beyond the expected extent of the broad-line region (BLR) and therefore challenges blazar-emission models that rely on inverse Compton up-scattering of seed photons from the BLR.

Figures (11)

• Figure 1: Selected uniformly weighted $43\,\mathrm{GHz}$ VLBA total intensity images of the FSRQ 4C $+$01.28 with the fitted Gaussian components overlaid. $S_{\mathrm{tot}}$ is the total integrated flux density, $S_{\mathrm{peak}}$ is the highest flux density per beam and $\sigma$ is the noise level. The gray ellipse in the bottom left corner corresponds to the beam. The contours begin at $3\sigma$ and increase logarithmically by a factor of 2. The image parameters are listed in Table \ref{['image']}. The images show two newly ejected jet components appearing in August 2015 (J4) and June 2018 (J5) that can be tracked back until April 2015 and February 2017, respectively. In this work we focus on these two newly ejected components. Additional plots of the epochs observed before April 2015 are shown in Appendix \ref{['app:source']} in Figs. \ref{['fig:app_images1']} to \ref{['fig:app_images2']}.
• Figure 2: Monthly binned $\gamma$-ray and radio light curves observed by Fermi/LAT, ALMA, SMA and OVRO and the VLBA total flux density light curve, showing similar variability behavior. In the upper panel red arrows indicate upper limits. The vertical dashed lines represent the ejection epochs of the jet components J4 (orange) and J5 (blue) with their $1\sigma$ uncertainties shown as the orange (J4) and blue (J5) bands. The ejection of the components J4 and J5 falls into the period of high activity starting in late 2013.
• Figure 3: Upper panel: Observed brightness temperatures of the jet components with relative uncertainties of $29\%$ plotted over time. The arrows denote lower limits for unresolved components. The horizontal dashed-dotted line represents the inverse Compton limit of $10^{12}\,\mathrm{K}$. The gray-shaded area denotes the range of brightness-temperature values for a jet in equipartition. The intrinsic brightness temperature of the core (blue bars) is mostly consistent with equipartition and lies only above equipartition close to the ejection epochs of moving jet components. Middle panel: Flux densities of the jet components with relative uncertainties of $5\%$ plotted over time. Lower panel: Distance of the jet components relative to the core component plotted over time. The solid lines are fitted via linear regression and their gradients represent the angular speed of the corresponding component. The dashed fitted line represents an alternative kinematics model for the components J1, J2 and J3 (see Sect. \ref{['sec:kin']}). Components J4 and J5 seem to accelerate and are therefore fitted by two separated linear regressions each with their transition points indicated by the two vertical dotted lines. At these transition points their brightness temperatures and flux densities show a steep increase.
• Figure 4: Upper panel: Jet width $D$, given by the FWHM size of the jet components, plotted as a function of their distance from the jet base. The dashed line is fitted via $D=C(d+d_{\mathrm{c,\,43,\,app}})^l$, where $d_{\mathrm{c,\,43,\,app}}$ is the apparent distance of the $43\,\mathrm{GHz}$ core to the jet base, $d$ is the distance from the core to the jet component, $C$ is a constant and $l$ is the power law index representing the jet geometry. The best fit results in $l=0.974\pm0.098$ which is consistent with a conical jet. Lower panel: Observed brightness temperature $T_\mathrm{B}$ of the jet components plotted as a function of the components' distances to the jet base. The dashed line is fitted via $\log(T_\mathrm{B})=s\cdot\log(d+d_{\mathrm{c,\,43,\,app}})+\log(C)$, in which $d_{\mathrm{c,\,43,\,app}}$ is the apparent distance of the $43\,\mathrm{GHz}$ core to the jet base and $s$ is the brightness-temperature gradient. For $d_{\mathrm{c,\,43,\,app}}$ we used the value derived in Sect. \ref{['sec:geometry']}. The best fit results in $s=-3.31\pm 0.31$ which corresponds to a conical jet in equilibrium between magnetic field strength density and electron energy density Burd2022.
• Figure 5: DCF (upper panel) and ICF (lower panel) cross-correlation coefficients between the Fermi/LAT $\gamma$-ray and ALMA 3 light curves plotted over time lag. For the DCF the bin size is chosen to be $20\,\mathrm{days}$, while the interpolation unit for the ICF is chosen to be $10\,\mathrm{days}$ (both calculated as explained in Sect. \ref{['sec:corr_function']}). Positive time lags mean that the radio light curve follows the Fermi/LAT $\gamma$-ray light curve. The time lags for the peak cross-correlation coefficients are marked by solid blue lines, with their $1\sigma$ uncertainties given by the shaded blue area. The dotted red, dashed-dotted orange and dashed green lines correspond to the two sided Gaussian equivalent $1\sigma$, $2\sigma$ and $3\sigma$ confidence intervals. The DCF and ICF cross-correlation coefficients between the Fermi/LAT and ALMA 7, SMA and OVRO light curves are plotted in Fig. \ref{['fig:corr_fermi-alma7']}, Fig. \ref{['fig:corr_fermi-sma']} and Fig. \ref{['fig:corr_fermi-ovro']}, respectively.