TXS 2013+370: Gamma-Ray Blazar Insights

• TXS 2013+370 is a γ-ray-loud blazar at z=0.859 known for its exceptional multiwavelength variability and relativistic jets.
• High-resolution VLBI imaging has resolved a compact, bright core and revealed moving and stationary jet components that trace its detailed kinematics and geometry.
• Temporal correlations between radio and γ-ray flares, coupled with stable polarization measures, localize the high-energy dissipation zone to the innermost parsec of the jet.

TXS 2013+370 is a γ-ray-loud blazar at redshift $z=0.859$, notable for its exceptional multiwavelength variability and highly relativistic jet. As an FSRQ exhibiting prominent radio and γ-ray outbursts, TXS 2013+370 has served as a key laboratory for probing the innermost structures and physical processes governing blazar emission. Multi-epoch very long baseline interferometry (VLBI) imaging and time-resolved polarimetry, in combination with coordinated single-dish radio and Fermi-LAT $\gamma$-ray monitoring, have enabled the localization of the high-energy dissipation zone, characterization of jet kinematics and geometry on sub-parsec to tens-of-parsec scales, and investigation of the relation between high-energy flares and jet activity (Traianou et al., 2019, Michailidis et al., 19 Nov 2025).

1. VLBI Imaging and Jet Morphology

High angular resolution VLBI imaging at 22, 43, and 86 GHz using the RadioAstron space antenna, ground-based arrays (VLBA, GMVA, Effelsberg, Yebes, Onsala, Green Bank, Jodrell Bank), and coordinated single-dish facilities (OVRO 40m, SMA) has resolved the inner jet of TXS 2013+370 with a linear resolution as fine as $\sim0.4$ pc. The observed morphology is characterized by a bright, unresolved radio core at the jet apex, followed by a gently bending jet hosting both moving and stationary components. During the 2020–2021 GeV outburst, new VLBI images captured a compact near-core knot (“N2”) at $r \simeq 40$–$60~\mu\mathrm{as}$ from the core concurrent with the flare, while stationary features A2 and C3 were recovered further downstream (Michailidis et al., 19 Nov 2025). The core maintains a flat, partially self-absorbed spectrum with $\langle \alpha_{\text{core}} \rangle \gtrsim -0.5$ across 22–86 GHz during major flares, indicating ongoing particle acceleration.

2. Jet Kinematics and Component Ejection

Model-fitting of VLBI visibilities with circular Gaussians has enabled tracking of distinct jet components epoch-by-epoch. Proper motions measured from the time evolution of feature-core separations yield apparent speeds as high as $\beta_{\text{app}}=13.9\pm0.9$ (component C2), with typical inner-jet speeds of $\beta_{\text{app}}=4.2\pm0.5$ (component A1, knot N2) and slower, quasi-stationary features at larger radii. Ejection epochs back-extrapolated for superluminal features align with multiwavelength flare timings, supporting a causal link between new component emergence and enhanced high-energy activity. The maximum observed speed sets a minimum bulk Lorentz factor $\Gamma_{\text{min}} \gtrsim 14$ and critical viewing angle $\theta_c \simeq 4.1^\circ$; inner-jet values near the core correspond to $\gamma$0–$\gamma$1 with Doppler factors $\gamma$2 for $\gamma$3 (Traianou et al., 2019).

3. Jet Geometry and Expansion Profile

Comprehensive analysis of stacked VLBI maps reveals that the jet width $\gamma$4 evolves according to a two-zone law: within $\gamma$5–$\gamma$6 mas ($\gamma$71–4 pc projected), $\gamma$8, consistent with parabolic collimation; beyond $\gamma$9–$\sim0.4$0 mas, a conical expansion with $\sim0.4$1 dominates. The parabolic-to-conical transition occurs at a deprojected distance $\sim0.4$2 pc ($\sim0.4$31.5%%%%24$\gamma$025%%%% Schwarzschild radii for $\sim0.4$6). Extrapolating the inner parabolic law to zero width and matching to the 86 GHz core FWHM locates the radio core at $\sim0.4$7 pc downstream of the true jet apex (Traianou et al., 2019).

4. Polarization Structure and Faraday Rotation

Full-polarization VLBI established that the core exhibits significant linear polarization ($\sim0.4$8–$\sim0.4$9) with a pronounced $r \simeq 40$0 rotation in the electric vector position angle (EVPA) between 43 and 86 GHz. Modeling the EVPA as a function of wavelength squared yields a uniform, extremely high rotation measure $r \simeq 40$1, unmatched by most blazar cores. This uniform RM, observed in both pixel- and integrated-Stokes analyses, indicates the presence of a highly magnetized, external Faraday screen, plausibly associated with circumnuclear material or the Galactic foreground (Michailidis et al., 19 Nov 2025). This stable RM signature persists through major flaring episodes, suggesting the Faraday screen location is not altered by rapid inner-jet events.

5. Radio–Gamma-Ray Temporal Correlations

Correlated radio and γ-ray activity is a hallmark of TXS 2013+370. Discrete cross-correlation of Fermi-LAT (0.1–300 GeV or 0.1–100 GeV) and SMA 235 GHz or OVRO 15 GHz light curves consistently reveals that γ-ray events lead millimeter and centimeter radio flares, establishing a temporal lag: $r \simeq 40$2 days and $r \simeq 40$3 days, respectively. Using jet kinematics ($r \simeq 40$4, $r \simeq 40$5), these lags translate to deprojected site separations of $r \simeq 40$6 pc and $r \simeq 40$7 pc (Traianou et al., 2019, Michailidis et al., 19 Nov 2025). Variability in the radio–γ-ray lag between epochs is attributed not to changes in the high-energy dissipation site, but instead to core-shift effects driven by changing opacity, resulting in the effective radio core moving downstream during flares while the true emission site remains spatially stable.

6. Localization of the Gamma-Ray Emission Region

Combining core–apex offsets with deprojected γ–radio separations confines the γ-ray production site to within the innermost parsec of the jet. For the 2021 outburst, the GeV emission zone lies between the jet apex and $r \simeq 40$8 pc downstream, consistent within $r \simeq 40$9 uncertainties with both the broad-line region (BLR, $60~\mu\mathrm{as}$0 pc) and the innermost edge of the dusty torus. This constrains viable external Compton (EC) seed photon scenarios to: (a) optical/UV photons from the BLR, or (b) infrared photons from hot dust in the torus. No evidence requires moving the dissipation zone far downstream across flares; instead, radiative delays are regulated by synchrotron opacity and associated core shifts (Michailidis et al., 19 Nov 2025).

7. Physical Interpretation and Implications

Multi-band VLBI, polarimetric, and cross-correlation data for TXS 2013+370 collectively support a leptonic EC scenario in which relativistic electrons, energized by shocks or magnetic reconnection within the magnetically dominated, accelerating jet zone, upscatter either BLR or torus photons to γ-ray energies. The observed flat spectrum and emergence of localized jet knots during flares demonstrate ongoing particle acceleration. RM and polarization properties indicate a persistently ordered, strongly magnetized circumnuclear environment. The observed jet opening angle ($60~\mu\mathrm{as}$1–$60~\mu\mathrm{as}$2) and bulk Lorentz factor ($60~\mu\mathrm{as}$3) satisfy $60~\mu\mathrm{as}$4 rad, in agreement with expectations from MHD jet models. The constancy of the γ-ray emission region across multiple flaring episodes indicates spatial stability of the high-energy dissipation process, modulated by core-shift–induced opacity variations rather than by migration of the radiative zone. This underscores the utility of multi-frequency, polarimetric VLBI for disentangling spatial from temporal effects in the high-energy physics of blazars (Traianou et al., 2019, Michailidis et al., 19 Nov 2025).