Catching the 2021 <i>γ</i> -ray flare in the blazar TXS 2013+370

The γ -ray–loud blazar TXS 2013+370, a powerful multiwavelength emitter at z = 0.859, underwent an exceptional gigaelectron volt outburst in late 2020 to early 2021. In this work, we present full polarization VLBI imaging at 22, 43, and 86 GHz (11 February 2021) together with contemporaneous single-dish monitoring (OVRO 15 GHz; SMA 226 GHz) and Fermi –LAT light curves to localize the high-energy dissipation site and probe the magnetic field of the inner jet. The images enabled us to study the jet structure and field topology on sub-parsec scales, revealing a compact near-core knot at r ≃ 40 − 60 μas along with the gigaelectron volt (GeV) flare and a flat core-dominated spectrum ( α ≳ −0.5). The core has strong linear polarization and exhibits a ∼50° electric vector polarization angle rotation at 86 GHz. The pixel-based and integrated fits we employed yielded a high, uniform rotation measure, RM = (7.8 ± 0.2)×10 4 rad m −2 , consistent with an external Faraday screen. Performing a cross-correlation of Fermi –LAT and 15 GHz light curves revealed a highly significant peak, with the γ rays leading by Δ t = (102 ± 12) d. Adopting β app = 4.2 ± 0.5 and θ = 4.1° ±0.2° implies a de-projected separation of Δ r γ − 15 = (2.71 ± 0.47) pc and locates the GeV emission between the jet apex and ∼0.42 pc (in the 1 σ range) downstream. Our results do not pinpoint the emission site; rather, they support two valid scenarios. The γ -ray production occurs within the broad-line region (∼0.07 pc), where external-Compton scatters optical/UV photons to γ -rays, and beyond the broad-line region, reaching ∼0.42 pc (1 σ ) within the inner parsecs, where external-Compton scattering of dusty-torus infrared photons dominates. Both scenarios are compatible in the allowed range of emission distances, while opacity-driven core shifts modulate the observed radio– γ delay without requiring large relocations of the dissipation zone.