Constraining the magnetic field strength of a flaring radio core in the compact steep spectrum source 3C 138

¹ Korea Astronomy and Space Science Institute, 776 Daedeok-daero, Yuseong-gu, Daejeon 34055, Korea
² University of Science and Technology, Korea, 217 Gajeong-ro, Yuseong-gu, Daejeon 34113, Korea
³ Department of Astronomy, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China
⁴ Joint ALMA Observatory, Alonso de Córdova 3107 Vitacura, Santiago 763-0355, Chile
⁵ National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
⁶ Department of Astronomy, School of Science, Graduate University for Advanced Studies (SOKENDAI), Tokyo 181-8588, Japan
⁷ European Southern Observatory, Alonso de Córdova 3107 Vitacura Casilla, 19001 Santiago de Chile, Chile

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Received: 9 March 2026
Accepted: 9 April 2026

Abstract

Context. Compact steep spectrum (CSS) sources generally show weak Doppler boosting, yet some exceptions show multi-year-scale radio flux variability and high-energy activity. Since 2022, the CSS quasar 3C 138 has been in a radio high state accompanied by multiple gamma-ray outbursts, offering unique opportunities to study changes in jet physical conditions.

Aims. We estimated the synchrotron self-absorption (SSA) magnetic field (B_SSA) in the SSA core of 3C 138 during its high state and compared it with the equipartition magnetic field (B_eq) to assess the core field environment.

Methods. Using extended Korean Very long-baseline interferometry Network (KVN) data at 22, 43, 86, and 129 GHz (2024–2025), we calibrated the visibilities and modeled resolved components with circular Gaussians. A single-zone SSA model fitted to the core spectrum provided the turnover frequency and peak flux density, from which we estimated the B_SSA and B_eq. We used Very Large Array and Atacama Large Millimeter/submillimeter Array data to constrain the broadband spectra with the same model.

Results. The KVN SSA core shows a turnover at about 33 GHz and a peak flux of about 1.45 Jy. The inferred B_SSA is far below equipartition, with B_SSA/B_eq ≈ 0.05.

Conclusions. The flux variability of 3C 138 is driven by a compact, particle-dominated core. Shock-driven particle injection in the inner jet could account for the core brightening and the production of X-ray/gamma-ray emissions through an inverse-Compton process without requiring extreme relativistic beaming effects.