Radio Follow-up Observations of a Weak-line Quasar Exhibiting Remarkable X-Ray Variability

SDSS J1539+3954 (z ≈ 1.935), a radio-quiet weak-line quasar (WLQ), exhibited exceptional X-ray variability in 2019–2020, with its X-ray flux increasing by over 20 times from 2013 to 2019 and subsequently dropping by at least a factor of 9 in 2020. Motivated by the empirical correlations between X-ray and radio emission in the cores of active galactic nuclei (AGNs), we carried out a follow-up radio study in the 0.3–10 GHz range using the Giant Metrewave Radio Telescope (GMRT; 2020, 2022, 2024) and Very Large Array (VLA; 2022), and analyzed archival Very Large Array Sky Survey (VLASS) 3 GHz data (2017–2023) to investigate the source’s radio properties and potential connection with the X-ray behavior. Our observations reveal a compact radio source with a spectral index of −0.65 ± 0.15 in the frequency range 0.3–1.4 GHz and −1.09 ± 0.16 in 3–10 GHz. While the source was undetected in VLA-FIRST (1994) and VLASS epochs, the GMRT and VLA observations show no statistically significant variability over the monitored period. The absence of detectable changes in the radio flux, despite strong X-ray variability, suggests no direct connection between the X-ray variability and the radio emission, consistent with the thick-disk-plus-outflow (TDO) model for WLQs. However, the sensitivity limit of the surveys prevents us from drawing definitive conclusions regarding variability on longer timescales between the VLA-FIRST and GMRT epochs. We further explore possible mechanisms driving the radio emission from this source. Our analysis rules out small-scale jets and coronal emission as the primary drivers of the radio emission, suggesting that extended emission from AGN winds and star formation is the more plausible mechanism.