Radio Follow-Up Observations of a Weak-Line Quasar Exhibiting Remarkable X-ray Variability

SDSSJ1539+3954 ($z\approx 1.935$), a radio-quiet weak-line quasar (WLQ), exhibited exceptional X-ray variability in 2019$-$2020, with its X-ray flux increasing by over 20 times from 2013 to 2019 and subsequently dropping by at least a factor of nine in 2020. Motivated by the empirical correlations between X-ray and radio emission in AGN cores, we carried out a follow-up radio study in the 0.3$-$10 GHz range using GMRT (2020, 2022, 2024) and VLA (2022), and analyzed archival VLASS 3 GHz data (2017-2023) to investigate the source's radio properties and potential connection with the X-ray behavior. Our observations reveal a compact radio source with a spectral index of -0.65$\pm$0.15 in the frequency range of 0.3$-$1.4 GHz and -1.09$\pm$0.16 in 3$-$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 longer timescale variability 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.