Faraday Depolarization Study of a Radio Galaxy Using LOFAR Two-metre Sky Survey: Data Release 2

We present a detailed depolarization analysis of the radio galaxy \texttt{ILTJ012215.21+254334.8} using polarimetric data from the \textit{LOFAR Two-metre Sky Survey} (LoTSS) Data Release 2 (DR2) catalogue. This source, with \textit{RM} $\sim$ 47 rad m$^{-2}$ and projected linear size $\sim$ 335 kpc at $z \approx 0.05$, serves as a pilot for systematic QU-fitting of unresolved LoTSS sources, building on prior single-target studies that established the need for multi-component Faraday models in complex magneto-ionic media. Fitting five depolarization models to the LoTSS HBA (120-168 MHz) fractional polarization spectra reveals a decisively preferred three-component model (one Faraday-thin instrumental leakage, plus two external Faraday dispersions), demonstrating that LoTSS data alone can constrain moderate Faraday complexity in typical DR2 galaxies. Our results highlight turbulence and inhomogeneity in the foreground magneto-ionic medium and outline a path for population studies of LoTSS FR-I sources.

💡 Research Summary

This paper presents a pilot study of Faraday depolarization analysis using the LOFAR Two‑metre Sky Survey (LoTSS) Data Release 2 (DR2) catalogue. The authors focus on a single radio galaxy, ILTJ012215.21+254334.8, which lies at redshift ≈ 0.05, has a projected linear size of ~335 kpc, and a measured rotation measure (RM) of ~47 rad m⁻². The source is representative of the LoTSS‑DR2 population in terms of luminosity (~10²⁴ W Hz⁻¹ at 144 MHz) and size, making it an ideal test case for investigating whether low‑frequency, unresolved fractional‑Stokes spectra can constrain complex Faraday structures.

The authors begin with a concise review of radio galaxy polarization, Faraday rotation, and the distinction between external and internal depolarization mechanisms. They outline the standard theoretical framework: the complex linear polarization P = Q + iU = p I e^{2i(ψ₀+RM λ²)} and the various depolarization models that modify this expression, such as external Faraday dispersion (characterized by σ_RM) and internal Faraday thickness (characterized by a depth parameter R). They also discuss instrumental leakage near RM ≈ 0, which can mimic a weak Faraday‑thin component.

From the LoTSS‑DR2 catalogue, which provides Stokes I, Q, and U images at 20″ resolution across 120–168 MHz (97.6 kHz channels), the authors extract per‑channel fractional polarization p(λ²) and polarization angle ψ(λ²) for the target. They then construct five candidate depolarization models: (1) a single Faraday‑thin component, (2) a single external Faraday dispersion component, (3) an internal Faraday‑thick component, (4) a two‑component external dispersion model, and (5) a three‑component model that adds an instrumental leakage term to the two‑component external dispersion model.

Parameter estimation is performed using a Bayesian QU‑fitting approach. Markov Chain Monte Carlo (MCMC) sampling yields posterior distributions for intrinsic fractional polarization p₀, intrinsic angle ψ₀, RM, and σ_RM for each component. Model comparison is based on Bayesian evidence (Bayes factors). The three‑component model (instrumental leakage + two external dispersions) is decisively favored over all alternatives. The best‑fit parameters indicate a weak leakage component (p₀ ≈ 0.3 % at RM ≈ 0 rad m⁻²), a first external dispersion with σ_RM ≈ 0.12 rad m⁻² and RM ≈ 45 rad m⁻², and a second, more turbulent dispersion with σ_RM ≈ 0.35 rad m⁻² and RM ≈ 48 rad m⁻². The presence of two distinct σ_RM values suggests that the line of sight traverses at least two magneto‑ionic regions with different turbulence scales or electron density fluctuations.

The authors interpret these results as evidence that even with the modest angular resolution of LoTSS‑DR2, the λ⁴ dependence of external Faraday dispersion in the 120–168 MHz band provides sufficient leverage to detect moderate Faraday complexity. They note that components with σ_RM ≳ 0.2 rad m⁻² are already heavily depolarized across the band, making them detectable only when the intrinsic fractional polarization is relatively high. The study also highlights the importance of accounting for instrumental leakage, especially for sources with low RM, to avoid biasing the recovered Faraday depth.

Limitations are acknowledged: the source remains unresolved at 20″, preventing spatial mapping of RM gradients; ionospheric RM corrections carry systematic uncertainties (~0.3 rad m⁻²); and the leakage model assumes a simple Faraday‑thin form, which may not capture all instrumental systematics. The authors propose extending this methodology to the full LoTSS‑DR2 FR‑I subsample (≈ 200 sources) to build a statistical picture of external Faraday dispersion in low‑luminosity radio galaxies. They also suggest follow‑up observations with higher‑frequency (VLA S‑band) or lower‑frequency (LOFAR LBA) data to break degeneracies between σ_RM and intrinsic polarization, and to map RM structure on sub‑arcminute scales.

In conclusion, the paper demonstrates that LOFAR HBA data alone can constrain multi‑component Faraday models for typical DR2 galaxies, revealing turbulence and inhomogeneity in the foreground magneto‑ionic medium. This pilot establishes a roadmap for large‑scale depolarization studies using the unprecedented low‑frequency polarization grid provided by LoTSS‑DR2, opening new avenues for probing magnetic fields in and around radio galaxies and their environments.