Polarisation and Faraday rotation measure imaging at metre wavelengths with sub-arcsecond resolution: a foundational calibration strategy

Technical Summary: Polarisation and Faraday Rotation Measure Imaging at Metre Wavelengths with Sub-arcsecond Resolution

Problem Statement
Low-frequency radio polarimetric observations are essential for probing magnetic fields in astrophysical sources and the intervening medium, as well as magnetospheric emission from compact objects. While the LOFAR telescope offers unique baselines up to 2000 km, enabling sub-arcsecond resolution, previous polarimetric studies with LOFAR have been limited to angular resolutions of approximately 6 arcseconds. This limitation results in significant beam depolarisation, obscuring the detailed polarisation structure of sources and reducing the detectable number of polarised sources. Furthermore, a comprehensive strategy for full-polarisation calibration and imaging at the full resolution of LOFAR's international (European) baselines had not yet been developed or demonstrated.

Methodology
The authors present a calibration strategy designed to enable full-resolution polarimetric imaging using the LOFAR pan-European array. The methodology involves three primary components:

1. Full-Jones Calibration with an Unpolarised Calibrator: The strategy applies full-Jones corrections to international stations using a high signal-to-noise ratio (S/N) in-field calibrator that is unpolarised in the HBA band (115–170 MHz). For the ELAIS-N1 field, the Seyfert 2 galaxy ICRF J160607.6+552135 was selected. This source is used to solve for instrumental leakage terms (RR/LL phase offsets and RL/LR cross-hand corrections) and differential Faraday rotation. The calibration utilizes facetselfcal with a point-source sky model, ignoring short baselines to mitigate incomplete sky model effects.
2. Faraday Depth Alignment with a Polarised Calibrator: To align multiple observing epochs in Faraday depth, the authors utilise a bright, linearly polarised reference source (7C 1604+5447). Residual offsets in polarisation angles between epochs (typically 0.1–0.3 rad m⁻²) are corrected by fitting the polarisation angle ($\chi$) as a function of wavelength squared ($\lambda^2$) for the reference source. These derived corrections (a rotation measure offset and a polarisation angle offset) are applied directly to the visibility data, allowing for deep combined imaging and deconvolution rather than simple image stacking.
3. RM-Synthesis and Imaging: The calibrated visibility data are imaged using WSClean. The authors perform two-dimensional RM-synthesis using RM-Tools to search for linearly polarised emission. To optimise sensitivity, they employ variance weighting and specific channel joining options. For detected sources, one-dimensional RM-synthesis is performed on integrated flux densities to allow for deeper cleaning and more accurate deconvolution.

Key Contributions

• Calibration Strategy: The paper establishes a validated workflow for full-Jones polarisation calibration on LOFAR international baselines, overcoming the limitations of previous lower-resolution studies.
• Visibility-Based Alignment: It demonstrates a method for aligning multi-epoch observations in Faraday depth by applying corrections directly to visibility data, facilitating deeper combined imaging.
• Sub-arcsecond Polarimetry: The study successfully applies this strategy to the ELAIS-N1 field, combining four 8-hour observations (32 hours total) to produce polarimetric images at resolutions of 0.3", 0.6", and 1.2".

Results
Applying this strategy to the ELAIS-N1 field yielded the following results:

• Noise Levels: At 0.3" resolution, the RMS noise levels for Stokes $I$, $Q$, $U$, and $V$ are approximately 14 $\mu$Jy beam⁻¹, indicating the images are effectively thermal-noise limited with minimal polarisation leakage contamination.
• Source Detection and Characterisation:
  • 7C 1604+5447: A known polarised source was resolved into distinct components. The polarised emission was found to originate predominantly from the southern hotspot, with a measured Rotation Measure (RM) of $6.285 \pm 0.008$ rad m⁻². The study detected wavelength-dependent depolarisation, with the polarisation fraction increasing from ~0.6% at long wavelengths to ~4% at short wavelengths.
  • 4C +55.32: A previously undetected polarised source at LOFAR frequencies was identified. The polarised emission originates from the southern lobe's double-hotspot region with an RM of $-1.25 \pm 0.01$ rad m⁻². The northern hotspot signal was determined to be dominated by instrumental leakage.
  • 7C 1607+5402: A giant radio galaxy was imaged, revealing polarised emission from a compact "spot" feature and the north-western lobe, with consistent RM values (~7.3 rad m⁻²).
  • CR Draconis: Circularly polarised (Stokes $V$) emission was detected from the binary M-dwarf system. The high angular resolution allowed for the measurement of the source's proper motion across epochs, consistent with Gaia DR3 data.
• Leakage Estimates: The study estimated the instrumental leakage from Stokes $I$ to linear polarisation ($Q/U$) at 0.11% and to circular polarisation ($V$) at 0.021%, approximately a factor of two lower than typical LoTSS leakage levels.

Significance
The authors claim that these results demonstrate that sub-arcsecond polarimetry at metre wavelengths is now feasible with LOFAR. By enabling the resolution of polarised structures on sub-kpc scales (e.g., resolving hotspots in radio galaxies) and detecting fainter sources previously lost to beam depolarisation, this work opens new scientific opportunities for the LOFAR2.0 era. The strategy provides a foundation for future large-area surveys, such as the planned International LoTSS (ILoTSS), and allows for ultra-deep polarimetric imaging of well-studied deep fields. The paper notes that the approach relies on the availability of suitable in-field calibrators (unpolarised and polarised) and suggests that the method can be automated for pipeline processing.