Properties of Polarized Radio Sources in the Wide Chandra Deep Field South from 2 to 4GHz

We present a study of the linear polarization properties of radio sources within the 10 deg$^2$ Wide Chandra Deep Field South (W-CDFS) in S-band (2-4 GHz). Our W-CDFS image has an angular resolution of 15 arcsec and a 1$σ$ RMS in Stokes $I$ of $\approx$50 $μ$Jy/beam. We detect 1920 distinct source components in Stokes $I$ and 175 in linear polarization. We examine the polarized source counts, Faraday Rotation measures, and fractional polarization of the sources in the survey. We show that sources with a total intensity above $\approx$10mJy have a mean fractional polarization value of $\approx$3% from modeling the polarized counts. We also calculate an estimate for the limit on the fractional polarization level of sources with a total intensity below 1mJy (mostly star-forming galaxies) of $\stackrel{<}{_{\sim}}$3% using stacking. The mean Faraday Rotation we measure is consistent with that due to the Milky Way. We also show that fractional polarization is correlated with in-band spectral index, consistent with a lower mean fractional polarization for the flat-spectrum population. In addition to characterizing the S-band polarization properties of sources in the W-CDFS, this study will be used to validate the shallower, but higher angular resolution S-band polarimetric information that the VLA Sky Survey will provide for the whole sky above Declination -40 degrees over the next few years.

💡 Research Summary

This paper presents a comprehensive study of linear polarization in the Wide Chandra Deep Field South (W‑CDFS) using the Karl G. Jansky Very Large Array (VLA) in S‑band (2–4 GHz). The authors observed a 10 deg² area with the VLA in C‑configuration, employing a hexagonal grid of 513 pointings spaced by 15 arcmin. Each pointing received roughly 110 seconds of integration, yielding a Stokes I rms of ≈ 50 µJy beam⁻¹ and Stokes Q/U rms of 70–120 µJy beam⁻¹ across four sub‑bands (2.243, 2.755, 3.243, 3.755 GHz). Data reduction was performed with the CASA pipeline (version 6.1) for standard gain, bandpass, and flux calibration, followed by a dedicated polarization calibration using 3C 84 as an unpolarized leakage calibrator (on‑axis leakage ≈ 0.5 %) and 3C 138 for R‑L phase calibration. Imaging employed multi‑frequency synthesis with three Taylor terms and Briggs weighting (robust = 0.5), producing a synthesized beam of 16.5″ × 11.0″ (PA = 8.3°).

Source extraction was carried out with PyBDSF at a 5σ threshold (≈ 250 µJy). The final catalog contains 1,920 Stokes I components and 175 linearly polarized components. Positional accuracy was verified against Gaia DR3, showing rms offsets of 0.4″ in RA and 0.5″ in Dec, well within the beam size. The authors measured polarized flux densities directly from the Q and U images of each sub‑band to avoid the non‑Gaussian noise properties of the polarized intensity image.

The paper provides detailed source count analyses for both total intensity and polarized intensity, comparing the results with several existing 3 GHz surveys: the S‑PASS (2.3 GHz), VLASS (1.4 GHz scaled to 3 GHz), S‑COSMOS, and ultra‑deep counts from Vernstrom et al. While VLASS counts are 20–40 % lower than the C‑configuration counts—consistent with expectations that VLASS resolves out extended emission—the authors find a local overdensity around 20 mJy that appears in both datasets, suggesting genuine cosmic variance rather than a calibration issue.

Polarization fractions (Π) were investigated as a function of total flux density. Sources brighter than ≈ 10 mJy (predominantly AGN) exhibit a mean Π ≈ 3 %, lower than the ≈ 5 % typical at 1.4 GHz, reflecting the higher contribution of flat‑spectrum core‑dominated AGN at S‑band frequencies. For sources below 1 mJy—where star‑forming galaxies dominate—the authors employed stacking techniques and derived an upper limit of Π ≲ 3 %, indicating that faint star‑forming systems are only weakly polarized.

Rotation measures (RMs) were derived from the four sub‑band polarization angles. The mean RM is ≈ +5 rad m⁻², in agreement with Galactic foreground models for the high‑latitude field, and the RM distribution shows modest scatter, implying limited contribution from extragalactic magneto‑ionic media.

A key result is the correlation between fractional polarization and in‑band spectral index. Steep‑spectrum sources (α < –0.7) have a higher mean Π (≈ 4 %) than flat‑spectrum sources (α > –0.5) with Π ≈ 2 %. This supports the physical picture that flat‑spectrum AGN are core‑dominated, experiencing stronger internal Faraday depolarization, whereas steep‑spectrum lobes retain higher intrinsic polarization.

The authors discuss the implications for the VLA Sky Survey (VLASS). VLASS, conducted at the same S‑band but with 2.5″ resolution and a shallower depth (≈ 150 µJy per epoch), will benefit from the deeper C‑configuration data as a validation set for completeness, flux scale, and polarization calibration, especially for compact (< 2″) sources. The W‑CDFS results thus provide a benchmark for assessing VLASS’s ability to recover polarized flux from both AGN and star‑forming populations across the sky.

In summary, this work delivers the first large‑area, moderate‑resolution (15″) polarization survey at 2–4 GHz, delivering robust source counts, polarization fractions, and RM statistics. It confirms that bright AGN retain modest polarization (~3 %) at S‑band, while faint star‑forming galaxies are largely unpolarized (< 3 %). The observed dependence of Π on spectral index and the agreement of RMs with Galactic expectations enhance our understanding of magnetic field structures in extragalactic sources. The dataset will serve as a critical calibration and validation resource for upcoming wide‑field polarimetric surveys such as VLASS, enabling more accurate studies of cosmic magnetism and the role of polarization in future radio weak‑lensing analyses.