Angular Correlation Analysis of Residual Faraday Rotation Measures in the NVSS Catalogue

This preprint presents a statistical analysis of angular correlations in foreground-subtracted extragalactic rotation measure (RM) data from the Taylor et al. (2009) NVSS catalogue (~37,000 sources), after subtraction of the Hutschenreuter et al. (2022) all-sky Bayesian Galactic RM template. Using several independent statistics — including the two-point amplitude correlation function CRM(θ)C_{RM}(\theta)CRM(θ), the sign correlation function Csign(θ)C_{sign}(\theta)Csign(θ), the RM structure function, and an approximate angular power spectrum — the analysis identifies a characteristic angular decorrelation scale at approximately θ ≈ 5.2°–5.4° in the residual RM sky. Five independent diagnostics support the robustness of this scale: • Agreement between amplitude and sign correlation zero-crossings• Bootstrap resampling showing stable recovery of the ~5° crossing scale• Complete invariance of the sign correlation under Galactic latitude cuts from |b| > 20° to |b| > 50°• Consistent behaviour across northern and southern sky jackknife tests• A spectral minimum in the angular power spectrum near multipole ℓ ≈ 25–30 with a rising blue-tilt spectrum at higher multipoles The Galactic RM template itself shows no zero crossing, indicating that the observed feature is not introduced by the subtraction procedure. Injection–recovery simulations constrain domain-like alternating-sign RM structures with amplitudes A ≲ 2 rad m⁻² at angular scales of 2°–20°. Update: Preliminary Application to POSSUM RM Data As an initial extension of this analysis, the same correlation pipeline has been applied to a publicly available subset of rotation measure data from the POSSUM survey. A qualitatively similar angular correlation structure is observed, characterised by: a minimum near ~5–6° a secondary maximum near ~10–12° This feature persists under multiple internal consistency tests, including: randomisation of sky positions (RA/Dec permutation) rotation measure value shuffling bootstrap resampling measurement uncertainty filtering Galactic latitude masking (|b| > 20° and |b| > 30°) In all cases, the structure remains detectable, with reduced amplitude but consistent angular scale under progressively stricter cuts. At this stage, the POSSUM result should be regarded as a preliminary, independent application of the pipeline, rather than a formal replication. The dataset used here is not a confirmed full-sky release, and further validation on independent RM catalogues (including NVSS re-analysis and future ASKAP data releases) is required. Nevertheless, the persistence of a comparable angular scale in an independent RM dataset suggests that the observed ~5° decorrelation scale may reflect a real property of the RM sky rather than a dataset-specific artefact. A related extension of this work proposes that the observed ~5° angular coherence scale may have implications for directional variation in cosmological parameters, including the Hubble constant (Ryder 2026c). Cross-Probe Validation Update — 25 March 2026 A controlled follow-up analysis was performed on the Pantheon+ Type Ia supernova dataset, restricted to the lowest redshift bin (zHD