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arxiv: 2605.25772 · v1 · pith:YBWNR2Z4new · submitted 2026-05-25 · 🌀 gr-qc · astro-ph.CO· astro-ph.IM

Polarized Anisotropic Stochastic Gravitational Wave Background Search with Ground-Based Detector Networks

T\"ore Boybeyi , Vuk Mandic This is my paper

Pith reviewed 2026-06-29 20:30 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.COastro-ph.IM
keywords stochastic gravitational wave backgroundStokes parameterspolarizationanisotropic SGWBLVK O3 datamap-making analysisfull-Stokes reconstructiongravitational wave foregrounds
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The pith

A full-Stokes analysis of stochastic gravitational wave backgrounds shows that intensity-only searches can be biased by polarized sky components.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper implements a joint maximum-likelihood reconstruction of the four Stokes parameters I, V, Q and U for anisotropic stochastic gravitational wave backgrounds using ground-based detector networks. Standard cross-correlation pipelines are extended to this full-Stokes map-making procedure and applied to LVK O3 data to place limits on the polarized angular power spectra. The central result is that the network response matrix does not orthogonalize the Stokes channels, so polarized signals leak into intensity estimates when polarization is ignored. The same non-orthogonality means polarized shot noise from compact binary coalescences is not parametrically smaller than intensity shot noise. The framework therefore both removes a modeling bias and opens access to polarization signatures that intensity-only methods cannot see.

Core claim

Gravitational waves admit a Stokes decomposition into intensity (I), circular polarization (V), and linear polarization (Q, U). A full-Stokes maximum-likelihood SGWB map-making analysis is implemented for ground-based detector networks that jointly reconstructs all four parameters from cross-correlation data products. Applied to LVK O3 data, the analysis constrains the polarized angular spectra C^{VV}_ℓ, C^{EE}_ℓ, C^{BB}_ℓ and |C^{IV}_ℓ|. An intensity-only model is shown to be biased when polarized sky components are present because the detector-network Fisher inner product does not generally make the Stokes responses orthogonal. For transient CBC foregrounds, polarized shot noise is not par

What carries the argument

The full-Stokes maximum-likelihood map-making procedure that jointly reconstructs the Stokes parameters I, V, Q, U from network cross-correlation data products via the detector-network Fisher inner product.

If this is right

  • An intensity-only SGWB analysis will return biased sky maps and spectra whenever polarized components are present.
  • Polarized shot noise from compact binary coalescences contributes at the same order as intensity shot noise and cannot be neglected.
  • Constraints become available on the angular power spectra of circular polarization (V), linear polarization E and B modes, and the I-V cross-spectrum.
  • Polarized anisotropies in the SGWB become detectable that remain invisible to intensity-only searches.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Existing upper limits on the anisotropic SGWB from O1-O3 data may need re-evaluation once polarized leakage is accounted for.
  • The method could be used with future detector networks to search for parity-violating signatures through a non-zero circular polarization spectrum.
  • The same non-orthogonality issue may appear in other map-making problems that involve vector or tensor fields observed by non-orthogonal detector responses.

Load-bearing premise

The detector-network Fisher inner product does not generally make the Stokes responses orthogonal.

What would settle it

Applying the full-Stokes pipeline and the intensity-only pipeline to the same LVK O3 dataset and finding statistically significant differences in the reconstructed intensity map, or finding non-zero polarized spectra C^{VV}_ℓ or C^{EE}_ℓ, would support the bias claim; identical results from both pipelines would falsify it.

Figures

Figures reproduced from arXiv: 2605.25772 by T\"ore Boybeyi, Vuk Mandic.

Figure 1
Figure 1. Figure 1: FIG. 1. Recovered clean maps in the spherical harmonic ba [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Angular power spectra for a CE+ET(2L) network [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Results from the full-Stokes analysis of the LVK O3 data at [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

Gravitational waves admit a Stokes decomposition into intensity ($I$), circular polarization ($V$), and linear polarization ($Q$, $U$), analogous to Cosmic Microwave Background (CMB) polarimetry. We implement a full-Stokes maximum-likelihood SGWB map-making analysis for ground-based detector networks, promoting the standard cross-correlation data products used in existing pipelines to a joint reconstruction of $I$, $V$, $Q$, $U$. Applied to LVK O3 data, we constrain the polarized angular spectra $C^{VV}_\ell$, $C^{EE}_\ell$, $C^{BB}_\ell$ and $|C^{IV}_\ell|$. We show that an intensity-only model is biased when polarized sky components are present, since the detector-network Fisher inner product does not generally make the Stokes responses orthogonal. For transient CBC foregrounds, polarized shot noise is not parametrically suppressed relative to ordinary CBC intensity shot noise. The full Stokes framework separates the Stokes sectors while providing access to polarized anisotropies invisible to conventional intensity-only searches.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The paper implements a full-Stokes maximum-likelihood SGWB map-making analysis for ground-based detector networks, extending standard cross-correlation pipelines to jointly reconstruct the Stokes parameters I, V, Q, U. Applied to LVK O3 data, it constrains the polarized angular spectra C^{VV}_ℓ, C^{EE}_ℓ, C^{BB}_ℓ and |C^{IV}_ℓ|. The central result is that intensity-only analyses are biased when polarized sky components are present, because the detector-network Fisher inner product does not make the Stokes responses orthogonal; the work further notes that polarized shot noise from transient CBC foregrounds is not parametrically suppressed relative to intensity shot noise.

Significance. If the maximum-likelihood implementation correctly propagates the off-diagonal Fisher blocks and the transient foreground model is complete, the result would be significant: it supplies the first joint constraints on polarized SGWB anisotropies with existing LVK data and supplies a concrete diagnostic for a previously unaccounted systematic in intensity-only searches. The approach re-uses existing cross-correlation data products, so the framework is immediately applicable to ongoing and future observing runs.

major comments (1)
  1. [Abstract / likelihood implementation] The claim that the full-Stokes reconstruction separates sectors without bias (Abstract) is load-bearing for both the O3 constraints and the assertion that intensity-only analyses are biased. The provided material does not describe an explicit simulation test or analytic propagation check confirming that the likelihood fully accounts for the off-diagonal Fisher blocks when polarized CBC shot noise is present; without such a check the reported spectra could acquire systematic offsets from incomplete foreground modeling.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thoughtful review and for highlighting the need for explicit validation of the full-Stokes likelihood. We address the major comment below and will revise the manuscript to incorporate the requested check.

read point-by-point responses

  1. Referee: [Abstract / likelihood implementation] The claim that the full-Stokes reconstruction separates sectors without bias (Abstract) is load-bearing for both the O3 constraints and the assertion that intensity-only analyses are biased. The provided material does not describe an explicit simulation test or analytic propagation check confirming that the likelihood fully accounts for the off-diagonal Fisher blocks when polarized CBC shot noise is present; without such a check the reported spectra could acquire systematic offsets from incomplete foreground modeling.

    Authors: The maximum-likelihood estimator is derived from the full covariance of the cross-correlation data products, so the Fisher matrix by construction includes all off-diagonal blocks between Stokes parameters I, V, Q, U. The analytic demonstration that intensity-only analyses are biased follows directly from the non-orthogonality of the network response functions under this inner product. We acknowledge, however, that the manuscript does not present an explicit end-to-end simulation injecting polarized CBC shot noise and recovering the input spectra. We will add such a validation section in the revised manuscript, using the same O3 noise curves and network geometry, to confirm unbiased recovery when the full Fisher is employed. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation extends standard cross-correlation methods independently

full rationale

The paper's derivation chain implements a full-Stokes maximum-likelihood map-making analysis by promoting existing cross-correlation data products to joint I/V/Q/U reconstruction, then applies this to LVK O3 data to obtain constraints on C^VV_ℓ, C^EE_ℓ, C^BB_ℓ and |C^IV_ℓ|. The key statement that the detector-network Fisher inner product does not generally orthogonalize Stokes responses is presented as an intrinsic property of the inner product rather than a fitted result or self-referential definition. No equations reduce by construction to the paper's own inputs, no predictions are statistically forced from subsets of the same data, and no load-bearing uniqueness theorems or ansatzes are imported via self-citation. The framework remains self-contained against external benchmarks of standard SGWB pipelines.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only abstract available, so no explicit free parameters, axioms, or invented entities can be identified from the provided text.

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discussion (0)

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Reference graph

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