Orientation-dependent sensitivity of the all-sky all-frequency gravitational-wave radiometer search to continuous-wave sources

Stavros Venikoudis, Giacomo Bruno

Oct 21, 2026arXiv:2610.29384v1

gr-qcastro-ph.IM

Scorecard· 16/16

4.5/10 impact

Clean, correct, practically useful refinement of ASAF interpretation, but largely incremental over known radiometer results and confined to a narrow subcommunity.

Abstract

The all-sky all-frequency (ASAF) gravitational-wave radiometer search cross-correlates the data of two detectors with equal weight on the $+$ and $\times$ tensor polarizations. This is optimal for an unpolarized stochastic background, but not for continuous-wave (CW) sources, whose polarization depends on the inclination angle $ι$ and the polarization angle $ψ$ . Unless the source is seen face-on, the search measures less power than a face-on source with the same intrinsic amplitude, and underestimates its strength. The ratio of the two powers, the projection factor $μ^{2} (ι, ψ)$ , is known from earlier radiometer studies. We show how $μ^{2}$ enters the ASAF statistic, derive its exact dependence on $ψ$ , and prove that its average over orientations is exactly $2 / 5$ , independent of sky position, baseline geometry, noise weighting, and frequency. We apply the formalism to four simulated pulsar signals at four sky positions, with polarization from circular to nearly linear, injected into the LIGO detectors during the second observing run (O2). A nearly edge-on injection is measured with a signal-to-noise ratio (SNR) of $5.20$ , below the threshold of $6.19$ , while the same signal seen face-on would have an SNR of $31.1 \pm 6.0$ . Bayesian upper limits on the strain amplitude $h_{0}$ , marginalized over orientation and calibration uncertainty, are $2.7$ to $2.9$ times the face-on values. For the $505$ sub-threshold candidates of the first part of the fourth LIGO-Virgo-KAGRA observing run (O4a), the upper limits increase by a factor of $2.5$ to $2.9$ , and a source of the same strength would reach threshold only when inclined by less than $34.7^{\circ}$ to $50.3^{\circ}$ from face-on. The measured SNR and the significance of every candidate are unchanged.

AI Impact Assessments

(1 model)

Core Contribution

The paper addresses an interpretive gap in the all-sky all-frequency (ASAF) radiometer search. The search weights the + and × polarizations equally, which suits an unpolarized stochastic background but not a continuous-wave (CW) source with a definite polarization. The authors define the projection factor μ²(ι,ψ) = h_eff²/h_0². The factor itself is not new: it appears in the Messenger and Meyers radiometer work, which the authors cite. The claimed new elements are:

1. An exact closed form, μ² = (A₊²+A×²)/2 + (A₊²−A×²)/2 · ε cos(4ψ+δ), valid for the full time-dependent, noise-weighted baseline statistic. All the ψ-dependence sits in a single 4ψ harmonic with a depth ε and phase δ fixed by baseline geometry and declination.

2. A proof that the isotropic average is exactly 2/5 for any sky position, weighting, or frequency, plus the location of the minimum, (1−ε)/8.

3. Propagation of μ² through strain, SNR, detection probability, orientation completeness, and orientation-marginalized Bayesian upper limits for every frequency-pixel pair. This yields a maximum detectable inclination ι_max and an orientation coverage 1−cos ι_max.

The headline results are practical. Marginalized upper limits are 2.5 to 2.9 times the published circular (face-on) limits. A candidate as strong as the O4a sub-threshold ones is detectable only within about 35° to 50° of face-on. The significance of every candidate is unchanged.

Methodological Rigor

The derivation is clean and short. The complex-phasor trick F⁺+iF× = z e^{2iψ} makes the algebra transparent. The 2/5 average follows directly from the structure of the expression, and the numerical claim ε ≤ 1 is checked for the O2 H1-L1 baseline. The Bayesian upper-limit extension reuses the published ASAF implementation and reproduces the published circular limits, which is a good consistency check. The paper explains why the marginalized-to-circular ratio exceeds √(5/2): the 95% limit is driven by the tail of the posterior at near-edge-on orientations.

The validation uses four hardware injections plus one O4a injection. The agreement is reasonable but not clean. Recovered h₀ matches the injection for two cases. For the other two, the authors invoke Doppler bin-edge loss and pixel-phase loss to explain deficits of 2.2× and 1.3×. These corrections are plausible and quantified approximately, but they are somewhat ad hoc and weaken the "confirmation" claim. The four injections are a very small sample for testing a formula that is essentially analytic. The ι_max analysis for candidates assumes ρ_ref = ρ̂/⟨μ²⟩, which is a hypothetical construct, and the authors flag this honestly. The time weights are assumed uniform over the sidereal day, which is reasonable but not exact. Spectral spreading at high frequency is not corrected for.

Potential Impact

The impact is narrow but real. The paper is directly useful to the LVK stochastic and CW radiometer community. It offers a concrete reporting recommendation: quote a range of upper limits over orientation, and report ι_max and C_orient alongside the SNR. It also gives an important caution that selecting follow-up candidates by SNR alone preferentially picks face-on sources. This could modestly change how future O4b/O5 ASAF results are presented and how candidates are prioritized for hierarchical follow-up with matched-filter CW searches. The closed form is easy to implement and applies to any baseline and run.

Outside the radiometer niche, the influence is limited. Matched-filter CW pipelines already handle ι and ψ. The finding is conceptually a bookkeeping correction, not a new search method. It does not improve sensitivity. It only clarifies interpretation and limits. Adjacent work such as the Boybeyi and Mandic Stokes-parameter analysis for polarized SGWB is conceptually related, but this paper does not generalize beyond CW sources.

Timeliness & Relevance

The paper is timely. O4a results have just been released with 505 sub-threshold candidates and published circular-polarization upper limits. O4b/O4c and O5 analyses are forthcoming. Interpreting those limits for physically motivated CW sources, including boson clouds and irregular neutron stars, is a real need. Nothing about the topic is a field-wide bottleneck, though.

Strengths

Exact, simple closed form with clear physical interpretation: the ε-modulation vanishes at the poles and peaks near ±19.5° declination.

Rigorous propagation through the full chain, including calibration-marginalized Bayesian upper limits.

Actionable recommendations, applied to real O4a catalog data.

Honest accounting of what is new versus what was known, and of which assumptions are hypothetical.

Clear writing, with a useful SNR taxonomy (measured, recovered, reference).

Limitations

Incremental novelty: the core factor and its isotropic average were known, and the marginalized upper limit has been used in narrowband radiometer searches. The new content is a generalization and proof for the full ASAF statistic.

Validation rests on four injections whose recovered amplitudes need ad hoc loss corrections, and one O4a injection.

No new search technique and no sensitivity gain. The upper limits still assume circular polarization in the published prescription.

The assumptions that the isotropic prior on orientation is appropriate and that candidates are real CW sources are untested.

The reporting recommendations may or may not be adopted by the LVK.

Code and data availability are not stated explicitly, although the inputs are public and the method is fully specified.

Overall this is a careful, well-presented technical note with moderate practical value for a specialized community, and low-to-moderate expected citation influence.

Rating:4.5/ 10

Significance 4Rigor 6.5Novelty 3.5Clarity 8

Generated Oct 22, 2026

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Scorecard· 16/16

4.5/10 impact

Clean, correct, practically useful refinement of ASAF interpretation, but largely incremental over known radiometer results and confined to a narrow subcommunity.