Search for continuous gravitational waves from the pulsar J0435+3233

Benjamin Steltner; Brian McGloughlin; Heinz-Bernd Eggenstein; Jianping Yuan; Jing Ming; Kartikey Sharma; Maria Alessandra Papa; Na Wang; Reinhard Prix

Search for continuous gravitational waves from the pulsar J0435+3233

T0 review · 0 major / 6 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read A targeted search with LIGO O4a data finds no continuous gravitational waves from the millisecond pulsar J0435+3233; if its spin-down is intrinsic, gravitational waves carry at most 0.5% of the rotational energy loss — the first such limit

desk verdict Solid non-detection and upper limits for J0435+3233, but the headline beat of the spin-down limit by >10x is conditional on an external assumption the authors themselves flag. read the letter →

arxiv 2607.18219 v2 pith:57KYZAE2 submitted 2026-07-20 gr-qc astro-ph.HE

Brian McGloughlin , Jing Ming , Maria Alessandra Papa , Kartikey Sharma , Reinhard Prix , Benjamin Steltner , Heinz-Bernd Eggenstein , Na Wang

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Jianping Yuan

This is my paper · ORCID

classification gr-qcastro-ph.HE

keywords continuousgravitationalwavesmillisecondpulsarJ0435+3233targetedsearchF-statisticspin-downlimitellipticityr-mode

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper searches for continuous gravitational waves from the millisecond pulsar J0435+3233, whose unusually large spin-down makes it a potentially strong emitter. Using LIGO O4a data and a coherent matched-filter search, it finds no signal. The most stringent 95% upper limit on the wave amplitude is 5.8×10^-27, corresponding to a neutron-star ellipticity below 1.6×10^-8 at an assumed distance of 1.2 kpc. Provided the observed spin-down is entirely intrinsic, gravitational waves would carry at most 0.5% of the rotational energy being lost — the first time any millisecond pulsar has beaten the spin-down limit by more than a factor of ten.

What carries the argument

The search rests on the multi-detector F-statistic, a maximum-likelihood matched filter for quasi-monochromatic signals whose phase follows a Taylor expansion in gravitational-wave frequency up to fifth order. The parameter space is shrunk by using precisely measured spin, astrometric, and binary orbital parameters, so the targeted f = 2ν search needs a single template; the narrow-band and r-mode searches add grids over frequency and first and second derivatives. The physical yardstick is the spin-down limit, h0^sd — the amplitude gravitational waves would need to carry away all observed rotational energy loss — and the paper also converts strain limits to ellipticity via the standard quadru

What would settle it

A multi-year timing campaign measuring the orbital-period derivative or the companion's radial acceleration: if it shows that dynamical acceleration from a third body provides most of the observed -4.77×10^-12 Hz/s spin-down, then the spin-down limit shrinks by roughly a factor of 66 and the paper's 'first >10× beat' claim is false, although the h0 and ellipticity upper limits remain valid.

Watch

Extended reading notes

Core claim

On the paper's own terms, the finding is a non-detection with unusually strong astrophysical consequences. For a signal locked to twice the spin frequency, the search returns 2F ≈ 2.74, consistent with noise, and the narrow-band and r-mode searches show no outlier. Injecting fake signals into the same cleaned data yields a 95% upper limit of h0 = 5.8×10^-27 on the intrinsic strain amplitude; at 1.2 kpc and Izz = 10^38 kg m^2 this corresponds to an ellipticity below 1.6×10^-8. Comparing with the spin-down limit of about 8×10^-26, the upper limit is ≈14 times smaller, meaning gravitational waves would remove at most 0.5% of the observed rotational-energy loss. The authors identify this as the

Load-bearing premise

The central comparison assumes that the measured spin-down of -4.77×10^-12 Hz/s reflects the star's own rotational slowing, not acceleration from a possible third companion; if most of it is kinematic, the spin-down-limit beat evaporates.

Editorial extensions

If this is right

An ellipticity upper limit of 1.6×10^-8 at 95% confidence excludes all but very small non-axisymmetric deformations of this neutron star.
If the spin-down is intrinsic, gravitational waves remove at most 0.5% of the rotational energy loss, so the spin-down torque must be dominated by electromagnetic or particle emission.
This is the first millisecond-pulsar targeted search to beat the spin-down limit by more than an order of magnitude, a substantial step beyond earlier ms-pulsar comparisons that reached only roughly the spin-down value.
The r-mode upper limits reach the predicted saturation-amplitude scale around 10^-5, making this the most restrictive targeted r-mode search for a known pulsar reported so far.
The excluded range of crustal anisotropy, computed as a function of crust-formation spin frequency, tightens constraints on the maximum size of crust-supported mountains in recycled pulsars.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If a third-body acceleration is confirmed by timing, the intrinsic spin-down could be as small as ~10^-15 Hz/s, shrinking the spin-down limit by about 66× and invalidating the 'first >10× beat' claim; the strain and ellipticity bounds would still stand.
The differential-rotation-aware r-mode band construction introduced here could be applied to other fast, high-spin-down pulsars, where conventional r-mode searches may miss the lowest-frequency emission.
Coherently including data from the rest of the fourth observing run could push the strain upper limit lower still, providing a direct test of whether the 0.5% energy-fraction bound tightens further.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The thing to know: this is a careful, standard targeted CW search for a newly discovered millisecond pulsar, and the non-detection result is solid. The h0 upper limit of 5.8e-27 and the ellipticity limit of 1.6e-8 are well supported by the F-statistic analysis with injection-based efficiency calibration on real O4a data. The r-mode band search is also a genuine step forward, first to include the differential-rotation correction κ3, and the resulting alpha upper limit of 1.7e-5 is the tightest from a targeted search.

What's new: first CW search for J0435+3233, and the r-mode treatment. The paper does the right things: uses an external timing solution, propagates uncertainties carefully, checks the 2F distributions against noise, and reports upper limits in sub-bands with lines accounted for.

The soft spot is the spin-down limit comparison, which drives the 'first source beaten by over an order of magnitude' claim and the 0.5% energy-budget statement. That comparison assumes the observed spin-down (-4.77e-12 Hz/s) is entirely intrinsic. The paper says so explicitly in Section 2 and the Conclusions, and even considers the alternative: if |ν-dot| is ~1e-15 Hz/s due to a hierarchical triple, the spin-down limit drops by ~66 and the limit sits above it. So the headline significance is conditional on an external astrophysical assumption that this analysis cannot test. That doesn't undermine the non-detection or the amplitude/ellipticity limits, but readers need to see the condition, and the abstract's 'If the observed spin-down is all intrinsic' does state it, though the 'first source' phrasing is easy to misread.

Minor issues: the 'smaller greater than' typo in the ellipticity sentence, and the ambiguous 'first source' – first millisecond pulsar? First pulsar? Worth cleaning up.

Bottom line: this is a solid, honest paper. The h0 and ellipticity upper limits are the real results; the spin-down limit beat is a conditional but well-flagged bonus. It deserves a serious referee and, with a revision that tightens the framing, is publishable. I'd happily cite the r-mode differential rotation treatment and the limits.

Referee Report

0 major / 6 minor

Summary. This paper presents a continuous gravitational-wave search for the millisecond pulsar J0435+3233 using LIGO O4a public data from Hanford and Livingston. Three template banks are used: a single-template search at exactly 2ν, a narrow-band search around 2ν with ~4×10^9 templates, and an r-mode band search centered on 4ν/3 with ~10^11 templates. No significant signal is found; the 95% upper limit from the targeted search is h0 = 5.8×10^-27, translating to an ellipticity bound ε < 1.6×10^-8 at d = 1.2 kpc and Izz = 10^38 kg m^2. The narrow-band and r-mode searches yield consistent non-detections. Under the explicit assumption that the observed spin-down is entirely intrinsic, the targeted upper limit is ~14 times below the spin-down limit, implying that gravitational waves carry at most 0.5% of the spin-down power; the authors note that a hierarchical triple companion could invalidate this interpretation.

Significance. The non-detection and the associated upper limits are technically sound and represent a useful addition to the targeted-CW literature. The analysis follows established methods: a coherent F-statistic with an external radio timing model, phase-metric template placement, and injection-based efficiency measurements on real data, with trials factors automatically included in the loudest-event upper limits. The ellipticity bound of <1.6×10^-8 is competitive with the best pulsar ellipticity constraints, and the r-mode amplitude and crustal-anisotropy bounds are also of astrophysical interest. The headline 'first source beaten by over an order of magnitude' is conditional on the observed spin-down being intrinsic; the paper discloses this condition explicitly in the abstract and Section 6. The strain and ellipticity upper limits are independent of that assumption. I regard the central result as reproducible from the description: the public data, the cited timing solution, and the cleaning/injection procedures are described in sufficient detail.

minor comments (6)

[Abstract] The phrase 'smaller greater than 1.6×10^-8' is a typo; it should read 'smaller than 1.6×10^-8'. Also, 'constraints' should be 'constrains'.
[Abstract and Introduction (Section 1)] The abstract's 'first source for which the spin-down upper limit is beaten by over an order of magnitude' is ambiguous and appears to conflict with the Introduction, which notes that Crab (0.02) and Vela (0.07) already beat the spin-down limit by more than an order of magnitude. Recommend rephrasing to 'first millisecond pulsar' or 'first source at spin frequency above ~300 Hz' for which this holds, to avoid an apparent overclaim.
[Table 2] The units in the 0.1% metric-mismatch row are formatted inconsistently (e.g., 'Hz/s3' without a superscript, and repeated units in the f^(3) column). Please standardize the table formatting.
[Section 5, first paragraph] The targeted search reports 2F ≈ 2.74 but no p-value or expected background quantile. Although the value is described as consistent with noise, quoting the p-value or the local significance would strengthen the presentation.
[Section 5.1] The text says 'We choose 90% confidence because the estimate of the detection efficiency is more robust than at 95%.' A brief explanation of why (e.g., fewer Monte Carlo injections required, or reduced fluctuations in the efficiency curve) would help the reader assess the trade-off.
[Author list] The author name 'Na W ang' contains an apparent spacing error; it should read 'Na Wang'.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the search parameters come from an external radio timing solution and the upper limits are injection-calibrated; the headline energy-budget claim is explicitly conditional on intrinsic spin-down.

full rationale

The central derivation is self-contained. The gravitational-wave phase model (f=2ν, frequency derivatives, binary orbital parameters) is taken from the external radio timing solution of Q. Wu et al. (2026), not fitted to LIGO data (Secs. 2 and 4.3). The h0 upper limits are obtained by injection-recovery efficiency simulations in real data (Sec. 5.1), so they are not constructed to match the spin-down limit. The comparison to the spin-down limit uses the standard external formula Eq. (19), and the ellipticity bound uses the standard quadrupole formula Eq. (20) with assumed distance and moment of inertia. The paper explicitly flags the one fragile link: Sec. 6 states that the energy-budget conclusions "assume that the observed spin-down is entirely intrinsic; any contribution from kinematic effects, such as radial acceleration due to a third body, would bias the inferred spin-down limit." This is a stated condition on the headline significance, not a hidden circular step. Self-citations (e.g., Steltner et al. 2022 for glitch removal, Fesik & Papa 2020 and Ming et al. 2025 for r-mode context) are auxiliary methodological references and are not used as a uniqueness theorem or as the source of the target result. No equation reduces by construction to its input, and no fitted parameter is renamed as a prediction. Score 1 reflects minor self-citation without load-bearing circularity.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The paper's central outputs are observational upper limits. No new particles or forces are introduced; the chief external inputs are the radio timing solution, the assumed distance, canonical neutron-star parameters, and literature r-mode model ranges. The most significant untested premise is the intrinsic-spin-down assumption, which the authors flag.

free parameters (4)

Source distance d = 1.2 kpc
Adopted from Wu et al. (2026); enters the ellipticity limit Eq. (20) and the spin-down limit linearly; no uncertainty quoted in this paper.
Moment of inertia Izz = 10^38 kg m^2
Canonical pulsar value used in Eq. (20) and Eq. (19); the ellipticity and spin-down limits scale inversely with Izz.
Neutron-star mass/radius for r-mode amplitude = M=1.4 Msun, R=11.7 km (canonical); M=1.17 Msun, R=9.6 km (conservative)
Chosen from the literature (Owen 2010; Martinez et al. 2015; Bauswein et al. 2019) to convert h0 upper limits to r-mode amplitude α via Eq. (21); results depend on these assumed values.
Crustal anisotropy conversion inputs = νK=1200 Hz, m_cr/M=0.01
Adopted canonical values in Eq. (22) to translate the ellipticity limit into a constraint on ⟨ϕ⟩; Section 5.1.

assumptions (6)

domain assumption Gravitational-wave phase follows the radio rotation phase with f=2ν (and derivatives)
Section 3, Eq. (4); the single-template targeted search assumes exact phase-locking; if differential rotation decouples GW and radio phases, this search loses sensitivity (narrow-band search partially mitigates).
domain assumption The Wu et al. (2026) radio timing solution accurately describes the spin and binary orbital phase over the O4a interval
Table 1 parameters are evolved to τ0 and used for all templates; if the timing model is incomplete, the matched filter SNR and resulting upper limits degrade.
domain assumption Observed spin-down is entirely intrinsic for the spin-down-limit comparison
Stated in the Conclusions: 'We emphasize that the energy-budget considerations assume that the observed spin-down is entirely intrinsic'; any kinematic acceleration from a third body would lower the true spin-down and the h_sd benchmark.
standard math Standard F-statistic noise model: 2F follows central chi-squared with 4 dof in stationary Gaussian noise
Section 4.2; the detection significance and noise histograms (Figs. 3-4) are assessed against this model.
domain assumption r-mode frequency model and parameter ranges (κ0, κ2, κ3, νK) from the literature
Appendix A, Eqs. (A1)-(A8); search band boundaries A_eff∈[1.276,1.567], B∈[0,0.195], νK,min=506 Hz, n≥3 are taken from prior r-mode studies and determine the coverage of the r-mode search.
domain assumption Upper-limit injection procedure gives valid confidence statements
Section 5.1: detection efficiency measured by injecting signals into real data; assumes simulated signals are representative and that data cleaning is correctly re-applied.

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Pith. "Pith review of Search for continuous gravitational waves from the pulsar J0435+3233." pith.science (2026). https://pith.science/paper/57KYZAE2

@misc{pith2026260718219,
  author       = {Pith},
  title        = {Pith review of: Search for continuous gravitational waves from the pulsar J0435+3233},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/57KYZAE2}},
  note         = {Machine review of arXiv:2607.18219}
}

abstract

We perform a search for continuous gravitational waves from J0435+3233 using LIGO O4a public data. J0435+3233 is unique among millisecond pulsars as it exhibits an exceptionally large spin-down and marks the first pulsar observed to date with a spin-down larger than $10^{-12}$ Hz/s in the sub $10$ ms spin period range, making it a potentially strong source of continuous gravitational waves. We target signals at exactly twice the rotation frequency, a narrow band around this frequency, and also signals corresponding to r-modes. Our results are consistent with a non-detection. Our most stringent upper limit on the intrinsic gravitational wave amplitude at 95\% confidence is $h_0=5.8\times10^{-27}$. With an estimated source distance of 1.2 kpc this upper limit constraints the ellipticity to be smaller greater than $1.6\times10^{-8}$. If the observed spin-down is all intrinsic, this is the first source for which the spin-down upper limit is beaten by over an order of magnitude and the ellipticity is constrained to the physically very interesting range of the low $10^{-8}$ region.

Figures

Figures reproduced from arXiv: 2607.18219 by the authors.

**Figure 1.** The spin and first spin derivative of Galactic pulsars from the Australia Telescope National Facility catalog (R. N. Manchester et al. 2005). The yellow star shows the uniquely large spin-down rate of J0435+3233 among millisecond pulsars. 3. THE SIGNAL MODEL This search targets quasi-monochromatic continuous gravitational-wave signals as described in P. Jaranowski et al. (1998). The detector response is amplitude… view at source ↗

**Figure 2.** Evolution of the orbital period of J0435+3233 from Q. Wu et al. (2026) (dashed line and uncertainties). We also mark the T Wu p used by Q. Wu et al. (2026) and given in [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Histogram of the maximum 2F results per 1-mHz sub-band for the narrow-band search around 2ν. search is shown in [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4: Histogram of the maximum 2F results per 10-mHz sub-band with fitted noise model for the r-mode search. The p-value of the most significant result is ≈ 0.10 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: , alongside the targeted and narrow-band gravitational wave amplitude upper limits from the search. The targeted search upper limit is a factor of ≈ 14 below the spin-down limit at the 95% confidence level. 624.5 625.0 625.5 626.0 626.5 f (Hz) 10 26 10 25 h 9 5 % 0 Ba…

**Figure 6.** Figure 6: Upper limits on the gravitational wave amplitude from r-modes in 0.5-Hz bands. Upper limits are not set in bands for which 95% detection efficiency could not be achieved, due to the presence of lines, near 420 Hz, 434 Hz and 480 Hz. spinning at a frequency ν and hosti…

**Figure 8.** Figure 8: 95% upper limits on the neutron star crustal anisotropy ⟨ϕ⟩. The gray shaded region corresponds to the ⟨ϕ⟩ values that are excluded by this work. For the Crab pulsar, the constraint on the ratio h UL 0 /hsd 0 reaches ≤ 0.8%, implying that at most ∼ 0.0064% of the avail…

**Figure 9.** Figure 9: The f (1) and f (2) parameter space ranges covered in the r-mode search. The shaded regions show the allowed ranges as a function of gravitational wave frequency f. Panel (a) shows the corresponding range in first frequency derivative f (1), while panel (b) shows the r…

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

On the triple nature of the PSR J0435+3233 system
astro-ph.HE 2026-07 conditional novelty 7.0 of 10

PSR J0435+3233 is a hierarchical triple: its anomalous spin-down is an acceleration artifact from a ~1.2 M⊙ outer companion on a ~70-year eccentric orbit.

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Pith tools

Reviewed August 1, 2026 · model on record in the stance chip above.

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