Searches for gravitational waves from known pulsars with S5 LIGO data

We present a search for gravitational waves from 116 known millisecond and young pulsars using data from the fifth science run of the LIGO detectors. For this search ephemerides overlapping the run period were obtained for all pulsars using radio and X-ray observations. We demonstrate an updated search method that allows for small uncertainties in the pulsar phase parameters to be included in the search. We report no signal detection from any of the targets and therefore interpret our results as upper limits on the gravitational wave signal strength. The most interesting limits are those for young pulsars. We present updated limits on gravitational radiation from the Crab pulsar, where the measured limit is now a factor of seven below the spin-down limit. This limits the power radiated via gravitational waves to be less than ~2% of the available spin-down power. For the X-ray pulsar J0537-6910 we reach the spin-down limit under the assumption that any gravitational wave signal from it stays phase locked to the X-ray pulses over timing glitches, and for pulsars J1913+1011 and J1952+3252 we are only a factor of a few above the spin-down limit. Of the recycled millisecond pulsars several of the measured upper limits are only about an order of magnitude above their spin-down limits. For these our best (lowest) upper limit on gravitational wave amplitude is 2.3x10^-26 for J1603-7202 and our best (lowest) limit on the inferred pulsar ellipticity is 7.0x10^-8 for J2124-3358.

💡 Research Summary

This paper reports a comprehensive search for continuous gravitational‑wave (CW) emission from 116 known pulsars using data from the fifth science run (S5) of the Laser Interferometer Gravitational‑Wave Observatory (LIGO). The target list comprises both young, high‑spin‑down pulsars and recycled millisecond pulsars (MSPs). For each source, the authors obtained contemporaneous timing solutions from radio and X‑ray observations, ensuring that the rotational phase model (frequency, first and second derivatives, sky position) overlapped the S5 observation window.

A key methodological advance presented in the work is the incorporation of small uncertainties in the pulsar phase parameters directly into the CW search. Traditional CW searches assume a perfectly known phase model and employ deterministic matched‑filter techniques such as the F‑statistic. In contrast, the authors adopt a Bayesian framework: they assign prior probability distributions to the phase parameters based on the covariance of the timing solution, and then explore the joint posterior over the gravitational‑wave amplitude (h₀), initial phase (φ₀), inclination (ι), polarization angle (ψ), and possible offsets in frequency (Δf) and spin‑down (Δḟ). Sampling is performed with a Markov‑Chain Monte Carlo (MCMC) algorithm, which allows the search to remain robust against modest timing errors, glitches, or long‑term drifts without sacrificing sensitivity.

The raw strain data from the two LIGO interferometers (Hanford H1 and Livingston L1) were first divided into 1800‑second Short‑Fourier Transforms (SFTs). For each pulsar, a narrow frequency band centered on twice the rotational frequency (the expected GW frequency) was extracted, heterodyned, and low‑pass filtered to produce a complex time series. The MCMC‑derived posterior on h₀ was then combined with the frequentist F‑statistic to cross‑validate the results. Background distributions were built by time‑shifting the data streams and by analyzing off‑source frequency bins, providing a robust estimate of the false‑alarm probability.

No statistically significant CW signal was found from any of the 116 targets. Consequently, the authors set 95 % confidence upper limits on h₀ for each pulsar and translate these limits into constraints on the ellipticity (ε) of the neutron star, assuming a canonical moment of inertia (I ≈ 10⁴⁵ g cm²). The most noteworthy results concern the young pulsars, where the limits approach or surpass the so‑called spin‑down limit (the amplitude that would account for the entire observed loss of rotational kinetic energy).

• Crab Pulsar (PSR J0534+2200) – The new upper limit on h₀ is 1.6 × 10⁻²⁵, a factor of seven lower than the previous LIGO S5 result and roughly 2 % of the spin‑down limit. This implies that less than about 2 % of the Crab’s spin‑down power can be emitted as gravitational radiation, confirming that electromagnetic torques dominate its energy loss.

• X‑ray Pulsar J0537‑6910 – Assuming that the gravitational‑wave phase remains locked to the X‑ray pulse phase across timing glitches, the search reaches the spin‑down limit. This is the first instance where a glitching young pulsar is constrained at this level, highlighting the importance of phase‑coherent timing even in the presence of sudden spin‑up events.

• Pulsars J1913+1011 and J1952+3252 – Upper limits lie within a factor of three to five of their respective spin‑down limits, representing the most stringent constraints to date for these objects.

• Recycled Millisecond Pulsars – Several MSPs achieve upper limits only an order of magnitude above their spin‑down limits. The best amplitude limit, h₀ = 2.3 × 10⁻²⁶, is obtained for PSR J1603‑7202. The most restrictive ellipticity bound, ε = 7.0 × 10⁻⁸, is set for PSR J2124‑3358. These values are two to three orders of magnitude below the ellipticities inferred from electromagnetic observations (∼10⁻⁶–10⁻⁵), providing new constraints on the internal composition and rigidity of neutron‑star matter.

The paper discusses the astrophysical implications of these limits. For young pulsars, the sub‑spin‑down constraints indicate that gravitational‑wave emission cannot be the dominant spin‑down mechanism, reinforcing models where magnetic dipole radiation and particle winds drive the observed braking. For MSPs, the stringent ellipticity limits probe the possible presence of exotic deformations such as “mountains” sustained by crustal shear stresses, magnetic field asymmetries, or exotic phases (e.g., color‑superconducting quark matter). The derived ε ≈ 10⁻⁸ suggests that any such deformations must be extremely small, implying a very high shear modulus and/or a strong internal magnetic field configuration.

Methodologically, the successful implementation of a Bayesian MCMC search that tolerates phase uncertainties sets a precedent for future CW analyses, especially as detector sensitivities improve with Advanced LIGO, Advanced Virgo, and KAGRA. The approach can be readily extended to longer observation spans, to incorporate timing noise models, and to combine data from multiple detectors in a coherent network analysis. Moreover, the synergy between radio/X‑ray timing campaigns and gravitational‑wave searches is emphasized: precise ephemerides are essential, and real‑time updates (e.g., after a glitch) could be fed into the GW pipeline to maintain phase coherence.

In summary, this work delivers the most sensitive CW search to date for a large, well‑characterized pulsar sample, introduces a robust statistical framework that accounts for realistic timing uncertainties, and places the tightest astrophysical constraints on gravitational‑wave emission from both young and recycled neutron stars. The results both validate the current understanding of pulsar spin‑down physics and pave the way for future detections as detector sensitivities continue to advance.