⚛️ general relativity

Search for continuous gravitational waves from the pulsar J0435+3233

Using LIGO O4a data, researchers conducted a search for continuous gravitational waves from the unique millisecond pulsar J0435+3233, resulting in a non-detection but establishing a stringent upper limit on the gravitational wave amplitude that surpasses the spin-down limit by a factor of approximately 14 and constrains the source's ellipticity to a physically interesting range of low $10^{-8}$ .

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

Published 2026-07-21

📖 4 min read🧠 Deep dive

CC BY 4.0

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

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a vast, silent ocean. For most of human history, we could only see the waves crashing on the surface—the light from stars and galaxies. But in 2015, we finally learned to listen to the ripples in the water itself. These ripples are gravitational waves, invisible distortions in the fabric of space and time caused by the most violent events in the cosmos, like colliding black holes. While we have caught these "tsunamis" from crashing giants, there is a quieter, more persistent sound we are hunting for: a continuous hum. This hum comes from neutron stars—city-sized corpses of dead stars that spin hundreds of times a second. If a spinning neutron star has a tiny bump on its surface, like a microscopic mountain, it should wobble as it spins, sending out a steady, monochromatic tone of gravitational waves. Finding this tone would be like hearing a single, pure note from a cosmic lighthouse, telling us secrets about the strange, super-dense matter inside these stars.

This paper is the story of a hunt for that specific note from a very special lighthouse: a pulsar named J0435+3233. This star is a bit of an oddball. It spins incredibly fast (over 300 times a second) and, more importantly, it is slowing down at a rate that is shockingly high for a star of its age. It's as if a spinning top is losing its speed so fast that it seems to be fighting against an invisible brake. The scientists behind this study wondered: Is this braking caused by the star emitting gravitational waves? If so, the "hum" should be loud enough for our detectors to hear.

The team used data from the LIGO detectors, which are essentially giant, ultra-sensitive ears listening to the universe, to search for this signal. They looked in three different ways: listening for the exact pitch expected from a spinning bump, scanning a slightly wider range of pitches in case the star is a bit wobbly, and listening for a specific type of internal wave (called an r-mode) that could also create a hum.

The result? Silence. The detectors did not hear the hum. However, this silence is actually a massive victory for science. Because the star is slowing down so fast, the scientists calculated how loud the gravitational wave hum would be if that braking were caused entirely by the waves. Their search was so sensitive that they could have heard it if it were there. Since they didn't, they can confidently say the hum is quieter than a specific threshold: an amplitude of $5.8 \times 10^{-27}$ .

This finding is a big deal because it places a strict limit on the "mountains" this star could have. The star's "braking" is so extreme that if it were caused by gravitational waves, the star would need to have a mountain so huge it would be physically impossible for the star's crust to hold it together. By proving the hum is too quiet to be the cause of the braking under the assumption that the braking is intrinsic, the paper tells us that either the star is slowing down for a different reason, or the braking we see is influenced by other factors. The authors note that if the star is actually part of a triple system, a hidden third companion could be tugging on it, creating a "kinematic" effect that mimics rapid braking. If that is the case, the true intrinsic braking might be much slower, and the gravitational wave signal would be even fainter than our current limits. Furthermore, the study sets a new record for how small a "mountain" on a neutron star can be. They calculated that any bump on this star must be smaller than $1.7 \times 10^{-8}$ (a tiny fraction of the star's size). This is the first time a search has been sensitive enough to rule out mountains in a physically interesting range, pushing our understanding of how strong neutron star crusts really are. In short, the star didn't sing, but by listening so carefully, we learned exactly how quiet it must be.

Technical Summary: Search for Continuous Gravitational Waves from Pulsar J0435+3233

Problem and Motivation
Continuous gravitational waves (CWs) are long-lived, nearly monochromatic signals expected from rapidly rotating neutron stars with non-axisymmetric mass quadrupoles (e.g., "mountains") or unstable oscillation modes (r-modes). While transient merger events have been detected, no CW signal has yet been confidently observed. Targeted searches for known pulsars offer the highest sensitivity because electromagnetic timing provides precise phase models, allowing for long, coherent integrations.

The pulsar J0435+3233 presents a unique target for such searches. Discovered recently by the Five-hundred-meter Aperture Spherical radio Telescope (FAST) and identified in gamma rays, it is a millisecond pulsar ( $\nu \approx 312.7$ Hz) exhibiting an exceptionally large observed spin-down rate ( $\dot{\nu} \approx -4.43 \times 10^{-12}$ Hz/s). This spin-down is the largest observed for a pulsar with a spin period under 10 ms. If intrinsic, this implies a high spin-down limit ( $h_0^{sd}$ ), the theoretical maximum amplitude if all rotational energy loss were due to gravitational radiation. The authors posit that J0435+3233 is a prime candidate for detection or for setting stringent constraints on neutron star ellipticity and r-mode amplitudes, potentially surpassing previous limits by an order of magnitude.

Methodology
The authors performed a targeted search for continuous gravitational waves using LIGO O4a public data (Hanford and Livingston detectors) spanning from May 24, 2023, to January 16, 2024. The analysis utilized the coherent multi-detector maximum-likelihood $F$ -statistic, a matched-filter method that maximizes the signal-to-noise ratio over the amplitude parameters while integrating over the observation time.

The search covered three distinct signal models based on the pulsar's parameters derived from FAST timing solutions (Q. Wu et al. 2026):

Targeted Search: Searched exactly at twice the rotation frequency ( $f = 2\nu \approx 625.4$ Hz), assuming the gravitational wave quadrupole rotates synchronously with the radio emission.
Narrow-band Search: Searched a frequency band of $\Delta f \approx 4 \times 10^{-3} \times f$ around $2\nu$ to account for small deviations from the strict phase model.
r-mode Search: Searched for signals at $f \approx 4\nu/3$ (approx. 417 Hz), accounting for corrections due to rapid rotation and differential rotation, which broaden the expected frequency range.

The analysis incorporated the pulsar's binary orbital parameters (an $\approx 8$ -day orbit) and proper motion. The authors evolved the spin and orbital parameters from the reference epoch of the timing solution to the mid-time of the O4a data run. To ensure computational feasibility, the search grid spacings were determined based on phase-metric mismatch calculations (targeting $<0.1\%$ mismatch), resulting in approximately $4 \times 10^9$ templates for the narrow-band search and $10^{11}$ for the r-mode search. Data cleaning involved removing known spectral lines and time-domain glitches.

Key Results
The search yielded no evidence of a continuous gravitational wave signal. The maximum $2\mathcal{F}$ values across all search configurations were consistent with Gaussian noise realizations. Consequently, the authors set upper limits on the intrinsic gravitational wave amplitude ( $h_0$ ) at 90% and 95% confidence levels:

Targeted Search ( $2\nu$ ): $h_0^{95\%} = 5.8 \times 10^{-27}$ .
Narrow-band Search: Mean $h_0^{95\%} = 2.2 \times 10^{-26}$ .
r-mode Search: Mean $h_0^{95\%} = 2.7 \times 10^{-26}$ .

Significance and Constraints
The primary significance of this work lies in the comparison between the observational upper limit and the spin-down limit ( $h_0^{sd}$ ). For J0435+3233, the targeted search upper limit is approximately 14 times lower than the spin-down limit. This represents the first time a targeted search has beaten the spin-down limit by more than an order of magnitude for a millisecond pulsar.

Assuming a source distance of 1.2 kpc and a canonical moment of inertia ( $I_{zz} = 10^{38}$ kg m $^2$ ), these amplitude limits translate into the following physical constraints:

Ellipticity ( $\epsilon$ ): The upper limit constrains the neutron star's ellipticity to $\epsilon < 1.7 \times 10^{-8}$ . This is a physically interesting value, lying in the low $10^{-8}$ region, and implies that if the observed spin-down is entirely intrinsic, gravitational waves carry away less than 0.5% of the lost rotational energy.
r-mode Amplitude ( $\alpha$ ): The search excludes r-mode amplitudes $\alpha > 1.7 \times 10^{-5}$ (canonical case) and $\alpha > 3.5 \times 10^{-5}$ (conservative case) across the search frequency range. These are the tightest constraints on r-mode amplitudes from a targeted search to date, surpassing previous limits for pulsars like J0537−6910 and J0534+2200.
Crustal Anisotropy ( $\langle \phi \rangle$ ): The authors set upper limits on the degree of macroscopic crustal anisotropy as a function of the birth spin frequency, providing new bounds on this parameter which is crucial for modeling neutron star deformations.

The authors note that these constraints rely on the assumption that the observed spin-down is intrinsic. If the large spin-down is partially due to kinematic acceleration (e.g., from a third body in a hierarchical triple system), the intrinsic spin-down limit would be lower, and the constraints on ellipticity would be correspondingly weaker. Nevertheless, the result significantly narrows the parameter space for the physical properties of J0435+3233 and demonstrates the capability of current detectors to probe the physics of rapidly rotating neutron stars beyond the spin-down limit.

More like this