Search for continuous gravitational waves from neutron stars in five globular clusters in the first part of the fourth LIGO-Virgo-KAGRA observing run

This paper reports the results of a directed search for continuous gravitational waves from unknown neutron stars in five Milky Way globular clusters using LIGO-Virgo-KAGRA data from the first eight months of the fourth observing run, finding no detections but setting the most sensitive upper limits to date across most of the explored parameter space.

The Gist

Imagine the universe is a giant, dark ocean. For decades, scientists have been trying to hear a specific, faint sound coming from deep within that ocean: the hum of a spinning neutron star. These stars are the dense, dead cores of massive stars, and if they have a tiny "bump" or wobble on their surface, they should emit a continuous, steady ripple in space-time called a gravitational wave.

However, these ripples are incredibly faint—like trying to hear a whisper in a hurricane.

This paper is a report from a team of scientists who went on a massive "listening expedition" to five specific neighborhoods in our galaxy called globular clusters. These clusters are like cosmic apartment buildings packed so tightly with stars that they are chaotic and crowded. The scientists hoped that in these crowded places, old neutron stars might get bumped around, develop new wobbles, and start "singing" loudly enough to be heard.

Here is the story of their search, broken down simply:

1. The Listening Post (The Data)

The scientists used the LIGO detectors (two giant "ears" in the US) to listen to the universe. They focused on data collected over eight months in 2023–2024. Think of this as recording 8 months of static from a radio, hoping to find a hidden song in the noise.

2. The Target List (The Neighborhoods)

They didn't listen to the whole galaxy; they picked five specific globular clusters: Terzan 10, NGC 104, NGC 6397, NGC 6544, and NGC 6540.

• Why these? Imagine you are looking for a lost coin. You wouldn't search the whole beach; you'd search where people usually drop things. These clusters are "high-traffic" areas where stars bump into each other, potentially creating the conditions for a neutron star to start spinning wildly and emitting waves.

3. The Search Method (The "Weave" Net)

Searching for these waves is like looking for a needle in a haystack, but the haystack is moving, and the needle might be changing shape.

• The Problem: If they tried to listen to every single second of data at once, the computer would explode from the sheer amount of math.
• The Solution: They used a clever software tool called Weave. Imagine the 8 months of data as a giant tapestry. Instead of looking at the whole thing at once, they cut the tapestry into small, manageable strips (7.5 days long). They analyzed each strip individually, looking for a signal, and then "wove" the results back together to see if a pattern emerged across the whole 8 months.

4. The Results (The Silence)

After running millions of calculations and filtering out the "static" (like the hum of the Earth's magnetic field or vibrations from nearby trucks), the result was... silence.

• No Signal Found: They did not detect any gravitational waves from these five clusters.
• The Veto: In one specific case, they thought they found a loud signal, but when they looked at the raw data, they realized it was just a glitch in the machine (an "instrumental line"), not a star.

5. Why This Matters (The "Upper Limits")

You might think, "If they didn't find anything, what's the point?"
Actually, this is a huge success. Here is the analogy:
Imagine you are trying to find a ghost in a house. You look everywhere, and you don't see one. You can't say, "There are no ghosts." But you can say, "If there were a ghost, it would have to be smaller than a dust mote to have escaped our notice."

In this paper, the scientists set strict limits on how "loud" a neutron star could be without them hearing it.

• They found that if a neutron star in these clusters is wobbling, it must be wobbling less than a specific tiny amount (measured as a strain of about $4.2 \times 10^{-26}$).
• This is the most sensitive search ever done for these specific targets. They have effectively ruled out the possibility of "loud" wobbling stars in these clusters.

6. The Future

This is just the beginning. The detectors are getting better (like upgrading from a tin can phone to a high-end microphone).

• The Promise: Even though they didn't find a signal this time, they have mapped out exactly where to look next and how quiet the universe is in these regions.
• The Goal: As the detectors improve, they will be able to hear even the faintest whispers. One day, they hope to catch that first continuous hum from a spinning neutron star, which would open a brand new window into how these extreme objects work.

In a nutshell: The scientists cast a massive, high-tech net into five crowded star clusters. They didn't catch a fish this time, but they proved their net is the finest ever made, and they now know exactly how small the fish would have to be to slip through the holes. The search continues!

Technical Summary

Here is a detailed technical summary of the paper "Search for continuous gravitational waves from neutron stars in five globular clusters in the first part of the fourth LIGO–Virgo–KAGRA observing run."

1. Problem and Motivation

Continuous gravitational waves (CWs) are faint, long-duration, quasi-monochromatic signals expected from rapidly rotating, non-axisymmetric neutron stars (NSs). Despite extensive searches, no CWs have been detected to date.

• Target Selection: Globular Clusters (GCs) are prime targets due to their high stellar densities, which facilitate dynamical interactions. These interactions can:
  1. Trigger bombardment of old, annealed NSs by debris disks or planets, inducing new non-axisymmetries and high spin-down rates (mimicking "young" stars).
  2. Form millisecond pulsars (MSPs) via binary accretion, which may later be disrupted to leave isolated, fast-spinning MSPs.
• The Challenge: Fully coherent searches over long observation periods are computationally intractable due to the vast parameter space (frequency, spin-down, sky position). Semi-coherent methods are required to balance sensitivity and computational cost.
• Objective: This study aims to perform directed searches for unknown NSs in the central regions of five specific GCs using data from the first eight months of the fourth LIGO-Virgo-KAGRA (LVK) observing run (O4a).

2. Methodology

Data Set

• Observing Run: O4a (May 24, 2023 – January 16, 2024).
• Detectors: LIGO Hanford (H1) and LIGO Livingston (L1). The Virgo and KAGRA detectors were not included as they joined the run later or were scheduled for the end.
• Data Quality: Only science-mode data was used (duty factors ~69% for L1, ~67.5% for H1). Data underwent cleaning to remove instrumental "lines" and "glitches" (short transients) using a gating algorithm.
• Frequency Band: 20 Hz to 475 Hz. The lower bound avoids seismic noise; the upper bound avoids "violin modes" (resonances of suspension fibers) and their non-linear sidebands.

Target Selection

Five GCs were selected based on two figures of merit (FoM) estimating the likelihood of hosting detectable CW sources:

1. $\Gamma^{1/2}d^{-1}$: Proportional to the number of "young" NSs formed by bombardment (depends on core density $\rho_c$, core radius $r_c$, and distance $d$).
2. $\gamma^{1/2}d^{-1}$: Proportional to the population of isolated MSPs formed via binary disruption (depends on binary encounter rate).

• Selected Targets: Terzan 10, NGC 104 (47 Tuc), NGC 6397, NGC 6544, and NGC 6540.
• Search Scope: The search covered the core radius ($r_c$) for Terzan 10 and NGC 104, and the tidal radius ($r_t$) for the others, to maximize source coverage.

Signal Model and Search Strategy

• Signal Model: The search assumes a signal phase $\Phi(t)$ expanded to the second order (frequency $f$, spin-down $\dot{f}$, and second derivative $\ddot{f}$). The search range for $\dot{f}$ and $\ddot{f}$ was defined by assuming a power-law spin-down model ($\dot{f} \propto -f^n$) with braking indices $n \in [2, 7]$ and a minimum source age of 300 years.
• Detection Statistic: The $\mathcal{F}$-statistic (Jaranowski et al. 1998) was used, which analytically marginalizes over unknown amplitude parameters (inclination, polarization, phase).
• Semi-coherent Approach (Weave):
  • The total observation time ($T_{obs} \approx 8$ months) was divided into $N_{seg} = 32$ coherent segments of $T_{coh} = 7.5$ days.
  • The Weave infrastructure was employed to map a fine semi-coherent grid to coarser segment grids, summing the $\mathcal{F}$-statistic values incoherently.
  • Mismatch Parameters: Coherent mismatch $m_{coh} = 0.1$ and semi-coherent mismatch $m_{semi} = 0.2$.
• Follow-up Procedure:
  1. Initial Search: Identified outliers exceeding a statistical threshold (based on a $\chi^2$ distribution) in 1-Hz bands.
  2. Hierarchical Follow-up: Surviving candidates were clustered and followed up in stages with increasing coherence time ($15, 30, 60, 120$ days).
  3. Validation: Candidates were vetted using spectrograms to identify instrumental artifacts. For Terzan 10 (largest angular radius), a 9-point sky grid was used in the first follow-up stage to mitigate signal loss from off-center sources.

3. Key Contributions

• First Directed Searches: This is the first directed CW search for Terzan 10 and NGC 104.
• Improved Sensitivity: The analysis covers a spin-down parameter space 1–2 orders of magnitude broader than previous searches (e.g., Dunn et al. 2025) while achieving 30–40% better strain sensitivity in the 100–475 Hz band.
• Age-Based Limits: The search sensitivity surpasses the "age-based" upper limit (assuming all rotational energy loss is GW emission) for sources younger than 50 kyr across all frequencies > 100 Hz.
• Comprehensive Constraints: The study provides the most stringent constraints to date on NS ellipticity ($\epsilon_0$) and r-mode amplitude ($\alpha_0$) for these specific targets.

4. Results

• No Detection: No statistically significant CW signal was detected in any of the five targets. All surviving candidates after the 4th follow-up stage (up to 120 days coherence) were identified as instrumental artifacts or noise outliers.
• Upper Limits:
  • Strain Amplitude ($h_0$): 95% confidence level upper limits were set for each 1-Hz band. The most sensitive limits reached $\sim 4.2 \times 10^{-26}$ near 282 Hz for NGC 6397.
  • Sensitivity Depth: The average sensitivity depth ($\mathcal{D}$) over 50–475 Hz ranged from 69.8 to 89.3 Hz$^{-1/2}$, with NGC 104 and NGC 6397 showing the highest depths.
  • Degradation Note: For targets with larger search radii (e.g., Terzan 10), upper limits degraded at higher frequencies due to the use of a single central sky template, which causes signal-to-noise ratio (SNR) loss for off-center sources.
• Astrophysical Constraints:
  • Ellipticity ($\epsilon_0$): Limits reached values below $10^{-5}$, entering the regime of theoretically predicted maximum ellipticities ($\sim 10^{-6}$to$10^{-4}$).
  • R-mode Amplitude ($\alpha_0$): Limits approached the theoretical maximum of $\sim 10^{-3}$.

5. Significance

This paper represents a significant step forward in the search for continuous gravitational waves from globular clusters. By leveraging the improved sensitivity of the O4a run and the computational efficiency of the Weave semi-coherent method, the authors have:

1. Excluded a vast volume of parameter space for unknown NSs in these clusters.
2. Set the new standard for sensitivity in directed GC searches, outperforming previous O3-based results by a substantial margin.
3. Provided critical constraints on the internal physics of neutron stars (deformation and r-modes), pushing the limits of detectability closer to theoretical predictions.
4. Demonstrated the viability of searching for "rejuvenated" old neutron stars and disrupted MSPs, validating the dynamical formation scenarios in dense stellar environments.

The results pave the way for future searches with even greater sensitivity as the LVK detectors continue to improve, bringing the community closer to the first detection of continuous gravitational waves.