Wide parameter-space O3 search for continuous gravitational waves from unknown neutron stars in binary systems

This paper presents the first wide parameter-space search for continuous gravitational waves from unknown neutron stars in binary systems using advanced detectors, covering frequencies above 520 Hz and orbital periods under 3 days, which yielded no detections but established the most stringent constraints to date on signal amplitudes, ellipticities, and r-mode amplitudes for such sources.

The Gist

Imagine the universe is filled with a constant, low hum, like the sound of a massive, spinning top that never stops. This is what scientists call a continuous gravitational wave. These waves are ripples in the fabric of space-time, created by neutron stars—tiny, incredibly dense city-sized stars—that are slightly lopsided. As they spin, that wobble sends out a steady signal, much like a lighthouse beam sweeping across the ocean.

However, finding these signals is like trying to hear a single whisper in a hurricane. Most of the time, we don't know exactly where to look, how fast the star is spinning, or if it's dancing around a partner (a binary system).

This paper describes a massive, high-tech "listening party" organized by scientists using the Advanced LIGO detectors. Here is what they did, explained simply:

1. The Search: Looking for a Needle in a Cosmic Haystack

The scientists decided to scan a huge, uncharted area of the "frequency map."

• The New Territory: Previous searches mostly looked at lower-pitched sounds (slower spins). This team pushed the search to much higher pitches, up to 1,000 Hz. Think of it as finally tuning a radio to a high-frequency station that no one had ever checked before.
• The Binary Challenge: Many neutron stars have a partner star they orbit. This adds a layer of complexity, like trying to hear a singer who is also spinning on a merry-go-round. The motion of the orbit changes the pitch of the sound (the Doppler effect), making it harder to find. This search looked for these "singers on merry-go-rounds" with orbital periods as short as 0.2 days (less than 5 hours).

2. The Method: The "Sieve" Strategy

Because the universe is so vast and the data is so huge, they couldn't listen to every second of data with perfect focus (that would take more computer power than exists). Instead, they used a semi-coherent strategy:

• The Rough Sweep: They broke the data into short chunks (15 minutes long) and looked for patterns. This is like using a coarse sieve to catch the big rocks.
• The Fine Filter: When they found a "rock" (a potential signal) in the rough sweep, they went back to that specific spot and looked at it with much higher precision, using longer chunks of data. This is like taking a magnifying glass to the rock to see if it's actually a diamond or just a stone.

3. The Result: Silence, but a Very Important Silence

They did not find any gravitational waves. No new neutron stars were discovered.

However, in science, a "null result" is still a victory if it tells us something important. Because they didn't find anything, they can now say with 95% confidence:

• The "No-Go" Zone: If there are any neutron stars within 100 light-years of Earth spinning faster than 495 Hz, they are not wobbling enough to be detected by our current technology.
• The Limit: They set the strictest rules yet on how "lumpy" these stars can be. If a star is that close and spinning that fast, its shape must be incredibly smooth (flatter than a pancake). If it were any bumpier, we would have heard it.

4. Why This Matters

Even though they didn't find a signal, this paper is a major milestone because:

• We Broke the Ceiling: They successfully searched frequencies twice as high as anyone had before.
• We Covered New Ground: They explored orbital periods (how fast stars orbit each other) that had never been searched with advanced detectors.
• We Proved the Tech Works: They showed that their computer methods can handle the massive complexity of searching for these specific, high-speed, binary stars.

In a nutshell: The scientists turned up the volume on their cosmic radio, scanned a brand-new, high-pitched frequency range for stars dancing in pairs, and found nothing. But by proving that nothing is there, they have drawn a very precise map of where these stars cannot be, narrowing down the search for the next generation of discoveries.

Technical Summary

Technical Summary: Wide Parameter-Space O3 Search for Continuous Gravitational Waves from Unknown Neutron Stars in Binary Systems

Problem and Motivation
Continuous gravitational waves (CWs) from asymmetric, spinning neutron stars remain undetected. While targeted searches for known pulsars and all-sky searches for isolated unknown objects have been conducted, searches for unknown neutron stars in binary systems present a unique computational challenge. The orbital motion of the source introduces additional parameters (orbital period, projected semi-major axis, time of ascension, etc.), significantly expanding the parameter space. Given that binary accretion is a natural mechanism for generating the required quadrupole asymmetry and that approximately half of known pulsars rotating above 25 Hz are in binary systems, expanding the search coverage to these systems is essential. Previous searches were limited by computational constraints, often restricting frequency ranges and orbital periods. This paper addresses the need to explore uncharted regions of the parameter space, specifically targeting higher gravitational-wave frequencies and shorter orbital periods than previously investigated with advanced detectors.

Methodology
The authors conducted a semi-coherent search using public data from the third observing run (O3) of the Advanced LIGO detectors (H1 and L1). The data was cleaned of non-Gaussian noise at 60 Hz harmonics and calibration lines, and short-duration glitches were removed via gating.

• Signal Model: The search utilized the Jaranowski et al. (1998) CW signal model, incorporating intrinsic amplitude parameters ($h_0, \cos \iota, \psi, \phi_0$) and phase-evolution parameters (frequency $f_0$, spin-down $f_1$, sky position, and binary orbital parameters: $P_{orb}, a_p, t_{asc}, \omega, e$).
• Parameter Space: The search covered gravitational-wave frequencies from 50 Hz to 1,000 Hz. To manage computational costs, the orbital parameter space $\{P_{orb}, a_p\}$ was divided into five distinct regions (A through E). Notably, Region E ($P_{orb} \in [0.2, 0.4]$ days, $a_p \in [0.03, 0.12]$ light-seconds) was completely unexplored prior to this work. The search assumed small orbital eccentricities ($e \leq 0.1$) and spin-down limits consistent with the observed binary neutron star population.
• Search Pipeline: The analysis employed the BinarySkyHouF semi-coherent pipeline.
  • Initial Stage: Data was split into $N_{seg} = 31,675$ segments of $T_{seg} = 900$ s. A detection statistic ($2\hat{F}_{AB}$) was calculated using a linear combination of statistics from templates with zero orbital parameters, weighted to track time-frequency patterns including non-zero orbital parameters. The grid spacings were optimized to keep the mismatch below 2%.
  • Follow-up: Candidates were selected based on significance and subjected to a coherent follow-up with $T_{seg} = 2,700$ s. A nested sampling algorithm was used to calculate a detection statistic and a robustness statistic ($\log_{10} \hat{B}_{1;S/GLtL}$) to distinguish astrophysical signals from instrumental lines and noise.
• Validation: Simulated test-signals were injected into the data to calibrate detection thresholds and estimate upper limits. Candidates were vetted against hardware injections and non-Gaussian disturbances.

Key Contributions

1. Extended Frequency Range: This is the first search to cover gravitational-wave frequencies above 520 Hz, extending up to 1,000 Hz. This is significant due to the "recycling" scenario where neutron stars gain angular momentum via accretion, potentially reaching high spin frequencies.
2. Short Orbital Periods: This is the first search using advanced detectors to explore orbital periods lower than 3 days, specifically targeting Region E ($P_{orb} \approx 0.2-0.4$ days).
3. Parameter Space Breadth: The search covers a parameter space approximately four orders of magnitude larger than any previous investigation using Advanced LIGO data.
4. Computational Strategy: The authors utilized a "breadth-first" approach, employing coarser template grids and shorter coherent baselines compared to sensitivity-optimized searches, allowing for the coverage of vast, previously unexplored regions within a fixed computational budget.

Results

• Detection: No astrophysical continuous gravitational wave signals were detected.
• Candidates: From an initial pool of ~127,500 candidates, 15 survived the follow-up vetoes. However, 12 were identified as associated with hardware injections (isolated neutron star signals at specific frequencies), and the remaining 3 were attributed to non-Gaussian disturbances. None were deemed defensible CW signals.
• Upper Limits: The authors established the most stringent constraints to date on the amplitude of such signals.
  • Sensitivity Depth: The average sensitivity depth was determined to be $\langle D_{95\%}^{low} \rangle = 18.1 \pm 1.1$ Hz$^{-1/2}$ (50–500 Hz) and $\langle D_{95\%}^{high} \rangle = 17.1 \pm 0.9$ Hz$^{-1/2}$ (500–1000 Hz).
  • Ellipticity Constraints: For neutron stars within 100 pc rotating faster than ~495 Hz, ellipticities above $5.2 \times 10^{-8}$ are excluded with 95% confidence (assuming $I_{zz} = 10^{38}$ kg m$^2$).
  • r-mode Constraints: For the same distance and rotation rates (> ~740 Hz), r-mode amplitudes above $1.5 \times 10^{-6}$ are excluded.

Significance
The paper claims that this work represents the most extensive search to date for CWs from unknown neutron stars in binary systems. By pushing the frequency limit to 1,000 Hz and exploring orbital periods down to 0.2 days, the search addresses critical gaps in the parameter space where accreting, recycled neutron stars are expected to reside. While no signals were found, the results provide the tightest constraints to date on the ellipticity and r-mode amplitudes of these sources. The authors position this search as a "blueprint" for investigating new, more sensitive datasets, demonstrating the capabilities of state-of-the-art techniques in the challenging high-frequency regime despite the computational scaling ($\propto f_0^5$). The work acknowledges that vast regions of the parameter space remain unexplored, but establishes a framework for future, more sensitive searches.