Search for Periodic Radio Signals from Double Neutron Star System Companions Using the Fast Folding Algorithm

Using the Fast Folding Algorithm and the PYSOLATOR resampling code on 272.2 hours of FAST telescope data, researchers searched for periodic radio signals from companions in 13 double neutron star systems but found no new companion signals among 197,962 candidates, despite successfully improving the detection of known pulsars.

The Gist

Imagine the universe as a giant, cosmic dance floor. On this floor, there are pairs of dancers called Double Neutron Star (DNS) systems. These are two incredibly dense, dead stars (neutron stars) locked in a tight, high-speed orbit around each other.

Usually, we can only see one of the dancers. This visible one is often a "recycled" pulsar—a star that has been spun up to incredible speeds by its partner, flashing radio beams like a lighthouse. The other dancer, the companion, is expected to be a "normal" pulsar. It spins much slower and is much dimmer, making it very hard to spot.

This paper is a report from a team of astronomers who used the world's biggest radio eye, the FAST telescope in China, to try and find these hidden, slow-spinning companions.

Here is the story of their search, explained simply:

1. The Problem: The "Spinning Top" Effect

Imagine trying to take a photo of a runner on a track, but the runner is on a merry-go-round that is speeding up and slowing down. If you try to take a long-exposure photo (which is what radio telescopes do to catch faint signals), the runner's image gets blurry because their speed keeps changing relative to you.

In space, the companion star is orbiting its partner. As it moves toward us and then away from us, its radio signal gets stretched and squeezed (like the sound of a passing siren). This "orbital modulation" blurs the signal, making the faint companion invisible to standard search methods.

2. The Solution: The "Fast Folding" Algorithm (FFA)

To find these slow, dim stars, the team used a special tool called the Fast Folding Algorithm (FFA).

• The Old Way (FFT): Imagine trying to find a pattern in a noisy room by listening for a specific frequency. If the person speaking changes their speed, you miss them. This is how older telescopes worked.
• The New Way (FFA): Imagine taking a stack of paper, each with a tiny piece of a sentence written on it. Instead of listening for a frequency, you fold the papers over and over, aligning the words perfectly. Even if the words are faint, once you fold them enough times, the sentence becomes clear. FFA does this with time data. It is much better at finding slow, long-period signals (like the companions) than the old methods.

3. The Secret Weapon: PYSOLATOR

Even with FFA, the "merry-go-round" effect (orbital motion) was still blurring the signals. So, the team used a piece of software called PYSOLATOR.

Think of PYSOLATOR as a time-traveling editor. It takes the messy, wobbling data and mathematically "rewinds" and "fast-forwards" the timeline to cancel out the wobble caused by the orbit. It resamples the data so that, from the telescope's perspective, the companion star appears to be standing still. This removes the blur and sharpens the image.

4. The Hunt

The team looked at 13 different double-star systems in the sky. They gathered over 272 hours of data from the FAST telescope.

• They processed the data to remove the orbital wobble.
• They used FFA to fold the signals and look for patterns.
• They found nearly 200,000 potential candidates (false alarms).

The Result: After checking every single candidate carefully, they found no new companion signals.

5. Why Didn't They Find Them?

Don't worry, this isn't a failure! Here is why they came up empty-handed, using a few metaphors:

• The "Flashlight" Problem: Neutron stars don't shine in all directions; they have a narrow beam, like a laser pointer. If the beam isn't pointing at Earth, we can't see it. The companions might be spinning so slowly that their beams are incredibly narrow (like a laser vs. a floodlight). If they are pointing away from us, they are invisible.
• The "Spinning Top" (Geodetic Precession): General Relativity predicts that these stars wobble like a spinning top as they orbit. Over time, this wobble changes the direction of their radio beams.
  • Some companions might have been visible in the past but have now wobbled out of our view.
  • Others might be invisible now but will wobble back into view in the future (like a lighthouse that only flashes once a year).
• The "Blur" Issue: For one specific system (J1946+0746), the team realized their "time-travel editor" (PYSOLATOR) wasn't quite precise enough. The star's orbit was so complex that the data was still slightly blurry. They suspect that if they use a different method, they might find it next time.

The Takeaway

Even though they didn't find a new companion, this paper is a success story for methodology.

1. They proved that combining FFA (the folding tool) with PYSOLATOR (the time editor) is a powerful way to hunt for these hidden stars.
2. They showed that the FAST telescope is sensitive enough to find these faint signals if the stars are pointing at us.
3. They identified specific systems (like J1906+0746 and J1946+2052) where the "wobble" might bring a companion into view in the coming years.

In short: They built a better net and a sharper lens, cast it into the ocean, and didn't catch the specific fish they were looking for yet. But they proved the net works, and they know exactly where to cast it again in the future when the fish might swim into view.

Technical Summary

Here is a detailed technical summary of the paper "Search for Periodic Radio Signals from Double Neutron Star System Companions Using the Fast Folding Algorithm."

1. Problem Statement

Double Neutron Star (DNS) systems are critical laboratories for testing gravitational theories and understanding binary evolution. While most known DNS systems contain one observed recycled pulsar, theoretical models suggest the companion should be a normal, long-period pulsar. However, these companions remain undetected in most systems, likely due to:

• Long Spin Periods: They often have periods ($P$) significantly longer than recycled pulsars, making them difficult to detect with standard Fast Fourier Transform (FFT) pipelines which lose sensitivity to long-period, low-duty-cycle signals.
• Orbital Modulation: The orbital motion of the binary induces Doppler shifts and phase smearing, which degrades the signal-to-noise ratio (S/N) in long-duration observations if not corrected.
• Geodetic Precession: The spin axis of the companion may precess, causing the radio beam to point away from Earth for extended periods.

The primary goal of this study was to search for these elusive companion signals in 13 known DNS systems within the sky of the Five-hundred-meter Aperture Spherical radio Telescope (FAST) using a methodology optimized for long-period signals and orbital correction.

2. Methodology

The authors developed a specialized search pipeline combining time-domain resampling with the Fast Folding Algorithm (FFA).

• Data Collection:

  • Source: 13 DNS systems (12 confirmed, 1 candidate) in the FAST sky.
  • Instrument: FAST 19-beam receiver (1.05–1.45 GHz).
  • Volume: 272.2 hours of observational data across 245 observation sessions.
  • Preprocessing: Data was processed using PRESTO (RFI masking, dedispersion). Eleven dedispersed time series were generated per observation to cover DM uncertainties.

• Orbital Correction (PYSOLATOR):

  • To mitigate orbital smearing, the code PYSOLATOR was employed.
  • It removes orbital modulation by subtracting the predicted Roemer delay and resampling the time series to the binary barycenter.
  • For systems lacking precise mass/inclination measurements, canonical masses ($1.35 M_{\odot}$) were assumed.
  • Special Case (PSR J1946+0746): Due to relativistic spin precession changing the pulse profile shape (single to double peak), a new timing solution was derived using FAST data (2019–2023) to ensure accurate orbital removal.

• Signal Search (FFA):

  • The Fast Folding Algorithm (FFA) was used via the RIPTIDE package.
  • Advantage over FFT: FFA performs phase-coherent folding in the time domain, making it superior for detecting long-period ($0.001 - 60$ s) and low-duty-cycle signals where FFT sensitivity drops due to red noise and limited harmonic summation.
  • Threshold: Candidates with $S/N \geq 7$ were selected for manual inspection.

3. Key Contributions

• Pipeline Integration: Successfully integrated PYSOLATOR (for orbital de-modulation) with FFA (for long-period sensitivity) specifically for DNS companion searches.
• Timing Refinement: Produced a high-precision timing solution for PSR J1946+0746, updating its orbital parameters and confirming a total system mass of $2.54(3) M_{\odot}$.
• Sensitivity Analysis: Demonstrated that the combined PYSOLATOR+FFA approach increases the S/N of known pulsar signals by at least 30% compared to uncorrected data. In one case (PSR B2127+11C), the companion signal was only detectable after orbital removal and FFA application.
• Geodetic Precession Modeling: Highlighted the role of geodetic precession in the visibility of companions, identifying specific systems (e.g., J1906+0746, J1946+0746, B2127+11C) where future observations may yield detections as precession brings the beam back into view.

4. Results

• Companion Detection: Zero companion signals were detected among the 197,962 candidates generated from the 13 systems.
• Validation: The method successfully recovered known pulsar signals with improved S/N. For example, the S/N for PSR B1913+16 increased from 227.0 to 1589.7 after resampling.
• Non-Detection Analysis: The lack of companion detections is attributed to:
  1. Narrow Beams: Companions likely have long spin periods and narrow beam opening angles ($\rho \propto P^{-0.5}$), reducing the probability of Earth-intersection.
  2. Precession: Geodetic precession may have tilted the companion's beam away from Earth.
  3. Timing Residuals: For J1946+0746, residual timing errors may still cause phase drift, potentially masking the companion; alternative methods (FFT or spectral stacking) might be required for this specific target.

5. Significance and Future Work

• Methodological Validation: The study confirms that FFA, when coupled with precise orbital resampling, is the optimal strategy for searching for long-period companions in compact binaries, outperforming traditional FFT-based acceleration searches.
• Future Targets: The authors identify PSR J1906+0746 and PSR J1946+0746 as high-priority targets for future "double pulsar" discoveries due to their high geodetic precession rates ($2.17^{\circ}$/yr and$7.96^{\circ}$/yr, respectively), which may bring their companion beams into alignment in the coming years.
• Next Steps: The team plans to:
  • Search for single pulses from companions to bypass period uncertainties.
  • Analyze newly discovered DNS systems (e.g., J1953+1847D in M71) once archival data becomes available.
  • Apply this pipeline to historical archival data from other telescopes (e.g., pre-2008 data for J0737-3039) to test the limits of the method.

In conclusion, while no new companions were found, the paper establishes a robust, high-sensitivity framework for future searches that could lead to the discovery of the second double pulsar system.