Evaluating the Prospects of Cyclic Deconvolution across 312 Pulsars

1. Problem Statement

Cyclic spectroscopy is a powerful signal processing technique that utilizes the periodicity of pulsar emission to extract information about the interstellar medium (ISM) and the intrinsic pulse profile. Specifically, it allows for the cyclic deconvolution of the pulse broadening function (caused by ISM scattering) from the intrinsic pulse profile.

However, achieving full cyclic deconvolution is not guaranteed for all pulsars or observing setups. It requires:

1. Sufficient Signal-to-Noise Ratio (S/N) and specific pulse characteristics to achieve a high "cyclic figure of merit" ($m_{cyc}$).
2. Observation within the "full deconvolution regime," defined by specific frequency boundaries where the scintillation bandwidth ($\Delta\nu_d$) is large enough to resolve the pulse structure but small enough to avoid undersampling.

The paper addresses the lack of a comprehensive survey determining which current and future radio telescopes, at which frequencies, are best suited to perform cyclic deconvolution on the known population of millisecond pulsars (MSPs).

2. Methodology

The authors conducted a systematic evaluation of 312 rapidly rotating pulsars (periods $P < 40$ ms) across 15 different telescope-frequency combinations.

• Source Selection: The sample was drawn from the ATNF pulsar catalog and the MeerKAT Pulsar Timing Array (MPTA), including 312 pulsars with measured pulse widths ($W_{50}$ or $W_{10}$).
• Metric Calculation:
  • The study utilized Cyclic Merit 2.0 ($m_{cyc, 2.0}$), a refined metric that estimates the likelihood of recovering the full transfer function. This metric accounts for the scintillation bandwidth ($\Delta\nu_d$) and equivalent pulse width ($W_e$).
  • $S/N$ was calculated using system temperatures, gains, and flux densities, incorporating galactic background noise (via PYGDSM) and Crab Nebula contributions where applicable.
  • Scintillation parameters were derived from NANOGrav data releases, literature measurements, or the NE2001 electron density model.
• Regime Boundaries:
  • Lower Bound: Determined by the condition where the scintillation bandwidth equals the pulsar spin frequency ($\Delta\nu_d \approx 1/P$). Below this, the cyclic spectrum becomes undersampled.
  • Upper Bound: Determined by the condition where the scintillation bandwidth equals the inverse of the intrinsic pulse width ($\Delta\nu_d \approx 1/W_{10}$). Above this, scattering tails become visible, preventing full deconvolution.
• Thresholds: Two thresholds were established for successful deconvolution:
  • Conservative: $m_{cyc} \geq 0.7$
  • Optimistic: $m_{cyc} \geq 0.3$
• Simulations: To project future capabilities, the authors simulated 10 populations of galactic MSPs (mean $\sim$31,400 sources) to estimate how many undiscovered sources could be viable for each instrument.

3. Key Contributions

• Comprehensive Survey: The first large-scale assessment of cyclic deconvolution feasibility across 10 major radio telescopes (GBT, DSA, MeerKAT, FAST, MWA, LWA, LOFAR, NenuFAR, CHIME, uGMRT) and 15 specific observing frequencies.
• Refined Metric Application: Application of the updated Cyclic Merit 2.0 metric to a large population, moving beyond simple phase slope recovery to full transfer function recovery.
• Instrument Ranking: A quantitative ranking of current and future instruments based on the number of viable sources for cyclic spectroscopy.
• Scintillation Analysis: An evaluation of which instruments can resolve scintles (interference patches in dynamic spectra), a prerequisite for studying ISM structure.

4. Key Results

Optimal Frequency Range

The study identifies $\sim$80–300 MHz as the optimal frequency range for achieving cyclic deconvolution across the largest number of pulsars. This range balances the need for high flux density (which increases at lower frequencies) with the requirement that the scintillation bandwidth remains within the full deconvolution regime.

Telescope Performance (Real Sources)

Based on the number of sources passing the conservative threshold ($m_{cyc} \geq 0.7$) while in the full deconvolution regime:

1. uGMRT (upgraded Giant Metrewave Radio Telescope): The clear leader, with 49 viable sources across its 150, 200, and 350 MHz bands. It offers the best combination of sensitivity, sky coverage, and low-frequency capability.
2. LOFAR: The second-best current instrument, with 15 unique viable sources (13 at 150 MHz).
3. MWA (Murchison Widefield Array): Strong performance in the southern hemisphere, with 9 unique viable sources across 150 and 200 MHz.
4. GBT (Green Bank Telescope): While it has fewer total viable sources (2) in the strict regime at 350 MHz, it is highlighted as a critical instrument because it will soon host the world's first real-time cyclic spectroscopy backend (expected late 2026).
5. DSA (Schmidt Sciences): Currently limited by high observing frequencies (800 MHz), but simulations predict it will become the top instrument for cyclic spectroscopy once a larger fraction of the galactic MSP population is discovered.

Notable Sources

• PSR B1937+21: Consistently shows high cyclic merit across all instruments, confirming it as the premier target for cyclic deconvolution.
• Crab Pulsar (PSR B0531+21): Surprisingly high cyclic merit in the 80–300 MHz range for GBT, MWA, LOFAR, and uGMRT. This suggests that some canonical (non-recycled) pulsars with fast spin rates may also be viable for cyclic deconvolution, expanding the potential target list beyond MSPs.
• PSR J1643−1224: Identified as a top candidate for GBT, DSA, and FAST.

Scintillation Resolution

The DSA at 800 MHz is predicted to be superior for resolving scintles (178 sources), followed by uGMRT and FAST. However, the study notes that for many of these high-frequency instruments, most viable sources have likely already been discovered.

5. Significance and Future Outlook

• Gravitational Wave Detection: Successful cyclic deconvolution allows for more precise measurement of scattering delays ($\tau_d$). This directly improves the timing precision of Pulsar Timing Arrays (PTAs), enhancing their sensitivity to nanohertz gravitational waves.
• ISM Science: The technique enables the reconstruction of the "dynamic wavefield," providing unprecedented detail on the structure and turbulence of the interstellar medium along specific lines of sight.
• Call to Action: The authors strongly advocate for the development of near real-time cyclic spectroscopy backends for current and upcoming low-frequency telescopes (specifically uGMRT, LOFAR, MWA, and the DSA). The GBT is already leading this effort; other facilities should follow to maximize the scientific return of the growing MSP population.
• Future Research: The paper suggests investigating faster-spinning canonical pulsars for cyclic deconvolution and utilizing the DSA's future sensitivity to unlock the potential of the undiscovered galactic MSP population.

In summary, this paper provides the roadmap for the next generation of pulsar timing and ISM studies, identifying uGMRT and LOFAR as the current workhorses for cyclic spectroscopy, while positioning the DSA and GBT as critical future assets for unlocking the full potential of this technique.