The NANOGrav 15 yr and 20 yr Datasets: Timing Events and Pulse Shape Changes

1. Problem Statement

Pulsar Timing Arrays (PTAs), such as NANOGrav, rely on the extreme stability of millisecond pulsar (MSP) pulse profiles to detect nanohertz gravitational waves. While pulse shapes are typically stable over decades, sudden, discrete changes in pulse morphology ("pulse shape change events") can introduce significant timing noise, mimicking or obscuring the gravitational wave background (GWB) signal.

Previous studies identified four such events in two NANOGrav pulsars (PSR J1713+0747 and PSR J1643−1224), but a systematic method to detect, characterize, and rank these events across the entire PTA sample was lacking. The challenge lies in distinguishing true astrophysical pulse shape changes from instrumental artifacts, single-epoch outliers, and intrinsic long-term variability (e.g., scattering).

2. Methodology

The authors developed a novel detection framework combining Principal Component Analysis (PCA) and matched filtering to identify "Fast Rise, Exponential Decay" (FRED) pulse shape events.

• Data Sample: The study analyzed nine NANOGrav pulsars, including the 15-year dataset and extended data for PSR J1713+0747 and PSR B1937+21. The sample included known event hosts, high-stability baselines (PSR J1909−3744, PSR J2234+0611), and pulsars with known scattering or intra-epoch variability.
• Preprocessing:
  • Pulse profiles were aligned via template matching and normalized.
  • Profiles were zeroed outside the central 50% of the pulse phase.
  • Data was sub-averaged into 100 MHz frequency bins to analyze chromaticity.
  • Signal-to-Noise (S/N) cutoffs were applied per pulsar to ensure sufficient data quality for PCA.
• Principal Component Analysis (PCA):
  • The dataset of pulse profile residuals ($\delta U$) was decomposed into eigenvectors (Principal Components, PCs).
  • Instead of projecting raw profiles, the authors projected the residuals (profile minus a frequency-dependent template) onto the PCs. This removes stable frequency-dependent shape variations, isolating morphological changes.
  • Time series of dot products ($D_i$) were generated for the first five PCs.
• Matched Filtering & Event Ranking:
  • To detect FRED-like events, the $D_i$ time series were cross-correlated with FRED templates (fast rise, exponential decay) and DERF templates (exponential rise, fast decay; the time-reversed version).
  • Discrimination: True FRED events produce a distinct asymmetry between the FRED and DERF cross-correlation function (CCF) responses, whereas single-epoch outliers (delta functions) produce symmetric responses.
  • Ranking Metric ($\zeta$): A score was derived based on two dimensionless parameters:
    1. Lag ($\ell$): The time lag between FRED and DERF CCF extrema (expected $\ell \approx 1$ for true events).
    2. Amplitude Ratio ($\alpha$): The ratio of FRED to DERF peak amplitudes (expected $\alpha \approx e/2$).
  • The final ranking score $\zeta$ combines deviations from these fiducial values, weighted by the number of frequency channels detecting the event. Lower $\zeta$ indicates a higher probability of a true FRED event.

3. Key Contributions

• Systematic Detection Algorithm: Introduced a robust, automated pipeline using PCA and dual-template matched filtering to search for pulse shape changes across multiple pulsars and frequency bands.
• Recovery of Known Events: Successfully recovered all four previously known FRED-like events in PSR J1713+0747 (three events) and PSR J1643−1224 (one event), validating the method's sensitivity.
• Discovery of New Candidates: Identified four new high-ranking candidate events in the sample:
  • Two attributed to long-term scattering variability in PSR B1937+21.
  • Two novel low-S/N candidates in PSR J1600−3053 (associated with anomalous DMX values) and PSR J0030+0451 (affecting both main pulse and interpulse).
• Recurrence of Scattering Events: Reported an unexpected recurrence of a specific pulse shape variation in PSR B1937+21 approximately 10 years after the first occurrence, challenging simple stochastic scattering models.
• Chromaticity Analysis: Demonstrated the utility of sub-band analysis in distinguishing between intrinsic magnetospheric changes (often achromatic or complex) and interstellar scattering (strongly chromatic, $\nu^{-x}$).

4. Key Results

• PSR J1713+0747: The method confirmed the three known events. Analysis suggests that while the events are chromatic, they do not follow a simple $\nu^{-2}$ dispersion measure law, supporting an intrinsic magnetospheric origin. The authors calculated that excising these events from timing data would create gaps totaling $\sim$6 years, highlighting the need for modeling rather than simple excision.
• PSR B1937+21: The study identified two distinct "scattering variability" events (one in 2011, one in 2021) separated by $\sim$10 years. The variation is strongest at 800 MHz and decays rapidly at higher frequencies. Instrumental errors and solar systematics were ruled out as causes. The recurrence suggests a periodic or quasi-periodic scattering source (e.g., a circumpulsar structure), though the source remains unidentified.
• PSR J1643−1224: The 2015 event was recovered, confirming its strong frequency dependence (detected at 1.4–1.8 GHz, absent at 800 MHz in NANOGrav data).
• Null Results: No FRED-like events were found in the most stable pulsars (PSR J1909−3744, PSR J2234+0611), confirming their suitability as baselines. PSR J1022+1001 showed no candidates due to high intrinsic noise and short observation baselines preventing reliable noise floor estimation.

5. Significance

• GWB Detection Mitigation: By characterizing the prevalence and nature of pulse shape changes, this work provides tools to mitigate timing noise in PTA datasets, crucial for the detection of the stochastic gravitational wave background.
• Physical Insights: The recurrence of the PSR B1937+21 event and the distinct chromaticity of various events offer new constraints on interstellar medium (ISM) scattering structures and pulsar magnetospheric physics.
• Future Observations: The paper emphasizes the importance of wide-frequency coverage (e.g., using the GBT's Ultra-Wideband Receiver) to isolate frequency bands unaffected by shape changes, allowing for "narrowband timing" strategies to bypass these events in future datasets.
• Methodological Advancement: The PCA-based approach offers a powerful, model-independent way to visualize and quantify pulse profile variability over timescales ranging from days to decades.