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Observations of Crab Pulsar Giant Pulses with the Parkes Ultra-Wideband (UWL) Receiver

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14 April 2026

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15 April 2026

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Abstract
We present a systematic study of giant pulses (GPs) from the Crab pulsar (PSR J0534+2200) using ultra-wideband observations with the Parkes radio telescope. We introduce an empirical classification scheme based on the cumulative distribution function (CDF) of pulse energy in frequency, separating the detected events into narrow-band and broadband GPs, with the former dominating the present sample. The narrow-band events concentrate most of their energy within limited frequency ranges, whereas broadband events show more extended spectral coverage. Spectral fitting shows that most narrow-band GPs have negative spectral indices, while a few events exhibit positive slopes, indicating substantial spectral diversity within the sample. The 3σ widths of narrow-band main pulse GPs appear to cluster around two characteristic ranges, although this feature should be interpreted with caution given the time resolution of the data. The energy distribution of narrow-band main pulse GPs is broadly consistent with a log-normal form at low-to-intermediate energies and a power-law-like tail at the high-energy end. The waiting-time distribution can be described by a Weibull function, while a sliding-window comparison with Monte Carlo Poisson realizations shows no statistically significant deviation from temporal independence over the present 18.9-minute observing span. These results provide observational constraints on the phenomenology of Crab giant pulses and may be useful for future studies of pulsar coherent emission and related radio transients.
Keywords: 
Crab pulsar
;  
giant pulses
;  
ultra-wideband observations
;  
spectral properties
;  
temporal structure
;  
energy statistics
Subject: 
Physical Sciences  -   Astronomy and Astrophysics

1. Introduction

The Crab pulsar (PSR J0534+2200) is one of the most prominent young pulsars in the Milky Way. Its extremely high spin-down power and strong magnetic field environment make it an ideal natural laboratory for studying particle acceleration and coherent radiation processes under extreme conditions [1,2]. The pulsar emits GPs, which are extremely short-duration bursts with instantaneous flux densities exceeding the average pulse by several orders of magnitude. Since their first discovery, GPs have been considered an important observational window for probing nonlinear plasma processes and coherent emission mechanisms in pulsar magnetospheres [3,4].
Over the past few decades, studies of Crab pulsar GPs have mainly focused on their extreme temporal structures, energy distributions, and associations with the main pulse and interpulse phases. Very Long Baseline Interferometry (VLBI) observations have confirmed that GPs emission originates within the pulsar magnetosphere rather than in the nebular shock regions [5]. Numerous observations indicate that the energy distribution of GPs often follows a power-law at the high-energy end, suggesting a generation process characterized by scale-free nonlinear amplification or critical behavior [6,7,8]. In the time domain, microsecond- and even nanosecond-scale fine structures have been repeatedly reported, implying extremely small emission regions and highly coherent radiation processes [9,10].
However, due to the limited bandwidth of early receivers, most studies were confined to relatively narrow frequency ranges (typically tens to hundreds of MHz), making it difficult to systematically characterize the spectral behavior of GPs over wide frequency ranges and their frequency-dependent emission properties. Existing observations indicate that GPs can exhibit significantly different spectral shapes and bandwidths at different frequencies, suggesting that their emission mechanisms or regions are not singular [8,11]. In recent broadband observations, a class of narrow-band GPs has been identified, with spectral widths significantly smaller than those of conventional broadband GPs when expressed as a fraction of the central frequency ( Δ ν / ν ). Using observations from the 46-m telescope in the 400–800 MHz range, Thulasiram & Lin (2021) identified a subpopulation of narrow-band GPs with Δ ν / ν ≃ 0.1 , appearing in both main pulse and interpulse phases. This finding supports an intrinsic emission mechanism rather than propagation effects [12]. Nevertheless, current distinctions between "narrow-band" and "broadband" GPs largely rely on empirical frequency coverage or subjective thresholds, lacking a unified and reproducible quantitative classification standard.
With the commissioning of the Parkes Ultra-Wideband Low receiver (UWL) [13], continuous coverage of 732–4032 MHz in a single observation has become possible. This provides an unprecedented opportunity to systematically study the time-frequency characteristics, spectral morphology, and statistical properties of Crab pulsar GPs under broadband conditions. At the same time, the increased data volume poses higher demands for objective GPs identification, bandwidth quantification, and statistical comparison of different emission properties.
PSR J0534+2200 is one of the most active known GP emitters [3,6,8], and its narrow-band and broadband emission properties under ultra-wideband conditions remain important observational issues. In this work, we present a systematic analysis of Crab pulsar GPs using Parkes UWL observations. Specifically, we: (1) introduce a reproducible empirical framework based on the cumulative distribution function (CDF) of pulse energy to characterize the frequency-domain extent of individual GPs; (2) compare narrow-band and broadband events in terms of spectral indices, temporal widths, and energy distributions within this framework; and (3) investigate their temporal behavior through waiting-time statistics and sliding-window burst-rate analysis [6,14]. Our aim is to provide observational constraints on the diversity of Crab GPs under wideband conditions, while also clarifying the statistical limitations of the current dataset.

2. Observations and Data Analysis

2.1. Observational Setup and Data Acquisition

The observational data used in this study were obtained from the PX500 project of the National Astronomical Observatories, Chinese Academy of Sciences. On 27 June 2024, targeted observations of the Crab pulsar (PSR J0534+2200) were carried out with the 64-m Parkes radio telescope in Australia. The observations employed the Ultra-Wideband Low (UWL) receiver [13], providing continuous frequency coverage from 732 to 4032 MHz, with a central frequency of 2382 MHz and an effective integration time of 18.9 minutes. Raw voltage data were recorded in real time by the Parkes digital backend. It should be noted that no absolute flux calibration was performed during the observations; thus, all intensity and energy analyses in this work are based on relative units, which are sufficient for comparing different GPs events and discussing emission mechanisms [11].During the data acquisition stage, coherent dedispersion was applied to remove the dispersive delays caused by the interstellar medium, using a dispersion measure of DM = 56.72 pc cm−3 [6,9]. The time resolution of the processed data is 128 μ s, which is adequate to resolve the emission structure within a single pulsar rotation. Subsequently, single-pulse folding was performed using the DSPSR software package [16], based on the precise ephemeris of PSR J0534+2200 (spin period P = 33.502 ms), with each rotation divided into 256 uniform phase bins. The resulting phase-aligned single-pulse profile sequence preserves the phase information of both the main pulse (MP) and interpulse (IP), providing a solid foundation for subsequent single-pulse statistics and broadband emission analysis.

2.2. Radio Frequency Interference Excision

Broadband radio observations are inevitably affected by various forms of radio frequency interference (RFI). To ensure reliable GPs identification and statistical analysis, a systematic RFI excision procedure was applied during data processing. RFI mitigation was primarily conducted using the PSRCHIVE software package [17,18]. In the frequency domain, persistently contaminated narrow-band channels were identified based on their statistical properties and subsequently masked. In the time domain, anomalous time samples deviating from the noise distribution were removed to eliminate transient strong interference events [19]. All thresholds applied in the RFI excision process were determined according to the statistical characteristics of the data itself, minimizing potential systematic biases on the genuine astrophysical signals. In addition, a subset of the automatically processed data was visually inspected, examining dynamic spectra and pulse profiles to further remove any remaining abnormal interference events. After these procedures, the data quality was deemed sufficient for subsequent GPs selection and broadband statistical analyses.

2.3. Giant Pulses Selection Criteria and Data Set Construction

To reliably extract GPs events from the large single-pulse dataset, a dual selection criterion based on relative intensity and signal-to-noise ratio (SNR) was employed. First, an initial selection was made based on pulse intensity. The peak of each candidate GPs profile was required to exceed 30 times the mean peak of all single-pulse profiles. This threshold ensures that selected events are significantly distinct from regular pulses in terms of emission strength, allowing clear separation from ordinary pulsar emission. Subsequently, to further exclude random noise fluctuations and low-SNR events, all candidate pulses were required to satisfy SNR > 9 . This dual criterion preserves the purity of the GPs sample while avoiding overly conservative selection bias.
Figure 1 presents two typical GPs examples identified through the above selection procedure.(a) shows an event with a signal-to-noise ratio (SNR) of 9.76, which is one of the weakest GPs that satisfy the selection criteria, yet its pulse profile remains clearly discernible.(b) displays a high-SNR, strong GPs event. Both exhibit peak features that are significantly enhanced relative to the average profile. For all candidate events selected based on both intensity and SNR, their peak phases were further checked to determine whether they fall within the known main pulse or interpulse phase windows. This phase consistency check effectively prevents residual radio frequency interference (RFI) events from being misclassified as genuine GPs, thereby improving the physical reliability of the sample. Using this procedure, a total of 372 high-confidence GPs were identified out of 33,531 pulse periods.

3. Results and Analysis

3.1. Narrow-Band Giant Pulses

3.1.1. Energy Cumulative Distribution Function (CDF) Method

To quantitatively characterize the energy distribution of GPs in the frequency domain and to distinguish between narrow-band and broadband GPs, we applied the cumulative distribution function (CDF) method to each individual GPs event. For each pulse, the on-pulse and off-pulse regions were selected from the two-dimensional time-frequency dynamic spectrum as the signal and background references, respectively. The on-pulse region is defined as the portion of the dynamic spectrum where the signal intensity exceeds the background noise by more than 3 σ , concentrating the main emission and energy of the GP. The off-pulse region, with the same width as the on-pulse window, contains no significant pulse emission and serves as a reference for background noise. By computing the cumulative distribution of signal energy across frequencies within the on-pulse region and subtracting the corresponding off-pulse cumulative energy, we obtain the net energy CDF curve. This curve describes the cumulative contribution of pulse energy as a function of frequency, directly reflecting whether the energy is concentrated or dispersed in the frequency domain. Subsequently, the net energy CDF curve is fitted using a piecewise linear approach. Candidate cutoff frequencies are uniformly selected from the middle portion of the cumulative energy range, excluding the lowest and highest 5% of data points to avoid edge effects. For each candidate cutoff frequency, the optimal piecewise linear fit is determined via the least-squares method, and the cutoff corresponding to the minimum residual sum of squares (RSS) is chosen as the best estimate. This cutoff frequency indicates the point where the cumulative energy behavior changes significantly and is used to characterize the effective frequency range of the pulse.To assess the statistical uncertainty of the cutoff frequency, an error band is constructed based on the mean and standard deviation of each fitting interval. The upper and lower boundaries of the error band are separately fitted, and the resulting intersection range provides an estimate of the cutoff frequency uncertainty. This method avoids subjective threshold selection while providing a quantifiable measure of uncertainty for subsequent statistical analyses.

3.1.2. Classification of Narrow-Band and Broadband Giant Pulses

Based on the CDF analysis described above, each detected GP was examined individually in the frequency domain. In this work, we adopt an empirical but reproducible classification scheme. Events whose net cumulative energy rises rapidly over a limited frequency interval and then approaches a plateau are classified as narrow-band GPs. In contrast, events whose net cumulative energy continues to increase over a much broader frequency range, without an early flattening trend, are classified as broadband GPs. The cutoff frequency derived from the piecewise fit is used as a convenient descriptor of the effective upper extent of the dominant emission.
Figure 2 presents representative examples of the two classes. In Figure 2(a), the emission is primarily concentrated within a restricted frequency range, and the net CDF becomes nearly flat above the main emitting band. In Figure 2(b), the emission extends over a substantially wider frequency interval, and the corresponding net CDF continues to increase to higher frequencies. Applying this empirical scheme to the full sample, we identify 353 narrow-band and 19 broadband GPs (Table 1). We stress that this classification is intended as a practical description of the present dataset rather than a unique physical taxonomy, and its robustness should be further examined with larger samples and alternative model-selection criteria. To provide a more detailed overview of the individual giant pulses, the measured parameters of all detected events, including normalized pulse energy, signal-to-noise ratio, central frequency, bandwidth, relative bandwidth, and spectral index, are listed in Appendix A1(Table A1).
Figure 2 highlights the contrast between the two spectral morphologies considered in this work. The narrow-band example shows that most of the pulse energy is confined to a limited spectral interval, whereas the broadband example exhibits enhanced emission over a much larger frequency span. The corresponding CDF curves provide a compact way to visualize how rapidly the pulse energy accumulates with frequency and where it begins to saturate. In this sense, the CDF-based representation is useful for comparing events with different spectral extents in a uniform manner.

3.1.3. Phase Distribution of Narrow-Band and Broadband Giant Pulses

After determining the bandwidth class of each GP, we further assigned each event to either the main pulse (MP) or interpulse (IP) phase window according to the phase of its peak. Among the 353 narrow-band GPs, 335 occur in the MP window and 18 in the IP window. Among the 19 broadband GPs, 17 are found in the MP window and 2 in the IP window (Table 1). Thus, both classes are dominated by MP events in the present dataset. Because the IP and broadband subsamples are both small, the apparent differences between phase categories should be interpreted with caution. A statistical comparison based on the current counts does not provide strong evidence for a significant association between pulse phase and bandwidth class. We therefore regard the present result mainly as a descriptive summary of the observed sample rather than a firm population-level conclusion.

3.1.4. Statistical Properties of Relative Bandwidth for Narrow-Band Giant Pulses

Based on the classification described above, we further performed a statistical analysis of the relative bandwidth of narrow-band GPs. The dimensionless parameter defined as the ratio of the frequency bandwidth to the central frequency was used to characterize the relative concentration of emission in the frequency domain. Figure 3(a) and Figure 3(b) show the histograms of the relative bandwidth distribution for narrow-band GPs in the main pulse and interpulse, respectively. For the main pulse sample, the relative bandwidth distribution exhibits a clear bimodal structure. A double-Gaussian model provides a good fit to describe this feature, with one peak centered around 0.65 with a relatively narrow width, and another peak around 0.74 with a broader spread. For the MP-narrow-band sample, the histogram shows a possible bimodal tendency, and a double-Gaussian function provides a visually reasonable description of the distribution. However, the statistical significance of this apparent bimodality should be tested more rigorously in future work using model-comparison criteria such as AIC, BIC, or bootstrap resampling. For the IP-narrow-band sample, only 18 events are available, and no robust statement about the underlying distribution can be made from the present data.

3.2. Spectral Index Properties of Giant Pulses

To further characterize the spectral behavior of narrow-band and broadband GPs, we performed a power-law fit to the energy spectrum of each individual GPs. The fit adopts the following form:
F ν = C ν α ,
where F ν is the peak flux at frequency ν , C is a normalization constant, and α is the spectral index used to describe the overall steepness of the spectrum.

3.2.1. Spectral Morphology of Representative Pulses

Despite the dominance of narrow-band GPs within the main pulse phase window (approximately 94.9%), their spectral behavior is not uniform and exhibits significant heterogeneity. Figure 4 shows the spectra of two representative narrow-band GPs, which display opposite trends in their frequency–flux relationships: one exhibits a typical power-law decay, while the other shows a power-law increase. Figure 4(a) presents a narrow-band GPs with a negative spectral slope. Its spectrum, spanning approximately 750–1900 MHz, clearly follows a power-law decay, with a fitted spectral index of α ≈ − 3.17 ± 0.30 , indicating a stable spectral structure with strong power-law characteristics and a significant decrease in flux with increasing frequency. In contrast, Figure 4(b) illustrates a narrow-band GPs with a positive spectral slope. In the low-frequency region, the flux increases monotonically with frequency, yielding a fitted spectral index of α ≈ 1.45 ± 0.22 . This “high-frequency enhanced” spectral feature is extremely rare among narrow-band GPs [20].

3.2.2. Statistical Distribution of Spectral Indices

A statistical analysis of the spectral indices for the full sample further quantifies the systematic differences in spectral characteristics between different types of giant GPs. Figure 5(a) shows the histogram of spectral indices for the main pulse and the corresponding single-Gaussian fit. The spectral indices of the MP-narrow-band sample span a wide range from − 4.56 to 1.45 , including both negative and positive values. This result is consistent with the observations of Karuppusamy et al. (2010) [11], reflecting the complexity of spectral evolution and particle acceleration in GPs emission. The single-Gaussian fit yields a mean μ = − 1.59 and standard deviation σ = 1.02 , which is in good agreement with the typical spectral index range of classical GPs, α ≈ − 1.5 to − 2.0 [21]. The MP–broadband GPs sample mainly occupies the central region of the distribution and overlaps closely with the narrow-window distribution, confirming the robustness of the measurement.
Figure 5(b) shows the spectral index distribution for the interpulse. Due to the limited number of observations, the distribution is relatively sparse and exhibits multiple peaks, with the core range approximately α ≈ − 3.2 to − 1.7 . The mean spectral index is more negative, reflecting the relative rarity of interpulse emission [22] and consistent with previous findings that the interpulse spectrum is steeper than that of the main pulse [23]. Comparison between the main pulse and interpulse distributions reveals notable differences in both the shape and central spectral index value.These findings should be interpreted with caution, as they may be influenced by the limited sample size as well as intrinsic differences in the emission physics of the two pulse types.

3.3. Statistical Analysis of the Giant Pulses Energy Distribution

To investigate the energy statistics of the giant GPs population, we analyzed the relative energy distribution of narrow-band main pulse GPs. Here, the relative energy is defined as E / 〈 E 〉 , where 〈 E 〉 denotes the mean energy of all pulses. Figure 6 shows the histogram of relative energies for narrow-band main pulse, with the horizontal axis representing E / 〈 E 〉 and the vertical axis representing the pulse counts in each energy bin.
As shown in Figure 6,The energy distribution of the narrow-band MP GPs is broadly consistent with a log-normal form at low-to-intermediate energies and a power-law-like tail at the high-energy end. At lower energies ( E / 〈 E 〉 ≲ 30 ), the number of pulses increases rapidly, while at higher energies ( E / 〈 E 〉 ≳ 30 ), the number of pulses decreases. The high-energy tail approximately follows a power-law distribution, though this result should be regarded as a phenomenological description due to the finite sample size and the influence of binning and fitting range on the histogram-based analysis. Given these limitations, the fitted models provide useful guidance for understanding the general behavior of the energy distribution, rather than a definitive statistical decomposition. To quantitatively describe this distribution, both a log-normal distribution and a power-law distribution were fitted to the observed data ( Figure 6).
(1) Log-normal fitting The red dashed line represents the fit using a log-normal distribution model, with best-fit parameters μ = 3.49 and σ = 0.29 . This model reproduces the overall shape of the observed distribution well in the mid-to-low energy range ( E / 〈 E 〉 ≲ 40 ), including the position of the distribution peak and the local statistical features. However, at the high-energy end, the fit systematically deviates from the observed data, indicating that the log-normal model cannot simultaneously describe the high-energy tail.
(2) Power-law fitting The blue dashed line represents the power-law model fitted to the high-energy tail, with a power-law index α = − 3.51 . In the high-energy region ( E / 〈 E 〉 ≳ 40 ), the power-law model matches the observed data significantly better than the log-normal model, capturing the rapid decline in GPs counts with increasing energy.
In summary, the energy distribution of narrow-band main pulse GPs exhibits distinct statistical behaviors in the mid-to-low and high-energy ranges: the former is well approximated by a log-normal distribution, while the latter is more consistent with a power-law distribution.

3.4. Statistical Analysis of Giant-Pulse Widths and Their Relation to Signal-to-Noise Ratio

To investigate the temporal characteristics of GPs, we analyzed the time-domain profiles of main pulse events using the 3 σ pulse width, defined as the effective duration over which the pulse intensity exceeds the background noise level by 3 σ . This quantity provides a practical measure of the observed temporal extent of each event within the processed single-pulse data.
The distribution of 3 σ widths is shown in Figure 7(a). For the narrow-band main pulse sample, the histogram can be empirically described by a double-Gaussian model, with two fitted centroids located near 0.33 ms and 0.41 ms. This fit provides a convenient phenomenological representation of the observed width distribution and suggests the presence of possible clustering within the range of measured widths. However, these fitted components should not be over-interpreted as fully resolved intrinsic width states. The processed data have a time resolution of 128 μ s, and each pulsar rotation is divided into 256 phase bins, corresponding to an effective sampling interval of about 0.13 ms per phase bin after folding. Therefore, although the formal uncertainties of the fitted centroids may be small, the effective uncertainty associated with width measurement is limited by the finite time sampling and is of the order of one phase bin. In this sense, the fitted centroids near 0.33 ms and 0.41 ms are better regarded as approximate locations of possible clustering in the histogram rather than as precise measurements of two sharply separated intrinsic timescales. Likewise, the Gaussian widths in the fit reflect the internal description of the histogram model and should not be interpreted directly as the observational resolving power of the dataset. Given these limitations, the apparent bimodal tendency in the narrow-band sample should be considered suggestive rather than conclusive. For the broadband main pulse sample, the measured 3 σ widths are more sparsely distributed, roughly between 0.33 and 0.41 ms, and no similarly clear double-peaked structure is evident. Because this subsample is much smaller, the current data do not support a strong comparative conclusion regarding intrinsic differences in temporal structure between narrow-band and broadband events.
To further examine whether pulse width is related to pulse strength, Figure 7(b) shows the scatter plot of 3 σ width versus SNR for the main pulse GPs. The SNR values span a broad range, while the widths are mainly distributed between approximately 0.30 and 0.45 ms. Across the observed parameter space, high-SNR events are not confined to a specific width interval, and lower-SNR events are likewise spread across the same width range. This indicates that no strong one-to-one correspondence is evident between pulse width and SNR in the present sample. Although relatively dense regions appear near the fitted centroids, this feature should be interpreted consistently with the finite time resolution discussed above. Overall, the width statistics suggest that narrow-band main pulse GPs may preferentially occupy a limited range of observed durations, with possible substructure in the histogram. However, higher time resolution and a larger sample will be required to determine whether this behavior reflects genuine intrinsic width components or is partly shaped by measurement discretization and finite-sampling effects[6].

3.5. Waiting-Time Statistics of Giant Pulses

To systematically characterize the temporal statistical behavior of GPs from the Crab pulsar, we analyzed the pulse waiting times from three perspectives: the distribution shape, logarithmic-scale properties, and the randomness of the time series.

3.5.1. Waiting-Time Distribution and Weibull Fitting

We first analyzed the waiting times ( Δ T ) between consecutive GPs. Figure 8 shows the normalized occurrence rate of waiting times as a function of Δ T in a log–log scale. As shown, the occurrence rate decreases monotonically with increasing Δ T , exhibiting a smooth and continuous distribution over several orders of magnitude in timescales. At short timescales ( Δ T ≲ 1 s), the occurrence rate drops rapidly, while at longer timescales ( Δ T ≳ 1 s), the distribution approximately follows a linear decay in log–log coordinates, though the slope changes.
To quantitatively characterize this distribution, we fitted the observed data using a Weibull distribution, whose probability density function is given by:
f ( t ; k , λ ) = k λ t λ k − 1 e − ( t / λ ) k ,
where t is the waiting time, k is the shape parameter, and λ is the scale parameter. The fit, shown as the red solid line in Figure 8, agrees well with the observed data across the full timescale range.
The best-fit shape parameter is k = 0.74 ± 0.11 ,indicating that the Weibull function provides a useful empirical description of the observed waiting-time distribution[24,25]. However, this does not by itself establish the presence of deterministic temporal memory or non-random triggering between successive pulses[26]. In the present work, the Weibull fit should be understood primarily as a compact phenomenological model for the waiting-time statistics.

3.5.2. Waiting Time Distribution and Temporal Independence of Giant Pulses

Considering that the waiting time Δ T spans several orders of magnitude, we further analyzed the distribution of log 10 Δ T . Figure 9 shows the histogram of log 10 Δ T and its Gaussian fit. The distribution exhibits an approximately symmetric, unimodal shape. Fitting with a Gaussian function yields a mean of μ = 0.21 ± 0.55 and a standard deviation of σ = 0.55 ± 0.01 . On the logarithmic timescale, this indicates that GPs waiting times are concentrated around a characteristic interval. Converting back to linear time, the typical waiting time is approximately 10 μ ≈ 1.62 s, with the main distribution range spanning roughly 0.46 s to 5.75 s, reflecting significant statistical dispersion within this scale.
To explore whether GPs bursts exhibit significant temporal dependence, we performed a sliding-window analysis on the full observation dataset (33,531 pulse periods) and compared it with random Poisson sequences. The window size was set to 1000 pulse periods, with a step size of 200 periods. The burst rate of GPs was calculated within each window, and Figure 10 shows the temporal evolution of the observed burst rate. To assess statistical significance, 1000 random Poisson sequences with the same mean burst rate were generated and subjected to the same sliding-window analysis. In Figure 10, the gray shaded region represents the 95% confidence interval of the random Poisson simulations, the gray dashed line indicates their mean burst rate, and the red horizontal line represents the global mean burst rate of the observed data (0.01). The results indicate that the observed burst rate series almost entirely falls within the 95% confidence interval of the random Poisson simulations and fluctuates around the global mean. Further statistical comparison shows that the variance of the observed series (1.20 × 10 − 5 ) closely matches the mean variance of the simulated Poisson sequences (1.07 × 10 − 5 ), with a Monte Carlo P-value of 0.25, exceeding the 0.05 significance threshold. Thus, we conclude that, within the current observation span of approximately 19 minutes, the GPs burst sequence does not show strong temporal dependence and is statistically indistinguishable from a random Poisson process. However, the apparent lack of temporal correlation may be due to the limited observation duration and sample size, and future studies with longer timescales and higher sensitivity are needed to further investigate potential temporal correlations or “memory effects” in the GPs bursts.

4. Discussion

Using a reproducible empirical classification scheme based on the cumulative distribution function (CDF) of pulse energy, this study distinguishes narrow-band and broadband giant pulses (GPs) under ultra-wideband observing conditions and shows that narrow-band events dominate the present sample. This result supports the view that Crab pulsar GPs do not constitute a single, uniform emission phenomenon, but instead encompass multiple forms of emission with distinct spectral characteristics, in agreement with previous studies of GP energy distributions and spectral behavior [4]. The observed differences in the energy distributions of different GP classes further suggest diversity in the underlying emission processes. In addition, the detection of a large population of narrow-band GPs reinforces earlier evidence for spectral differentiation within the Crab GP population [12]. In the frequency domain, narrow-band GPs concentrate most of their energy within a limited spectral range and exhibit a wide spread of spectral indices, including both negative and positive values. While negative spectral slopes are consistent with the conventional low-frequency-dominated trend, the rare positive slopes depart from this picture and may point to less explored or atypical excitation processes. The relative-bandwidth distribution likewise indicates clear frequency localization and selectivity, highlighting the spectral heterogeneity and complexity of narrow-band GP emission.
These properties are consistent with an origin in localized, frequency-selective coherent emission regions within the pulsar magnetosphere [12], potentially associated with plasma-instability-driven processes such as turbulent wave-packet collapse [4]. Such an interpretation is also compatible with a highly stratified magnetospheric environment, in which emission generated at different heights or under different plasma conditions gives rise to distinct spectral signatures [27]. By contrast, broadband GPs distribute their energy across a much wider frequency range, and their spectra are generally not well described by a single power-law model [11,23]. This behavior suggests a more complex emission picture, possibly involving multiple overlapping components or large-scale coherent structures capable of radiating efficiently over broad frequency intervals. Previous work has likewise shown that Crab GPs can display broadband characteristics and broad spectral-index distributions that are difficult to explain within a single unified framework [9,11]. Therefore, the spectral contrast between narrow-band and broadband GPs lends further support to the idea that multiple emission components or mechanisms may coexist in the Crab pulsar. In this respect, the phenomenological distinction between the two classes may also offer a useful point of comparison with the diversity observed in narrow-band and broadband fast radio bursts (FRBs) [28]. Overall, the systematic spectral differences identified here provide additional observational constraints for evaluating multi-component or multi-mechanism models of GP emission and help clarify the possible physical origins of these two classes.
The high-energy tail of the narrow-band main pulse energy distribution, at E / 〈 E 〉 > 40 , shows an approximate power-law behavior with an index of about − 3.51 . Scale-free tails of this kind are common in complex systems and are often associated with nonlinear amplification or cross-scale energy-release processes [14], suggesting that the strongest GPs are not governed by a single characteristic energy scale. Instead, they may arise from episodic energy release when magnetospheric conditions approach a critical state, with event sizes spanning a broad dynamic range [29,30]. At the same time, the good agreement between the mid-to-low-energy part of the distribution and a log-normal form may reflect the combined influence of multiple stochastic factors in the buildup or modulation of the radiated energy [6,7]. Taken together, these results suggest that the energy statistics of narrow-band main pulse GPs may encode contributions from more than one physical regime, although the limited sample size and the histogram-based fitting procedure mean that this interpretation should remain phenomenological at the present stage.
The 3 σ pulse-width distribution of narrow-band main pulse GPs shows two apparent concentrations near 0.33 ms and 0.41 ms, with neither component exhibiting a strong dependence on signal-to-noise ratio (SNR). This may indicate that pulse width is a more intrinsic observational characteristic than peak intensity and may be linked more directly to the characteristic timescale of the emission process [7,11]. Narrower events could correspond to smaller or more coherent emission regions whose temporal extent is constrained by local physical conditions, such as the geometric scale or coherence length of the emitting region [31]. Slightly broader events, on the other hand, may reflect lateral expansion of the emitting region, propagation effects, or instabilities operating on somewhat different characteristic scales [32,33,34]. However, this interpretation should be treated with caution because the effective time sampling of the present data is limited, and the apparent bimodality may be influenced in part by finite time resolution and measurement discretization.
The waiting-time analysis shows that GP intervals are well described empirically by a Weibull distribution with shape parameter k < 1 , indicating a form that differs from a simple exponential law [24,25]. However, the sliding-window analysis and Monte Carlo comparisons show that, over the approximately 19-minute observing span, the observed burst sequence is statistically indistinguishable from a temporally independent Poisson process [25,35]. Thus, the current dataset does not provide strong evidence for significant temporal correlations or deterministic memory effects in the GP sequence [11]. The apparent tension between the Weibull-like waiting-time distribution and the Poisson-consistent burst-rate fluctuations may arise from a combination of limited observing duration, finite sample size, and selection or threshold effects. Longer observations with improved sensitivity will be needed to determine more reliably whether Crab GPs exhibit genuine temporal correlations on particular timescales.

5. Conclusions

Based on Parkes UWL observations, we have carried out a phenomenological analysis of the spectral, temporal, and statistical properties of giant pulses from the Crab pulsar. The main results can be summarized as follows:
1.
Using the cumulative distribution function of pulse energy in frequency, we introduce a reproducible empirical scheme to describe the spectral extent of individual GPs. Under this scheme, 353 events are classified as narrow-band and 19 as broadband, indicating that narrow-band events dominate the present sample.
2.
The spectral indices of narrow-band MP GPs cover a broad range, with most events showing negative slopes and a few showing positive slopes. This indicates substantial spectral diversity within the observed sample, although detailed physical interpretation requires caution because no absolute flux calibration is available.
3.
The 3 σ widths of narrow-band MP GPs show two apparent concentrations near 0.33 ms and 0.41 ms. At the current time resolution, this feature is best regarded as suggestive of possible preferred width ranges rather than conclusive evidence for discrete intrinsic timescales.
4.
The energy distribution of narrow-band MP GPs is broadly consistent with a log-normal form at lower energies and a power-law-like tail at higher energies, providing a useful empirical description of the sample.
5.
The waiting-time distribution can be described by a Weibull function, while the burst-rate fluctuations over the 18.9-minute observing span are statistically consistent with a Poisson-like process. Taken together, these results do not provide strong evidence for temporal memory in the present dataset.
Overall, this work provides a wideband observational description of Crab giant pulses and highlights several trends that merit further investigation with longer observations, larger samples, improved calibration, and higher time resolution.

Author Contributions

Author Contributions: Conceptualization, R.Z. and H.L.; methodology, R.Z.; software, L.W., R.Z. and H.L.; validation, L.W.; formal analysis, Z.T.,H.X. and R.T.; investigation, R.T. and Q.Z.; resources, R.Z. and H.L.; data curation, L.W.; writing–original draft preparation,L.W. and R.Z.; writing–review and editing, L.W.,R.Z.,H.L. and D.Y.; visualization, L.W.,K.Y.,J.F. and Y.Z.; supervision, R.Z. and H.L.; project administration, R.Z. and H.L. All authors have read and agreed to the published version of the manuscript.

Funding

We gratefully acknowledge support from the following agencies and programs: National Natural Science Foundation of China (Grant Nos. 12563008, 11988101, U1731238, U2031117, 11565010, 11725313, 1227308, 12041303, 12588202); National Key R&D Program of China (No. 2023YFE0110500); National SKA Program of China (Nos. 2020SKA0120200, 2022SKA0130100, 2022SKA0130104); Science and Technology Foundation of Guizhou Provincial Department of Education (No. KY(2023)059); Youth Innovation Promotion Association CAS (ID: 2021055); Youth Scientists Project of Basic Research in CAS (YSBR-006); Foreign Talents Program (No. QN2023061004L; E.G.); Scientific and Technological Innovation Team of Higher Education Institutions under the Education Department of Guizhou Province (Grant No. QJJ[2023]093); Natural Science Research Support Project of the Education Department of Guizhou Province (No. [2024]350, KY[2018]006); CAS Youth Interdisciplinary Team; Liupanshui Science and Technology Development Project (No. 52020-2024-PT-01); the Cultivation Project for FAST Scientific Payoff and Research Achievement of CAMS-CAS. P.W. acknowledges additional support from the CAS Youth Interdisciplinary Team, the Youth Innovation Promotion Association CAS, and the Cultivation Project for FAST Scientific Payoff and Research Achievement of CAMS-CAS. D.L. is supported as a New Cornerstone Investigator. These supports were instrumental in the successful completion of this work.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Acknowledgments

The authors would like to express their sincere gratitude to [Name] for insightful discussions and valuable support throughout this study. During the preparation of this manuscript, artificial intelligence tools were employed to assist in the translation of content. All outputs generated with the assistance of artificial intelligence were carefully reviewed, refined, and edited by the authors, who take full responsibility for the final manuscript.

Conflicts of Interest

The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

Appendix A

Appendix A.1

Table A1 presents the measured parameters of identified giant pulses, including normalized pulse energy ( E / < E > ), signal-to-noise ratio (SNR), central frequency ( ν c ), bandwidth (BW), relative bandwidth (BW/ ν c ), and spectral index ( α ). The table includes all four categories: MP-Narrow-band, MP-broadband, IP-Narrow-band, and IP-broadband.
Table A1. Parameters of Identified Giant Pulses.
Table A1. Parameters of Identified Giant Pulses.
Number E / < E > SNR Vc(MHz) BW(MHz) BW/Vc α
MP-Narrow-band
19 29.64  15.57  1333.50  873.00  0.65  -1.52±0.35
60 79.27  70.65  1643.50  1493.00  0.91  -0.95±0.23
79 29.24  16.93  1355.00  916.00  0.68  -2.41±1.17
139 54.12  28.02  1410.00  1026.00  0.73  -0.21±0.47
163 27.05  13.34  1281.50  769.00  0.60  -1.38±0.25
171 15.59  12.03  1442.00  1090.00  0.76  -1.37±0.41
207 22.73  15.74  1412.50  1031.00  0.73  -0.90±0.28
254 59.88  32.27  1359.00  924.00  0.68  -1.18±0.87
446 41.82  18.32  1246.00  698.00  0.56  -1.44±1.02
648 47.12  28.49  1443.50  1093.00  0.76  -0.81±0.51
749 28.27  20.35  1492.50  1191.00  0.80  -2.11±0.32
998 24.16  16.67  1491.50  1189.00  0.80  -0.77±0.26
1013 16.15  10.36  1471.50  1149.00  0.78  -1.62±0.48
1042 40.44  19.04  1292.00  790.00  0.61  0.19±0.36
1144 34.19  19.40  1308.50  823.00  0.63  -3.14±0.85
1277 18.89  14.12  1558.50  1323.00  0.85  -1.17±0.45
1308 73.96  38.26  1422.50  1051.00  0.74  -1.18±0.34
1335 55.43  37.01  1415.00  1036.00  0.73  -1.48±0.51
1447 30.72  14.60  1405.00  1016.00  0.72  -0.99±0.41
1449 49.25  10.21  1009.00  224.00  0.22  0.27
1544 15.62  9.76  1318.50  843.00  0.64  -3.24±0.71
1656 83.77  54.51  1475.50  1157.00  0.78  -2.33±0.25
1804 24.60  19.01  1545.50  1297.00  0.84  -0.89±0.15
1873 21.09  13.41  1321.50  849.00  0.64  -2.70±0.63
1890 27.10  12.32  1307.00  820.00  0.63  -0.66±0.38
2019 64.07  37.27  1567.00  1340.00  0.86  -2.33±0.76
2023 52.38  29.07  1462.00  1130.00  0.77  -0.82±0.58
2034 30.24  17.13  1350.50  907.00  0.67  -0.23±0.23
2102 35.94  19.82  1374.50  955.00  0.69  -2.60±0.51
2171 23.59  14.98  1371.50  949.00  0.69  -1.21±0.69
2244 48.09  31.45  1516.00  1238.00  0.82  -1.40±0.24
2274 81.96  45.03  1357.00  920.00  0.68  -0.08±0.26
2341 33.47  15.52  1284.00  774.00  0.60  -3.80±0.42
2342 39.38  27.46  1514.50  1235.00  0.82  -0.37±0.17
2408 26.05  15.42  1489.00  1184.00  0.80  -0.56±0.44
2548 73.95  41.54  1431.00  1068.00  0.75  -1.00±0.30
2679 39.72  19.92  1338.00  882.00  0.66  0.59±0.46
2689 52.56  30.04  1387.50  981.00  0.71  -1.97±0.45
2713 84.13  49.85  1324.00  854.00  0.65  -1.13±0.75
2785 62.46  39.09  1520.00  1246.00  0.82  -0.90±0.19
2833 27.64  15.73  1457.00  1120.00  0.77  -1.12±0.34
2899 94.40  62.72  1427.50  1061.00  0.74  -0.42±0.59
2905 57.72  29.93  1428.00  1062.00  0.74  -1.10±0.58
2945 68.96  36.55  1319.00  844.00  0.64  -3.01±0.49
2990 24.65  17.17  1422.00  1050.00  0.74  -2.88±0.58
3006 60.65  36.30  1410.00  1026.00  0.73  -1.73±0.36
3077 46.21  23.51  1412.50  1031.00  0.73  -1.73±0.53
3087 39.29  27.34  1432.50  1071.00  0.75  -0.20±0.60
4125 28.06  16.63  1369.50  945.00  0.69  -2.50±1.14
4160 29.16  19.61  1376.00  958.00  0.70  -1.54±0.42
4209 31.04  19.91  1384.50  975.00  0.70  -1.98±0.10
4241 20.52  16.20  1437.50  1081.00  0.75  -2.13±0.43
4253 23.37  12.72  1327.50  861.00  0.65  -1.43±0.67
4275 20.18  9.95  1152.50  511.00  0.44  0.85±2.18
4279 32.11  23.66  1503.50  1213.00  0.81  -1.15±0.34
4292 34.36  21.65  1432.00  1070.00  0.75  -1.68±0.83
4442 30.39  14.50  1320.00  846.00  0.64  -1.84±0.65
4587 36.57  21.26  1364.00  934.00  0.68  -0.81±0.63
4618 32.54  18.59  1503.00  1212.00  0.81  -2.29±0.27
4631 51.40  29.35  1345.50  897.00  0.67  -2.28±0.37
4696 22.57  14.00  1359.00  924.00  0.68  -0.97±1.14
4699 33.10  21.27  1447.00  1100.00  0.76  -1.46±0.25
4852 31.70  18.04  1328.50  863.00  0.65  -1.91±0.47
4885 63.65  29.00  1319.50  845.00  0.64  -1.72±0.77
4903 29.15  13.54  1268.50  743.00  0.59  -2.05±0.93
4995 45.37  23.21  1450.00  1106.00  0.76  -0.38±0.44
5022 45.19  25.40  1316.00  838.00  0.64  -3.48±0.48
5071 49.63  27.55  1398.00  1002.00  0.72  -1.13±0.63
5075 16.77  10.37  1313.50  833.00  0.63  -1.43±0.90
5315 16.39  13.28  1633.50  1473.00  0.90  -1.00±0.14
5333 57.54  31.33  1280.50  767.00  0.60  -1.28±0.24
5402 42.04  24.25  1414.50  1035.00  0.73  -2.49±0.21
5420 37.78  20.57  1390.00  986.00  0.71  -1.89±0.85
6335 38.52  22.06  1383.00  972.00  0.70  -1.08±0.29
6461 22.94  14.79  1578.00  1362.00  0.86  -1.42±0.43
6483 30.06  20.40  1436.00  1078.00  0.75  -1.34±0.28
6507 29.13  17.39  1346.50  899.00  0.67  -2.19±0.83
6515 48.33  25.67  1326.50  859.00  0.65  -0.06±0.22
6779 12.65  10.02  1667.50  1541.00  0.92  -1.67±0.24
6988 19.88  11.03  1333.50  873.00  0.65  -0.01±0.31
7026 55.72  23.75  1317.50  841.00  0.64  -1.12±0.43
7039 34.23  21.00  1437.00  1080.00  0.75  -1.81±0.52
7243 56.71  30.04  1390.00  986.00  0.71  -2.31±0.53
7291 31.78  17.15  1302.00  810.00  0.62  -2.19±0.52
7355 34.52  29.58  1700.00  1606.00  0.94  -1.83±0.43
7708 63.35  44.42  1502.00  1210.00  0.81  -1.65±0.30
7798 23.56  13.59  1367.50  941.00  0.69  -1.05±0.49
7852 91.85  50.14  1479.50  1165.00  0.79  -0.58±0.47
7893 21.66  13.43  1385.00  976.00  0.70  -2.66±0.40
7956 21.46  13.35  1539.00  1284.00  0.83  -1.03±0.35
7972 21.50  13.86  1340.00  886.00  0.66  -2.50±0.39
8057 36.77  22.96  1370.00  946.00  0.69  -1.53±0.61
8187 47.63  27.06  1393.50  993.00  0.71  -2.30±0.30
8359 30.47  16.43  1348.50  903.00  0.67  -1.64±0.52
8428 33.44  12.48  1122.00  450.00  0.40  0.58±0.27
8505 38.95  27.05  1432.50  1071.00  0.75  -1.88±0.19
8528 29.00  18.73  1410.50  1027.00  0.73  -3.17±0.30
8535 38.59  18.80  1257.00  720.00  0.57  -3.19±0.94
8567 92.92  54.32  1372.00  950.00  0.69  -2.32±0.53
8607 45.23  24.48  1406.50  1019.00  0.72  -1.76±0.14
8753 43.71  25.51  1367.00  940.00  0.69  -1.71±0.38
8887 31.25  17.84  1538.00  1282.00  0.83  -1.38±0.20
8890 36.04  21.07  1279.00  764.00  0.60  -3.12±0.75
9060 46.66  31.25  1542.00  1290.00  0.84  -1.71±0.58
9092 27.22  13.21  1324.50  855.00  0.65  -2.09±0.52
9141 24.94  16.98  1474.00  1154.00  0.78  -0.45±0.46
9396 35.33  25.15  1487.50  1181.00  0.79  -1.84±0.23
9532 24.93  16.67  1604.50  1415.00  0.88  -0.56±0.47
9615 35.79  18.77  1397.50  1001.00  0.72  -0.92±0.47
9633 22.41  28.07  1857.00  1920.00  1.03  -1.31±0.48
9790 34.18  20.79  1309.50  825.00  0.63  -2.01±0.17
9830 34.54  19.12  1310.00  826.00  0.63  -1.77±0.87
9886 139.77  86.81  1330.50  867.00  0.65  -1.74±0.37
10064 34.32  18.28  1326.50  859.00  0.65  -1.52±0.36
10350 26.68  16.65  1375.50  957.00  0.70  -2.63±0.87
10368 65.25  31.75  1403.00  1012.00  0.72  -1.34±0.18
10373 30.59  18.72  1416.50  1039.00  0.73  -1.83±0.50
10432 60.88  37.45  1326.00  858.00  0.65  -2.03±0.38
10450 49.60  26.86  1357.50  921.00  0.68  -1.42±0.37
10496 26.76  18.72  1410.00  1026.00  0.73  -1.78±0.60
10721 30.83  15.84  1328.50  863.00  0.65  -1.30±0.50
10725 25.67  19.13  1664.00  1534.00  0.92  -0.30±0.47
10841 28.30  14.84  1291.00  788.00  0.61  -3.13±0.48
10958 39.81  28.22  1511.00  1228.00  0.81  -2.91±0.27
10970 37.86  17.18  1258.00  722.00  0.57  -2.30±0.70
11071 67.25  40.08  1388.00  982.00  0.71  -1.80±0.22
11096 17.45  12.84  1687.00  1580.00  0.94  -1.88±0.31
11102 39.72  25.78  1492.00  1190.00  0.80  -0.89±0.38
11138 24.24  13.25  1338.50  883.00  0.66  -4.22±0.32
11335 26.28  13.60  1328.50  863.00  0.65  -2.65±1.37
11419 34.87  22.49  1458.50  1123.00  0.77  -1.95±0.22
11521 96.42  53.04  1333.00  872.00  0.65  -2.34±0.46
11624 38.46  23.34  1353.50  913.00  0.67  -2.07±0.40
11650 49.16  27.55  1510.50  1227.00  0.81  -0.59±0.46
11842 22.39  11.28  1317.50  841.00  0.64  -2.95±0.11
11950 91.97  46.76  1460.50  1127.00  0.77  -1.86±0.39
11989 51.59  28.27  1308.00  822.00  0.63  -1.92±0.32
12052 62.80  28.43  1326.50  859.00  0.65  -2.68±0.76
12434 31.94  17.15  1349.00  904.00  0.67  -3.13±0.96
12476 37.85  17.22  1369.50  945.00  0.69  -0.86±0.98
12505 37.57  21.85  1316.50  839.00  0.64  -1.62±0.41
12520 38.24  26.32  1558.50  1323.00  0.85  -1.74±0.54
12841 52.62  35.05  1483.00  1172.00  0.79  -0.76±0.18
12911 28.46  17.35  1433.00  1072.00  0.75  -1.71±0.39
12955 60.12  35.80  1392.50  991.00  0.71  -1.74±0.32
12968 49.08  21.92  1324.50  855.00  0.65  -3.35±0.57
13034 64.67  44.64  1449.50  1105.00  0.76  -1.74±0.20
13036 45.54  23.35  1323.50  853.00  0.64  -2.64±0.86
13174 43.68  25.59  1455.50  1117.00  0.77  -2.25±0.50
13285 43.84  14.79  1118.00  442.00  0.40  -3.14±3.18
13463 51.68  30.71  1415.50  1037.00  0.73  -1.09±0.18
13710 27.99  16.60  1430.50  1067.00  0.75  -2.98±0.24
13821 46.49  23.49  1317.50  841.00  0.64  -4.12±0.43
14333 26.68  12.92  1400.50  1007.00  0.72  -0.45±0.37
14379 119.03  79.46  1496.00  1198.00  0.80  -1.21±0.36
14778 33.22  20.56  1333.50  873.00  0.65  -0.77±0.35
14878 69.15  31.87  1302.00  810.00  0.62  -4.37±0.94
14931 75.13  33.90  1311.00  828.00  0.63  -1.3±0.79
15107 40.33  24.05  1302.50  811.00  0.62  -1.27±0.85
15112 60.39  37.85  1315.50  837.00  0.64  -2.43±0.38
15160 32.46  22.62  1458.50  1123.00  0.77  -1.24±0.27
15274 46.59  28.99  1496.00  1198.00  0.80  -0.42±0.42
15285 27.62  21.12  1341.00  888.00  0.66  -0.77±0.46
15288 32.22  17.44  1366.00  938.00  0.69  -0.24±0.67
15322 24.22  15.83  1457.50  1121.00  0.77  -2.47±0.29
15333 37.65  19.94  1414.50  1035.00  0.73  -0.45±0.41
15356 29.95  20.74  1446.00  1098.00  0.76  -0.38±0.40
15397 61.57  37.45  1415.50  1037.00  0.73  -2.26±0.36
15422 26.88  17.53  1344.00  894.00  0.67  -2.53±0.20
15462 40.59  18.93  1244.50  695.00  0.56  -1.71±0.94
15498 86.32  46.73  1321.50  849.00  0.64  -1.24±0.75
15565 86.02  59.33  1490.00  1186.00  0.80  -2.46±0.51
15861 32.53  12.36  1184.50  575.00  0.49  -2.00±0.50
16098 43.49  25.84  1328.00  862.00  0.65  -0.14±0.52
16210 109.10  63.64  1334.50  875.00  0.66  -2.72±0.34
16240 94.69  46.97  1424.50  1055.00  0.74  0.14±0.55
16266 48.44  24.53  1327.50  861.00  0.65  -1.19±0.65
16284 35.16  21.92  1419.50  1045.00  0.74  -0.23±0.26
16291 40.35  23.37  1391.50  989.00  0.71  -1.55±0.65
16335 46.82  27.95  1496.00  1198.00  0.80  -0.42±0.44
16357 36.42  24.55  1457.50  1121.00  0.77  -0.90±0.31
16431 58.58  31.51  1362.00  930.00  0.68  -0.11±0.41
16744 32.32  19.37  1366.00  938.00  0.69  -1.39±0.43
16834 38.79  26.33  1523.00  1252.00  0.82  -0.20±0.59
17130 24.02  17.43  1358.00  922.00  0.68  -2.52±0.43
17187 32.97  17.24  1312.00  830.00  0.63  -3.44±0.70
17330 45.29  30.86  1434.00  1074.00  0.75  -2.37±0.38
17555 32.74  18.87  1423.50  1053.00  0.74  -1.82±0.35
17558 43.55  29.37  1507.50  1221.00  0.81  -1.23±0.36
17617 24.85  16.34  1320.00  846.00  0.64  -0.20±0.71
17676 21.36  19.52  1684.00  1574.00  0.93  -0.43±0.35
17819 81.78  43.92  1316.00  838.00  0.64  -0.78±0.67
17980 25.70  15.18  1350.00  906.00  0.67  -3.33±0.79
17985 27.00  16.17  1479.00  1164.00  0.79  -2.81±0.36
18094 31.42  17.72  1319.00  844.00  0.64  -3.05±0.87
18313 24.99  16.63  1452.50  1111.00  0.76  -1.08±0.75
18343 26.85  15.00  1406.00  1018.00  0.72  -2.31±0.82
18512 20.69  16.06  1616.00  1438.00  0.89  -0.54±0.39
18570 28.24  20.13  1463.00  1132.00  0.77  -0.78±0.41
18814 26.68  14.72  1338.00  882.00  0.66  0.84±0.61
18883 36.05  26.72  1503.00  1212.00  0.81  -2.11±0.46
18922 47.68  27.48  1451.50  1109.00  0.76  -0.97±0.23
19237 24.09  16.89  1459.00  1124.00  0.77  -1.03±0.68
19299 31.49  17.66  1391.00  988.00  0.71  -1.86±0.67
19453 31.41  18.32  1325.00  856.00  0.65  -2.25±0.95
19513 35.54  22.49  1481.50  1169.00  0.79  -1.55±0.46
19639 91.67  60.59  1449.50  1105.00  0.76  -2.52±0.50
19761 33.03  19.00  1341.50  889.00  0.66  0.32±0.42
19829 35.63  16.38  1336.00  878.00  0.66  -1.83±0.62
19881 32.72  18.42  1343.00  892.00  0.66  -2.17±0.79
19911 28.37  18.73  1453.50  1113.00  0.77  -0.05±0.28
19941 148.91  57.29  1207.00  620.00  0.51  -0.35±0.22
20113 34.62  23.45  1446.50  1099.00  0.76  -1.88±0.19
20287 59.61  40.24  1528.00  1262.00  0.83  -0.98±0.59
20322 35.80  22.32  1354.50  915.00  0.68  -0.96±0.79
20404 23.55  15.87  1547.50  1301.00  0.84  -0.33±0.12
20465 29.19  18.42  1423.00  1052.00  0.74  -1.76±0.56
20481 50.91  28.44  1346.50  899.00  0.67  -1.36±0.31
20556 32.03  16.45  1440.50  1087.00  0.75  -0.10±0.18
20626 60.81  38.20  1391.50  989.00  0.71  -0.39±0.30
20628 19.63  13.38  1572.50  1351.00  0.86  -1.53±0.42
20647 38.13  16.86  1244.00  694.00  0.56  1.45±0.22
20921 88.43  48.51  1457.50  1121.00  0.77  -2.34±0.59
20981 27.37  13.86  1352.50  911.00  0.67  -0.62±0.63
20988 53.26  26.95  1393.00  992.00  0.71  -1.62±0.91
21010 29.59  17.90  1330.50  867.00  0.65  -2.40±0.16
21321 58.98  31.80  1374.00  954.00  0.69  -3.27±0.46
21370 74.08  44.09  1373.00  952.00  0.69  -1.73±0.55
21695 20.19  17.99  1559.00  1324.00  0.85  -1.33±0.47
21710 36.22  15.48  1309.50  825.00  0.63  -1.17±0.32
21795 37.21  25.81  1691.00  1588.00  0.94  -1.45±0.32
21913 40.92  24.41  1403.00  1012.00  0.72  -1.61±0.30
22813 25.35  15.73  1326.00  858.00  0.65  -2.70±0.81
22944 49.15  30.45  1314.00  834.00  0.63  -2.05±1.08
23011 30.75  19.69  1312.50  831.00  0.63  -3.47±0.29
23025 29.97  19.80  1455.00  1116.00  0.77  0.08±0.12
23317 26.02  13.26  1335.00  876.00  0.66  -3.32±0.32
23320 36.19  19.15  1422.00  1050.00  0.74  -1.89±0.59
23322 23.35  15.26  1364.50  935.00  0.69  -2.61±0.11
23326 38.81  13.95  1294.50  795.00  0.61  -2.31±0.55
23330* 9.89  9.89  1307.50  821.00  0.63  -2.53±0.78
23333 42.27  25.02  1318.00  842.00  0.64  -1.73±1.00
23431 55.16  34.74  1397.00  1000.00  0.72  -2.48±0.28
23457 49.37  25.79  1315.00  836.00  0.64  -1.80±0.17
23514 26.53  17.47  1590.00  1386.00  0.87  -2.27±0.40
23571 44.54  28.89  1472.00  1150.00  0.78  0.11±0.21
23574 34.59  20.07  1355.00  916.00  0.68  0.28±0.25
23658 23.71  15.82  1645.00  1496.00  0.91  -2.22±0.44
23727 48.28  28.38  1321.00  848.00  0.64  -3.20±0.72
23917 29.54  17.20  1418.50  1043.00  0.74  -0.40±0.32
23919 26.08  17.49  1316.50  839.00  0.64  -1.08±0.21
24347 61.17  34.00  1284.00  774.00  0.60  -2.42±0.33
24406 49.20  26.01  1397.00  1000.00  0.72  -1.69±0.40
24583 94.80  57.18  1343.50  893.00  0.66  -0.60±0.40
24632 38.86  22.24  1338.00  882.00  0.66  -2.22±0.32
24653 35.70  24.79  1516.00  1238.00  0.82  -1.52±0.31
25102 57.44  33.68  1398.50  1003.00  0.72  0.11±0.56
25138 50.97  34.74  1417.50  1041.00  0.73  -2.25±0.42
25334 31.98  13.77  1318.00  842.00  0.64  -2.28±0.77
25487 33.04  16.61  1302.00  810.00  0.62  -0.92±0.78
25566 27.51  16.93  1424.50  1055.00  0.74  -0.46±0.52
25673 29.84  15.90  1315.00  836.00  0.64  -0.76±0.35
25861 66.56  32.63  1395.50  997.00  0.71  -2.47±0.35
26051 72.08  39.90  1471.50  1149.00  0.78  -2.00±0.32
26135 58.74  31.66  1437.00  1080.00  0.75  -1.07±0.43
26175 28.09  15.19  1429.00  1064.00  0.74  -1.41±0.30
26265 34.66  17.54  1222.00  650.00  0.53  -4.56±0.66
26369 35.82  16.90  1235.50  677.00  0.55  -2.95±0.37
26377 44.52  21.72  1264.50  735.00  0.58  -3.44±0.49
26504 48.78  24.68  1409.50  1025.00  0.73  -2.12±0.42
26512 36.28  22.28  1358.50  923.00  0.68  -2.01±0.72
26748 34.62  14.38  1169.00  544.00  0.47  0.92±0.78
26798 37.42  22.68  1358.50  923.00  0.68  -0.83±0.45
27109 25.36  10.44  1235.50  677.00  0.55  1.04±0.72
27209 102.55  51.86  1336.00  878.00  0.66  -0.11±0.67
27286 77.81  46.90  1410.50  1027.00  0.73  -1.85±0.54
27528 34.74  24.93  1464.50  1135.00  0.78  -0.80±0.36
27550 67.16  42.11  1443.00  1092.00  0.76  -1.27±0.35
27583 46.57  27.68  1479.50  1165.00  0.79  -1.74±0.21
27704 37.67  22.49  1432.00  1070.00  0.75  -0.39±0.35
27744 39.18  21.75  1391.00  988.00  0.71  -2.49±0.90
27833 46.88  31.20  1405.50  1017.00  0.72  -2.16±0.61
27838 33.26  19.15  1373.50  953.00  0.69  -2.44±0.42
27921 66.86  37.56  1330.00  866.00  0.65  -1.80±0.83
28033 38.12  21.53  1305.00  816.00  0.63  -0.54±0.54
28303 32.86  22.21  1396.00  998.00  0.71  -2.47±0.44
28368 50.47  24.11  1317.50  841.00  0.64  -2.22±1.06
28620 40.52  16.41  1171.50  549.00  0.47  -2.98±0.27
28772 35.62  22.04  1411.00  1028.00  0.73  -3.04±0.36
28781 32.84  18.72  1353.50  913.00  0.67  -2.31±0.36
28820 33.94  18.53  1384.00  974.00  0.70  -2.27±0.51
28838 38.75  20.03  1308.50  823.00  0.63  -2.66±0.62
28943 33.39  20.36  1328.50  863.00  0.65  -3.26±1.04
28948 104.97  64.86  1488.00  1182.00  0.79  -2.14±0.21
29047 125.17  64.94  1493.00  1192.00  0.80  -0.37±0.45
29053 40.11  23.86  1501.50  1209.00  0.81  -1.05±0.16
29058 171.03  107.28  1466.50  1139.00  0.78  -1.88±0.34
29061 43.28  20.29  1310.00  826.00  0.63  -2.9±0.80
29344 72.79  39.58  1321.00  848.00  0.64  -2.19±0.24
29520 46.41  30.11  1341.50  889.00  0.66  -1.15±0.33
29574 37.66  18.70  1411.50  1029.00  0.73  0.52±0.34
29580 113.03  69.79  1479.00  1164.00  0.79  -0.38±0.47
29681 64.88  38.69  1355.00  916.00  0.68  -2.52±0.42
29736 49.34  25.78  1410.50  1027.00  0.73  -1.63±0.47
29928 61.79  37.78  1413.50  1033.00  0.73  -3.26±0.89
30030 42.50  23.57  1427.50  1061.00  0.74  -1.84±0.22
30144 57.72  36.62  1402.00  1010.00  0.72  -2.42±0.47
30184 41.02  27.10  1470.00  1146.00  0.78  0.29±0.51
30275 34.87  16.04  1273.00  752.00  0.59  -3.38±0.87
30364 126.52  73.47  1466.50  1139.00  0.78  -2.37±0.26
30450 34.37  19.27  1427.00  1060.00  0.74  -1.00±0.46
30473 23.86  10.71  1406.00  1018.00  0.72  0.01±0.23
30631 33.68  19.85  1405.00  1016.00  0.72  -1.75±0.60
30878 25.74  19.24  1503.00  1212.00  0.81  -1.16±0.50
30898 40.55  22.93  1331.50  869.00  0.65  -1.04±0.22
30933 38.81  24.22  1358.50  923.00  0.68  0.97±0.40
31002 46.66  27.81  1514.00  1234.00  0.82  -0.99±0.42
31338 72.90  37.63  1401.00  1008.00  0.72  0.36±0.45
31360 27.48  17.94  1460.00  1126.00  0.77  1.09±1.40
31592 36.33  14.48  1160.00  526.00  0.45  0.48±1.00
31809 45.03  25.52  1316.50  839.00  0.64  -2.06±0.24
31965 60.25  37.81  1340.50  887.00  0.66  -1.26±0.48
31994 44.95  25.41  1326.00  858.00  0.65  -3.21±0.44
32023 24.46  12.96  1343.50  893.00  0.66  -1.85±1.34
32032 34.43  19.53  1351.50  909.00  0.67  -0.04±0.34
32093 43.79  29.46  1352.50  911.00  0.67  -1.54±0.41
32298 83.81  44.70  1346.00  898.00  0.67  -1.57±0.60
32304 27.94  14.92  1353.00  912.00  0.67  -1.19±0.88
32350 44.83  28.31  1294.00  794.00  0.61  -2.31±0.63
32374 33.22  13.76  1260.50  727.00  0.58  -3.52±1.76
32450 141.02  67.46  1336.00  878.00  0.66  -0.68±0.73
32859 158.16  94.59  1525.50  1257.00  0.82  -1.11±0.26
32949 32.75  22.60  1501.50  1209.00  0.81  -0.48±0.60
33168 38.05  21.76  1446.00  1098.00  0.76  -0.65±0.19
33367 48.13  36.10  1384.00  974.00  0.70  -1.25±0.31
MP-broadband
4777 32.54  40.47  2382.00  2970.00  1.25  -1.57±0.18
5483 21.42  31.92  2382.00  2970.00  1.25  -1.19±0.19
10039 71.93  73.61  2382.00  2970.00  1.25  -1.84±0.13
11797 124.24  147.00  2382.00  2970.00  1.25  -1.45±0.15
12411 42.27  46.80  2382.00  2970.00  1.25  -2.07±0.25
13694 115.79  140.49  2382.00  2970.00  1.25  -0.24±0.18
13869 25.16  28.30  2382.00  2970.00  1.25  -1.11±0.23
18626 27.03  25.38  2382.00  2970.00  1.25  -0.27±0.12
20995 84.19  102.89  2382.00  2970.00  1.25  -1.72±0.19
21017 35.08  38.51  2382.00  2970.00  1.25  -1.19±0.20
23087 10.74  14.14  2382.00  2970.00  1.25  -0.07±0.34
23883 26.47  33.35  2382.00  2970.00  1.25  -1.14±0.15
24281 36.08  43.74  2382.00  2970.00  1.25  -1.18±0.33
24331 120.65  138.09  2382.00  2970.00  1.25  -1.00±0.16
27211 35.54  38.59  2382.00  2970.00  1.25  -1.70±0.19
27884 26.79  36.93  2382.00  2970.00  1.25  -1.04±0.19
32644 79.98  83.67  2382.00  2970.00  1.25  -2.03±0.25
IP-Narrow-band
552 81.97  11.90  1396.00  998.00  0.71  -1.54±0.57
578 90.95  15.73  1416.00  1038.00  0.73  0.60±0.11
5723 380.92  59.07  1524.00  1254.00  0.82  -1.67±0.46
7082 99.60  16.25  1380.00  966.00  0.70  -0.77±0.5
11405 229.34  37.09  1499.50  1205.00  0.80  -1.18±0.45
13783 107.22  16.30  1294.00  794.00  0.61  -3.19±0.45
13863 184.08  26.83  1299.00  804.00  0.62  -2.17±0.95
16617 126.29  12.99  1228.00  662.00  0.54  -3.92±0.45
20814 169.95  26.45  1332.50  871.00  0.65  -3.09±0.45
21192 206.55  29.45  1402.00  1010.00  0.72  -1.78±0.5
23330* 197.48  33.60  1432.00  1070.00  0.75  -2.66±0.55
24375 168.30  29.39  1530.50  1267.00  0.83  -2.85±0.55
25523 110.47  20.00  1274.00  754.00  0.59  -3.26±0.69
26138 112.47  14.14  1235.00  676.00  0.55  -2.18±0.36
26496 124.93  15.46  1366.00  938.00  0.69  -1.40±0.37
28059 138.73  25.02  1457.50  1121.00  0.77  -2.18±0.64
29808 161.04  24.48  1381.50  969.00  0.70  -1.79±0.25
30268 121.05  16.41  1403.50  1013.00  0.72  0.16±0.38
MP-broadband
14956 126.18  26.79  2382.00  2970.00  1.25  -1.82±0.13
22556 142.62  50.68  2382.00  2970.00  1.25  -2.00±0.22
Note: * Radiation windows exist in both the main pulse and interpulse phases within one pulse period.

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Preprints 208281 g001
Figure 1. This figure shows two GPs events selected through the dual selection procedure in this observation. The black solid line represents the intensity variation of each GPs across 256 phase bins, while the blue dashed line shows 30 times the mean profile of all pulses, illustrating the significant enhancement of the GPs relative to the average emission. (a) The event has a signal-to-noise ratio (SNR) of 9.76, satisfying both criteria of SNR > 9 and a peak exceeding 30 times the mean profile peak, representing one of the weakest GPs that still exhibits a clearly discernible profile. (b) The event is a high-SNR GPs, with SNR well above 9.
Figure 1. This figure shows two GPs events selected through the dual selection procedure in this observation. The black solid line represents the intensity variation of each GPs across 256 phase bins, while the blue dashed line shows 30 times the mean profile of all pulses, illustrating the significant enhancement of the GPs relative to the average emission. (a) The event has a signal-to-noise ratio (SNR) of 9.76, satisfying both criteria of SNR > 9 and a peak exceeding 30 times the mean profile peak, representing one of the weakest GPs that still exhibits a clearly discernible profile. (b) The event is a high-SNR GPs, with SNR well above 9.
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Figure 2. Typical features of a narrow-band and a broadband GPs from the Crab pulsar, shown in panels (a) and (b), respectively. The upper sub-panels display the spectra, while the lower sub-panels show the cumulative energy distribution (CDF) curves. In the CDF plots, the black curve represents the cumulative energy in the on-pulse region, the light blue curve represents the cumulative energy in the off-pulse region, and the orange curve represents the net energy obtained by subtracting the off-pulse CDF from the on-pulse CDF. The red curve shows the piecewise linear fit to the data, and the dark blue curve indicates the fitting uncertainty. The red star marks the “cutoff frequency” of the pulse energy, while the blue triangle denotes the associated uncertainty range.
Figure 2. Typical features of a narrow-band and a broadband GPs from the Crab pulsar, shown in panels (a) and (b), respectively. The upper sub-panels display the spectra, while the lower sub-panels show the cumulative energy distribution (CDF) curves. In the CDF plots, the black curve represents the cumulative energy in the on-pulse region, the light blue curve represents the cumulative energy in the off-pulse region, and the orange curve represents the net energy obtained by subtracting the off-pulse CDF from the on-pulse CDF. The red curve shows the piecewise linear fit to the data, and the dark blue curve indicates the fitting uncertainty. The red star marks the “cutoff frequency” of the pulse energy, while the blue triangle denotes the associated uncertainty range.
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Figure 3. Histograms of the relative bandwidth (ratio of narrow-band bandwidth to central frequency) for narrow-band GPs in the main pulse and interpulse , shown in panels (a) and (b), respectively. In panel (a), the red curve represents the double-Gaussian fit to the main pulse distribution. The green and purple curves represent single-Gaussian fits to the same main pulse distribution.
Figure 3. Histograms of the relative bandwidth (ratio of narrow-band bandwidth to central frequency) for narrow-band GPs in the main pulse and interpulse , shown in panels (a) and (b), respectively. In panel (a), the red curve represents the double-Gaussian fit to the main pulse distribution. The green and purple curves represent single-Gaussian fits to the same main pulse distribution.
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Figure 4. Spectral morphology of two representative narrow-band GPs, shown in panels (a) and (b), respectively. Blue circles indicate the peak flux at different frequency bands, while the red curves represent the power-law fits to the data. The spectral index α characterizes the slope of each fit.
Figure 4. Spectral morphology of two representative narrow-band GPs, shown in panels (a) and (b), respectively. Blue circles indicate the peak flux at different frequency bands, while the red curves represent the power-law fits to the data. The spectral index α characterizes the slope of each fit.
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Figure 5. Histograms of the spectral indices for GPs in the main pulse and interpulse , shown in panels (a) and (b), respectively. In the plots, the blue histogram represents main pulse GPs, and the pink histogram represents interpulse GPs. The red curve indicates a Gaussian fit to the narrow-band GPs distribution.
Figure 5. Histograms of the spectral indices for GPs in the main pulse and interpulse , shown in panels (a) and (b), respectively. In the plots, the blue histogram represents main pulse GPs, and the pink histogram represents interpulse GPs. The red curve indicates a Gaussian fit to the narrow-band GPs distribution.
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Figure 6. Figure 6 shows the statistical distribution of the relative energy for narrow-band main pulse. The solid black line represents the observational data, while the red dashed line (log-normal distribution) and the blue dashed line (power-law distribution) correspond to the fits from two different models, respectively.
Figure 6. Figure 6 shows the statistical distribution of the relative energy for narrow-band main pulse. The solid black line represents the observational data, while the red dashed line (log-normal distribution) and the blue dashed line (power-law distribution) correspond to the fits from two different models, respectively.
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Figure 7. (a) Histogram of 3 σ widths for main pulse GPs. The red curve shows an empirical double-Gaussian fit to the narrow-band sample, with fitted centroids near 0.33 ms and 0.41 ms. Because the effective sampling interval after folding is about 0.13 ms per phase bin, these fitted components should be interpreted as approximate clustering locations in the observed width distribution rather than fully resolved intrinsic width states. (b) Scatter plot of 3 σ width versus signal-to-noise ratio (SNR) for narrow-band main pulse GPs.
Figure 7. (a) Histogram of 3 σ widths for main pulse GPs. The red curve shows an empirical double-Gaussian fit to the narrow-band sample, with fitted centroids near 0.33 ms and 0.41 ms. Because the effective sampling interval after folding is about 0.13 ms per phase bin, these fitted components should be interpreted as approximate clustering locations in the observed width distribution rather than fully resolved intrinsic width states. (b) Scatter plot of 3 σ width versus signal-to-noise ratio (SNR) for narrow-band main pulse GPs.
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Figure 8. Statistical distribution of waiting times between GPs from the Crab pulsar. The horizontal axis represents the pulse intervals ( Δ T ), and the vertical axis represents the corresponding occurrence rates, with both axes in logarithmic scale. Blue points indicate the observed data, while the red solid line shows the fit using a Weibull distribution model.
Figure 8. Statistical distribution of waiting times between GPs from the Crab pulsar. The horizontal axis represents the pulse intervals ( Δ T ), and the vertical axis represents the corresponding occurrence rates, with both axes in logarithmic scale. Blue points indicate the observed data, while the red solid line shows the fit using a Weibull distribution model.
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Figure 9. Histogram of the logarithm (base 10) of waiting times ( Δ T ) between GPs from the Crab pulsar, shown as log 10 Δ T . The horizontal axis represents log 10 Δ T , and the vertical axis represents the corresponding pulse counts. Blue bars indicate the observed data, while the red solid line shows the Gaussian fit to the distribution.
Figure 9. Histogram of the logarithm (base 10) of waiting times ( Δ T ) between GPs from the Crab pulsar, shown as log 10 Δ T . The horizontal axis represents log 10 Δ T , and the vertical axis represents the corresponding pulse counts. Blue bars indicate the observed data, while the red solid line shows the Gaussian fit to the distribution.
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Figure 10. Comparison of the observed burst rate of GPs from the Crab pulsar with Monte Carlo simulated Poisson sequences. The gray shaded region represents the 95% confidence interval of the burst rates derived from 1000 Monte Carlo simulations of random Poisson sequences. The gray dashed line indicates the mean burst rate of the simulated sequences. Blue points with error bars show the observed burst rate and its statistical uncertainty in each sliding window. The red horizontal line represents the global mean burst rate of the observed data over the full observation period (0–33,530 pulse periods), equal to 0.01.
Figure 10. Comparison of the observed burst rate of GPs from the Crab pulsar with Monte Carlo simulated Poisson sequences. The gray shaded region represents the 95% confidence interval of the burst rates derived from 1000 Monte Carlo simulations of random Poisson sequences. The gray dashed line indicates the mean burst rate of the simulated sequences. Blue points with error bars show the observed burst rate and its statistical uncertainty in each sliding window. The red horizontal line represents the global mean burst rate of the observed data over the full observation period (0–33,530 pulse periods), equal to 0.01.
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Table 1. Numbers of narrow-band and broadband giant pulses detected in the main pulse (MP) and interpulse (IP) phase windows.
Table 1. Numbers of narrow-band and broadband giant pulses detected in the main pulse (MP) and interpulse (IP) phase windows.
Narrow-band Broadband Total
MP 335 17 352
IP 18 2 20
Total 353 19 372
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