Multi-scale Memory and Regime Shift in the Hyperactive Repeating FRB 20240114A

Abstract: We present a statistical analysis of FRB~20240114A, a hyperactive repeating fast radio burst, based on 11,553 bursts detected by FAST over 214 days. Our main findings are fourfold. (1) On the most active day (MJD~60381, 3,197 bursts in 4.38 hr), event-rate coherence analysis reveals persistent correlated activity extending up to 3600~s, the longest reported for any repeating FRB, showing memory persists even in intense bursting epochs. (2) The waiting-time distribution on this day is well described by three exponentials, whereas the full 214-day sample develops a threshold power-law tail, indicating burst statistics depend on the observational baseline, with long-range correlations emerging only over longer timescales, a hallmark of self-organized criticality. (3) Rescaled range (R/S) analysis of waiting times reveals a broken power law, with Hurst exponents $H_1=0.63\pm0.02$ (short-lag weak memory) and $H_2=1.04\pm0.02$ (long-lag non-stationary drift). The break corresponds to $\sim$1 hour, consistent with the 3600~s coherence limit. R/S analysis of energies similarly exhibits a break ($H_1=0.60\pm0.01$, $H_2=1.10\pm0.05$) at a different lag, reinforcing that non-stationarity affects both temporal and energetic properties. (4) Energy distributions exhibit waiting-time-dependent slopes that are consistent with the full and daily samples, and the high-energy cutoff remains constant across waiting-time groups, suggesting that the maximum energy scale is an intrinsic source property. Together, these results establish a multi-scale memory framework: the source behaves stochastically on short timescales but exhibits systemic non-stationarity over months, providing benchmarks for burst models and highlighting the need for long-term, high-cadence monitoring to capture temporal complexity.

• The paper analyzes 11,553 FAST-detected bursts and identifies coherent rate growth lasting at least 3,600 seconds, showing that deterministic memory can persist despite locally exponential waiting times.
• The paper finds a baseline-dependent regime shift: a three-exponential model fits the densest four-hour epoch, while the full 214-day sample requires two exponentials plus a power-law tail beyond roughly 30 seconds.
• The paper links broken R/S scaling and waiting-time-dependent energy indices to multi-scale, non-stationary dynamics, while noting that instrumental incompleteness and the single-source sample limit physical interpretation.

Dataset and motivation

This paper presents a statistical characterization of the hyperactive repeating fast radio burst (FRB) 20240114A, using 11,553 bursts detected with FAST over MJD 60337–60552 (214 days, 33.86 hr on-source), the largest single-source FRB sample assembled to date (2608.19713). The source was discovered by CHIME/FRB [2026ApJ...997..334S] and lies at $z=0.1306$ behind a galaxy cluster [2025ApJ...980L..24C]. The mean burst rate is $\sim341~\mathrm{hr^{-1}}$, peaking at $729~\mathrm{hr^{-1}}$ on MJD 60381, when 3,197 bursts were recorded in a single 4.38 hr window. The authors use this densest epoch as a short-baseline benchmark and contrast it with the full seven-month sample to test whether burst statistics depend on the observational timescale — a question motivated by conflicting prior results: some analyses report clustering and power-law tails consistent with self-organized criticality (SOC) [2023ApJ...949L..33W, 2024ApJ...975..188W], while others find nearly Poissonian behavior [Sang2024, 2024SciBu..69.1020Z].

Four complementary diagnostics are applied: event-rate coherence analysis, waiting-time distribution fitting (with BIC-based model selection), rescaled range (R/S) analysis yielding Hurst exponents, and waiting-time-conditioned energy distributions fit with a low-break cutoff power law (Lb-CPL). All parameters are estimated via MCMC with uniform priors.

Coherent rate growth up to one hour

On MJD 60381, the coherence analysis identifies 87 structures of at least four consecutive bins with strictly increasing burst rate, across time resolutions from 20 s to 3800 s; some fitted nonlinearity indices satisfy $p \ge 2.0$, indicating super-linear growth. The longest coherent structure extends to $\delta T = 3600$ s, exceeding the previous record of 2200 s for FRB 20121102A [2023ApJ...949L..33W]. Because the search is bounded by the 4.38 hr observing window, this value is explicitly a lower limit on the true memory timescale.

The implication is significant: even when the waiting-time distribution is purely exponential — nominally Poissonian — the burst rate retains a deterministic memory component operating from minutes up to roughly an hour. Exponential inter-arrival statistics and coherent rate evolution are therefore not mutually exclusive descriptions of the same process.

Waiting-time distributions depend on the observational baseline

The two baselines yield qualitatively different fits. On MJD 60381, the differential waiting-time distribution is best described by three exponentials (3Exp), with $\Delta\mathrm{BIC} > 10$ over both the 2Exp and Exp+TPL alternatives; no power-law tail is required. This multi-exponential structure implies a superposition of Poisson-like processes with distinct characteristic rates, independently corroborated by L.-X. Zhang et al. (in prep.) using a different burst identification criterion.

In contrast, the full 214-day sample requires two exponentials plus a threshold power-law tail (2Exp+TPL), again with $\Delta\mathrm{BIC} > 10$: exponentials govern $\Delta t \lesssim 0.3$ s, while the tail beyond $\Delta t \gtrsim 30$ s follows $(x+x_0)^{-\alpha}$. The emergence of a scale-free tail only when the baseline extends from hours to months is presented as a hallmark of SOC behavior, resolving the apparent contradiction between memory-reporting and Poisson-reporting studies: long-range correlations become manifest only above a threshold observational span.

Broken R/S scaling and non-stationarity

R/S analysis of the waiting-time sequence indexed by burst order gives a single power law with $\sim341~\mathrm{hr^{-1}}$0 on MJD 60381 — near-random — but a broken power law for the full sample:

Sequence	Short-lag $\sim341~\mathrm{hr^{-1}}$1	Long-lag $\sim341~\mathrm{hr^{-1}}$2	Break lag
Waiting time	$\sim341~\mathrm{hr^{-1}}$3	$\sim341~\mathrm{hr^{-1}}$4	$\sim341~\mathrm{hr^{-1}}$5 ($\sim341~\mathrm{hr^{-1}}$6 min)
Energy	$\sim341~\mathrm{hr^{-1}}$7	$\sim341~\mathrm{hr^{-1}}$8	$\sim341~\mathrm{hr^{-1}}$9

The long-lag exponents exceed unity in both cases, which the authors interpret as non-stationary fractional-Brownian-like drift rather than stationary persistence. Converting the waiting-time break via the average burst rate gives $729~\mathrm{hr^{-1}}$0 s, closely matching the 3600 s coherence limit — although the authors caution that this conversion is approximate given the strongly variable burst rate, so the coincidence should be treated as suggestive rather than definitive. The energy-sequence break occurs at a different lag ($729~\mathrm{hr^{-1}}$1 hr), consistent with waiting times and energies probing triggering dynamics versus energy release, respectively. That both sequences independently show $729~\mathrm{hr^{-1}}$2 supports the claim that the non-stationarity is systemic rather than an artifact of a single statistic.

These results extend earlier R/S work on FRB 20121102A and 20201124A, where only stationary values ($729~\mathrm{hr^{-1}}$3 and $729~\mathrm{hr^{-1}}$4) were found [2023ApJ...949L..33W]; the detection of $729~\mathrm{hr^{-1}}$5 requires the longer 214-day baseline and would be inaccessible to shorter campaigns. The results also complement global stochasticity diagnostics based on the Pincus index and Lyapunov exponents [Xu2026]: the source appears nearly random on short lags but exhibits structural non-stationarity that entropy-based global measures do not capture.

Waiting-time-dependent energy indices

Splitting bursts into short-wait ($729~\mathrm{hr^{-1}}$6 s) and long-wait ($729~\mathrm{hr^{-1}}$7 s) groups, Lb-CPL fits give $729~\mathrm{hr^{-1}}$8 for the full sample and $729~\mathrm{hr^{-1}}$9 for MJD 60381 — consistent within uncertainties, suggesting a scale-invariant feature. The shallower index during rapid bursting parallels the decrease of the Gutenberg–Richter $p \ge 2.0$0-value with increasing shear stress in earthquakes [1956BuSSA..46..105G], supporting a stress-dependent SOC interpretation. The high-energy cutoff $p \ge 2.0$1 remains constant between wait-time groups in both samples, implying that the maximum energy scale is an intrinsic source property independent of instantaneous burst rate. The measured indices $p \ge 2.0$2–1.56 are consistent with the fractal-diffusive SOC prediction of $p \ge 2.0$3 for three-dimensional energy dissipation [2012A&A...539A...2A].

Limitations

The authors identify several caveats that bear directly on the strength of these conclusions. First, R/S analysis indexes sequences by burst order rather than physical time, so the inferred break timescale depends on an approximate conversion through the average burst rate. Second, low-energy incompleteness may bias the energy indices: missed faint bursts in dense sequences would artificially steepen $p \ge 2.0$4 and reduce the true $p \ge 2.0$5. If the intrinsic $p \ge 2.0$6 is smaller than measured, the stress-dependent SOC interpretation weakens and the waiting-time dependence could be predominantly a selection effect. Against a purely instrumental origin, however, $p \ge 2.0$7 does not increase on the densest day, where pulse-overlap incompleteness should be most severe. Third, the 3600 s coherence limit is a lower bound set by the 4.38 hr window. Fourth, all results derive from a single source; generalization to the broader repeating-FRB population remains untested. Whether the $p \ge 2.0$81 hr timescale is intrinsic to the magnetar or imposed by the observing configuration is left open, as is whether the R/S break correlates with source properties such as spin period or magnetic field strength in other repeaters.

Conclusion

Using the largest burst sample available for any repeating FRB, this work establishes a multi-scale memory framework for FRB 20240114A: coherent rate growth to at least 3600 s, a transition from multi-exponential to power-law waiting-time statistics as the baseline lengthens, broken R/S scaling with $p \ge 2.0$9 in both waiting-time and energy sequences, and a scale-invariant, Gutenberg–Richter-like dependence of the energy index on waiting time with a fixed high-energy cutoff. Collectively, these results indicate a regime shift from locally random, Poisson-like behavior on seconds-to-hours timescales to systematic non-stationarity over weeks to months, with the $\delta T = 3600$01 hour scale emerging as a candidate fundamental timescale of the burst dynamics whose physical origin remains undetermined.