An invariant energy release hierarchy in a repeating fast radio burst

Abstract: Fast radio bursts (FRBs) are luminous millisecond radio transients whose physical origin remains unsettled. A key diagnostic is whether their burst-energy distributions retain characteristic physical scales that are intrinsic and temporally stable within an individual engine. Here we report a 3.2-year monitoring campaign of the hyperactive repeater FRB~20220529 with FAST and Parkes, yielding more than 1,300 bursts spanning nearly five orders of magnitude in spectral energy density. The cumulative burst-rate distribution is described by an exponential-plus-power-law (EXP+PL) form, linking a low-energy exponential component with characteristic scale (E_0) to a scale-free bright-end tail. This scale remains invariant despite the burst rate declining by more than an order of magnitude, revealing a stable dissipation scale decoupled from the source's macroscopic trigger activity. Within a magnetar interpretation, this phenomenology is consistent with localized sub-critical reconnection episodes coexisting with plasmoid-mediated magnetic avalanches in a twisted magnetosphere. The invariant (E_0) constrains the dissipation region to the inner-to-middle magnetosphere and reveals a robust energy-release hierarchy beneath the variable activity of repeating FRBs, providing an observational benchmark for relativistic reconnection in an ultra-magnetized neutron-star environment.

• The paper Uses observations of repeating fast radio burst FRB 20220529 over 3.2 years to show that these bursts maintain a stable energy release distribution despite variability in burst rates.
• The consistent results obtained model the burst energy distribution as two components: an exponential low-energy part and a power-law high-energy tail.
• Results argue in favor of a magnetar recombination hierarchy, suggesting bursts are generated by reconnection events in a twisted magnetar magnetosphere.

Observational dataset

The paper presents a 3.2-year monitoring campaign of the hyperactive repeating FRB 20220529, conducted from 22 June 2022 to 8 September 2025 with the Five-hundred-meter Aperture Spherical radio Telescope (FAST) and the Parkes 64-m telescope. The FAST sample comprises 1,265 bursts (1,215 from on-source pointings, giving a mean on-source rate of 20.0 bursts per hour), spanning spectral energy densities from $2.3\times10^{27}$ to $2.6\times10^{31}$ erg Hz$^{-1}$. Two outburst epochs centered on August 2022 and March 2023 reached peak rates of 134 and 204 bursts per hour; excluding these, the quiescent mean rate is 7.6 bursts per hour, and the source exhibits a clear secular fading trend across the baseline. The Parkes Ultra-Wideband Low receiver contributed 58 bursts over 204.2 hours of integration, extending the energy coverage to $8.6\times10^{31}$ erg Hz$^{-1}$. The combined dynamic range spans nearly five orders of magnitude in spectral energy density.

Flux calibration used the radiometer equation with measured system temperatures and gains, and completeness was established by injecting 10,000 mock bursts into real data; the 95% detection thresholds are 22.6 mJy ms (FAST) and 398.1 mJy ms (Parkes). All core statistical fits were restricted to energies above the FAST completeness threshold to suppress selection bias, and the Parkes dataset was deliberately excluded from the primary fitting and reserved for independent validation of the high-energy tail.

A two-component energy distribution and its statistical preference

The cumulative burst-rate distribution $R(>E)$ is modeled as a sum of an exponential and a power-law component,

$$R(>E)=A\exp\!\left(-E/E_0\right)+B(E/10^{30}\,\mathrm{erg\ Hz^{-1}})^{-\gamma},$$

fitted with Bayesian MCMC under Poisson count statistics. Head-to-head comparisons against five alternatives—single power law, single exponential, broken power law, smoothly broken power law, and double exponential—show that the EXP+PL model is decisively preferred: it achieves $\chi^2/\mathrm{dof}=0.7$ and BIC = 17.9, versus BIC values of 52.3–416.4 for all competing models. This preference persists when the analysis is restricted to the 651 bursts whose bandwidth falls entirely within the FAST passband ($E_0 = 5.14\times10^{28}$ erg Hz$^{-1}$), ruling out band-limited detection effects as a driver of the two-component morphology.

The high-energy branch was verified independently: Parkes-only bursts follow a power law with index $2.6\times10^{31}$0, consistent with continuation of the FAST bright-end tail rather than an exponential cutoff. A complementary Tsallis $2.6\times10^{31}$1-Gaussian analysis of the energy return distribution shows that the full sample lacks scale invariance, as expected when a characteristic scale dominates, while the subset above $2.6\times10^{31}$2 erg Hz$2.6\times10^{31}$3 approaches scale-invariant statistics consistent with avalanche-like behavior. Together these results establish a robust decomposition into a low-energy exponential component with e-folding scale $2.6\times10^{31}$4 and a scale-free bright-end tail.

Temporal invariance of the characteristic scale

The central result concerns temporal stability. Dividing the FAST sample into four chronological epochs of roughly 300 bursts each, the EXP+PL morphology persists throughout, but the component normalizations $2.6\times10^{31}$5 and $2.6\times10^{31}$6 decline substantially in the final low-activity epoch. In contrast, $2.6\times10^{31}$7 remains confined to $2.6\times10^{31}$8–$2.6\times10^{31}$9 erg Hz$^{-1}$0—a variation of less than a factor of 1.5—while the global burst rate drops by more than an order of magnitude. This decoupling of the characteristic dissipation scale from the macroscopic trigger rate indicates that the source fades by activating fewer reconnection sites rather than by shifting the local energy scale of each event.

Robustness checks support this inference: alternative epoch-splitting schemes (equal-time and activity-based), a 300-burst rolling window analysis, fixed-$^{-1}$1 refits (Epoch 4 with $^{-1}$2 yields $^{-1}$3 erg Hz$^{-1}$4), and the full-bandwidth subsample all give consistent results. The high-energy index $^{-1}$5 remains within 0.74–0.99 during the three burst-rich epochs but flattens to 0.39 in Epoch 4; the authors attribute this to small-number statistics at low activity and adopt the full-sample value $^{-1}$6 as fiducial. A logarithmic stability budget derived from $^{-1}$7 implies that, if microphysical factors are stable, the emission radius can drift by at most about 10% over the baseline—a strong constraint on any model invoking evolving dissipation geometry.

Comparison with other hyperactive repeaters

Applying the identical fitting framework to published samples of other active repeaters yields one clear counterpart. For FRB 20220912A (696 bursts spanning roughly four orders of magnitude), EXP+PL is again statistically preferred ($^{-1}$8, BIC = 19.2), with $^{-1}$9 erg Hz$8.6\times10^{31}$0 and $8.6\times10^{31}$1. The phenomenological alignment between the two sources, despite differing instruments, frequency coverage, and selection functions, argues against an instrumental or purely source-specific origin for the hierarchy.

However, no significant EXP+PL preference was found for FRB 20121102, FRB 20201124A, or FRB 20240114A. The authors treat these nulls cautiously: resolving a two-component structure requires the completeness threshold to lie near or below $8.6\times10^{31}$2, sufficient dynamic range, and uniform cadence, conditions met mainly by the two best-monitored sources. These sources are therefore classified as currently inconclusive rather than population-level counterexamples. Whether $8.6\times10^{31}$3 is similarly invariant in FRB 20220912A remains an open question answerable only with epoch-resolved analysis.

Interpretation as a thresholded reconnection hierarchy

The theoretical framework interprets each burst as a reconnection episode in a twisted magnetar magnetosphere, characterized by an effective avalanche size $8.6\times10^{31}$4 mapped to observed spectral energy density via $8.6\times10^{31}$5, where $8.6\times10^{31}$6 absorbs geometry, coherent radiative efficiency, beaming, and propagation. Using a Galton–Watson branching process with Poisson offspring of mean $8.6\times10^{31}$7, subcritical episodes ($8.6\times10^{31}$8) produce Borel-distributed avalanche sizes with an exponential cutoff at $8.6\times10^{31}$9, naturally generating the low-energy exponential component. A power law emerges if the event-to-event distribution of branching ratios has support approaching criticality: a mixture over $^{-1}$0 yields $^{-1}$1 without requiring every event to sit exactly at $^{-1}$2. Notably, macroscopic current sheets have global Lundquist numbers of order $^{-1}$3, far above the plasmoid threshold $^{-1}$4; the exponential component therefore reflects confined propagation of local triggers, not globally stable sheets.

Anchoring the full-sample value $^{-1}$5 erg Hz$^{-1}$6 to the local magnetic free-energy reservoir constrains the emission radius to $^{-1}$7 cm for canonical magnetar fields, placing the dissipation layer in the inner-to-middle magnetosphere. Because $^{-1}$8, this conclusion depends only weakly on the composite nuisance parameter encapsulating beaming, efficiency, reconnecting-field fraction, and volume. The required effective active-volume factor ($^{-1}$9) exceeds the single-plasmoid minimum $R(>E)$0 by many orders of magnitude, indicating a mesoscopic reconnecting region. The authors emphasize that the conversion of dissipated magnetic energy into coherent GHz radiation remains model dependent, so the mapping is phenomenological rather than calorimetric.

Limitations and open questions

Several caveats qualify these results. The late-time flattening of the power-law index rests on few bright bursts, and although fixed-$R(>E)$1 checks preserve the stability of $R(>E)$2, the behavior of the high-energy tail during extended quiescence is not well characterized. The branching-ratio interpretation treats $R(>E)$3 as phenomenological; if $R(>E)$4 were controlled by a drift in a single effective branching ratio, the allowed variation would shrink to $R(>E)$5 near criticality—but this limiting case should not be read as evidence that all bursts share one narrowly distributed $R(>E)$6. The comparison sample is limited: FRB 20220912A's epoch-resolved invariance of $R(>E)$7 is untested, and the null results for other repeaters may reflect sampling rather than intrinsic differences. Finally, the frequency dependence of $R(>E)$8—a predicted diagnostic of emission geometry—and correlations with rotation measure, dispersion measure, or polarization variations remain untested with present data.

Conclusion

Using more than 1,300 bursts from a 3.2-year dual-telescope campaign, this work establishes that the burst-energy distribution of FRB 20220529 follows a stable exponential-plus-power-law form whose characteristic scale $R(>E)$9 varies by less than a factor of 1.5 while the burst rate declines by more than an order of magnitude. The invariance elevates the characteristic scale from a fitting parameter to a persistent engine property, constraining the localized dissipation region to the inner-to-middle magnetosphere within a thresholded magnetar reconnection picture. Whether such invariant energy-release hierarchies are common among repeating FRBs is now a well-posed empirical question for future multi-year, multi-frequency, completeness-characterized monitoring campaigns.