The energy structure function of fast radio bursts supports a stochastic origin model

The origin of fast radio bursts (FRBs) has remained a mystery up to now. There are two kinds of process invoking neutron stars as an origin of FRBs, namely inner-driven starquakes and outer-driven collisions with interstellar objects (ISOs). The former origin should exhibit an earthquake-like statistical behavior while the latter should show a stochastic process. In this paper, we introduce a new statistical method by making use of the energy structure function of active repeating FRBs and earthquakes. We find that the energy structure function of FRBs exhibits a very different statistical behavior compared to that of earthquakes. On small time-interval scales, the energy of an earthquake show a tendency to decay with time-interval and the energy difference of a pair of events increases with time-interval. Such a behavior is not found in FRBs, whose energy function is very similar to those of a stochastic process. Our result shows that repeating FRBs may have an origin process differing from that of earthquakes, i.e., FRBs arise from a series of unrelated events such as collisions of a neutron star with ISOs.

💡 Research Summary

This paper presents a novel statistical analysis aimed at deciphering the physical origin of Fast Radio Bursts (FRBs), particularly the repeating class. The central mystery revolves around whether FRBs are generated by internal processes of neutron stars (magnetars), analogous to “starquakes,” or by external, random events such as collisions with interstellar objects (ISOs) like asteroids. The former predicts a correlated, earthquake-like sequence of events, while the latter predicts a stochastic, memoryless process.

To distinguish between these models, the authors introduce and apply the “Energy Structure Function (ESF),” a statistical tool adapted from fluid dynamics and time-series analysis. The ESF quantifies how the difference in energy between two events changes as a function of the time interval (τ) separating them. The first-order ESF, S1(τ), measures the average directional change in energy, while the second-order ESF, S2(τ), measures the variance or fluctuation of these energy differences. If event energies are correlated in time, the ESF will show a systematic variation with τ; if they are independent, the ESF will remain constant.

The study utilizes high-quality data from several actively repeating FRBs (FRB 20121102A, 20201124A, 20220912A, 20240114A) observed with the high-sensitivity Five-hundred-meter Aperture Spherical radio Telescope (FAST). For comparison, seismic data from the 2019 Southern California and 2011 Tohoku earthquakes are meticulously processed, and a synthetic dataset of completely random events is generated as a stochastic benchmark.

The results reveal a striking dichotomy. The second-order ESF for earthquake data exhibits a characteristic shape: it rises sharply at small time intervals (τ < ~10^4 s) and then plateaus. This indicates that earthquakes occurring close in time tend to have similar energies (small energy difference), but as the time gap increases, the energy difference becomes larger and eventually stabilizes, reflecting the stress accumulation and release process of seismic sequences. The first-order ESF for earthquakes also shows a clear evolution with τ.

In stark contrast, the ESF for all four repeating FRB sources remains remarkably flat across the entire observed range of time intervals, from milliseconds to days. Both S1(τ) and S2(τ) hover around constant values, showing no significant trend or scaling with τ. This pattern is statistically indistinguishable from that of the purely stochastic synthetic data.

The authors interpret this clear divergence as strong evidence against the starquake model for the observed repeating FRBs. The earthquake-like temporal correlations predicted by an internal, driven process are absent. Instead, the “memoryless” and stochastic nature of the FRB energy sequences aligns perfectly with the predictions of the external ISO collision model. In this scenario, each FRB is triggered by an independent encounter between the neutron star and a randomly encountered ISO, with no causal link or energy correlation between successive bursts.

The paper further demonstrates the robustness of the result by testing different energy thresholds and time windows for the seismic data, confirming that the observed difference is intrinsic. It argues that the ESF provides a more integrated, multi-parameter view of event sequences compared to traditional univariate analyses (like waiting time or energy distributions alone), successfully capturing the lack of spatio-temporal correlation in FRB energies.

In conclusion, this work provides a compelling statistical argument based on the Energy Structure Function that the burst sequences of active repeating FRBs are fundamentally stochastic. This finding significantly favors an origin involving random external triggers, such as collisions with interstellar objects, over an internal starquake mechanism for these sources. It offers a fresh methodological perspective in the ongoing quest to unravel the FRB enigma.