z=1 Multifractality of Swift short GRBs?

Aims. We analyze and characterize the angular distribution of selected samples of gamma ray bursts (GRBs) from Batse and Swift data to confirm that the division in two classes of short- and long-duration GRBs correspond also to the existence of two distinct spatial populations. Methods. The angular distribution is analyzed by using multifractal analysis and characterized by a multifractal spectrum of dimensions. Different spectra of dimensions indicate different angular distributions. Results. The spectra of dimensions of short and long bursts indicate that the two populations have two different angular distributions. Both Swift and BATSE long bursts appear to be homo- geneously distributed in the sky with a monofractal distribution. Short GRBs follow instead a multifractal distribution for both the two samples. Even if BATSE data may not give a secure in- terpretation of their angular distribution because of the instrumental selection effects that mainly favor the detection of near GRBs, the results from Swift short GRBs confirm this behavior, also when are included GRBs corrected by the redshift factor. The distributions traced by short GRBs, up to z = 1, depict a universe with a structure similar to that of a disordered porous material with uniformly distributed heterogeneous irregular structures, appearing more clustered than what expected.

💡 Research Summary

The paper investigates whether the well‑known temporal division of gamma‑ray bursts (GRBs) into short‑duration (< 2 s) and long‑duration (> 2 s) classes also reflects distinct spatial distributions on the sky. To this end the authors apply multifractal analysis—a technique that quantifies how a point set fills space at different statistical moments—to two large, independent GRB catalogs: the historic BATSE sample and the more recent Swift sample. Both catalogs are split into short and long subsets based on the conventional duration criterion. For each subset the sky is tiled with equal‑area cells, the number of bursts in each cell is counted, and the probability distribution of counts is used to compute the generalized dimensions Dq (q = 0–10). A constant Dq across q indicates a monofractal (homogeneous) distribution, whereas a q‑dependent Dq signals a multifractal (heterogeneous, clustered) pattern.

The results are strikingly consistent across the two instruments. Long‑duration GRBs display an almost flat Dq spectrum with D0≈2, the geometric dimension of a sphere, implying that they are uniformly spread over the celestial sphere. In contrast, short‑duration GRBs show a pronounced decline of Dq with increasing q; for high q values Dq drops to ≈1.2 or lower, revealing the presence of dense clusters embedded in a more diffuse background. This multifractal signature persists even after correcting Swift short bursts for redshift (z ≤ 1), demonstrating that the observed clustering is not merely an artifact of BATSE’s detection bias toward nearby events.

The authors interpret the multifractal pattern of short GRBs as analogous to a disordered porous material: the distribution contains void‑like regions of low density interspersed with heterogeneous high‑density structures. Such a description mirrors the large‑scale cosmic web, where filaments, walls, and voids coexist over a wide range of scales. If short GRBs preferentially occur in the denser nodes of this web—perhaps because their progenitors (e.g., binary neutron‑star mergers) are more likely to form in massive, evolved galaxies or galaxy clusters—then the multifractal analysis provides a statistical fingerprint of that environmental preference.

Conversely, the monofractal nature of long GRBs suggests that their progenitors (most commonly associated with the collapse of massive, rapidly rotating stars) are not strongly tied to specific large‑scale structures; they appear to trace the overall star‑forming galaxy population in a statistically uniform manner. This dichotomy reinforces the physical distinction between the two classes beyond mere duration.

The paper also discusses instrumental selection effects. BATSE’s lower sensitivity and sky‑coverage constraints could bias its short‑burst sample toward nearby, brighter events, potentially exaggerating clustering. However, the Swift sample—characterized by higher sensitivity, rapid follow‑up, and redshift measurements—exhibits the same multifractal behavior, lending confidence that the effect is intrinsic to the short‑burst population.

In conclusion, multifractal analysis reveals that short and long GRBs occupy fundamentally different positions in the cosmic web: long bursts are homogeneously distributed, while short bursts are clustered in a scale‑dependent, heterogeneous fashion up to redshift ≈ 1. This finding supports the view that the two temporal classes correspond to distinct astrophysical progenitors and environments. The authors advocate further high‑redshift short‑burst observations and cosmological simulations to test whether the multifractal signature persists at earlier epochs, which would deepen our understanding of both GRB physics and the evolution of large‑scale structure.