Constraining Circumburst Environments of GRBs with Jet Break Features in X-Ray Afterglows

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Abstract The nature of the circumburst medium serves as a key diagnostic for probing the progenitor systems and the physics of relativistic jet propagation in gamma-ray bursts (GRBs). In this work, we systematically infer the density profile index k (where n ∝ r − k ) from the change in the temporal decay index at the jet break (Δ α ). Within the framework of the uniform jet model, the two quantities are linked by the relation Δ α = (3 − k )/(4 − k ). We apply this diagnostic to a substantial and uniformly selected sample of 170 GRBs with clear jet breaks, identified from over 1400 Swift/XRT X-ray afterglows observed from 2004 to 2024. By fitting the light curves with a broken power-law model, we obtain Δ α for each burst and subsequently derive the corresponding k value. We then use the derived k values to classify the circumburst environment of each GRB. Our results reveal a near-even split: 82 bursts (∼48%) are consistent with a constant-density interstellar medium (ISM, k ≈ 0), while 88 bursts (∼52%) favor a wind environment ( k ≈ 2). For the 35 bursts with optical data, our X-ray-based classifications are generally consistent with independent multiband analyses. Additionally, we derive jet opening angles and true beaming-corrected energies for bursts with known redshifts.

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