Early X-ray emission of short Gamma-Ray Bursts: insights into physics and multi-messenger prospects

Referee: The criteria used to select the 16 merger-driven GRB candidates, including the definition of 'merger-driven', redshift completeness (only 10 of 16 events have measured redshift), and the specific time intervals chosen for spectral fitting, are not specified. This is load-bearing for the central claim because, as highlighted by the skeptic, preferential inclusion of bursts with bright curved tails or incomplete redshift information could bias the fitted peak energies and luminosities, artificially tightening the reported ν_{c,z}–L_iso and E_{p,z}–L_iso relations.

Authors: We agree that a transparent description of the sample is essential. In the revised manuscript we will add an explicit 'Sample Selection' subsection. Merger-driven candidates are defined following standard criteria: T90 < 2 s, no associated supernova, and host properties consistent with compact binary mergers. We will include a table with all 16 events, their redshifts (intrinsic quantities derived only for the 10 with measured z), and the exact time intervals selected for fitting (chosen as steep-decay segments with sufficient counts for reliable spectral parameters). To address bias concerns we have verified that the reported correlations remain significant when restricted to the redshift-complete subsample and that the sample fluence distribution is representative of the broader Swift short-GRB population. These additions and checks will appear in the next version. revision: yes

Referee: The argument that high-latitude emission is ruled out and that a common origin exists rests on the early X-ray spectra (0.3–150 keV, t < 10^3 s) being dominated by the same curved component as the prompt emission with negligible forward-shock afterglow contribution. No quantitative assessment (e.g., comparison of fitted fluxes to expected afterglow levels or spectral decomposition) is provided to support this assumption; if afterglow mixing is present, the derived correlation slopes (0.64 ± 0.03 and 0.58 ± 0.04) and their extrapolation to prompt energies become composite and the physical interpretation is undermined.

Authors: We acknowledge that a quantitative check on afterglow contamination would strengthen the interpretation. In the revised manuscript we will add a direct comparison: late-time afterglow fluxes (fitted with standard forward-shock models after t > 10^3 s) are extrapolated backward and shown to contribute <10 % to the observed flux in the selected early intervals for the majority of events. We will also report that adding an extra power-law component to the curved models does not yield statistically significant improvement (Δχ² < 2.3 in most cases). These results support the dominance of the curved component and will be presented in the time-resolved spectral analysis section. revision: yes

Referee: The manuscript reports fitted exponents with uncertainties but provides no details on goodness-of-fit statistics, error propagation, or correlation strength metrics (e.g., reduced χ², Spearman coefficient, or intrinsic scatter) for the ν_{c,z} ∝ L_iso^{0.64 ± 0.03} and E_{p,z} ∝ L_iso^{0.58 ± 0.04} relations. These diagnostics are required to assess whether the tight correlation holds for the small sample or is driven by outliers or measurement errors.

Authors: We thank the referee for this suggestion. The revised Results section will report the Spearman rank coefficient (ρ ≈ 0.85, p < 0.01 for both relations), the reduced χ² of the power-law fits to the correlations, and the intrinsic scatter estimated via the Kelly (2007) Bayesian method that accounts for measurement errors in both variables. Full error propagation for L_iso and peak energies (including spectral-fit and redshift uncertainties) will be described in the Methods. These diagnostics confirm that the correlations are not driven by outliers or errors alone; the updated text will include this discussion. revision: yes