A Full-width-at-half-maximum Method for Measuring Spectral Time Lags in Gamma-Ray Bursts

Abstract Spectral time lag is an important temporal property of gamma-ray bursts (GRBs) and provides insight into both emission physics and potential propagation effects. Conventional methods for extracting spectral lags, such as cross-correlation or pulse fitting, typically rely on comparisons between narrow energy bands and require relatively high signal-to-noise ratios. In this work, we propose a new method to estimate spectral time lag based on the Full Width at Half Maximum (FWHM) of GRB light curve structures. By combining light curves from multiple energy bands and optimizing their relative offsets to minimize the normalized FWHM of the merged signal, this method exploits information from a broad energy range and is therefore suitable for relatively faint GRBs. We demonstrate the procedure using GRB 131030A and estimate uncertainties through Monte Carlo simulations. A statistically consistent time lag is obtained between adjacent energy bands. Assuming, as an extreme case, that the measured lag is entirely attributed to Lorentz invariance violation, we derive a corresponding lower limit on the quantum gravity energy scale. This method provides a complementary approach to existing lag extraction techniques and may enable spectral timing studies for GRBs that are inaccessible with traditional methods.