Discovery of the linear energy dependence of the spectral lag of X-ray bursts from SGR J1935+2154

Spectral lag of the low-energy photons with respect to the high-energy ones is a common astrophysical phenomenon (such as gamma-ray bursts and the Crab Pulsar) and may serve as a key probe to the underlying radiation mechanism. However, spectral lag in keV range of the magnetar bursts has not been systematically studied yet. In this work, we perform a detailed spectral lag analysis with the Li et al.'s Cross-Correlation Function (Li-CCF) method for SGR J1935+2154 bursts observed by Insight-Hard X-ray Modulation Telescope (HXMT), Gravitational Wave High-energy Electromagnetic Counterpart All-sky Monitor (GECAM), and Fermi/Gamma-ray Burst Monitor (GBM) from 2014 July to 2022 January. We discover that the spectral lags of about 61 per cent (non-zero significance >1σ) bursts from SGR J1935+2154 are linearly dependent on the photon energy (E) with t_lag(E) = α(E/keV) + C, which may be explained by a linear change of the temperature of the blackbody-emitting plasma with time. The distribution of the slope (α) approximately follows a Gaussian function with mean and standard deviation of 0.02 ms keV^-1 (i.e. high-energy photons arrive earlier) and 0.02 ms keV^-1, respectively. We also find that the distribution can be well fitted with three Gaussians with mean values of ~-10.009, 0.013, and 0.039 ms keV^-1, which may correspond to different origins of the bursts. These spectral lag features may have important implications on the magnetar bursts.