A Comprehensive Analysis of Insight-HXMT Gamma-Ray Burst Data. I. Power Density Spectrum

Power Density Spectrum (PDS) is one of the powerful tools to study light curves of gamma-ray bursts (GRBs). We show the average PDS and individual PDS analysis with {\it Hard X-ray Modulation Telescope} (also named \insighthxmt) GRBs data. The values of power-law index of average PDS ($\alpha_{\bar{P}}$) for long GRBs (LGRBs) vary from 1.58-1.29 (for 100-245, 245-600, and 600-2000 keV). The \insighthxmt\ data allow us to extend the energy of the LGRBs up to 2000 keV, and a relation between $\alpha_{\bar{P}}$ and energy $E$, $\alpha_{\bar{P}}\propto E^{-0.09}$ (8-2000 keV) is obtained. We first systematically investigate the average PDS and individual PDS for short GRBs (SGRBs), and obtain $\alpha_{\bar{P}}\propto E^{-0.07}$ (8-1000 keV), where the values of $\alpha_{\bar{P}}$ vary from 1.86 to 1.34. The distribution of power-law index of individual PDS ($\alpha$) of SGRB, is consistent with that of LGRB, and the $\alpha$ value for the dominant timescale group (the bent power-law, BPL) is higher than that for the no-dominant timescale group (the single power-law, PL). Both LGRBs and SGRBs show similar $\alpha$ and $\alpha_{\bar{P}}$, which indicates that they may be the result of similar stochastic processes. The typical value of dominant timescale $\tau$ for LGRBs and SGRBs is 1.58 s and 0.02 s, respectively. It seems that the $\tau$ in proportion to the duration of GRBs $T_{90}$, with a relation $\tau \propto T_{90}^{0.86}$. The GRB light curve may result from superposing a number of pulses with different timescales. No periodic and quasi-periodical signal above the 3$\sigma$ significance threshold is found in our sample.