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

Abstract The power density spectrum (PDS) is a powerful tool to study light curves of gamma-ray bursts (GRBs). We show the average PDS and individual PDS analysis with GRB data from the Hard X-ray Modulation Telescope (also named Insight-HXMT). The values of the power-law index of the average PDS ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> </mml:msub> </mml:math> ) for long GRBs (LGRBs) vary from 1.58 to 1.29 (for 100–245, 245–600, and 600–2000 keV). The Insight-HXMT data allow us to extend the energy of the LGRBs up to 2000 keV, and a relation between <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> </mml:msub> </mml:math> and energy E is obtained: <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> </mml:msub> <mml:mo>∝</mml:mo> <mml:msup> <mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.09</mml:mn> </mml:mrow> </mml:msup> </mml:math> (8–2000 keV). We first systematically investigate the average PDS and individual PDSs for short GRBs (SGRBs), and obtain <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> </mml:msub> <mml:mo>∝</mml:mo> <mml:msup> <mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.07</mml:mn> </mml:mrow> </mml:msup> </mml:math> (8–1000 keV), where the values of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> </mml:msub> </mml:math> vary from 1.86 to 1.34. The distribution of the power-law index of an individual PDS ( α ) of an SGRB is consistent with that of an LGRB, and the α value for the group with a dominant timescale (the bent power law) is higher than that for the group with no dominant timescale (the single power law). Both LGRBs and SGRBs show similar α and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> </mml:msub> </mml:math> , which indicates that they may be the result of similar stochastic processes. Typical values of the dominant timescale τ for LGRBs and SGRBs are 1.58 s and 0.02 s, respectively. It seems that τ varies in proportion to the duration of GRBs T 90 , with a relation <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>τ</mml:mi> <mml:mo>∝</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>90</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>0.86</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> . The GRB light curve may result from superposing a number of pulses with different timescales. No periodic or quasi-periodic signal above the 3 σ significance threshold is found in our sample.