Stepwise Filter Correlation Method and Evidence of Superposed Variability Components in GRB Prompt Emission Lightcurves

Abstract

Gamma-ray bursts (GRBs) have variable lightcurves. Although most models attribute the observed variability to one physical origin (e.g. central engine activity, clumpy circumburst medium, relativistic turbulence), some models invoke two physically distinct variability components. We develop a method, namely, the stepwise filter correlation (SFC) method, to decompose the variability components in a GRB lightcurve. Based on a low-pass filter technique, we progressively filter the high frequency signals from the lightcurve, and then perform a correlation analysis between each adjunct pair of filtered lightcurves. Our simulations suggest that if a mock lightcurve contains a slow variability component superposed on a rapidly varying time sequence, the correlation coefficient as a function of the filter frequency would display a prominent dip feature around the frequency of the slow component. Through simulations, we demonstrate that this method can identify significant clustering structures of a lightcurve in the frequency domain, and proved that it can catch superposed signals that are otherwise not easy to retrieve based on other methods (e.g. the power density spectrum analysis method). We apply this method to 266 BATSE bright GRBs. We find that the majority of the bursts have clear evidence of such a superposition effect. We perform a statistical analysis of the identified variability components, and discuss the implications for GRB physics.