[Paper Review] Variability in the Prompt Emission of Swift-BAT Gamma-Ray Bursts

T. N. Ukwatta, K. S. Dhuga+9 more|ArXiv.org|Jun 17, 2009

Gamma-ray bursts and supernovae3 references3 citations

TL;DR

This study uses Fast Fourier Transform (FFT) analysis on Swift-BAT gamma-ray burst (GRB) light curves to extract a threshold frequency as a proxy for variability time scales. It finds a significant correlation (r = 0.69 ± 0.03, p = 3.4×10⁻⁴) between this threshold frequency and isotropic peak luminosity, suggesting a potential link to GRB microphysics and a possible redshift estimator.

ABSTRACT

We present the results of our study of the variability time scales of a sample of 27 long Swift Gamma-Ray Bursts (GRBs) with known redshifts. The variability time scale can help our understanding of fundamental GRB parameters such as the initial bulk Lorentz factor and the characteristic size associated with the emission region. Fast Fourier Transform (FFT) techniques were used to extract a noise threshold crossing frequency, which we associate with a variability time scale. The threshold frequency appears to show a correlation with the peak isotropic luminosity of GRBs.

Motivation & Objective

• To establish a consistent, physically motivated measure of variability time scale in long GRBs using Fourier analysis.
• To investigate whether the threshold frequency—defined as the point where red noise crosses white noise in the power spectrum—correlates with fundamental GRB parameters.
• To assess the potential of the threshold frequency as a probe of GRB emission mechanisms and as a redshift estimator.
• To evaluate observational biases, such as flux dependence and redshift distribution, that may affect the observed correlation.

Proposed method

• Applied Fast Fourier Transform (FFT) to event-by-event light curves of 27 Swift-BAT GRBs with known redshifts to compute power spectra.
• Fitted the power spectra with a broken power-law model: P(f) = A(f/f_th)^(-α) for f < f_th and P(f) = A(f/f_th)^(-β) for f ≥ f_th.
• Identified the threshold frequency f_th as the intersection point between the low-frequency red noise (signal) and high-frequency white noise (background).
• Calculated isotropic peak luminosity L_iso using observed flux, luminosity distance d_L, and redshift correction, with d_L computed from cosmological parameters (Ω_M = 0.27, Ω_L = 0.73, H₀ = 70 km s⁻¹ Mpc⁻¹).
• Used Monte Carlo simulations to estimate uncertainties in correlation coefficients and significance levels.
• Applied z-correction to the threshold frequency to account for time dilation, yielding f_th(z+1) as the corrected variability timescale proxy.

Experimental results

Research questions

• RQ1 Is there a statistically significant correlation between the FFT-derived threshold frequency and the isotropic peak luminosity of GRBs?
• RQ2 To what extent is the observed correlation influenced by observational biases such as flux or redshift distribution?
• RQ3 Can the threshold frequency serve as a reliable proxy for intrinsic GRB variability time scales and a potential redshift estimator?
• RQ4 How do the spectral indices α and β of the broken power-law fit relate to the physical properties of GRB emission regions?
• RQ5 What is the minimum intrinsic variability time scale implied by the observed threshold frequencies in the sample?

Key findings

• The threshold frequency f_th is significantly correlated with isotropic peak luminosity L_iso, with a Pearson correlation coefficient of 0.69 ± 0.03 and a chance probability of 3.4×10⁻⁴.
• The best-fit relation is log L_iso = (52.0 ± 0.2) + (1.4 ± 0.2) log[f_th(z+1)], indicating a strong dependence on the redshift-corrected threshold frequency.
• The average spectral index α for the low-frequency red noise component is 1.12 ± 0.05, while β is consistent with zero across all fits.
• The lowest redshift-corrected threshold frequency in the sample is ~0.2 Hz, implying a minimum intrinsic variability time scale of approximately 50 milliseconds.
• The distribution of redshifts is uneven, with roughly half of the sample concentrated between z = 1.5 and z = 3.5, which may influence the observed correlation with luminosity.
• Potential observational bias from burst brightness is noted, as higher flux enhances red noise and may inflate f_th, though the observed slope (1.4) exceeds what would be expected from α (1.12), suggesting additional physical drivers.