[Paper Review] The lag-luminosity relation in the gamma-ray burst source-frame

T. N. Ukwatta, K. S. Dhuga+5 more|arXiv (Cornell University)|Mar 1, 2010

Gamma-ray bursts and supernovae3 citations

TL;DR

This study investigates the lag-luminosity relation in the rest frame of gamma-ray bursts (GRBs) using fixed source-frame energy bands (100–200 keV and 300–400 keV), projected to the observer frame to avoid redshift-dependent energy band ambiguity. It finds a significant anti-correlation between spectral lag and isotropic peak luminosity (correlation coefficient −0.76 ± 0.06), with a power-law index of −0.9 ± 0.1, representing an improvement over prior observer-frame studies.

ABSTRACT

We have investigated the empirical lag-luminosity relation in the Gamma-ray Burst (GRB) source-frame. We selected two energy bands (100-200 keV and 300-400 keV) in the GRB source-frame, which after redshift correction, lie in the observer-frame energy range of the Swift Burst Alert Telescope (BAT). The spectral lags between these energy channels are then presented as a function of the isotropic peak luminosity of the GRBs in the sample.

Motivation & Objective

• To eliminate redshift-induced variability in energy band selection by defining fixed energy bands in the GRB source frame.
• To improve the consistency and physical interpretability of the lag-luminosity relation by avoiding arbitrary observer-frame energy bands.
• To re-express spectral lags and luminosities in the source frame to reduce systematic uncertainties from redshift effects.
• To test whether the lag-luminosity correlation remains significant and quantitatively consistent when analyzed in the rest frame of GRBs.
• To enhance the precision of spectral lag measurements using both mask-weighted and non-mask-weighted light curves from the Swift BAT instrument.

Proposed method

• Defined two fixed energy bands in the GRB source frame: 100–200 keV and 300–400 keV, to avoid redshift-dependent energy band shifts.
• Projected these source-frame bands to the observer frame using the relation $ E_{\text{observer}} = E_{\text{source}} / (1+z) $, ensuring alignment with the Swift BAT energy range (15–350 keV).
• Extracted spectral lags using an improved cross-correlation function (CCF) method, fitting a Gaussian to the CCF to determine the time delay corresponding to the global maximum.
• Calculated lag uncertainties via Monte Carlo simulation of 1,000 synthetic light curves, using the standard deviation of resulting lag values.
• Corrected observed spectral lags for cosmological time dilation using $ \tau_{\text{source}} = \tau_{\text{observer}} / (1+z) $ to obtain source-frame lags.
• Computed isotropic peak luminosity $ L_{\text{iso}} $ using spectral-fit parameters and luminosity distance, integrating over 1.0 keV to 10,000 keV in the source frame.

Experimental results

Research questions

• RQ1 Does the lag-luminosity relation remain significant when analyzed in the GRB source frame using fixed energy bands?
• RQ2 How does the correlation between spectral lag and isotropic peak luminosity in the source frame compare to previous observer-frame results?
• RQ3 Can the use of fixed source-frame energy bands reduce systematic uncertainties introduced by redshift-dependent energy band projections?
• RQ4 What is the strength and slope of the lag-luminosity relation when derived from both mask-weighted and non-mask-weighted Swift BAT light curves?
• RQ5 Does the improved method yield a more consistent and precise lag-luminosity correlation than prior studies using arbitrary observer-frame bands?

Key findings

• The final sample comprises 22 GRBs with redshifts ranging from 0.54 to 5.46, selected based on sufficient signal-to-noise for lag extraction.
• A significant anti-correlation was found between source-frame spectral lag and isotropic peak luminosity, with a correlation coefficient of −0.76 ± 0.06.
• The best-fit power-law index for the lag-luminosity relation is −0.9 ± 0.1, which is shallower than previous observer-frame results (e.g., −1.14 from Norris et al. 2000 and −1.4 from Ukwatta et al. 2009).
• The use of non-mask-weighted light curves extended the usable redshift range down to 0.2, improving sample coverage compared to mask-weighted light curves (z ≥ 1).
• The correlation coefficient of −0.76 represents a notable improvement over the average of −0.68 reported in the reference study (Ukwatta et al. 2009), indicating enhanced statistical significance.
• The method successfully mitigates redshift-induced energy band ambiguity, providing a more physically consistent framework for studying the lag-luminosity relation.