The Lag-Luminosity Relation in the GRB Source Frame T. N. Ukwatta 1,2, K. S. Dhuga 1, M. Stamatikos 3, W. C. Parke 1, T. Sakamoto 2, S. D. Barthelmy 2, and N. Gehrels 2 Introduction Spectral lag is a common feature in Gamma-ray Bursts (GRBs). The lag is defined as the difference in time of arrival of high and low energy photons. Norris et al. reported a correlation between spectral lag and the isotropic peak luminosity of GRBs based on a limited sample. In order to better elucidate the microphysics of GRBs, we extract the spectral lag in the GRB source frame. We selected two energy bands ( keV and keV) in the GRB source frame, which after redshift correction, lie in the detectable 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. 1 The George Washington University, 2 NASA/Goddard Space Flight Center, 3 The Ohio State University Due to cosmological redshift (z) photons have less energy at the observer frame. Cosmological Redshift Swift Satellite Gamma-ray Burst time counts keV Energy Band Spectral Lag at the source frame time counts time counts Spectral Lag at the observer frame time counts keV Energy Band keV Energy Band keV Energy Band 15 keV 350 keV Variable Energy Bands at the Observer Frame Fixed Energy Band at the GRB Source Frame keV keV keV For a GRB with redshift of keV For a GRB with redshift of 2.0 For a GRB with redshift of keV keV keV keV References: Ukwatta (2009); Norris (2000) Isotropic Luminosity vs. Spectral Lag  We have investigated the spectral lag between keV and keV energy bands at the source-frame by projecting these bands to the observer frame.  We have selected the source-frame energy bands in such a way that when projected to the observer frame they will lie in the BAT energy range.  For mask weighted light curves, the effective energy range of the BAT reduces to keV, which implies a GRB redshift range of 1 to 5.7. For non-mask weighted light curves (i.e. full BAT energy range), the redshift lower limit can be as low as 0.2.  Our sample of 22 GRBs have redshift ranging from 0.54 to  After correcting for the time dilation, the spectral lag is correlated with isotropic peak luminosity with a correlation coefficient of ±  The index of the best-fit power-law is -0.9 ± 0.1. Methodology We used the mask weighted, background-subtracted light curves, as well as non-mask weighted light curves in our analysis. The non-mask weighted light curves have about 30% better signal-to-noise ratio than the mask weighted light curves. Hence, when the signal-to-noise ratio of mask weighted light curves was too small, non-mask weighted light curves were used to extract spectral lags. Swift BAT Energy Band Summary We used the cross-correlation function (CCF) analysis method to extract spectral lags as outlined in Ukwatta, Autocorrelation function (ACF) analyses were used to determine suitable time bins for the light curves. The value of the spectral lag is the time delay corresponding to the maximum value of the CCF. A Gaussian curve was fitted to the CCF to extract the spectral lag. The uncertainty in the spectral lag is obtained by simulating 1,000 light curves and repeating the aforementioned procedure. The standard deviation of the simulated spectral lag values is taken as the lag uncertainty. The isotropic peak luminosity (Liso), for each GRB, is obtained by calculating the peak flux for the source– frame energy range, 1.0 keV to 10,000 keV, using the observed spectral-fit parameters and the luminosity distance. The spectral lag is time dilated by a factor of (z+1) at the observer frame.