We analyze the time profiles of individual gamma-ray burst (GRB) pulses, that are longer than 2 s, by modelling them with analytical functions that are based on physical first principles and well-established empirical descriptions of GRB spectral evolution. These analytical profiles are independent of the emission mechanism and can be used to model both the rise and decay profiles allowing for the study of the entire pulse light-curve. Using this method, we have studied a sample of 77 individual GRB pulses, allowing us to examine the fluence, pulse width, asymmetry, and rise and decay power-law distributions. We find that the rise phase is best modelled with a power law of average index r = 1.31 ± 0.11 and that the average decay phase has an index of d = 2.39 ± 0.12. We also find that the ratio between the rise and decay times (the pulse asymmetry) exhibited by the GRB pulse shape has an average value of 0.47 which varies little from pulse to pulse and is independent of pulse duration or intensity. Although this asymmetry is largely uncorrelated to other pulse properties, a statistically significant trend is observed between the pulse asymmetry and the decay power law index, possibly hinting at the underlying physics. We compare these parameters with those predicted to occur if individual pulse shapes are created purely by relativistic curvature effects in the context of the fireball model, a process that -2makes specific predictions about the shape of GRB pulses. The decay index distribution obtained from our sample shows that the average GRB pulse fades faster than the value predicted by curvature effects, with only 39% of our sample being consistent with the curvature model. We discuss several refinements of the relativistic curvature scenario that could naturally account for these observed deviations, such as symmetry breaking and varying relative time-scales within individual pulses.

We estimate the luminosity evolution and formation rate for over 900 GRBs by using redshift and luminosity data calculated by Band, Norris, & Bonnell (2004) via the lag-luminosity correlation. By applying maximum likelihood techniques, we are able to infer the true distribution of the parent GRB population's luminosity function and density distributions in a way that accounts for detector selection effects. We find that after accounting for data truncation, there still exists a significant correlation between the average luminosity and redshift, indicating that distant GRBs are on average more luminous than nearby counterparts. This is consistent with previous studies showing strong source evolution and also recent observations of under luminous nearby GRBs. We find no evidence for beaming angle evolution in the current sample of GRBs with known redshift, suggesting that this increase in luminosity can not be due to an evolution of the collimation of gamma-ray emission. The resulting luminosity function is well fit with a single power law of index L ′−1.5 , which is intermediate between the values predicted by the power-law and Gaussian structured jet models. We also find that the GRB comoving rate density rises steeply with a broad peak between 1 < z < 2 followed by a steady decline above z > 3. This rate density qualitatively matches the current estimates of the cosmic star formation rate, favoring a short lived massive star progenitor model, or a binary model with a short delay between the formation of the compact object and the eventual merger.

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Abstract. We analyze the spectral lags of a sample of bright gamma-ray burst pulses observed by CGRO BATSE and compare these with the results of high-resolution spectroscopical investigations. We find that pulses with hard spectra have the largest lags, and that there is a similar, but weaker correlation between hardness-intensity correlation index, η, and lag. We also find that the lags differ considerably between pulses within a burst. Furthermore, the peak energy mainly decreases with increasing lag. Assuming a lag-luminosity relation as suggested by Norris et al., there will thus be a positive luminosity-peak-energy correlation. We also find that the hardness ratio, of the total flux in two channels, only weakly correlates with the spectral evolution parameters. These results are consistent with those found in the analytical and numerical analysis in Paper I. Finally, we find that for these bursts, dominated by a single pulse, there is a correlation between the observed energy-flux, F, and the inverse of the lag, ∆t: F ∝ ∆t −1 . We interpret this flux-lag relation found as a consequence of the lag-luminosity relation and that these bursts have to be relatively narrowly distributed in z. However, they still have to, mainly, lie beyond z ∼ 0.01, since they do not coincide with the local super-cluster of galaxies. We discuss the observed correlations within the collapsar model, in which the collimation of the outflow varies. Both the thermal photospheric emission as well as non-thermal, optically-thin synchrotron emission should be important.