On the Kinetic Energy and Radiative Efficiency of Gamma-Ray Bursts

Using measured X-ray luminosities to 17 Gamma-Ray Bursts (GRBs) during the afterglow phase and accounting for radiative losses, we calculate the kinetic energy of these bursts and investigate its relation to other GRB properties. We then use the observed radiated energy during the prompt phase to determine the radiative efficiency of these bursts, and explore how the efficiency relates to other GRB observables. We find that the kinetic energy in the afterglow phase is directly correlated with the radiated energy, total energy as well as possibly the jet opening angle and spectral peak energy. More importantly, we find the intriguing fact that the efficiency is correlated with the radiated energy, and mildly with the total energy, jet opening angle and spectral peak energy. XRF020903 also seems to follow the trends we find for our GRB sample. We discuss the implications of these results for the GRB radiation and jet models.Comment: 9 pages, 7 figures; Revised version, accepted to Ap

The Extent of the Spectral Bias in BATSE: The True Distribution of the nu F_nu Peak Energy

The distributions of spectral characteristics and their correlations with fluence, peak flux, or duration, are essential in understanding the nature of GRBs. However, the selection effects involved in detecting GRBs can distort these distributions. Here, we discuss how to deal with selection effects involving the peak energy E_p of the GRB nu F_nu spectrum, which suffers from both an upper and lower threshold. We describe a new method to account for this double-sided truncation, and show that the true distribution of E_p is significantly different from the observed distribution.Comment: 5 pages, 3 postscript figures. To appear in the proceedings of the 4th Huntsville Gamma Ray Burst Symposium, C.A.Meegan, P.Cushman, ed

Synchrotron Radiation as the Source of GRB Spectra, Part I: Theory

We investigate synchrotron emission models as the source of gamma ray burst spectra. We show that allowing for synchrotron self absorption and a ``smooth cutoff'' to the electron energy distribution produces a wide range of low energy spectral behavior. We show that there exists a correlation between the value of the peak of the $\nu F_{\nu}$ spectrum, $E_{p}$, and the low energy spectral index $\alpha$ as determined by spectral fits over a finite bandwidth. Finally, we discuss the implications of synchrotron emission from internal shocks for GRB spectral evolution.Comment: To appear in the proceedings of the 5th Huntsville Symposium on Gamma Ray Burst

Synchrotron Emission as the Source of GRB Spectra, Part II: Observations

We test the models of synchrotron emission presented in Part I of this series (Lloyd & Petrosian, these proceedings) against the distributions and evolution of GRB spectral parameters (particularly the low energy index, $\alpha$). With knowledge of the $E_{p}$ distribution and the correlation between $\alpha$ and $E_{p}$ presented in Part I, we show how to derive the expected distribution of $\alpha$ from fits to optically thin synchrotron spectra, and compare this with the observed distribution. We show that there is no difficulty explaining bursts below the ``line of death'', $\alpha < -2/3$, and that these bursts indicate that the spectrum of accelerated electrons must flatten or decline at low energies. Bursts with low energy spectral indices that fall above this limit are explained by the synchrotron self-absorption frequency entering the lower end of the BATSE window. Finally, we discuss a variety of spectral evolution behavior seen in GRBs and explain this behavior in the context of synchrotron emission from internal shocks.Comment: To appear in the proceedings of the 5th Huntsville Symposium on Gamma Ray Burst

On the Structure of Quasi-Universal Jets for Gamma-Ray Bursts

The idea that GRBs originate from uniform jets has been used to explain numerous observations of breaks in the GRB afterglow lightcurves. We explore the possibility that GRBs instead originate from a structured jet that may be quasi-universal, where the variation in the observed properties of GRBs is due to the variation in the observer viewing angle. We test how various models reproduce the jet data of Bloom, Frail, & Kulkarni (2003), which show a negative correlation between the isotropic energy output and the inferred jet opening angle (in a uniform jet configuration). We find, consistent with previous studies, that a power-law structure for the jet energy as a function of angle gives a good description. However, a Gaussian jet structure can also reproduce the data well, particularly if the parameters of the Gaussian are allowed some scatter. We place limits on the scatter of the parameters in both the Gaussian and power-law models needed to reproduce the data, and discuss how future observations will better distinguish between these models for the GRB jet structure. In particular, the Gaussian model predicts a turnover at small opening angles and in some cases a sharp cutoff at large angles, the former of which may already have been observed. We also discuss the predictions each model makes for the observed luminosity function of GRBs and compare these predictions with the existing data.Comment: 13 pages, including 10 figures; To appear in Ap