The Importance of Off-Axis Beaming in Jet Models

Gamma-Ray Bursts (GRBs) are widely thought to originate from collimated jets of material moving at relativistic velocities. Emission from such a jet should be visible even when viewed from outside the angle of collimation. Using Monte Carlo population synthesis methods and including the effects of this off-axis beaming, we can compare various GRB jet models against the global properties of observed bursts. We explore whether or not the X-Ray Flashes (XRFs) seen by HETE-2 and BeppoSAX can be explained as classical GRBs viewed off-axis, and begin to address the more general question of the importance of off-axis beaming in current burst samples.Comment: 4 pages, 1 figure. Poster presented at the 4th Workshop Gamma-Ray Bursts in the Afterglow Era, Rome,18-22 October 2004. Editors: L. Piro, L. Amati, S. Covino, and B. Gendre. Il Nuovo Cimento, in pres

Jet Models of X-Ray Flashes

One third of all HETE-2--localized bursts are X-Ray Flashes (XRFs), a class of events first identified by Heise in which the fluence in the 2-30 keV energy band exceeds that in the 30-400 keV energy band. We summarize recent HETE-2 and other results on the properties of XRFs. These results show that the properties of XRFs, X-ray-rich gamma-ray bursts (GRBs), and GRBs form a continuum, and thus provide evidence that all three kinds of bursts are closely related phenomena. As the most extreme burst population, XRFs provide severe constraints on burst models and unique insights into the structure of GRB jets, the GRB rate, and the nature of Type Ib/Ic supernovae. We briefly mention a number of the physical models that have been proposed to explain XRFs. We then consider two fundamentally different classes of phenomenological jet models: universal jet models, in which it is posited that all GRBs jets are identical and that differences in the observed properties of the bursts are due entirely to differences in the viewing angle; and variable-opening angle jet models, in which it is posited that GRB jets have a distribution of jet opening angles and that differences in the observed properties of the bursts are due to differences in the emissivity and spectra of jets having different opening angles. We consider three shapes for the emissivity as a function of the viewing angle theta_v from the axis of the jet: power-law, top hat (or uniform), and Gaussian (or Fisher). We then discuss the effect of relativistic beaming on each of these models. We show that observations can distinguish between these various models.Comment: 8 pages, 7 figures, 1 table. Invited review talk at the 4th Workshop Gamma-Ray Bursts in the Afterglow Era, Rome,18-22 October 2004. Editors: L. Piro, L. Amati, S. Covino, and B. Gendre. Il Nuovo Cimento, in pres

Gamma-Ray Burst Jet Profiles And Their Signatures

HETE-II and BeppoSAX have produced a sample of GRBs and XRFs with known redshifts and $E_{pk}$. This sample provides four important empirical constraints on the nature of the source jets: Log $E_{iso}$ is approximately uniformly distributed over several orders of magnitude; the inferred prompt energy Log $E_{\gamma}$ is narrowly distributed; the Amati relation holds between $E_{iso}$ and $E_{pk}$; and the Ghirlanda relation holds between $E_{\gamma}$ and $E_{pk}$. We explore the implications of these constraints for GRB jet structure during the prompt emission phase. We infer the underlying angular profiles from the first two of the above constraints assuming all jets have the same profile and total energy, and show that such ``universal jet'' models cannot satisfy both constraints. We introduce a general and efficient method for calculating relativistic emission distributions and $E_{pk}$ distributions from jets with arbitrary (smooth) angular jet profiles. We also exhibit explicit analytical formulas for emission from top-hat jets (which are not smooth). We use these methods to exhibit $E_{pk}$ and $E_{iso}$ as a function of viewing angle, for several interesting families of GRB jet profiles. We use the same methods to calculate expected frequency distributions of $E_{iso}$ and $E_{\gamma}$ for the same families of models. We then proceed to explore the behavior of universal jet models under a range of profile shapes and parameters, to map the extent to which these models can conform to the above four empirical constraints.Comment: 71 page, 33 figures. Submitted to Ap

Likelihood Analysis of GRB Evolution with Redshift

We present a likelihood approach to modeling multi-dimensional GRB Epeak--fluence--redshift data that naturally incorporates instrument detection thresholds. The treatment of instrument thresholds is essential for analyzing evidence for GRB evolution. The method described here compares the data to a uniform jet model, in which the jet parameters are allowed to vary with redshift. Data from different experiments may be modeled jointly. In addition, BATSE data (for which no redshift information is available) may be incorporated by ascribing to each event a likelihood derived from the full model by integrating the probability density over the unknown redshift. The loss of redshift information is mitigated by the large number of available bursts. We discuss the implementation of the method, and validation of it using simulated data.Comment: 4 pages, 1 figure. Poster presented at the 4th Workshop Gamma-Ray Bursts in the Afterglow Era, Rome,18-22 October 2004. Editors: L. Piro, L. Amati, S. Covino, and B. Gendre. Il Nuovo Cimento, in pres

GRB Redshift Evolution Within the Unified Jet Model

HETE-2 has provided new evidence that gamma-ray bursts may evolve with redshift. We investigate the consequences of this possibility for the unified jet model of XRFs and GRBs. We find that burst evolution with redshift can be naturally explained within the unified jet model, and the resulting model provides excellent agreement with existing HETE-2 and BeppoSAX data sets. In addition, this evolution model produces reasonable fits to the BATSE peak photon number flux distribution -- something that cannot be easily done without redshift evolution.Comment: 5 pages, 4 figures, to appear in proc. 2003 GRB Conference, Santa Fe, N

Unifying XRFs and GRBs with a Fisher-Shaped Universal Jet Model

We show analytically that GRB jets with an emissivity profile given by the Fisher distribution, epsilon(theta) = A * e^(B cos(theta)), have the unique property of producing equal numbers of bursts per logarithmic interval in Eiso, and therefore in most burst properties. Since this broad distribution of burst properties is a key feature found by HETE-2, a Fisher-shaped universal jet model can explain many of the observed properties of XRFs, X-ray-rich GRBs, and GRBs reasonably well, in contrast to a power-law universal model. For small viewing angles, the Fisher distribution can be approximated by a Gaussian, whose properties have been explored by Zhang et al. (2004). We also show that the Fisher universal jet model produces a broad distribution in the inferred radiated energy Egamma_inf, in contrast to the narrow distribution predicted by the uniform variable opening-angle jet model Lamb, Donaghy & Graziani (2005). Here we present Monte Carlo simulations of both a Fisher-shaped universal jet model and a Fisher-shaped variable opening-angle jet model.Comment: 4 pages, 2 figures. Poster presented at the 4th Workshop Gamma-Ray Bursts in the Afterglow Era, Rome,18-22 October 2004. Editors: L. Piro, L. Amati, S. Covino, and B. Gendre. Il Nuovo Cimento, in pres