A Unified Jet Model of X-Ray Flashes, X-Ray-Rich Gamma-Ray Bursts, and Gamma-Ray Bursts: I. Power-Law-Shaped Universal and Top-Hat-Shaped Variable Opening-Angle Jet Models

HETE-2 has provided strong evidence that the properties of X-Ray Flashes (XRFs), X-ray-rich GRBs, and GRBs form a continuum, and therefore that these three kinds of bursts are the same phenomenon. A key feature found by HETE-2 is that the density of bursts is roughly constant per logarithmic interval in burst fluence S_E and observed spectral peak energy Ep_obs, and in isotropic-equivalent energy Eiso and rest frame spectral peak energy Epeak. In this paper, we explore a unified jet model of all three kinds of bursts, using population synthesis simulations of the bursts and detailed modeling of the instruments that detect them. We show that both a variable jet opening-angle model in which the emissivity is a constant independent of the angle relative to the jet axis and a universal jet model in which the emissivity is a power-law function of the angle relative to the jet axis can explain the observed properties of GRBs reasonably well. However, if one tries to account for the properties of all three kinds of bursts in a unified picture, the extra degree of freedom available in the variable jet opening-angle model enables it to explain the observations reasonably well while the power-law universal jet model cannot. The variable jet opening-angle model of XRFs, X-ray-rich GRBs, and GRBs implies that the energy Egamma radiated in gamma rays is ~ 100 times less than has been thought, and that most GRBs have very small jet opening angles (~ half a degree). It also implies that there are ~ 10^4 - 10^5 more bursts with very small jet opening angles for every burst that is observable. If this is the case, the rate of GRBs could be comparable to the rate of Type Ic core collapse supernovae.Comment: 51 pages, 19 figures, accepted by ApJ; revised; condensed abstrac

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

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

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

Evidence for Two Distinct Morphological Classes of Gamma-Ray Bursts from their Short Timescale Variability

We have analyzed the 241 bursts for which peak counts \C exist in the publicly available Burst and Transient Source Experiment (BATSE) catalog. Introducing peak counts in 1024 ms as a measure of burst brightness \B and the ratio of peak counts in 64 and 1024 ms as a measure of short timescale variability \V, we find a statistically significant correlation between the brightness and the short timescale variability of \g-ray bursts. The bursts which are smoother on short timescales are both faint and bright, while the bursts which are variable on short timescales are faint only, suggesting the existence of two distinct morphological classes of bursts.Comment: 9 pages + 2 Postscript figures available upon request; LATEX v. 2.0

Galaxy formation with radiative and chemical feedback

Here we introduce GAMESH, a novel pipeline which implements self-consistent radiative and chemical feedback in a computational model of galaxy formation. By combining the cosmological chemical-evolution model GAMETE with the radiative transfer code CRASH, GAMESH can post process realistic outputs of a N-body simulation describing the redshift evolution of the forming galaxy. After introducing the GAMESH implementation and its features, we apply the code to a low-resolution N-body simulation of the Milky Way formation and we investigate the combined effects of self-consistent radiative and chemical feedback. Many physical properties, which can be directly compared with observations in the Galaxy and its surrounding satellites, are predicted by the code along the merger-tree assembly. The resulting redshift evolution of the Local Group star formation rates, reionisation and metal enrichment along with the predicted Metallicity Distribution Function of halo stars are critically compared with observations. We discuss the merits and limitations of the first release of GAMESH, also opening new directions to a full implementation of feedback processes in galaxy formation models by combining semi-analytic and numerical methods.Comment: This version has coloured figures not present in the printed version. Submitted to MNRAS, minor revision

Evidence Against an Association Between Gamma-Ray Bursts and Type I Supernovae

We present a rigorous method, based on Bayesian inference, for calculating the odds favoring the hypothesis that any particular class of astronomical transients produce gamma-ray bursts over the hypothesis that they do not. We then apply this method to a sample of 83 Type Ia supernovae and a sample of 20 Type Ib-Ic supernovae. We find overwhelming odds against the hypothesis that all Type Ia supernovae produce gamma-ray bursts, whether at low redshift ($10^{9}:1$) or high-redshift ($10^{12}:1$), and very large odds ($6000:1$) against the hypothesis that all Type Ib, Ib/c, and Ic supernovae produce observable gamma-ray bursts. We find large odds ($34:1$) against the hypothesis that a fraction of Type Ia supernovae produce observable gamma-ray bursts, and moderate odds ($6:1$) against the hypothesis that a fraction of Type Ib-Ic supernovae produce observable bursts. We have also re-analyzed both a corrected version of the Wang & Wheeler sample of Type Ib-Ic SNe and our larger sample of 20 Type Ib-Ic SNe, using a generalization of their frequentist method. We find no significant evidence in either case of a correlation between Type Ib-Ic SNe and GRBs, consistent with the very strong evidence against such a correlation that we find from our Bayesian analysis.Comment: 45 pages, 2 PostScript figures. Uses AASTEX macros. Submitted to The Astrophysical Journa