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 From HETE-2 For GRB Evolution With Redshift

After taking into account threshold effects, we find that the isotropic-equivalent energies E_iso and luminosities L_iso of gamma-ray bursts (GRBs) are correlated with redshift at the 5% and 0.9% signficance levels, respectively. Our results are based on 10 BeppoSAX GRBs and 11 HETE-2 GRBs with known redshifts. Our results suggest that the isotropic-equivalent energies and luminosities of GRBs increase with redshift. They strengthen earlier clues to this effect from analyses of the BATSE catalog of GRBs, using the variability of burst time histories as an estimator of burst luminosities (and therefore redshifts), and from an analysis of BeppoSAX bursts only. If the isotropic-equivalent energies and luminosities of GRBs really do increase with redshift, it suggests that GRB jets at high redshifts may be narrower and thus the cores of GRB progenitor stars at high redshifts may be rotating more rapidly. It also suggests that GRBs at very high redshifts may be more luminous -- and therefore easier to detect -- than has been thought, which would make GRBs a more powerful probe of cosmology and the early universe than has been thought.Comment: 5 pages, 3 figures, to appear in proc. 2003 GRB Conference, Santa Fe, N

Observation and implications of the Epeak - Eiso correlation in Gamma-Ray Bursts

The availability of a few dozen GRB redshifts now allows studies of the intrinsic properties of these high energy transients. Amati et al. recently discovered a correlation between Epeak, the intrinsic peak energy of the $\nu f \nu$ spectrum, and Eiso, the isotropic equivalent energy radiated by the source. Lamb et al. have shown that HETE-2 data confirm and extend this correlation. We discuss here one of the consequences of this correlation: the existence of a 'spectral standard candle', which can be used to construct a simple redshift indicator for GRBs.Comment: Proceedings of the GRB 2003 Conference in SantaFe, 5 pages, 4 figure

Statistical Analysis of Spectral Line Candidates in Gamma-Ray Burst GRB870303

The Ginga data for the gamma-ray burst GRB870303 exhibit low-energy dips in two temporally distinct spectra, denoted S1 and S2. S1, spanning 4 s, exhibits a single line candidate at ~ 20 keV, while S2, spanning 9 s, exhibits apparently harmonically spaced line candidates at ~ 20 and 40 keV. We evaluate the statistical evidence for these lines, using phenomenological continuum and line models which in their details are independent of the distance scale to gamma-ray bursts. We employ the methodologies based on both frequentist and Bayesian statistical inference that we develop in Freeman et al. (1999b). These methodologies utilize the information present in the data to select the simplest model that adequately describes the data from among a wide range of continuum and continuum-plus-line(s) models. This ensures that the chosen model does not include free parameters that the data deem unnecessary and that would act to reduce the frequentist significance and Bayesian odds of the continuum-plus-line(s) model. We calculate the significance of the continuum-plus-line(s) models using the Chi-Square Maximum Likelihood Ratio test. We describe a parametrization of the exponentiated Gaussian absorption line shape that makes the probability surface in parameter space better-behaved, allowing us to estimate analytically the Bayesian odds. The significance of the continuum-plus-line models requested by the S1 and S2 data are 3.6 x 10^-5 and 1.7 x 10^-4 respectively, with the odds favoring them being 114:1 and 7:1. We also apply our methodology to the combined (S1+S2) data. The significance of the continuum-plus-lines model requested by the combined data is 4.2 x 10^-8, with the odds favoring it being 40,300:1.Comment: LaTeX2e (aastex.cls included); 41 pages text, 10 figures (on 11 pages); accepted by ApJ (to be published 1 Nov 1999, v. 525

STOCHASTIC DYNAMICS OF LARGE-SCALE INFLATION IN DE~SITTER SPACE

In this paper we derive exact quantum Langevin equations for stochastic dynamics of large-scale inflation in de~Sitter space. These quantum Langevin equations are the equivalent of the Wigner equation and are described by a system of stochastic differential equations. We present a formula for the calculation of the expectation value of a quantum operator whose Weyl symbol is a function of the large-scale inflation scalar field and its time derivative. The unique solution is obtained for the Cauchy problem for the Wigner equation for large-scale inflation. The stationary solution for the Wigner equation is found for an arbitrary potential. It is shown that the large-scale inflation scalar field in de Sitter space behaves as a quantum one-dimensional dissipative system, which supports the earlier results. But the analogy with a one-dimensional model of the quantum linearly damped anharmonic oscillator is not complete: the difference arises from the new time dependent commutation relation for the large-scale field and its time derivative. It is found that, for the large-scale inflation scalar field the large time asymptotics is equal to the `classical limit'. For the large time limit the quantum Langevin equations are just the classical stochastic Langevin equations (only the stationary state is defined by the quantum field theory).Comment: 21 pages RevTex preprint styl