Unifying XRFs and GRBs with a Fisher-Shaped Universal Jet Model
Abstract
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.
Keywords
Cite
@article{arxiv.astro-ph/0505151,
title = {Unifying XRFs and GRBs with a Fisher-Shaped Universal Jet Model},
author = {T. Q. Donaghy and C. Graziani and D. Q. Lamb},
journal= {arXiv preprint arXiv:astro-ph/0505151},
year = {2010}
}
Comments
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 press