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

T. Q. Donaghy·C. Graziani·D. Q. Lamb
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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.

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T. Q. Donaghy, C. Graziani, D. Q. Lamb. 2005-05-08. Unifying XRFs and GRBs with a Fisher-Shaped Universal Jet Model. https://doi.org/10.1393/ncc%2Fi2005-10069-5

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