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 SE and observed spectral peak energy Eobs peak, and in isotropic-equivalent energy Eiso and spectral peak energy Epeak in the rest frame of the burst. 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 XRFs, X-ray-rich GRBs, and GRBs in a unified picture, the extra degree of freedom available

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