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X-ray flashes from off-axis nonuniform jets

It is widely believed that outflows of gamma-ray bursts are jetted. Some people also suggest that the jets may have structures like $ε(θ)\proptoθ^{-k}$. We test the possibility of X-ray flashes coming from such jets in this paper. Both qualitative and quantitative analyses have shown that this model can reproduce most observational features for both X-ray flashes and gamma-ray bursts. Using common parameters of gamma-ray bursts, we have done both uniform and nonuniform jets' numerical calculations for their fluxes, spectra and peak energies. It seems that nonuniform jets are more appropriated to these observational properties than uniform ones. We also give a spectrum and flux fit to the most significant X-ray flash, XRF971019 by our model. We also have shown that in our model the observational ratio of gamma-ray bursts to X-ray flashes is about several.