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Constraints on Off-Axis X-Ray Emission from Beamed Gamma-Ray Bursts

We calculate the prompt X-ray emission as a function of the viewing angle for beamed gamma-ray burst (GRB) sources. Prompt X-rays are inevitable owing to the less highly blueshifted photons emitted at angles ≳1/γ relative to the beam symmetry axis, where γ is the expansion Lorentz factor. The observed flux depends on the combinations γΔθ and γθv, where Δθ is the beaming angle and θv is the viewing angle. We use the observed source counts of γ-ray-selected GRBs to predict the minimum detection rate of prompt X-ray bursts as a function of limiting sensitivity. We compare our predictions with the results from the Ariel 5 catalog of fast X-ray transients and find that Ariel's sensitivity is not great enough to place significant constraints on γ and Δθ. We estimate that a detector with fluence limit ~10-7 ergs cm-2 in the 2-10 keV channel will be necessary in order to distinguish between geometries. Because the X-ray emission is simultaneous with the GRB emission, our predicted constraints do not involve any model assumptions about the emission physics but simply follow from special relativistic considerations.