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 greater than or similar to 1/y relative to the beam symmetry axis, where gamma is the expansion Lorentz factor. The observed flux depends on the combinations gamma Delta theta and gamma theta(v), where Delta theta is the beaming angle and theta(v) is the viewing angle. We use the observed source counts of gamma-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 gamma and Delta theta. We estimate that a detector with fluence limit similar to 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 hut simply follow from special relativistic considerations.