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Long-lived high-energy (>100MeV) emission, a common feature of most Fermi-LATdetected gamma-ray burst, is detected up to \sim 10^2 s in the short GRB090510. We study the origin of this long-lived high-energy emission, usingbroad-band observations including X-ray and optical data. We confirm that thelate > 100 MeV, X-ray and optical emission can be naturally explained viasynchrotron emission from an adiabatic forward shock propagating into ahomogeneous ambient medium with low number density. The Klein-Nishina effectsare found to be significant, and effects due to jet spreading and magneticfield amplification in the shock appear to be required. Under the constraintsfrom the low-energy observations, the adiabatic forward shock synchrotronemission is consistent with the later-time (t>2s) high-energy emission, butfalls below the early-time (t < 2s) high energy emission. Thus we argue that anextra high energy component is needed at early times. A standard reverse shockorigin is found to be inconsistent with this extra component. Therefore, weattribute the early part of the high-energy emission (t< 2s) to the promptcomponent, and the long-lived high energy emission (t>2s) to the adiabaticforward shock synchrotron afterglow radiation. This avoids the requirement foran extremely high initial Lorentz factor.

On the High Energy Emission of the Short GRB 090510