A Stacking Analysis of Faint Short GRBs Observed by Fermi-LAT and Cooling-Regime Constraints on GRB 090510

Abstract We perform a stacking analysis of 15 faint short GRBs observed by \emph{Fermi}-LAT and compare their $>100$~MeV afterglow with GRB~090510. Because individual faint bursts contain only a few selected LAT photons, stacking is required to measure their average temporal behavior. The stacked light curve decays as $\alpha = 0.89 \pm 0.06$, consistent with, though not uniquely diagnostic of, a slow-cooling forward-shock interpretation. In contrast, GRB~090510 shows two much steeper decay phases, $\alpha_1 = 2.13 \pm 0.24$ and $\alpha_2 = 2.31 \pm 0.81$, after accounting for a possible plateau-like feature, indicating that it is not representative of the faint short-GRB population. If the LAT band lies above the cooling frequency, the condition $h\nu_c < 0.1$~GeV gives $\epsilon_B \gtrsim 3\times10^{-4}-7\times10^{-3}$ for $n\sim10^{-5}-10^{-3}$~cm$^{-3}$. GRB~090510 may therefore be an unusual event, possibly involving efficient magnetic-field amplification, favorable viewing geometry, or additional emission components.