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Gravitational waves from a merger of two neutron stars (NSs) were discoveredfor the first time in GW170817, together with diverse electromagneticcounterparts, providing a direct clue to the origin of short gamma-ray bursts(sGRBs). The associated sGRB 170817A was much fainter than typical, suggestingoff-axis emission from a relativistic jet. However the observed prompt spectrumis inconsistent with the spectral (Amati) relation and causes the compactnessproblem in the simplest off-axis model. We focus on this spectral puzzle andsuggest a possible key that the off-axis emission generally comes from theoff-center jet, neither the jet core nor the line-of-sight jet, if the jetstructure is exponentially faint outward as inferred from observations. Theoff-center jet could be loaded with baryon or cocoon. The off-axis modelpredicts that roughly $\sim 10\%$ events are brighter at smaller viewing anglesthan sGRB 170817A, although the exact event rate sensitively depends onuncertainties of the off-center structure. The model also predicts outliers toAmati relation, providing future tests to reveal the central engine activities.

Spectral Puzzle of the Off-Axis Gamma-Ray Burst in GW170817