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

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