Inverse reconstruction of jet structure from off-axis gamma-ray burst afterglows

The gravitational wave event GW 170817 and the slowly rising afterglows of short gamma-ray burst (GRB) 170817A clearly suggest that the GRB jet has an angular structure. However the actual jet structure remains unclear as different authors give different structures. We formulate a novel method to inversely reconstruct the jet structure from off-axis GRB afterglows, without assuming any functional form of the structure in contrast to the previous studies. The jet structure is uniquely determined from the rising part of a light curve for a given parameter set by integrating an ordinary differential equation, which is derived from the standard theory of GRB afterglows. Applying to GRB 170817A, we discover that a non-trivial hollow-cone jet is consistent with the observed afterglows, as well as Gaussian and power-law jets within errors, which implies the Blandford-Znajek mechanism or ejecta-jet interaction. The current observations only constrain the jet core, not in principle the outer jet structure around the line of sight. More precise and high-cadence observations with our inversion method will fix the jet structure, providing a clue to the jet formation and propagation.