Jet Structure in the Afterglow Phase for Gamma-ray Bursts with a Precessing Jet

The structured jet is involved to explain the afterglows and even the prompt emission of GRB 170817A. In this paper, we stress that for a precessing jet, the jet structure in the prompt emission phase and that in the afterglow phase may be different. The jet structure in the afterglow phase can be non-uniform even if a narrow-uniform jet is presented in the prompt emission phase. We estimate the jet structure in the afterglow phase under the situation that a narrow-uniform-precessing jet is launched from the central engine of gamma-ray burst. With different precession angles, it is found that the structured jet can be roughly described as follows: a narrow uniform core with power-law wings and sharp cut-off edges, a Gaussian profile, a ring shape, or other complex profile in energy per solid angle. Correspondingly, the afterglows for our obtained structured jets are also estimated. We find that the estimates of the intrinsic kinetic energy, the electron index, and the jet opening angle based on the afterglows formed in a precessing system may be incorrect. Our obtained structured jet is likely to be revealed by future observations for a fraction of gravitational wave detected merging compact binary systems (e.g., black hole-neutron star mergers).