We perform a series of relativistic magnetohydrodynamics simulations to
investigate how a hot magnetic jet propagates within the dynamical ejecta of a
binary neutron star merger, with the focus on how the jet structure depends on
the delay time of jet launching with respect to the merger time, Δtjet. We find that regardless of the jet launching delay time, a structured
jet with an angle-dependent luminosity and Lorentz factor is always formed
after the jet breaks out the ejecta. On the other hand, the jet launching delay
time has an impact on the jet structure. If the jet launching delay time is
relatively long, e.g., ≥0.5 s, the line-of-sight material has a dominant
contribution from the cocoon. On the other hand, for a relatively short jet
launching delay time, the jet penetrates through the ejecta early on and
develops an angular structure afterward. The line-of-sight ejecta is dominated
by the structured jet itself. We discuss the case of GW170817/GRB 170817A
within the framework of both long and short Δtjet. Future more
observations of GW/GRB associations can help to differentiate between these two
scenarios.Comment: 6 pages, 4 figures, 1 table, accepted by ApJ