Numerical Simulations of an Initially Top-hat Jet and the Afterglow of GW170817/GRB170817A

The afterglow of GRB 170817A/GW170817 was very unusual, slowly rising as , peaking at days, and sharply decaying as . Very-long-baseline interferometry observations revealed an unresolved radio afterglow image whose flux centroid apparently moved superluminally with v _app ≈ 4c between 75 and 230 days, clearly indicating that the afterglow was dominated by a relativistic jet's compact core. Different jet angular structures successfully explained the afterglow light curves: Gaussian and steep power-law profiles with narrow core angles θ _c ≲ 5° and significantly larger viewing angles θ _obs/θ _c ∼3-5. However, a top-hat jet (THJ; conical with sharp edges at θ =θ ₀) was ruled out because it appeared to produce an early flux rise much steeper ( with a ⪆ 3) than observed. Using 2D relativistic hydrodynamic simulations of an initially THJ, we show that the initial steep flux rise is an artifact caused by the simulation's finite start time, t ₀, missing its flux contributions from t <t ₀ and sometimes "compensated" using an analytic THJ. While an initially THJ is not very physical, such simulations are particularly useful at when the afterglow emission is dominated by the jet's core and becomes insensitive to its exact initial angular profile if it drops off sharply outside of the core. We demonstrate that an initially THJ fits GW170817/GRB 170817A's afterglow light curves and flux centroid motion at , for θ _obs/θ ₀ ≈ 3 and may also fit the earlier light curves for Γ₀ =Γ(t ₀) ⪆ 10^2.5. We analytically express the degeneracies between the model parameters, and find a minimal jet energy of erg and circumburst medium density of .