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

Abstract

The afterglow of GRB 170817A/GW 170817 was very unusual, slowly rising as F ν ∝ t 0.8 obs ν −0.6 , peaking at t obs,pk ∼ 150 days, and sharply decaying as ∼ t −2.2 obs . VLBI 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 lightcurves: 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 (conical with sharp edges at θ = θ 0 ) was ruled out since it appeared to produce an early flux rise much steeper (∝ t a obs with a 3) than observed. Using 2D relativistic hydrodynamic simulations of an initially top-hat jet 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 top-hat jet. While an initially top-hat jet is not very physical, such simulations are particularly useful at t obs t obs,pk 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 top-hat jet fits GW 170817/GRB 170817A's afterglow lightcurves and flux centroid motion at t obs t obs,pk , for θ obs /θ 0 ≈ 3 and may also fit the earlier lightcurves for Γ 0 = Γ(t 0 ) 10 2.5 . We analytically express the degeneracies between the model parameters, and find a minimal jet energy of E min ≈ 5.3 × 10 48 erg and circum-burst medium density of n min ≈ 5.3 × 10 −6 cm −3 .1 Here νm is the synchrotron frequency of minimal energy electrons and νc of electrons that cool on the dynamical time (Sari et al. 1998).

Neutron star mergers and how to study them

“…Magnetic fields can accelerate charged particles in a preferential direction, where ordered poloidal fields can also contribute to jet collimation (e.g., Rezzolla et al 2011). These interactions impart structure onto the jet where dependencies on the amount and distribution of polar material and the jet launch time are important (e.g., Xie et al 2018;Geng et al 2019;Kathirgamaraju et al 2019;Gill et al 2019). GW observations provide new information to investigate this question and additional constraints to be met with future models and simulation.…”

Constraints on Hořava–Lifshitz gravity from GRB 170817A

“…We assume In [67], the second energetic photon with E high = 11.16 GeV of GRB 090902B was chosen to calculate E L I V,1 , compared to [66] where E high = 33.4 GeV E high,an = E peak (the peak energy of the Band fit of the GBM data), which implies those photons have the maximum probabilities to undergo the absorption with the highestenergy photons (E high ). For the Lorentz factor, we employ the estimated values (100−10 2.5 ) as suggested in the literatures [81][82][83][84], leading to an estimation that the range of the highest energy E high is (10 − 200) GeV (the observations E peak = (185 ± 62) keV and z 0.001 in [22]). Based on this estimation and (36), we expect that the GRB 170817A suggests a possible LV effect | υ| ∼ (10 −19 − 10 −18 ) if the most stringent constraint E LV,1 ∼ 10 20 GeV [67] is used.…”

“…We assume E high,an = E peak (the peak energy of the Band fit of the GBM data), which implies those photons have the maximum probabilities to undergo the absorption with the highest-energy photons (E high ). For the Lorentz factor, we employ the estimated values (100 − 10 2.5 ) as suggested in the literatures [79][80][81][82], leading to an estimation that the range of the highest energy E high is (10 − 200) GeV (the observations E peak = (185 ± 62) keV and z ≃ 0.001 in [22]). Based on this estimation and 36…”

Afterglow light curves from misaligned structured jets

“…The latter can reduce the effective parameter space and point towards the unknown parameters (or combinations of those) that may be well constrained by observations (e.g. Gill et al 2019).…”