Abstract
ABSTRACT Very long baseline interferometry radio images recently proved to be essential in breaking the degeneracy in the ejecta model for the neutron star merger GW170817. We discuss the properties of synthetic radio images of merger jet afterglows by using semi-analytical models of laterally spreading or non-spreading jets. The image centroid initially moves away from the explosion point in the sky with apparent superluminal velocity. After reaching a maximum displacement, its motion is reversed. This behaviour is in line with that found in full hydrodynamic simulations. We show that the evolution of the centroid shift and the image size are significantly different when lateral spreading is considered. For Gaussian jet models with plausible model parameters, the morphology of the laterally spreading jet images is much closer to circular. The maximum displacement of the centroid shift and its occurrence time are smaller/earlier by a factor of a few for spreading jets. Our results indicate that it is crucial to include lateral spreading effects when analysing radio images of neutron star merger jets. We also obtain the viewing angle θobs by using the centroid shift of radio images provided the ratio of the jet core size θc and θobs is determined by afterglow light curves. We show that a simple method based on a point-source approximation provides reasonable angular estimates ($10{-}20{{\ \rm per\ cent}}$ errors at most). By taking a sample of laterally spreading structured Gaussian jets, we obtain θobs ∼ 0.32 for GW170817, consistent with previous studies.
Highlights
After the detection of gravitational waves (GWs) from the binary neutron star (NS) merger, GW170817, its electromagnetic (EM) counterpart was discovered in the S0 galaxy NGC 4993 (e.g. Coulter et al 2017; Soares-Santos et al 2017)
We have presented radio image calculations from semi-analytical modelling, focusing on comparison between spreading and nonspreading approximations
We have shown a comparison of these models to the analytical point-source approximation and a comparison of the spreading-jet semi-analytical model to the observations of GW170817
Summary
After the detection of gravitational waves (GWs) from the binary neutron star (NS) merger, GW170817, its electromagnetic (EM) counterpart was discovered in the S0 galaxy NGC 4993 (e.g. Coulter et al 2017; Soares-Santos et al 2017). Nakar & Piran (2020) showed that afterglow light curves observed around their peak time Tp cannot constrain the observing angle, θ obs, but only determine the ratio of the observing angle θ obs to the jet opening angle, θ c (or core size for a core-dominated structured jet) This leads to degeneracy among the parameters {θ obs, θ c, l, B}, where l ∼ (E/nmpc2)1/3 is the Sedov length, n is the ambient density, mp is the proton mass, and B is the fraction of shock energy in the magnetic fields. As lateral spreading is most significant at late times, after the light-curve peaks, this effect is often not included in semi-analytical modelling (e.g. Ghirlanda et al 2019; Salafia et al 2019; Beniamini, Granot & Gill 2020).
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