Inclination Estimates from Off-Axis GRB Afterglow Modelling

Abstract

For gravitational wave (GW) detected neutron star mergers, one of the leading candidates for electromagnetic (EM) counterparts is the afterglow from an ultra-relativistic jet. Where this afterglow is observed, it will likely be viewed off-axis, such as the afterglow following GW170817/GRB 170817A. The temporal behaviour of an off-axis observed GRB afterglow can be used to reveal the lateral jet structure, and statistical model fits can put constraints on the various model free-parameters. Amongst these parameters is the inclination of the system to the line of sight. Along with the GW detection, the afterglow modelling provides the best constraint on the inclination to the line-of-sight and can improve the estimates of cosmological parameters, for example, the Hubble constant, from GW-EM events. However, modelling of the afterglow depends on the assumed jet structure and—often overlooked—the effects of lateral spreading. Here we show how the inclusion of lateral spreading in the afterglow models can affect the estimated inclination of GW-EM events.

Extragalactic fast X-ray transient candidates discovered byChandra(2000–2014)

“…6. For an off-axis scenario, a delay between the gamma-ray trigger and its peak X-ray afterglow depends on both intrinsic (e.g., the off-axis angle and the deceleration timescale of the outflow) and extrinsic (e.g., the low densities density of the BNS environment and the observer location) properties (e.g., Granot et al 2002Granot et al , 2018aTroja et al 2020;Lamb et al 2021), effectively spanning all timescales. Strong X-ray flares have been known to occur on top of X-ray afterglow emission, but these typically occur during the early phase of the afterglow ( 10 3 -10 4 s; e.g., Yi et al 2016).…”

Multi-Messenger Constraints on the Hubble Constant through Combination of Gravitational Waves, Gamma-Ray Bursts and Kilonovae from Neutron Star Mergers

“…On the EM side, possible source of systematic uncertainties come from estimates of peculiar velocities in nearby events [57][58][59] and viewing-angle selection effects biasing discovery of EM counterparts towards systems viewed close to face-on [163]. Secondly, additional source of systematics are introduced by the uncertainties on models used to fit GRB [87,[90][91][92][93][94] and KN [144][145][146][147] observables to constrain the inclination. In a recent study, Chen et al [163] showed that the viewing-angle effects are likely to dominate the systematics budget and be a major challenge to resolve the H 0 tension with GWs and light from NS mergers.…”

“…The uncertainties in the modelling of the GRB afterglow light curves can potentially bias the inclination estimates and introduce systematics in the H 0 measurement. In particular, different studies [87,[90][91][92][93][94] have highlighted a clear degeneracy between the observer viewing angle and the jet structure adopted. For instance, Ryan et al [87] and Takahashi & Yota [90] showed that for both a Gaussian and a power-law jet the ratio θ obs /θ j is much better constrained than any of the two angles individually.…”

“…The value θ obs /θ j ∼ 5.8 required to fit the peak of GW170817 was found to be in good agreement with the θ obs /θ j ratio derived from the aforementioned studies fitting for the two angles individually. Moreover, Lamb et al [93] showed that the inclusion/omission of a lateral spreading of the blastwave can shift θ obs by up to a factor of 2. All these studies caution against using viewing-angle constraints from the light curve fitting alone, unless systematic uncertainties are properly modelled and taken into account.…”

An analytic derivation of the empirical correlations of gamma-ray bursts

“…Luckily, a recent study suggests that E p and the flux will not change much regardless of the choice of a top-hat jet or a not-too-complicated structured jet (Farinelli et al 2021). However, in some more complicated scenarios, structured jets may further have an angle-dependent energy density (Lamb et al 2021). They may be choked jets or even in jet-cocoon systems (Ioka & Nakamura 2018;Mooley et al 2018;Troja et al 2019).…”