Zusammenfassung
We present an analytic model for measuring the jet core angle ($þeta_c$)
and viewing angle ($þeta_obs$) of off-axis gamma-ray bursts independently
of the jet angular structure outside of the core. We model the images of
off-axis jets and using this model we show that $þeta_obs$ and $þeta_c$
can be measured using any two of the three following observables: the afterglow
light curve, the flux-centroid motion, and the image width. The model is
calibrated using 2D relativistic hydrodynamic simulations with a broad range of
jet angular structures. We study the systematic errors due to the uncertainty
in the jet structure and find that when using the light curve and centroid
motion to determine $þeta_obs$ and $þeta_c$, our formulae can be accurate
to a level of $5-10\%$ and $30\%$, respectively. In light of the Hubble
tension, the systematic error in $\cosþeta_obs$ in GRBs originating in a
binary compact object merger is of special interest. We find that the
systematic uncertainty on the measurement of $\cosþeta_obs$ due to the
unknown jet structure is smaller than $1.5\%$ for well-observed events. A
similar error is expected if the microphysical parameters evolve at a level
that is not easily detected by the light curve. Our result implies that this
type of systematic uncertainty will not prevent measurement of $H_0$ to a level
of $2\%$ with a sample of well-observed GW events with resolved afterglow image
motion. Applying our model to the light curve and centroid motion observations
of GW170817 we find $þeta_obs=19.22~\deg$ (1$\sigma$) and
$þeta_c=1.5-4~\deg$.
Nutzer