Christopher Berry edited sky.tex  almost 9 years ago

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\section{Sky localization} \section{Source location}  Having discussed how GW observations can measure the intrinsic properties of their source systems, we now consider the measurement of extrinsic parameters such as source location. parameters, specifically the sky position (section \ref{sec:sky}) and the distance (section \ref{sec:distance}).  On their own, these are not useful for understanding the physics of compact objects, but they are central to the success of multimessenger astronomy. The sky position is required in order to direct telescopes for electromagnetic follow-up and to verify that any observed transients do coincide with the source of the gravitational waves. The distance also aids electromagnetic follow-up as it allows cross-reference with galaxy catalogues to find the most probably source locations \citep{Nissanke_2012,Fan_2014}. Even without an observed counterpart, the posterior for the (three-dimensional) position allows us to assign a probability that the source resided in given galaxies; combined the redshift of these galaxies (measured electromagnetically) with the gravitational-wave luminosity distance gives a measure of the Hubble constant free of the usual systematics \citep{Schutz_1986,Del_Pozzo_2012}. For our population of slowly spinning neutron stars, we do not expect measurement of the extrinsic parameters to be affected by the inclusion of spin in the analysis.  \subsection{Sky localization}\label{sec:sky}  We characterize sky localization using credible regions, the smallest sky area that encompasses a given total posterior probability. The credible region for a total posterior probability $p$ is defined as  \begin{equation}