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Update ms.tex
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thomasckng committed Oct 30, 2023
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\acro{PE}{parameter estimation}
\acro{FAR}{false-alarm rate}
\acro{SNR}{signal-to-noise ratio}
\acro{2D}{two-dimensional}
\end{acronym}

\section{Introduction}
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\includegraphics[width=\columnwidth]{figures/corner_Gaussian.pdf}
\caption{
The posterior of the $\kappa$ population hyperparameters $\mu$ and $\sigma$, including (blue) and excluding (orange) GW200129 from the collection of events.
The \ac{2D} contours correspond to the $39.35\%$ and $90\%$ credible levels.
The two-dimensional (2D) contours correspond to the $39.35\%$ and $90\%$ credible levels.
The plot shows that the population constraint on $\kappa$ is consistent with no birefringence ($\mu=\sigma=0$) at the 90\% credible level.
}
\label{fig:corner_Gaussian}
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GW200129 posterior on $\kappa$, luminosity distance $d_L$, and inclination $\cos{\iota}$, including different sets of detectors in the analysis per the legend.
The marginalized posterior on $\chi_p$ is shown in the top right panel.
The main run with all three detectors (HLV, filled blue), shows a preference for $\kappa < 0$, as in Fig.~\ref{fig:violin_kappa}; this preference is more pronounced for two-detector runs that include Virgo (HV and LV, orange and green); however, it disappears if we remove Virgo (HL, dashed black).
The \ac{2D} contours correspond to the $90\%$ credible level.
The 2D contours correspond to the $90\%$ credible level.
}
\label{fig:corner_GW200129}
\end{figure}
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