Thesis: Radio Interferometry: competitive with FD

documents/thesis/chapters/radio_interferometry.tex

@@ -20,9 +20,9 @@ For suitable frequencies, an array of radio antennas can be used as an interfero
 Therefore, air showers can be analysed using radio interferometry.
 Note that since the radio waves are mainly caused by processes involving electrons (see Section~\ref{sec:airshowers}), any derived properties are tied to the electromagnetic component of the air shower.
 \\
-In \cite{Schoorlemmer:2020low}, a technique was developed to obtain properties of an air shower using interferometry.%
+In Reference~\cite{Schoorlemmer:2020low}, a technique was developed to obtain properties of an air shower using radio interferometry.%
 \footnote{
-	Available as a python package at \url{gitlab}\Todo{url}.
+	Available as a python package at \url{https://gitlab.com/harmscho/asira}.
 }
 Figure~\ref{fig:radio_air_shower} shows a power mapping of a simulated air shower.
 It reveals the air shower in one vertical and three horizontal slices.
@@ -32,33 +32,36 @@ From these, the energy, composition and direction of the cosmic particle can be
 
 The accuracy of the technique is primarily dependent on the timing accuracy of the detectors.
 In Figure~\ref{fig:xmax_synchronise}, the estimated atmospheric depth resolution as a function of detector synchronisation is shown as simulated for different inclinations of the air shower.
-For detector synchronisations above $1\ns$, the atmospheric depth resolution is degrading rapidly.
+For detector synchronisations under $2\ns$, the atmospheric depth resolution is competitive with techniques from fluorescence detectors ($\sigma(\Xmax) ~ 25\,\mathrm{g/cm^2}$ at \gls{Auger} \cite{Deligny:2023yms}).
+With a difference in $\langle \Xmax \rangle$ of $\sim 100\,\mathrm{g/cm^2}$ between iron and proton initiated air showers, this depth of shower maximum resolution allows to study the mass composition of cosmic rays.
+However, for worse synchronisations, the $\Xmax$ resolution for radio antennas degrades linearly.
 \\
-Note that the values in Figure~\ref{fig:xmax_synchronise} are particular to the simulation setup of \cite{Schoorlemmer:2020low}.
-Generally, this will depend on the antenna density of the array.
+An advantage of radio antennas with respect to fluorescence detectors is the increased duty-cycle.
+Fluorescence detectors require clear, moonless nights, resulting in a duty-cycle of about $10\%$ whereas radio detectors have a near permanent duty-cycle.
 \\
 
 \begin{figure}
 	\centering
-	\begin{minipage}{0.47\textwidth}
+	\begin{minipage}[t]{0.47\textwidth}
 		\centering
 		\includegraphics[width=\textwidth]{2006.10348/fig01.no_title}%
 		\captionof{figure}{
 			From \protect \cite{Schoorlemmer:2020low}.
 			Radio interferometric power analysis of a simulated air shower.
-			\textit{a)} shows the normalised power of $S(\vec{x})$ mapped onto a vertical plane.
+			\textit{a)} shows the normalised power of $S(\vec{x})$ mapped onto a vertical planer,
 				while \textit{b)}, \textit{c)} and \textit{d)} show the horizontal slices on different heights.
 			On \textit{b)}, \textit{c)} and \textit{d)}, the orange and blue dot indicate the true shower axis and the maximum power respectively.
 		}
 		\label{fig:radio_air_shower}
 	\end{minipage}
 	\hfill
-	\begin{minipage}{0.47\textwidth}
+	\begin{minipage}[t]{0.47\textwidth}
 		\centering
 		\includegraphics[width=\textwidth]{2006.10348/fig03_b}%
 		\captionof{figure}{
 			From \protect \cite{Schoorlemmer:2020low}.
 			$\Xmax$ resolution as a function of detector-to-detector synchronisation.
+			Note that this figure shows a first-order effect with values particular to the antenna density of the simulated array.
 		}
 		\label{fig:xmax_synchronise}
 	\end{minipage}
@@ -95,7 +98,7 @@ This requires us to compute the time delays for each test location $\vec{x}$ sep
 \\
 
 % Features in S
-Features in the summed waveform $S(\vec{x})$ are enhanced according\Todo{word} to the coherence of that feature in the recorded waveforms with respect to the time delays.
+Features in the summed waveform $S(\vec{x})$ are enhanced according to the coherence of that feature in the recorded waveforms with respect to the time delays.
 \\
 Figures~\ref{fig:trace_overlap:best} and~\ref{fig:trace_overlap:bad} show examples of this effect for the same recorded waveforms.
 At the true source location, the recorded waveforms align and sum coherently to result in a summed waveform with enhanced features and amplitudes.
@@ -108,23 +111,25 @@ The signal in the summed waveform grows linearly with the number of detectors, w
 
 \begin{figure}% fig:trace_overlap %<<<
 	\centering
-	\begin{minipage}[c][9cm][t]{0.47\textwidth}
+	\begin{minipage}[b][9cm][t]{0.47\textwidth}
 		\begin{subfigure}{\textwidth}
 			\includegraphics[height=8cm, width=\textwidth]{radio_interferometry/rit_schematic_far.pdf}%
 			\caption{}
 			\label{fig:rit_schematic}
 		\end{subfigure}
-	\end{minipage}
-	\hfill
-	\begin{minipage}[c][9cm][t]{.47\textwidth}
+	\end{minipage}\hfill%
+	\begin{minipage}[b][9cm][t]{.47\textwidth}
+			\vskip 1cm
 		\begin{subfigure}{\textwidth}
 			\includegraphics[height=2.5cm, width=\textwidth]{radio_interferometry/trace_overlap_best.png}
+			\vskip 0.3cm
 			\caption{}
 			\label{fig:trace_overlap:best}
 		\end{subfigure}
-		\vfill
+		\vskip 0.7cm
 		\begin{subfigure}{\textwidth}
 			\includegraphics[height=2.5cm, width=\textwidth]{radio_interferometry/trace_overlap_bad.png}
+			\vskip 0.3cm
 			\caption{}
 			\label{fig:trace_overlap:bad}
 		\end{subfigure}
@@ -157,4 +162,5 @@ An example of this power distribution of $S\vec{x}$ is shown in Figure~\ref{fig:
 The region of high power identifies strong coherent signals related to the air shower.
 By mapping this region, the shower axis and shower core can be resolved.
 Later, with the shower axis identified, the power along the axis is used to compute \Xmax.
+\Todo{Longitudinal grammage?}
 \end{document}