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