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% Define document class
\documentclass[twocolumn]{aastex631}
\documentclass[twocolumn,tighten,linenumbers]{aastex631}
\usepackage{showyourwork}
\usepackage{subfigure}
\usepackage{amsmath}
\usepackage{hyperref}

\sloppy % citations were over-running the margins of a column, this fixes that

\shorttitle{Time-Variable Elemental Abundances in Loops}
\shortauthors{Reep et al.}

% Begin!
\begin{document}
Expand Down Expand Up @@ -65,17 +73,17 @@ \section{Loop Simulations}
Figure \ref{fig:L40} shows a comparison of evolution for 40 Mm loops, with the electrons heated by a 20 s heating pulse on a triangular profile (10 s rise, 10 s decay), for maximum heating rates of 0.01, 0.03, 0.1, and 1.0 erg s$^{-1}$ cm$^{-3}$ (each row, respectively). The columns respectively show the evolution of the electron temperature $T_{e}(t)$, density $n(t)$, and abundance factor $f(t)$. The different lines show the three cases of abundances: time-variable abundance factor (blue), time-fixed photospheric abundances ($f=1$, orange), and time-fixed coronal abundances ($f=4$, green).
\begin{figure*}
\centering
\includegraphics[width=0.32\linewidth]{Figures/temperature_L40_H0.01_t20.png}
\includegraphics[width=0.32\linewidth]{Figures/density_L40_H0.01_t20.png}
\includegraphics[width=0.32\linewidth]{Figures/abundance_L40_H0.01_t20.png}
\includegraphics[width=0.32\linewidth]{Figures/temperature_L40_H0.03_t20.png}
\includegraphics[width=0.32\linewidth]{Figures/density_L40_H0.03_t20.png}
\includegraphics[width=0.32\linewidth]{Figures/abundance_L40_H0.03_t20.png} \includegraphics[width=0.32\linewidth]{Figures/temperature_L40_H0.1_t20.png}
\includegraphics[width=0.32\linewidth]{Figures/density_L40_H0.1_t20.png}
\includegraphics[width=0.32\linewidth]{Figures/abundance_L40_H0.1_t20.png}
\includegraphics[width=0.32\linewidth]{Figures/temperature_L40_H1.0_t20.png}
\includegraphics[width=0.32\linewidth]{Figures/density_L40_H1.0_t20.png}
\includegraphics[width=0.32\linewidth]{Figures/abundance_L40_H1.0_t20.png}
\includegraphics[width=0.32\linewidth]{figures/temperature_L40_H0.01_t20.png}
\includegraphics[width=0.32\linewidth]{figures/density_L40_H0.01_t20.png}
\includegraphics[width=0.32\linewidth]{figures/abundance_L40_H0.01_t20.png}
\includegraphics[width=0.32\linewidth]{figures/temperature_L40_H0.03_t20.png}
\includegraphics[width=0.32\linewidth]{figures/density_L40_H0.03_t20.png}
\includegraphics[width=0.32\linewidth]{figures/abundance_L40_H0.03_t20.png} \includegraphics[width=0.32\linewidth]{figures/temperature_L40_H0.1_t20.png}
\includegraphics[width=0.32\linewidth]{figures/density_L40_H0.1_t20.png}
\includegraphics[width=0.32\linewidth]{figures/abundance_L40_H0.1_t20.png}
\includegraphics[width=0.32\linewidth]{figures/temperature_L40_H1.0_t20.png}
\includegraphics[width=0.32\linewidth]{figures/density_L40_H1.0_t20.png}
\includegraphics[width=0.32\linewidth]{figures/abundance_L40_H1.0_t20.png}
\caption{The evolution of the electron temperature (left column), density (center column), and abundance factor (right column) for a 40 Mm coronal loop, heated with 0.01, 0.03, 0.1, and 1.0 erg s$^{-1}$ cm$^{-3}$ (rows), for a 20 s heating pulse. The blue lines show the case with time-variable abundances $f(t)$, while orange lines show time-fixed photospheric abundances ($f=1$), and green time-fixed coronal abundances ($f=4$). \label{fig:L40}}
\end{figure*}

Expand All @@ -85,30 +93,30 @@ \section{Loop Simulations}
In Figure \ref{fig:L80}, we show a similar comparison with 80 Mm loops. Since the cooling time depends on loop length ($\propto L^{5/6}$, \citealt{cargill1995}), we expect that the differences should be exaggerated here. While the overall trends are similar to the previous case, there are a few differences worth noting. The first is that the coronal density does not grow as large with the same heating rates, and as a consequence the abundance factor remains somewhat higher. The second is that the duration of evaporation is somewhat longer, as the flows must travel a longer distance to fill the loop, so the rate of change of the abundance factor is generally slower.
\begin{figure*}
\centering
\includegraphics[width=0.32\linewidth]{Figures/temperature_L80_H0.01_t20.png}
\includegraphics[width=0.32\linewidth]{Figures/density_L80_H0.01_t20.png}
\includegraphics[width=0.32\linewidth]{Figures/abundance_L80_H0.01_t20.png}
\includegraphics[width=0.32\linewidth]{Figures/temperature_L80_H0.03_t20.png}
\includegraphics[width=0.32\linewidth]{Figures/density_L80_H0.03_t20.png}
\includegraphics[width=0.32\linewidth]{Figures/abundance_L80_H0.03_t20.png}
\includegraphics[width=0.32\linewidth]{Figures/temperature_L80_H0.1_t20.png}
\includegraphics[width=0.32\linewidth]{Figures/density_L80_H0.1_t20.png}
\includegraphics[width=0.32\linewidth]{Figures/abundance_L80_H0.1_t20.png}
\includegraphics[width=0.32\linewidth]{Figures/temperature_L40_H1.0_t20.png}
\includegraphics[width=0.32\linewidth]{Figures/density_L80_H1.0_t20.png}
\includegraphics[width=0.32\linewidth]{Figures/abundance_L80_H1.0_t20.png}
\includegraphics[width=0.32\linewidth]{figures/temperature_L80_H0.01_t20.png}
\includegraphics[width=0.32\linewidth]{figures/density_L80_H0.01_t20.png}
\includegraphics[width=0.32\linewidth]{figures/abundance_L80_H0.01_t20.png}
\includegraphics[width=0.32\linewidth]{figures/temperature_L80_H0.03_t20.png}
\includegraphics[width=0.32\linewidth]{figures/density_L80_H0.03_t20.png}
\includegraphics[width=0.32\linewidth]{figures/abundance_L80_H0.03_t20.png}
\includegraphics[width=0.32\linewidth]{figures/temperature_L80_H0.1_t20.png}
\includegraphics[width=0.32\linewidth]{figures/density_L80_H0.1_t20.png}
\includegraphics[width=0.32\linewidth]{figures/abundance_L80_H0.1_t20.png}
\includegraphics[width=0.32\linewidth]{figures/temperature_L40_H1.0_t20.png}
\includegraphics[width=0.32\linewidth]{figures/density_L80_H1.0_t20.png}
\includegraphics[width=0.32\linewidth]{figures/abundance_L80_H1.0_t20.png}
\caption{Similar to Figure \ref{fig:L40}, showing the results for an 80 Mm loop heated impulsively for 20 s. \label{fig:L80}}
\end{figure*}

We finally show two examples of nanoflare trains \citep{reep2013,cargill2014,barnes2016b}, where a series of nanoflare heating events occur in close succession before ceasing and allowing the loop to cool. Figure \ref{fig:train} shows two cases for loops of 40 and 80 Mm, with 5 heating events of 0.01 erg s$^{-1}$ cm$^{-3}$, spaced 300 s apart. The loops oscillate around temperatures of around 2.5 and 3.5 MK, respectively, during the heating period, before rapidly cooling. In both cases, the evaporation is prolonged for more than 30 minutes, causing the abundance factor to continue to fall, reaching a minimum of around $f=2$. As with single heating events, the effect of time-variable abundance on temperature and density becomes most noticeable during the cooling phase.
\begin{figure*}
\centering
\includegraphics[width=0.32\linewidth]{Figures/temperature_train_L40_H0.01_t20.png}
\includegraphics[width=0.32\linewidth]{Figures/density_train_L40_H0.01_t20.png}
\includegraphics[width=0.32\linewidth]{Figures/abundance_train_L40_H0.01_t20.png}
\includegraphics[width=0.32\linewidth]{Figures/temperature_train_L80_H0.01_t20.png}
\includegraphics[width=0.32\linewidth]{Figures/density_train_L80_H0.01_t20.png}
\includegraphics[width=0.32\linewidth]{Figures/abundance_train_L80_H0.01_t20.png}
\includegraphics[width=0.32\linewidth]{figures/temperature_train_L40_H0.01_t20.png}
\includegraphics[width=0.32\linewidth]{figures/density_train_L40_H0.01_t20.png}
\includegraphics[width=0.32\linewidth]{figures/abundance_train_L40_H0.01_t20.png}
\includegraphics[width=0.32\linewidth]{figures/temperature_train_L80_H0.01_t20.png}
\includegraphics[width=0.32\linewidth]{figures/density_train_L80_H0.01_t20.png}
\includegraphics[width=0.32\linewidth]{figures/abundance_train_L80_H0.01_t20.png}
\caption{Similar to Figure \ref{fig:L40}, showing examples of nanoflare trains, with 5 heating events spaced 300 s apart, for loops of 40 and 80 Mm. \label{fig:train}}
\end{figure*}

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