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showyourwork committed May 9, 2024
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Expand Up @@ -109,16 +109,14 @@ \section{Loop Simulations}
\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.
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 $f$ to fall successively with each heating event (and thus evaporation event), 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}
\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}}
\includegraphics[width=0.47\linewidth]{figures/temperature_train_L40_H0.01_t20.png}
\includegraphics[width=0.47\linewidth]{figures/abundance_train_L40_H0.01_t20.png}
\includegraphics[width=0.47\linewidth]{figures/temperature_train_L80_H0.01_t20.png}
\includegraphics[width=0.47\linewidth]{figures/abundance_train_L80_H0.01_t20.png}
\caption{Two examples of nanoflare trains, with 5 heating events spaced 300 s apart, for loops of 40 and 80 Mm. The abundance factor $f$ falls with each successive heating event. \label{fig:train}}
\end{figure*}

\section{Discussion}
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