\documentclass[border=10pt]{standalone}
\usepackage{pgfplots, amsmath}
\usepackage{filecontents}

%\definecolor{color1}{rgb}{0.9,0.9,0.9}
%\definecolor{color2}{rgb}{0.7,0.7,0.7}
%\definecolor{color3}{rgb}{0.5,0.5,0.5}
%\definecolor{color4}{rgb}{0.3,0.3,0.3}
%\definecolor{color5}{rgb}{0.1,0.1,0.1}

\usetikzlibrary{colorbrewer}
\usepgfplotslibrary{colorbrewer}
%\usepgfplotslibrary{colormaps}
%\usepackage{pgfplotstable}
 \usepgfplotslibrary{external}
 \tikzexternalize[shell escape=-shell-escape]


%\pgfplotsset{every axis plot/.append style={line width=1pt}}
\pgfplotsset{every axis plot/.append style={line width=1pt},compat=1.8}

\begin{document}
	\begin{tikzpicture}
	\begin{axis}[
	xlabel= $t/t_\text{esc}$,
	ylabel=$\sigma_K(t)$,
	width = 6cm,
	height = 4cm,
	ymin = 0,
	minor tick style={draw=none},
	cycle list/Paired-5,
	%ymin = 1,
	%domain = 3.5:450,
	%transpose legend,
	%legend columns=-1,
	%legend style={at={(0.5,1.30)},anchor=north},
	minor tick style={draw=none},
	legend columns=1,
	legend entries ={$0$, $0.25$, $0.5$,$0.75$,$1$},
	legend style={font=\small,at={(1.3,1.0)},anchor=north},
	]
	\addplot +[mark=none] table[x expr=\thisrowno{0}/600,y index=1] {data_P_0.txt};
	\addplot +[mark=none] table[x expr=\thisrowno{0}/600,y index=1] {data_P_25.txt};
	\addplot +[mark=none] table[x expr=\thisrowno{0}/600,y index=1] {data_P_50.txt};
	\addplot +[mark=none] table[x expr=\thisrowno{0}/600,y index=1] {data_P_75.txt};
	\addplot +[mark=none] table[x expr=\thisrowno{0}/600,y index=1] {data_P_100.txt};
	%\legend{P=0, P=0.25, P=0.5,P=0.75,P=1}
	\end{axis}
	\end{tikzpicture}
\end{document}