A comparative study of non-thermal parameters of the X-class solar flare plasma obtained from cold and warm thick-target models; error estimation by Monte Carlo simulation method

The electron transport and relaxation in the non-thermal plasma of solar flare are often described by cold thick-target model. Recently introduced warm thick-target model however is also found to be more consistent for describing it and hence provide the accurate estimate of parameters of non-thermal solar flare plasma. In this study, we evaluate the consistency of cold and warm thick-target models by estimating non-thermal parameters viz., low-energy cutoff (Ec/Ewc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${E_{c}/E_{wc}} $\end{document}), kinetic power of non-thermal electrons (Pnth/Pwnth\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${P _{nth}/P_{wnth}} $\end{document}) and non-thermal energy (Enth/Ewnth\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${E_{nth}/E_{wnth}} $\end{document}), along with standard error (SE) and their linear statistical analysis with respect to flare duration (tf\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${t _{f}}$\end{document}). We further evaluate the accuracy of these parameters using Monte Carlo simulation data in 2σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$2 \sigma $\end{document} limits. We found that cold thick-target model gives high values of mean and SE of the estimated parameters compare to warm thick-target model those were also found consistent with the Monte Carlo data (in both cases). Here, we also found that the variation of Ec/Ewc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${E_{c}/E_{wc}} $\end{document} and Pnth/Pwnth\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${P _{nth}/P_{wnth}} $\end{document} with respect to tf\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${t_{f}} $\end{document} give a negative/positive and positive values of correlation coefficient (r\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$r$\end{document}) and slope (b\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$b$\end{document}) respectively which account for upper and lower limits of Ec/Ewc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${E_{c}/E_{wc}} $\end{document} and high and slow rate of thermalization of non-thermal electrons. Our results show that the warm thick-target model is more consistent model compare to cold thick-target model that could also lead a multi-temperature component in the thermalized plasma.