The Origin of Superflares on G-Type Dwarf Stars of Various Ages

We analyze new observations of superflares on G-stars discovered in the optical and near-IR ranges with the Kepler mission. An evolution of solar-type activity is discussed. We give an estimate of the maximal total energy, Etot=1034erg\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$E_{\mathrm{tot}} = 10^{34}~\mbox{erg}$\end{document}, of a flare that could have occurred on the young Sun at its age of 1 Gyr when the cycle was formed. We believe that the main source of the flare optical continuum is a low-temperature condensation forming in the course of the response of the chromosphere to an impulsive heating. For a superflare on the young Sun, we adopt an accelerated electron flux, Fe(E>20keV)=3×1011ergcm−2s−1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$F_{e}\ (E> 20~\mbox{keV}) = 3 \times 10^{11}~\mbox{erg}\,\mbox{cm}^{-2}\,\mbox{s}^{-1}$\end{document}, that is limited by the return current and obtain that the area of the optical continuum source on a G-star is S≈1019cm2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$S \approx 10^{19}~\mbox{cm}^{2}$\end{document}. This value is close to the area of the Hα\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathrm{H}\alpha$\end{document} ribbons in the largest solar flares, while the area of bright patches of a white-light flare on the contemporary Sun is lower by about two orders of magnitude. At the same electron flux and hard electron spectrum, a stellar flare of similar energy should be accompanied by a microwave source of about 2 mJy at frequencies 10 – 100 GHz at a distance of 100 pc. We discuss the possible detection of the flare-produced lithium in the course of spallation reactions. The detection of the flare microwave source and the emission in the Li resonant line could demonstrate how effective particle acceleration can be on stars in the lower part of the main sequence.