The minimum mass ratio of W UMa-type contact binaries—a new calculation

Abstract

A model is developed to establish the relationship between the critical gyration radius k of the primary component and the mass ratio (q) by considering the different dimensionless gyration radii of main-sequence stars with varying masses. The next step involves obtaining the low mass ratio limit (qmin=0.038∼0.041\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${q_{\ ext{min}}} = 0.038 \\sim 0.041$$\\end{document} for overcontact degree f=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f = 0$$\\end{document}~ 1) of W UMa-type contact binaries. Furthermore, the radial density distributions are estimated within the range of 0.3M⊙∼4.0M⊙\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0.3 M_{\\odot } \\sim 4.0 M_{\\odot }$$\\end{document}, based on the mass-radius relationship of main-sequence stars. Subsequently, the physical meaning of the minimum k value is proposed, which leads to an explanation for the cause of the minimum mass ratio. Finally, a stability criterion is proposed, which is based on both the mass ratio (q) and the total mass of the two components (Mtot\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_{tot}$$\\end{document}).