Constraints on primordial black holes in the mixed dark matter scenarios using the ratio (3He+D)/H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathrm (^3{He}+D)/H$$\\end{document}

Abstract

We derive the upper limit on the dark matter (DM) fraction in primordial black holes (PBHs) in the mixed DM scenarios. In this scenarios, a PBH can accrete weakly interacting massive particles (WIMPs) to form a ultracompact minihalo (UCMH) with a density profile of ρDM(r)∼r-9/4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho _{\ extrm{DM}}(r)\\sim r^{-9/4}$$\\end{document}. The energy released from UCMHs due to dark matter annihilation has influence on the photodissociation of 4He\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{4}{\ extrm{He}}$$\\end{document}, producing the 3He\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{3}{\ extrm{He}}$$\\end{document} and the D. By requiring that the ratio (3He+D)/H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(^3\ ext {He}+\ ext {D})/\ ext {H}$$\\end{document} caused by UCMHs does not exceed the measured value, we derive the upper limit on the dark matter fraction in PBHs. For the canonical value of DM thermally averaged annihilation cross section σv=3×10-26cm3s-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left<\\sigma v\\right>=3\ imes 10^{-26}\ ext {cm}^{3}\\,\ ext {s}^{-1}$$\\end{document}, we find that the upper limit is fPBH<0.35(0.75)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_{\ extrm{PBH}} < 0.35(0.75)$$\\end{document} for DM mass mχ=1(10)GeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_{\\chi }=1(10)~ \ ext {GeV}$$\\end{document}. Compared with other limits obtained by different astronomical measurements, although our limit is not the strongest, we provide a different way of constraining the cosmological abundance of PBHs.