Binary pulsars in magnetic field versus spin period diagram

We analyzed 186 binary pulsars (BPSRs) in the magnetic field versus spin period (B-P) diagram, where their relations to the millisecond pulsars (MSPs) can be clearly shown. Generally, both BPSRs and MSPs are believed to be recycled and spun-up in binary accreting phases, and evolved below the spin-up line setting by the Eddington accretion rate (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\dot{M}{\simeq}10^{18}~\mbox{g/s}$\end{document}). It is noticed that most BPSRs are distributed around the spin-up line with mass accretion rate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\dot{M}=10^{16}~\mbox{g/s}$\end{document} and almost all MSP samples lie above the spin-up line with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\dot{M}\sim10^{15}~\mbox{g/s}$\end{document}. Thus, we calculate that a minimum accretion rate (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\dot{M}\sim10^{15}~\mbox{g/s}$\end{document}) is required for the MSP formation, and physical reasons for this are proposed. In the B-P diagram, the positions of BPSRs and their relations to the binary parameters, such as the companion mass, orbital period and eccentricity, are illustrated and discussed. In addition, for the seven BPSRs located above the limit spin-up line, possible causes are suggested.