On the structure of quasi-Keplerian accretion discs surrounding millisecond X-ray pulsars

In this study, we investigated the time-independent dynamics (disc structure, forces and torques) of a quasi-Keplerian disc around a millisecond pulsar (MSP) with an internal dynamo. We considered the disc around a MSP to be divided into the inner, middle and outer regions. By assuming that the disc matter flows in a quasi-Keplerian motion, we derived analytical equations for a complete structure (temperature, pressure, surface density, optical depth and magnetic field) of a quasi-Keplerian thin accretion disc, and the pressure gradient force (PGF). In our model, the MSP-disc interaction results into magnetic and material torques, such that for a given dynamo (ϵ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}) and quasi-Keplerian (ξ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\xi $$\end{document}) parameter, we obtained enhanced spin-up and spin-down torques for a chosen star spin period. Results obtained reveal that PGF results into episodic torque reversals that contribute to spinning-up or spinning-down of a neutron star, mainly from the inner region. The possibility of a quasi-Keplerian disc is seen and these results can explain the observed spin variations in MSPs like SAX J1808.4-3658 and XTE J1814-338.