# The Structure of a Quasi-Keplerian Accretion Disk around Magnetized Stars

## TL;DR

This paper develops a detailed model of a quasi-Keplerian accretion disk around magnetized neutron stars, highlighting the significant impact of pressure gradients on disk structure and star spin dynamics.

## Contribution

It introduces a comprehensive model incorporating pressure gradient forces in quasi-Keplerian disks, revealing their influence on disk structure and neutron star spin behavior.

## Key findings

- Pressure gradient force significantly alters disk structure near the neutron star.
- Corotation radius shifts depending on the deviation factor be;
- Pressure gradients affect spin-up and spin-down torques.

## Abstract

In this paper, we present the complete structure of a quasi-Keplerian thin accretion disk with an internal dynamo around a magnetized neutron star. We assume a full quasi-Keplerian disk with the azimuthal velocity deviating from the Keplerian fashion by a factor of $\xi$ ($0<\xi<2$). In our approach, we vertically integrate the radial component of the momentum equation to obtain the radial pressure gradient equation for a thin quasi-Keplerian accretion disk. Our results show that, at large radial distance, the accretion disk behaves in a Keplerian fashion. However, close to the neutron star, pressure gradient force (PGF) largely modifies the disk structure, resulting into sudden dynamical changes in the accretion disk. The corotation radius is shifted inward (outward) for $\xi>1$ (for $\xi<1$), and the position of the inner edge with respect to the new corotation radius is also relocated accordingly, as compared to the Keplerian model. The resulting PGF torque couples with viscous torque (when $\xi<1$) to provide a spin-down torque and a spin-up torque (when $\xi>1$) while in the advective state. Therefore, neglecting the PGF, as has been the case in previous models, is a glaring omission. Our result has the potential to explain the observable dynamic consequences of accretion disks around magnetized neutron stars.