The magnetospheric radius of an inclined rotator in the magnetically threaded disk model

TL;DR

This paper compares different models for estimating the magnetospheric radius in neutron star X-ray binaries, showing that the revised Wang model predicts smaller radii, especially at high inclination angles, which better explains low-luminosity pulsations.

Contribution

It provides a detailed comparison of the Ghosh & Lamb and Wang models, highlighting the impact of inclination angle and revised calculations on magnetospheric radius estimates.

Findings

Revised Wang model predicts smaller magnetospheric radii than Ghosh & Lamb.

High inclination angles further decrease the estimated radius.

Application to transitional pulsars explains low-luminosity pulsations without strong propeller outflows.

Abstract

The estimate of the magnetospheric radius in a disk-fed neutron star X-ray binary is a long standing problem in high energy Astrophysics. We review the magnetospheric radius calculations in the so-called magnetically threaded disk model, comparing the simplified approach originally proposed by Ghosh & Lamb (1979) with the revised version proposed by Wang (1987), Wang (1995), and Wang (1997). We show that for a given set of fixed parameters (assuming also a comparable screening factor of the neutron star magnetic field by the currents induced on the disk surface) the revised magnetically threaded disk model predicts a magnetospheric radius that is significantly smaller than that derived from the Ghosh & Lamb (1979) treatment. For a fixed value of the neutron star magnetic field and a wide range of mass accretion rates, the inclusion of a large inclination angle between the neutron star rotation and magnetic field axes ($\chi$$\gtrsim$60 deg) leads to a further decrease of the magnetospheric radius. To illustrate the relevance of these calculations, we consider, as an example, the case of the transitional pulsars. During the so-called "high mode" of their sub-luminous accretion disk state, these sources have shown X-ray pulsations interpreted as due to accretion at an unprecedented low luminosity level compared to other neutron stars in X-ray binaries. In the context of the magnetic threaded disk model, we show that accretion at luminosities of $\sim$10$^{33}$ erg s$^{-1}$ (and thus accretion-driven X-ray pulsations) can be more easily explained when the prescription of the magnetospheric radius provided by Wang (1997) is used. This avoids the need of invoking very strong propeller outflows in the transitional pulsars, as proposed in other literature works.