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 with the revised version proposed by , , and .
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 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 is used .
This avoids the need of invoking very strong propeller outflows in the transitional pulsars , as proposed in other literature works .