Induced Magnetic Field in Accretion Disks Around Neutron Stars: Main Equations

Table of Links

Abstract and Introduction

Model of Disk and Neutron Star

Main Equations

The Solution for the Induced Field

Discussion

Conclusion and References

3. MAIN EQUATIONS

We shall start with the magnetic field induction equation (e.g., Naso and Miller 2010, 2011):

3.1. Equation of field diffusion

To estimate the strongest possible induced field inside the disk, I assume that the NS dipolar field penetrates the disk without screening (the assumption is discussed further).

The equation requires boundary conditions, but the expression in the last brackets in (6) is not suitable for setting them. It is convenient to make a substitution:

The non-dipolar component of the field is expected to be of the same order below and above the surface, thereby:

Thus, assuming turbulent diffusion in the magnetosphere, one may ignore the induced field derivative there. I follow this approach because the presence of corona seems very likely. From (13) we get:

It is remarkable how little the result depends on the choice for setting the boundary conditions.

The boundary condition at the lower surface of the disk may be set in the same fashion. At the inner radius of the disk, by analogy, one may write: