Effect of variable crustal density on the surface magnetic field of Radio Pulsars

Abstract

We study the surface magnetic field fluctuations due to radial oscillations as a viable cause for the micro structures of the radio pulsar pulse patterns. The electrical conductivity of matter in the outer layer of the crust of a neutron star (NS) plays a crucial role in the resulting surface magnetic field if we assume that the magnetic field is confined to this layer. This outer layer has a rapidly varying matter density - that changes the micro-physics of the material affecting the electrical conductivity at every stage of the density change. In this study, the varying electrical conductivity in this rapidly varying density regime of the outer layer of the NS crust - from $\sim 10^{11}~g~cm^{-3}$ to about $10^4~g~cm^{-3}$ - has been used to calculate the surface magnetic field using the induction equation. A finite effect of the strong gravitational field at the NS surface has also been taken into account. The equations have been solved in MATLAB using the method of lines. Any minor radial fluctuation due to stellar oscillation, in particular the radial oscillations, leads to a fluctuation of the electrical conductivity in the outer layer of the crust. This leads to fluctuations in the surface magnetic field with a frequency equal to the frequency of the stellar oscillation. We find that not only the variation of the surface magnetic field is substantial, but also it does not remain constant throughout the lifetime of the NS.