Screening of the Magnetic Field of Disk Accreting Stars

An analytical model is developed for the screening of the external magneticfield of a rotating, axisymmetric neutron star due to the accretion of plasmafrom a disk. The decrease of the field occurs due to the electric current inthe infalling plasma. The deposition of this current carrying plasma on thestar's surface creates an induced magnetic moment with a sign opposite to thatof the original magnetic dipole. The field decreases independent of whether thestar spins-up or spins-down. The time-scale for an appreciable decrease (factorof $>100$) of the field is found to be $\sim 1.6 \times 10^7$ yr, for a massaccretion rate $\dot{M}=10^{-9} M_\odot/$yr and an initial magnetic moment$\mu_i = 10^{30}{\rm G cm}^3$ which corresponds to a surface field of $10^{12}$G if the star's radius is $10^6$ cm. The time-scale varies approximately as$\mu_i^{3.8}/\dot{M}^{1.9}$. The decrease of the magnetic field does not have asimple relation to the accreted mass. Once the accretion stops the field leaksout on an Ohmic diffusion time scale which is estimated to be $ > 10^9$ yr.Comment: 11 pages, 7 figure