An accreting neutron star of mass and radius has a surface dipole field and accretes at

PHYSICS · Multi-part · Fermi University Physics · Astrophysics & Cosmology · Stellar death and compact objects · Astrophysical fluid dynamics and plasmas

Stars from the Inside, Ch Accretion power: mass transfer, discs and the weighing of black holes

Problem

An accreting neutron star of mass

M = 1.5\,M_\odot

and radius

R = 12\,\mathrm{km}

has a surface dipole field

B_* = 5.0\times10^{7}\,\mathrm{T}

and accretes at

\dot M = 5.0\times10^{13}\,\mathrm{kg\,s^{-1}}

. Infalling matter is stopped where the magnetic pressure of the dipole field,

B(r)^2/2\mu_0

with

B(r) = B_*(R/r)^3

, balances the ram pressure of matter falling freely from rest at infinity,

\rho v^2

with

\rho = \dot M/4\pi r^2 v

and

v = \sqrt{2GM/r}

. ((a)) Find the magnetospheric radius

r_m

. ((b)) Find the spin period at which the star would corotate with matter at

r_m

(the equilibrium spin period).

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