Ballooning Instability in Polar Caps of Accreting Neutron Stars

We assess the stability of Kruskal-Schwarzschild (magnetic Rayleigh-Taylor) type modes for accreted matter on the surface of a neutron star confined by a strong (>= 1.E12 G) magnetic field. Employing the energy principle to analyze the stability of short-wavelength ballooning modes, we find that line-tying to the neutron star crust stabilizes these modes until the overpressure at the top of the neutron star crust exceeds the magnetic pressure by a factor ~ 8(a/h), where a and h are respectively the lateral extent of the accretion region and the density scale height. The most unstable modes are localized within a density scale height above the crust. We calculate the amount of mass that can be accumulated at the polar cap before the onset of instability.