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 b y a strong (greater than or similar to 10(12) G) magnetic field. Employing the energy principle to analyze the stability of short-wavelength balloonin g 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 similar to8(a/h), where a and h are, resp ectively, 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 a t the polar cap before the onset of instability.