Unstable nonradial oscillations on helium-burning neutron stars

Material accreted onto a neutron star can stably burn in steady state only when the accretion rate is high ( typically super-Eddington) or if a large flux from the neutron star crust permeates the outer atmosphere. For such situations we have analyzed the stability of nonradial oscillations, finding one unstable mode for pure helium accretion. This is a shallow surface wave that resides in the helium atmosphere above the heavier ashes of the ocean. It is excited by the increase in the nuclear reaction rate during the oscillations, and it grows on the timescale of a second. For a slowly rotating star, this mode has a frequency omega/(2pi) (20-30 Hz)[l + 1)/2](1/2), and we calculate the full spectrum that a rapidly rotating (>>30 Hz) neutron star would support. The short-period X-ray binary 4U 1820-30 is accreting helium-rich material and is the system most likely to show this unstable mode, especially when it is not exhibiting X-ray bursts. Our discovery of an unstable mode in a thermally stable atmosphere shows that nonradial perturbations have a different stability criterion than the spherically symmetric thermal perturbations that generate type I X-ray bursts.