Title:Instabilities, turbulence, and mixing in the ocean of accreting neutron stars

Abstract: We consider the stability properties of the ocean of accreting magnetic neutron stars. It turns out that the ocean is always unstable due to the combined influence of the temperature and chemical composition gradients along the surface and of the Hall effect. Both the oscillatory and non-oscillatory modes can be unstable in accreting stars. The oscillatory instability grows on a short timescale of the order os 0.1-10 s depending on the lengthscale of a surface inhomogeneity and the wavelength of perturbations. The instability of non-oscillatory modes is typically much slower and can develop on a timescale of hours or days. Instability generates a weak turbulence that can be responsible for mixing between the surface and deep ocean layers and for spreading the accreted material over the stellar surface. Spectral features of heavy elements can be detected in the atmospheres of accreting stars due to mixing, and these features should be different in neutron stars with stable and unstable burning. Motions caused by instability can also be the reason for slow variations in the luminosity.