  Hydrogen and/or helium accreted by a neutron star from a binary companion may
undergo thermonuclear fusion. At different mass accretion rates different
burning regimes are discerned. Theoretical models predict helium fusion to
proceed as a thermonuclear runaway for accretion rates below the Eddington
limit and as stable burning above this limit. Observations, however, place the
boundary close to 10% of the Eddington limit. We study the effect of
rotationally induced transport processes on the stability of helium burning.
For the first time detailed calculations of thin helium shell burning on
neutron stars are performed using a hydrodynamic stellar evolution code
including rotation and rotationally induced magnetic fields. We find that in
most cases the instabilities from the magnetic field provide the dominant
contribution to the chemical mixing, while Eddington-Sweet circulations become
important at high rotation rates. As helium is diffused to greater depths, the
stability of the burning is increased, such that the critical accretion rate
for stable helium burning is found to be lower. Combined with a higher heat
flux from the crust, as suggested by recent studies, turbulent mixing could
explain the observed critical accretion rate. Furthermore, close to this
boundary we find oscillatory burning, which previous studies have linked to mHz
QPOs. In models where we continuously lower the heat flux from the crust, the
period of the oscillations increases by up to several tens of percents, similar
to the observed frequency drift, suggesting that this drift could be caused by
the cooling of deeper layers.
