Regimes Of Helium Burning
  The burning regimes encountered by laminar deflagrations and ZND detonations propagating through helium-rich compositions in the presence of buoyancy-driven turbulence are analyzed. Particular attention is given to models of X-ray bursts which start with a thermonuclear runaway on the surface of a neutron star, and the thin shell helium instability of intermediate-mass stars. In the X-ray burst case, turbulent deflagrations propagating in the lateral or radial directions encounter a transition from the distributed regime to the flamlet regime at a density of 10^8 g cm^{-3}. In the radial direction, the purely laminar deflagration width is larger than the pressure scale height for densities smaller than 10^6 g cm^{-3}. Self-sustained laminar deflagrations travelling in the radial direction cannot exist below this density. Similarily, the planar ZND detonation width becomes larger than the pressure scale height at 10^7 g cm^{-3}, suggesting that a steady-state, self-sustained detonations cannot come into existance in the radial direction. In the thin helium shell case, turbulent deflagrations travelling in the lateral or radial directions encounter the distributed regime at densities below 10^7 g cm^{-3}, and the flamelet regime at larger densities. In the radial direction, the purely laminar deflagration width is larger than the pressure scale height for densities smaller than 10^4 g cm^{-3}, indicating that steady-state laminar deflagrations cannot form below this density. The planar ZND detonation width becomes larger than the pressure scale height at 5 10^4 g cm^{-3}, suggesting that steady-state, self-sustained detonations cannot come into existance in the radial direction. 
F.X. Timmes and J.C. Niemeyer