Regimes of helium burning

The burning regimes encountered by laminar deflagrations and Zeldovich von Neumann Döring (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 that start with a thermonuclear runaway on the surface of a neutron star and to the thin-shell helium instability of intermediate-mass stars. In the X-ray burst case, turbulent deflagrations propagating in the lateral or radial direction encounter a transition from the distributed regime to the flamelet regime at a density of ∼10⁸ g cm^-3. In the radial direction, the purely laminar deflagration width is larger than the pressure scale height for densities smaller than ∼10⁶ g cm^-3. Self-sustained laminar deflagrations traveling in the radial direction cannot exist below this density. Similarly, the planar ZND detonation width becomes larger than the pressure scale height at ∼10⁷ g cm^-3, suggesting that steady state, self-sustained detonations cannot come into existence in the radial direction. In the thin helium shell case, turbulent deflagrations traveling in the lateral or radial direction encounter the distributed regime at densities below ∼10⁷ 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 ∼10⁴ 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 × 10⁴ g cm^-3, suggesting that steady state, self-sustained detonations cannot come into existence in the radial direction.