Regimes of helium burning

The burning regimes encountered by laminar deflagrations and Zeldovich von Neumann Doring (ZND) detonations propagating through helium-rich compositio ns in the presence of buoyancy-driven turbulence are analyzed. Particular a ttention 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 inst ability of intermediate-mass stars. In the X-ray burst case, turbulent defl agrations propagating in the lateral or radial direction encounter a transi tion from the distributed regime to the flamelet regime at a density of sim ilar to 10(8) g cm(-3). In the radial direction, the purely laminar deflagr ation width is larger than the pressure scale height for densities smaller than similar to 10(6) g cm(-3). Self-sustained laminar deflagrations travel ing in the radial direction cannot exist below this density. Similarly, the planar ZND detonation width becomes larger than the pressure scale height at similar to 10(7) 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 rad ial direction encounter the distributed regime at densities below similar t o 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 pressu re scale height for densities smaller than similar to 10(4) g cm(-3), indic ating that steady state laminar de deflagrations cannot form below this den sity. The planar ZND detonation width becomes larger than the pressure scal e height at similar to 5 x 10(4) g cm(-3), suggesting that steady state, se lf-sustained detonations cannot come into existence in the radial direction .