Accreted helium layers on white dwarfs have been highlighted for many decades as a possible site for a detonation triggered by a thermonuclear runaway .
In this paper , we find the minimum helium layer thickness that will sustain a steady laterally propagating detonation and show that it depends on the density and composition of the helium layer , specifically ^ { 12 } C and ^ { 16 } O. Detonations in these thin helium layers have speeds slower than the Chapman-Jouget ( CJ ) speed from complete helium burning , v _ { CJ } = 1.5 \times 10 ^ { 9 } cm/s .
Though gravitationally unbound , the ashes still have unburned helium ( \approx 80 \% in the thinnest cases ) and only reach up to heavy elements such as ^ { 40 } Ca , ^ { 44 } Ti , ^ { 48 } Cr , and ^ { 52 } Fe .
It is rare for these thin shells to generate large amounts of ^ { 56 } Ni .
We also find a new set of solutions that can propagate in even thinner helium layers when ^ { 16 } O is present at a minimum mass fraction of \approx 0.07 .
Driven by energy release from \alpha captures on ^ { 16 } O and subsequent elements , these slow detonations only create ashes up to ^ { 28 } Si in the outer detonated He shell .
We close by discussing how the unbound helium burning ashes may create faint and fast “ .Ia ” supernovae as well as events with virtually no radioactivity , and speculate on how the slower helium detonation velocities impact the off-center ignition of a carbon detonation that could cause a Type Ia supernova in the double detonation scenario .