  The double-detonation explosion scenario of Type Ia supernovae has gained
increased support from the SN Ia community as a viable progenitor model, making
it a promising candidate alongside the well-known single degenerate and double
degenerate scenarios. We present delay times of double-detonation SNe, in which
a sub-Chandrasekhar mass carbon-oxygen white dwarf accretes non-dynamically
from a helium-rich companion. One of the main uncertainties in quantifying SN
rates from double-detonations is the (assumed) retention efficiency of He-rich
matter. Therefore, we implement a new prescription for the treatment of
accretion/accumulation of He-rich matter on white dwarfs. In addition, we test
how the results change depending on which criteria are assumed to lead to a
detonation in the helium shell. In comparing the results to our standard case
(Ruiter et al. 2011), we find that regardless of the adopted He accretion
prescription, the SN rates are reduced by only 25% if low-mass He shells (<
0.05 Msun) are sufficient to trigger the detonations. If more massive (0.1
Msun) shells are needed, the rates decrease by 85% and the delay time
distribution is significantly changed in the new accretion model - only SNe
with prompt (< 500 Myr) delay times are produced. Since theoretical arguments
favour low-mass He shells for normal double-detonation SNe, we conclude that
the rates from double-detonations are likely to be high, and should not
critically depend on the adopted prescription for accretion of He.
