The double-detonation explosion model has been considered a candidate for explaining astrophysical transients with a wide range of luminosities. In this model, a carbon-oxygen white dwarf star explodes following detonation of a surface layer of helium. One potential signature of this explosion mechanism is the presence of unburned helium in the outer ejecta, left over from the surface helium layer. In this paper we present simple approximations to estimate the optical depths of important He I lines in the ejecta of double-detonation models. We use these approximations to compute synthetic spectra, including the He I lines, for double-detonation models obtained from hydrodynamical explosion simulations. Specifically, we focus on photospheric-phase predictions for the near-infrared 10830 AA~and 2 $mu$m lines of He I. We first consider a double detonation model with a luminosity corresponding roughly to normal SNe Ia. This model has a post-explosion unburned He mass of 0.03 $M_{odot}$ and our calculations suggest that the 2 $mu$m feature is expected to be very weak but that the 10830 AA~feature may have modest opacity in the outer ejecta. Consequently, we suggest that a moderate-to-weak He I 10830 AA~feature may be expected to form in double-detonation explosions at epochs around maximum light. However, the high velocities of unburned helium predicted by the model ($sim 19,000$~km~s$^{-1}$) mean that the He I 10830 AA~feature may be confused or blended with the C I 10690~AA~line forming at lower velocities. We also present calculations for the He I 10830 AA~and 2 $mu$m lines for a lower mass (low luminosity) double detonation model, which has a post-explosion He mass of 0.077 $M_{odot}$. In this case, both the He I features we consider are strong and can provide a clear observational signature of the double-detonation mechanism.
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