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The double-detonation explosion model has been considered a candidate forexplaining astrophysical transients with a wide range of luminosities. In thismodel, a carbon-oxygen white dwarf star explodes following detonation of asurface layer of helium. One potential signature of this explosion mechanism isthe presence of unburned helium in the outer ejecta, left over from the surfacehelium layer. In this paper we present simple approximations to estimate theoptical depths of important He I lines in the ejecta of double-detonationmodels. We use these approximations to compute synthetic spectra, including theHe I lines, for double-detonation models obtained from hydrodynamical explosionsimulations. Specifically, we focus on photospheric-phase predictions for thenear-infrared 10830 \AA~and 2 $\mu$m lines of He I. We first consider a doubledetonation model with a luminosity corresponding roughly to normal SNe Ia. Thismodel has a post-explosion unburned He mass of 0.03 $M_{\odot}$ and ourcalculations suggest that the 2 $\mu$m feature is expected to be very weak butthat 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 beexpected to form in double-detonation explosions at epochs around maximumlight. 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 beconfused or blended with the C I 10690~\AA~line forming at lower velocities. Wealso present calculations for the He I 10830 \AA~and 2 $\mu$m lines for a lowermass (low luminosity) double detonation model, which has a post-explosion Hemass of 0.077 $M_{\odot}$. In this case, both the He I features we consider arestrong and can provide a clear observational signature of the double-detonationmechanism.

Helium in Double-Detonation Models of Type Ia Supernovae