Recent studies have argued that the progenitor system of type Iax supernovae
must consist of a carbon-oxygen white dwarf accreting from a helium star
companion. Based on existing explosion models invoking the pure deflagration of
carbon-oxygen white dwarfs, we investigate the likelihood of producing spectral
features due to helium in type Iax supernovae. From this scenario, we select
those explosion models producing ejecta and 56Ni masses that are broadly
consistent with those estimated for type Iax supernovae (0.014 -
0.478~M⊙ and ∼0.003 - 0.183~M⊙, respectively). To this
end, we present a series of models of varying luminosities (−18.4≲MV≲−14.5~mag) with helium abundances accounting for up to
∼36\% of the ejecta mass, and covering a range of epochs beginning a few
days before B−band maximum to approximately two weeks after maximum. We find
that the best opportunity for detecting \ion{He}{i} features is at
near-infrared wavelengths, and in the post-maximum spectra of the fainter
members of this class. We show that the optical spectrum of SN~2007J is
potentially consistent with a large helium content (a few 10−2M⊙),
but argue that current models of accretion and material stripping from a
companion struggle to produce compatible scenarios. We also investigate the
presence of helium in all objects with near-infrared spectra. We show that
SNe~2005hk, 2012Z, and 2015H contain either no helium or their helium
abundances are constrained to much lower values
(≲10−3M⊙). Our results demonstrate the differences in
helium content among type Iax supernovae, perhaps pointing to different
progenitor channels. Either SN~2007J is an outlier in terms of its progenitor
system, or it is not a true member of the type Iax supernova class.Comment: 15 pages, 12 figures, 2 tables. Accepted for publication in Astronomy
and Astrophysic