Evidence for sub-Chandrasekhar-mass progenitors of Type Ia supernovae at
  the faint end of the width-luminosity relation
  The faster light-curve evolution of low-luminosity Type Ia supernovae (SNe
Ia) suggests that they could result from the explosion of white dwarf (WD)
progenitors below the Chandrasekhar mass ($M_{\rm Ch}$). Here we present 1D
non-LTE time-dependent radiative transfer simulations of pure central
detonations of carbon-oxygen WDs with a mass ($M_\rm{tot}$) between 0.88
M$_{\odot}$ and 1.15 M$_{\odot}$, and a $^{56}\rm{Ni}$ yield between 0.08
M$_{\odot}$ and 0.84 M$_{\odot}$. Their lower ejecta density compared to
$M_{\rm Ch}$ models results in a more rapid increase of the luminosity at early
times and an enhanced $\gamma$-ray escape fraction past maximum light.
Consequently, their bolometric light curves display shorter rise times and
larger post-maximum decline rates. Moreover, the higher
$M(^{56}\rm{Ni})/M_\rm{tot}$ ratio at a given $^{56}\rm{Ni}$ mass enhances the
temperature and ionization level in the spectrum-formation region for the less
luminous models, giving rise to bluer colours at maximum light and a faster
post-maximum evolution of the $B-V$ colour. For sub-$M_{\rm Ch}$ models fainter
than $M_B\approx -18.5$ mag at peak, the greater bolometric decline and faster
colour evolution lead to a larger $B$-band post-maximum decline rate, $\Delta
M_{15}(B)$. In particular, all of our previously-published $M_{\rm Ch}$ models
(standard and pulsational delayed detonations) are confined to $\Delta
M_{15}(B) < 1.4$ mag, while the sub-$M_{\rm Ch}$ models with
$M_\rm{tot}\lesssim 1$ M$_{\odot}$ extend beyond this limit to $\Delta
M_{15}(B)\approx 1.65$ mag for a peak $M_B\approx -17$ mag, in better agreement
with the observed width-luminosity relation (WLR). Regardless of the precise
ignition mechanism, these simulations suggest that fast-declining SNe Ia at the
faint end of the WLR could result from the explosion of WDs whose mass is
significantly below the Chandrasekhar limit.
