Carnegie Supernova Project: kinky $i$-band light-curves of Type Ia
  supernovae
  We present detailed investigation of a specific $i$-band light-curve feature
in Type Ia supernovae (SNe Ia) using the rapid cadence and high signal-to-noise
ratio light-curves obtained by the Carnegie Supernova Project. The feature is
present in most SNe Ia and emerges a few days after the $i$-band maximum. It is
an abrupt change in curvature in the light-curve over a few days and appears as
a flattening in mild cases and a strong downward concave shape, or a "kink", in
the most extreme cases. We computed the second derivatives of Gaussian Process
interpolations to study 54 rapid-cadence light-curves. From the second
derivatives we measure: 1) the timing of the feature in days relative to
$i$-band maximum; tdm$_{2}$($i$) and 2) the strength and direction of the
concavity in mag d$^{-2}$ ; dm$_{2}$($i$). 76$\%$ of the SNe Ia show a negative
dm$_{2}$($i$), representing a downward concavity - either a mild flattening or
a strong "kink". The tdm$_{2}$($i$) parameter is shown to correlate with the
color-stretch parameter s$_{\mathrm{BV}}$, a SN Ia primary parameter. The
dm$_{2}$($i$) parameter shows no correlation with s$_{\mathrm{BV}}$ and
therefore provides independent information. It is also largely independent of
the spectroscopic and environmental properties. Dividing the sample based on
the strength of the light-curve feature as measured by dm$_{2}$($i$), SNe Ia
with strong features have a Hubble diagram dispersion of 0.107 mag, 0.075 mag
smaller than the group with weak features. Although larger samples should be
obtained to test this result, it potentially offers a new method for improving
SN Ia distance determinations without shifting to more costly near-infrared or
spectroscopic observations.
