Effects of Explosion Asymmetry and Viewing Angle on the Type Ia
  Supernova Color and Luminosity Calibration
  Phenomenological relations exist between the peak luminosity and other
observables of type Ia supernovae (SNe~Ia), that allow one to standardize their
peak luminosities. However, several issues are yet to be clarified: SNe~Ia show
color variations after the standardization. Also, individual SNe~Ia can show
residuals in their standardized peak absolute magnitude at the level of $\sim
0.15$ mag. In this paper, we explore how the color and luminosity residual are
related to the wavelength shift of nebular emission lines observed at $\gsim
150$ days after maximum light. A sample of 11 SNe Ia which likely suffer from
little host extinction indicates a correlation ($3.3\sigma$) between the peak
$B-V$ color and the late-time emission-line shift. Furthermore, a nearly
identical relation applies for a larger sample in which only three SNe with
$B-V \gsim 0.2$ mag are excluded. Following the interpretation that the
late-time emission-line shift is a tracer of the viewing direction from which
an off-centre explosion is observed, we suggest that the viewing direction is a
dominant factor controlling the SN color and that a large part of the color
variations is intrinsic, rather than due to the host extinction. We also
investigate a relation between the peak luminosity residuals and the wavelength
shift in nebular emission lines in a sample of 20 SNe. We thereby found a hint
of a correlation (at $\sim 1.6 \sigma$ level). The confirmation of this will
require a future sample of SNe with more accurate distance estimates. Radiation
transfer simulations for a toy explosion model where different viewing angles
cause the late-time emission-line shift are presented, predicting a strong
correlation between the color and shift, and a weaker one for the luminosity
residual.
