Dependences of Type Ia Supernovae Lightcurve Parameters on the Host
  Galaxy Star Formation Rate and Metallicity
  We present the dependences of the properties of type Ia Supernovae (SNe Ia)
on their host galaxies by analyzing the multi-band lightcurves of 118
spectroscopically confirmed SNe Ia observed by the Sloan Digital Sky Survey
(SDSS) Supernova Survey and the spectra of their host galaxies. We derive the
equivalent width of the \rm{H}$\alpha$ emission line, star formation rate, and
gas-phase metallicity from the spectra and compare these with the lightcurve
widths and colors of SNe Ia. In addition, we compare host properties with the
deviation of the observed distance modulus corrected for lightcurve parameters
from the distance modulus determined by the best fit cosmological parameters.
This allows us to investigate uncorrected systematic effects in the magnitude
standardization. We find that SNe Ia in host galaxies with a higher star
formation rate have synthesized on average a larger $^{56}$Ni mass and show
wider lightcurves. The $^{56}$Ni mass dependence on metallicity is consistent
with a prediction of Timmes et al. 2003 based on nucleosynthesis. SNe Ia in
metal-rich galaxies ({$\log_{10}(O/H)+12>8.9$) have become 0.13 $\pm$ 0.06
magnitude brighter after corrections for their lightcurve widths and colors,
which corresponds to up to 6% uncertainty in the luminosity distance. We
investigate whether parameters for standardizing SN Ia maximum magnitude differ
among samples with different host characteristics. The coefficient of the color
term is larger by 0.67 $\pm$ 0.19 for SNe Ia in metal-poor hosts than those in
metal-rich hosts when no color cuts are imposed.
