Near-infrared K corrections of Type Ia Supernovae and their errors
  In this paper we use near-infrared (NIR) spectral observations of Type Ia
supernovae (SNe Ia) to study the uncertainties inherent to NIR K corrections.
To do so, 75 previously published NIR spectra of 33 SNe Ia are employed to
determine K-correction uncertainties in the YJHK_s passbands as a function of
temporal phase and redshift. The resultant K corrections are then fed into an
interpolation algorithm that provides mean K corrections as a function of
temporal phase and robust estimates of the associated errors. These
uncertainties are both statistical and intrinsic --- i.e., due to the diversity
of spectral features from object to object --- and must be included in the
overall error budget of cosmological parameters constrained through the use of
NIR observations of SNe Ia. Intrinsic variations are likely the dominant source
of error for all four passbands at maximum light. Given the present data, the
total Y-band K-correction uncertainties at maximum are smallest, amounting to
+/- 0.04 mag at a redshift of z = 0.08. The J-band K-term errors are also
reasonably small (+/- 0.06 mag), but intrinsic variations of spectral features
and noise introduced by telluric corrections in the H band currently limit the
total K-correction errors at maximum to +/- 0.10 mag at z = 0.08. Finally,
uncertainties in the K_s-band K terms at maximum amount to +/- 0.07 mag at this
same redshift. These results are largely constrained by the small number of
published NIR spectra of SNe Ia, which do not yet allow spectral templates to
be constructed as a function of the light curve decline rate.
