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.
To appear in PASP. 34 pages, including 5 figures and 3 tables