Towards a quantitative analysis of high-redshift Type Ia supernova spectra

We use a new technique to extract the spectrum of a supernova from that of the contaminating background of its host galaxy, and apply it to the specific case of high-redshift Type Ia supernova (SN Ia) spectroscopy. The algorithm is based on a two-channel iterative technique employing the Richardson-Lucy restoration method and is implemented in the IRAF code specinholucy. We run the code both on simulated (SN Ia at z = 0.5 embedded in a bright host galaxy) and observed (SNe Ia at various phases up to z = 0.236) data taken with VLT+FORS1 and show the advantages of using such a deconvolution technique in comparison with less elaborate methods. This paper is motivated by the need for optimal supernova spectroscopic data reduction in order to make meaningful comparisons between the low and high-redshift SN Ia samples. This may reveal subtle evolutionary and systematic effects that could depend on redshift and bias the cosmological results derived from comparisons of local and high-z SNe Ia in recent years. We describe the various aspects of the extraction in some detail as guidelines for the first-time user and present an optimal observing strategy for successful implementation of this method in future high-z SN Ia spectroscopic follow-up programmes.