A Generalized K Correction for Type IA Supernovae: Comparing R-band Photometry beyond z=0.2 with B, V, and R-band Nearby Photometry

Photometric measurements show that as a group nearby type Ia supernovaefollow similar lightcurves and reach similar peak magnitudes Thus, thesesupernovae can serve as standard candles or calibrated candles at cosmologicaldistances. Magnitudes of local and distant supernovae, both in the same filterband, are compared using a $K$ correction to account for the different spectralregions incident on that filter. A generalized approach compares magnitudes indifferent bands for the nearby and distant supernova, bands that are selectedto give sensitivity in corresponding regions of the redshifted and unredshiftedspectra. Thus at a redshift of $z \approx 0.5$, local $B$ magnitudes arecompared with distant $R$ magnitudes. We compute these generalized $K$corrections over a range of redshifts and bandpass pairs and discuss theiradvantages over the traditional single-band $K$ correction. In particular,errors near maximum light can be kept below 0.05 mag out to at least $z=0.6$,whereas the traditional $K$ correction is difficult to use beyond $z > 0.2$.