Applying the expanding photosphere and standardized candle methods to Type II-Plateau supernovae at cosmologically significant redshifts - The distance to SN 2013eq

Based on optical imaging and spectroscopy of the Type II-Plateau SN 2013eq, we present a comparative study of commonly used distance determination methods based on Type II supernovae. The occurrence of SN 2013eq in the Hubble flow ( z = 0.041 ± 0.001) prompted us to investigate the implications of the difference between “angular” and “luminosity” distances within the framework of the expanding photosphere method (EPM) that relies upon a relation between flux and angular size to yield a distance. Following a re-derivation of the basic equations of the EPM for SNe at non-negligible redshifts, we conclude that the EPM results in an angular distance. The observed flux should be converted into the SN rest frame and the angular size, θ , has to be corrected by a factor of (1 + z ) 2 . Alternatively, the EPM angular distance can be converted to a luminosity distance by implementing a modification of the angular size. For SN 2013eq, we find EPM luminosity distances of D L  = 151 ± 18 Mpc and D L = 164 ± 20 Mpc by making use of different sets of dilution factors taken from the literature. Application of the standardized candle method for Type II-P SNe results in an independent luminosity distance estimate ( D L = 168 ± 16 Mpc) that is consistent with the EPM estimate.