Distance determinations using type II supernovae and the expanding photosphere method

Abstract

Due to their high intrinsic brightness, type II supernovae (SN) can be used as lighthouses to constrain distances in the Universe using variants of the Baade-Wesselink method. Based on a large set of CMFGEN models (Hillier & Miller 1998) covering the photospheric phase of type II SN, we study the various concepts entering one such technique, the Expanding Photosphere Method (EPM). We compute correction factors $ξ$ needed to approximate the synthetic Spectral Energy Distribution (SED) with that of a blackbody at temperature $T$. Our $ξ$, although similar, are systematically greater, by $\sim 0.1$, than the values obtained by Eastman et al. (1996). This translate into a systematic enhancement of 10-20% in EPM-distances. We find that line emission and absorption, not directly linked to color temperature variations, can considerably alter the synthetic magnitude, and cause above-unity $ξ$-values. Optically-thick lines, present in the optical at late-times, can also introduce a strong wavelength-dependence of the photospheric radius, invalidating the use of the Baade method. Both the impact of line-blanketing on the SED and the photospheric radius at low $T$ suggest that the EPM is best used at early times, when the outflow is fully ionized and line-opacity mostly confined to the UV range. We also investigate how reliably one can measure the photospheric velocity from P-Cygni line profiles. Contrary to the usually held belief, the velocity at maximum absorption in the P-Cygni trough of optically-thick lines can both {\it overestimate or underestimate} the photospheric velocity, with a magnitude that depends on the SN outflow density gradient and the optical thickness of the line.