Distance determinations using type II supernovae and the expanding photosphere method

¹ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85748 Garching bei München, Germany
² Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721, USA e-mail: luc@as.arizona.edu
³ Department of Physics and Astronomy, University of Pittsburgh, 3941 O'Hara Street, Pittsburgh, PA 15260, USA

Received: 9 April 2005
Accepted: 17 May 2005

Abstract

Due to their high intrinsic brightness, caused by the disruption of the progenitor envelope by the shock-wave initiated at the bounce of the collapsing core, hydrogen-rich (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 ~0.1, than the values obtained by Eastman et al. (1996) and 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: in particular, line-blanketing attributable to Fe ii and Ti ii is the principal cause for above-unity correction factors in the B and V bands in hydrogen-recombining models.
Following the dominance of electron-scattering opacity in type II SN outflows, the blackbody SED arising at the thermalization depth is diluted, by a factor of approximately 0.2 to 0.4 for fully- or partially-ionized models, but rising to unity as hydrogen recombines for effective temperatures below 9000 K. For a given effective temperature, models with a larger spatial scale, or lower density exponent, have a larger electron-scattering optical depth at the photosphere and consequently suffer enhanced dilution. We also find that when lines are present in the emergent spectrum, the photospheric radius in the corresponding wavelength range can be enhanced by a factor of 2–3 compared to the case when only continuum opacity is considered. Lines can thus nullify the uniqueness of the photosphere radius and invalidate the Baade method at the heart of the EPM. 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 overestimate or underestimate the photospheric velocity, with a magnitude that depends on the SN outflow density gradient and the optical thickness of the line. This stems from the wavelength-shift, toward line-center, of the location of maximum line-absorption for rays with larger impact parameters. This has implications for the measurement of expansion rates in SN outflows, especially at earlier times when only fewer, broader, and blue-shifted lines are present. This investigation should facilitate more reliable use of the EPM and the determination of distances in the Universe using type II SN.