The spectral temperature of optically thick outflows with application to light echo spectra from η Carinae's giant eruption

The detection by Rest et al. of light echoes from eta Carinae has provided important new observational constraints on the nature of its 1840s era giant eruption. Spectra of the echoes suggest a relatively cool spectral temperature of about 5500 K, lower than the lower limit of about 7000 K suggested in the optically thick wind-outflow analysis of Davidson. This has led to a debate about the viability of this steady wind model relative to alternative, explosive scenarios. Here we present an updated analysis of the wind-outflow model using newer low-temperature opacity tabulations and accounting for the stronger mass-loss implied by the >10 M-circle dot mass now inferred for the Homunculus. A major conclusion is that, because of the sharp drop in opacity due to recombination loss of free electrons for T < 6500 K, a low temperature of about 5000 K is compatible with, and indeed expected from, a wind with the extreme mass-loss inferred for the eruption. Within a spherical grey model in radiative equilibrium, we derive spectral energy distributions for various assumptions for the opacity variation of the wind, providing a basis for comparisons with observed light echo spectra. The scaling results here are also potentially relevant for other highly optically thick outflows, including those from classical novae, giant eruptions of luminous blue variables and supernovae Type IIn precursors. A broader issue therefore remains whether the complex, variable features observed from such eruptions are better understood in terms of a steady or explosive paradigm, or perhaps a balance of these idealizations.