The Multi-temperature Blackbody of Kilonovae

The early spectra of the kilonova AT2017gfo have a remarkably smooth blackbody continuum, which reveals information on the thermal properties and radioactive heating within the ejecta. However, the widespread use of a single-temperature blackbody to fit kilonova data is theoretically invalid, because 1) the significant travel-time delays for a rapidly cooling surface result in a broad distribution of temperatures and 2) the relativistic Doppler correction varies across different surface elements. Thus, the observed spectrum will be a modified blackbody with a range of temperatures over the surface. In this paper we quantify the impact of these effects and illustrate the typical wavelength-dependent spectral corrections. We apply the multi-temperature blackbody framework to the first epoch X-shooter AT2017gfo spectrum, to deconvolve the underlying physical temperature at the photosphere from the relativistic Doppler shift. We show that cooling and Doppler effect individually results in a variation of temperatures over the photosphere of up to 30%, but in combination these effects nearly cancel and produce the single-temperature blackbody observed. Furthermore, we show that for more rapidly expanding ejecta, $v \approx 0.4-0.5c$, one may be able to constrain the cooling rate and the expansion velocity purely from the spectral shape.