The Dust Echo Emission of Fast Blue Optical Transients and Application to the Near-Infrared Excess of AT 2018cow

A near-infrared (NIR) excess has been discovered in the emission of the representative fast blue optical transient (FBOT): AT 2018cow. It was suggested that this NIR excess could be emitted by the dust surrounding the source and, thus, could provide a probe into the nature of its progenitor. We develop a model to describe the influence of the FBOT emission on the environmental dust and, as a result, a dust-free evaporation cavity can be formed on a timescale of one day. Outside this cavity, the surviving dust grains can have different size distributions at different distances to the source. With such a special dust environment, we fit the multi-wavelength light curves of AT 2018cow by taking into account the evolutionary dust echo of the FBOT emission. It is found that the dust temperature can vary with time along with the evolution of the irradiating FBOT emission. Even at a fixed time, the dust temperature can be distributed in a wide range rather than having only a unique value. Furthermore, both the mass of the dust shell and its distance to the FBOT are found to be much larger than those derived with a direct empirical fitting of the NIR spectra but without considering the evolutionary relationship between the spectra.