Top two panels: synthetic observations at 1.3 and 3.2 mm of the core-collapse simulation used in this analysis. The radiative transfer is performed using the POLARIS code. The flux is in Jy pixel⁻¹. The pixel size is 1 au. Bottom: spectral indices α_1−3mm derived fromthe simulation. The parameter α_1−3mm is defined as log (F_ν0 / F_ν1) / log (ν0 / ν1), where ν0 and ν1 are 231 and 94 GHz, respectively. The inset shows a zoom on the central 200 au region.