FAUST XX. The chemical structure and temperature profile of the IRAS 4A2 hot corino at 20-50 au

Young low-mass protostars often possess hot corinos, which are compact, hot, and dense regions that are bright in interstellar complex organic molecules (iCOMs). In addition to their prebiotic role, iCOMs can be used as a powerful tool to characterize the chemical and physical properties of hot corinos. Using ALMA/FAUST data, our aim was to explore the iCOM emission at $<$ 50 au scale around the Class 0 prototypical hot corino IRAS 4A2. We imaged IRAS 4A2 in six abundant common iCOMs (CH_3OH, HCOOCH_3, CH_3CHO, CH_3CH_2OH, CH_2OHCHO, and NH_2CHO), and derived their emitting sizes. The column density and gas temperature for each species were derived at 1σ from a multi-line analysis by applying a non-LTE approach for CH_3OH, and LTE population or rotational diagram analysis for the other iCOMs. Thanks to the unique estimates of the absorption from foreground millimeter dust toward IRAS 4A2, we derived for the first time unbiased gas temperatures and column densities. We resolved the IRAS 4A2 hot corino, and found evidence for a chemical spatial distribution in the inner 50 au, with the outer emitting radius increasing from ∼ 22-23 au for NH_2CHO and CH_2OHCHO, followed by CH_3CH_2OH (∼ 27 au), CH_3CHO (∼ 28 au), HCOOCH_3 (∼ 36 au), and out to ∼ 40 au for CH_3OH. Combining our estimate of the gas temperature probed by each iCOM with their beam-deconvolved emission sizes, we inferred the gas temperature profile of the hot corino on scales of 20-50 au in radius, and found a power-law index q of approximately --1. We observed, for the first time, a chemical segregation in iCOMs of the IRAS 4A2 hot corino, and derived the gas temperature profile of its inner envelope. The derived profile is steeper than when considering a simple spherical collapsing and optically thin envelope, hinting at a partially optically thick envelope or a gravitationally unstable disk-like structure.