Chemical abundance gradients of organic molecules within a protostellar disk

Observations of low-mass protostellar systems show evidence of rich complex organic chemistry. Their low luminosity, however, makes determining abundance distributions of complex organic molecules (COMs) within the water snowline challenging. However, the excitation conditions sampled by differing molecular distributions may produce substantive changes in the resulting emission. Thus, molecular excitation may recover spatial information from spatially unresolved data. By analyzing spatially-unresolved NOrthern Extended Millimeter Array (NOEMA) observations of CH$_3$OH and CH$_3$CN, we aim to determine if CH$_3$OH and CH$_3$CN are distributed differently in the protostellar disk around HOPS-370, a highly-luminous intermediate mass protostar. Rotational diagram analysis of CH$_3$OH and CH$_3$CN yields rotational temperatures of $198 \pm 1.2$ K and $448 \pm 19$ K, respectively, suggesting the two molecules have different spatial distributions. Source-specific 3D LTE radiative transfer models are used to constrain the spatial distribution of CH$_3$OH and CH$_3$CN within the disk. A uniform distribution with an abundance of $4\times10^{-8}$ reproduces the CH$_3$OH observations. In contrast, the spatial distribution of CH$_3$CN needs to be either more compact (within $\sim120$ au versus $\sim240$ au for CH$_3$OH) or exhibiting a factor of $\gtrsim 15$ increase in abundance in the inner $\sim55$ au. A possible explanation for the difference in spatial abundance distributions of CH$_3$OH and CH$_3$CN is carbon-grain sublimation.