Correlations among complex organic molecules around protostars: Effects of physical structure

Context. Complex organic molecules have been observed toward many protostars. Their column density ratios are generally constant across protostellar systems, with some low-level scatter. However, the scatter in the column density ratio of formamide (NH2CHO) to methanol (CH3OH), N-NH2CHO/N-CH3OH, is one of the highest compared to other ratios. The larger scatter for N-NH2CHO/N-CH3OH (or weak correlation of these two molecules) is sometimes interpreted as evidence of gas-phase formation of NH2CHO.Aims. In this work, we propose an alternative interpretation in which this scatter is produced by differences in the snowline locations related to differences in binding energies of these species (formamide typically has a greater than or similar to 2000 K larger binding energy than methanol) and the small-scale structure of the envelope and the disk system. Therefore, we do not include chemistry in our models in order to isolate the effect of physical factors. We also include CH3CN in our work as a control molecule, as it has a similar binding energy to CH3OH.Methods. We used radiative transfer models to calculate the emission from NH2CHO, CH3OH, and CH3CN in protostellar systems with and without disks. The abundances of these species were parameterized in our models, and we fit the calculated emission lines to find the column densities and excitation temperatures of these species, as done in real observations.Results. Given the difference in binding energies of NH2CHO and CH3OH, we find the gas-phase N-NH2CHO/N-CH3OH needs to be multiplied by a correction factor of approximately ten in order to give the true abundance ratio of these two species in the ices. This factor is much smaller (i.e., similar to 2) for NCH3CN/NCH3OH (the control molecule). We find that models with different disk sizes, luminosities, and envelope masses produce a scatter in this correction factor, and hence in N-NH2CHO/N-CH3OH comparable with that of observations. The scatter in N-NH2CHO/N-CH3OH is larger than that of N-CH3CN/N-CH3OH in models consistent with the observations. However, the scatter in the models for N-CH3CN/N-CH3OH is smaller than observations by a factor of around two, as expected from the similar binding energies of CH3OH and CH3CN pointing to the need for some chemical effects in the gas or ice to explain the observed ratios. We show that the scatter in N-NH2CHO/N-CH3OH will be lower than previously measured if we correct for the difference in sublimation temperatures of these two species in observations of similar to 40 protostellar systems with ALMA.Conclusions. The scatter in N-NH2CHO/N-CH3OH (or the ratio of any two molecules with a large binding energy difference) can be partially explained by the difference in their binding energies. Correction for this bias makes the scatter in this ratio similar to that in ratios of other complex organics in the observations, making NH2CHO a "normal" molecule. Therefore, we conclude that gas-phase chemistry routes for NH2CHO are not necessary to explain the larger scatter of N-NH2CHO/N-CH3OH compared with other ratios.