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

Column density ratios of complex organic molecules are generally constant across protostellar systems with some low-level scatter. However, the scatter in formamide (NH_2CHO) to methanol (CH_3OH) column density ratio is one of the highest. This larger scatter is sometimes interpreted as evidence of gas-phase formation of NH_2CHO. 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 and the small-scale structure of the envelope and the disk system. We also include CH_3CN in our work as a control molecule which has a similar binding energy to CH_3OH. We use radiative transfer models to calculate the emission from these species in protostellar systems with and without disks. The abundances of these species are parameterized in our models. Then we fit the calculated emission lines to find the column densities as done in real observations. We find a correction factor of  10 to be multiplied by gas-phase N_NH_2CHO/N_CH_3OH to give the true abundance ratio of these two species in the ices. We find that models with different physical parameters produce a scatter in N_NH_2CHO/N_CH_3OH, comparable with that of observations. The scatter in N_NH_2CHO/N_CH_3OH is larger than that of N_CH_3CN/N_CH_3OH in models consistent with the observations. We show that the scatter in N_NH_2CHO/N_CH_3OH will be lower if we correct for the difference in sublimation temperatures of these two species in observations of  40 protostellar systems with ALMA. The scatter in N_NH_2CHO/N_CH_3OH can be partially explained by the difference in their binding energies. We conclude that gas-phase chemistry routes for NH_2CHO are not necessary to explain the larger scatter of N_NH_2CHO/N_CH_3OH compared with other ratios.