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 (NH 2 CHO) to methanol (CH 3 OH), N NH 2 CHO / N CH 3 OH , is one of the highest compared to other ratios. The larger scatter for N NH 2 CHO / N CH 3 OH (or weak correlation of these two molecules) is sometimes interpreted as evidence of gas-phase formation of NH 2 CHO. 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 ≳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 CH 3 CN in our work as a control molecule, as it has a similar binding energy to CH 3 OH. Methods. We used radiative transfer models to calculate the emission from NH 2 CHO, CH 3 OH, and CH 3 CN 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 NH 2 CHO and CH 3 OH, we find the gas-phase N NH 2 CHO / N CH 3 OH 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., ~2) for N CH 3 CN / N CH 3 OH (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 NH 2 CHO / N CH 3 OH comparable with that of observations. The scatter in N NH 2 CHO / N CH 3 OH is larger than that of N CH 3 CN / N CH 3 OH in models consistent with the observations. However, the scatter in the models for N CH 3 CN / N CH 3 OH is smaller than observations by a factor of around two, as expected from the similar binding energies of CH 3 OH and CH 3 CN 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 NH 2 CHO / N CH 3 OH will be lower than previously measured if we correct for the difference in sublimation temperatures of these two species in observations of ~40 protostellar systems with ALMA. Conclusions. The scatter in N NH 2 CHO / N CH 3 OH (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 NH 2 CHO a “normal” molecule. Therefore, we conclude that gas-phase chemistry routes for NH 2 CHO are not necessary to explain the larger scatter of N NH 2 CHO / N CH 3 OH compared with other ratios.