The Robustness of Synthetic Observations in Producing Observed Core Properties: Predictions for the TolTEC Clouds to Cores Legacy Survey

We use hydrodynamical simulations of star-forming gas with stellar feedback and sink particles-proxies for young stellar objects (YSOs)-to produce and analyze synthetic 1.1 mm continuum observations at different distances (150-1000 pc) and ages (0.49-1.27 Myr). We characterize how the inferred core properties, including mass, size, and clustering with respect to diffuse natal gas structure, change with distance, cloud evolution, and the presence of YSOs. We find that atmospheric filtering and core segmentation treatments have distance-dependent impacts on the resulting core properties for d < 300 pc and 500 pc, respectively, which dominate over evolutionary differences. Concentrating on synthetic observations at further distances (650-1000 pc), we find a growing separation between the inferred sizes and masses of cores with and without YSOs in the simulations, which is not seen in recent observations of the Monoceros R2 (Mon R2) cloud at 860 pc. We find that the synthetic cores cluster in smaller groups, and that their mass densities are correlated with gas column density over a much narrower range, than those in the Mon R2 observations. Such differences limit the applicability of the evolutionary predictions we report here, but will motivate our future efforts to adapt our synthetic observation and analysis framework to next generation simulations, such as Star Formation in Gaseous Environments (STARFORGE). These predictions and systematic characterizations will help to guide the analysis of cores on the upcoming TolTEC Clouds to Cores Legacy Survey on the Large Millimeter Telescope Alfonso Serrano.