Co-Evolution of Stars and Gas: Using Analysis of Synthetic Observations to Investigate the Star-Gas Correlation in STARFORGE

We explore the relationship between stellar surface density and gas surface density (the star-gas or S-G correlation) in a 20,000 M$_{\odot}$ simulation from the STAR FORmation in Gaseous Environments (STARFORGE) Project. We create synthetic observations based on the Spitzer and Herschel telescopes by modeling active galactic nuclei contamination, smoothing based on angular resolution, cropping the field-of-view, and removing close neighbors and low-mass sources. We extract star-gas properties such as the dense gas mass fraction, the Class II:I ratio, and the S-G correlation ($\Sigma_{\rm YSO}/\Sigma_{\rm gas}$) from the simulation and compare them to observations of giant molecular clouds, young clusters, and star-forming regions, as well as to analytical models. We find that the simulation reproduces trends in the counts of young stellar objects and the median slope of the S-G correlation. This implies that the S-G correlation is not simply the result of observational biases but is in fact a real effect. However, other statistics, such as the Class II:I ratio and dense gas mass fraction, do not always match observed equivalents in nearby clouds. This motivates further observations covering the full simulation age range and more realistic modeling of cloud formation.