Simultaneously Modelling Dusty Star Forming Galaxies and Massive Quiescents: A Calibration Framework for Galaxy Formation Models

Abstract Galaxy formation models, particularly semi-analytic models (SAMs), rely on differential equations with free parameters to describe the physical mechanisms governing galaxy formation and evolution. Traditionally, most SAMs calibrate these parameters manually to match observational data. However, this approach fails to fully explore the multidimensional parameter space, resulting in limited robustness and inconsistency with some observations. In contrast, the L-Galaxies SAM features a unique Markov Chain Monte Carlo (MCMC) mode, enabling robust model calibration. Using this functionality, we address a long-standing tension in galaxy formation models: simultaneously reproducing the number densities of dusty star-forming galaxies (DSFGs) and high-redshift massive quiescent galaxies (MQs). We test nine combinations of observational constraints — including stellar mass functions, quiescent fractions, neutral hydrogen mass functions, and DSFG number densities — across different redshifts. We then analyze the resulting galaxy property predictions and discuss the underlying physical mechanisms. Our results identify a model that reasonably matches the number density of DSFGs while remaining consistent with observationally-derived lower limits on the number density of high-redshift MQs, though limitations remain. This model requires high star formation efficiencies in mergers and a null dependency of supermassive black hole (SMBH) cold gas accretion on halo mass, facilitating rapid stellar mass and SMBH growth. Additionally, our findings highlight the importance of robust calibration procedures to address the significant degeneracies inherent to multidimensional galaxy formation models.