Large-scale numerical simulations of star formation put to the test Comparing synthetic images and actual observations for statistical samples of protostars

Context. Both observations and simulations of embedded protostars have progressed rapidly in recent years. Bringing them together is an important step in advancing our knowledge about the earliest phases of star formation. Aims. To compare synthetic continuum images and spectral energy distributions (SEDs), calculated from large-scale numerical simulations, to observational studies, thereby aiding in both the interpretation of the observations and in testing the fidelity of the simulations. Methods. The adaptive mesh refinement code, RAMSES, is used to simulate the evolution of a 5 pc x 5 pc x 5 pc molecular cloud. The simulation has a maximum resolution of 8AU, resolving simultaneously the molecular cloud on parsec scales and individual protostellar systems on AU scales. The simulation is post-processed with the radiative transfer code RADMC-3D, which is used to create synthetic continuum images and SEDs of the protostellar systems. In this way, more than 13 000 unique radiative transfer models, of a variety of different protostellar systems, are produced. Results. Over the course of 0 : 76 Myr the simulation forms more than 500 protostars, primarily within two sub-clusters. The synthetic SEDs are used to calculate evolutionary tracers T-bol and L-smm/L-bol. It is shown that, while the observed distributions of the tracers are well matched by the simulation, they generally do a poor job of tracking the protostellar ages. Disks form early in the simulation, with 40% of the Class 0 protostars being encircled by one. The flux emission from the simulated disks is found to be, on average, a factor similar to 6 too low relative to real observations; an issue that can be traced back to numerical effects on the smallest scales in the simulation. The simulated distribution of protostellar luminosities spans more than three order of magnitudes, similar to the observed distribution. Cores and protostars are found to be closely associated with one another, with the distance distribution between them being in excellent agreement with observations. Conclusions. The analysis and statistical comparison of synthetic observations to real ones is established as a powerful tool in the interpretation of observational results. By using a large set of post-processed protostars, which make statistical comparisons to observational surveys possible, this approach goes beyond comparing single objects to isolated models of star-forming cores.