Final Report Summary - FEEDGAL (Feedback Regulated Star Formation in Diverse Galactic Environments) An outstanding question in modern astrophysics is whether the distribution of the masses of stars at their birth (the so-called initial mass function, or in short, the IMF) is universal or whether there are significant cluster-to-clusters variations in the IMF of stellar clusters in the Milky Way galaxy and in neighboring galaxies. In the field of the Galaxy, the IMF rises steeply from the low stellar mass regime until it reaches a shallow maximum in the mass range around 0.1-0.5 solar masses, after which it declines, approximately following a power law, in the high stellar mass regime. The universality of the IMF, or lack of it, has important consequences for the evolution of molecular clouds, the distribution of sizes of protoplanetary disks in stellar clusters, the radiative and mechanical feedback from stars into the interstellar medium, and the dynamical and chemical evolution of galaxies. A central goal of the Feedgal project was to investigate the origin of the stellar initial mass function and to assess its universality in star forming regions and in young clusters in the Milky Way galaxy. To achieve this goal, we used a combination of numerical simulations, analytical models, and statistical methods. The results of these models/simulations are compared to state-of-the art observational data. Numerical simulations are performed using the Copenhagen version of the magnetohydrodynamical code RAMSES. The code is used to perform three-dimensional simulations of turbulent, magnetized, and self-gravitating molecular clouds. It has been upgraded to include a sink particle implementation that encapsulates the mass of gravitationally collapsing, high density regions, representing newborn stars. The code is also coupled to a chemistry module, KROME, which tracks the non-equilibrium formation and destruction of complex molecules in the clouds. We used numerical simulations performed with the RAMSES code to study the scaling laws of turbulence in the clouds using different chemical species to trace the behavior in different density regimes. Our goal was to understand how the scaling laws of turbulence (size of structures in the clouds versus their velocity dispersion) depend on mass density, as tracked by the various molecules. This numerical approach has been complemented by the development of a Bayesian statistic code which was used to directly infer the most likely parameters that characterize the shape of the IMF (i.e. the slopes at the low and high mass ends and the characteristic mass) for 8 young Galactic stellar clusters. A complementary approach using a specially designed Monte Carlo code has been pursued in order to infer the distributions of parameters of the IMF for a larger population of Galactic clusters (341 clusters). The method is based on the comparison of the fractions of isolated massive O stars in the population of young Galactic clusters in the Milky Way Stellar Cluster survey and in populations of young stellar clusters constructed with various cluster mass functions and different assumed distribution functions for the IMF parameters. The simulated clusters include corrections for the fraction of binary stars, stellar evolution, and for the fraction of O stars ejected from the clusters by dynamical interactions. Using this code, we showed, for the first time that the fraction of isolated O stars in Galactic clusters can only be reproduced when the parameters of the IMF of the clusters have broad distributions (e.g. dispersion of the power law slope at the high mass end of ~0.6). The IMF is one out of the many outcomes of the star formation process. The star formation rate and efficiency are other crucial quantities that quantify the rate and efficiency with which star forming regions and whole galaxies convert their gas reservoirs into stars. In the framework of Feedgal, I have developed a theoretical model to analyze the local gravitational stability in galactic disks. The models predicts the star formation rate as a function of the local gas and star properties (surface densities, velocity dispersions, scaling laws of turbulence). The model has been successfully used to explain the star formation rates in a number on nearby galaxies. Another Monte Carlo star cluster formation code (The Clafoutis code) is under development. Clafoutis follows the turbulent fragmentation of a population of protocluster clumps, the build of the IMF within the clumps, and the quenching of star formation by the combined feedback effects from outflows, radiation pressure and stellar winds. One of the major findings of this projects is that the initial mass function of the young stellar populations in the Milky Way can not be described by a single, universal distribution function. Instead, each of the parameters that characterize the IMF in a given stellar mass range is described by a broad Gaussian distribution. The broad distributions of the IMF parameters inferred in this work very likely reflect the existence of equally broad distributions of the initial conditions under which these clusters have formed in Galactic proto-cluster clumps. The implications of our results are manifold. For example, the probabilistic IMF proposed in this work, in lieu of a fixed IMF, is expected to influence the modeling of star formation and stellar feedback in sub-grid models that are employed in galactic and cosmological simulations. Broad distributions of the IMF parameters imply less feedback and chemical enrichment in star forming regions with a steep slope of the IMF in the high mass regime versus more feedback and chemical enrichment in star forming regions with a shallow slope in this mass regime. Furthermore, the resulting inter-cluster variations of the feedback from supernovae significantly affects the driving of turbulence in molecular clouds and in the interstellar medium. The website where the project results are disseminated: http://sites.google.com/site/astronosami
