Simulating galaxy formation with the IllustrisTNG model

We review recent determinations of the present day and initial mass functions in various components of the Galaxy, disk, spheroid, young and globular clusters. As a general feature, the IMF is well described by a power-law form for \(m\ga 1 \msol\) and a lognormal form below. The extension of the disk IMF into the brown dwarf (BD) regime is in good agreement with observations and yields a disk BD number-density comparable to the stellar one \(\sim 0.1 \pc3\). The IMF of young clusters is found to be consistent with the disk field IMF, providing the same correction for unresolved binaries. The spheroid IMF relies on much less robust grounds. Within all the uncertainties, it is found to be similar to the one derived for globular clusters, and is well represented also by a lognormal form with a characteristic mass slightly larger than for the disk. The IMF characteristic of early star formation remains undetermined, but different observational constraints suggest that it does not extend below \(\sim 1 \msol\). These IMFs allow a reasonably robust determination of the Galactic present-day and initial stellar and brown dwarf contents. They also have important galactic implications in yielding more accurate mass-to-light ratio determinations. The M/L ratios obtained with the disk and the spheroid IMF yield values 1.8 and 1.4 smaller than a Salpeter IMF, respectively. This general IMF determination is examined in the context of star formation theory. (shortened)