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We examine various physical processes that may explain the shallow high-mass slope of the initial mass function (IMF), as well as the low star formation rate (SFR) in star-forming molecular clouds (MCs) in the Central Molecular Zone (CMZ). We show that the strong tidal field and shear experienced by the CMZ have opposite effects on the collapse of density fluctuations and cannot explain these properties. Similarly, we show that the intense magnetic field in the CMZ provides a negligible pressure support and, for the high densities at play, should not modify the probability density function of the turbulent gas flow, thus affecting negligibly the IMF. However, we show that, in contrast to the MCs in the Galactic disk, the ones in the CMZ experience only one single episode of turbulence cascade. Indeed, their rather short lifetime, due to their high mean densities, is similar to one typical turbulence crossing time. Consequently, according to the Hennebelle–Chabrier theory of star formation, within this “single turbulence cascade episode,” the cloud experiences one single field of turbulence-induced density fluctuations, leading eventually to gravitationally unstable cores. As shown in Hennebelle & Chabrier (2013), this yields a shallower IMF than usual and leads to the correct observed slope for the CMZ star-forming clouds. Similarly, this single large-scale turbulence event within the cloud lifetime yields a 5–6 times lower SFR than under usual conditions, in agreement with the observed values. Therefore, we suggest that this “single turbulence cascade” scenario can explain both the shallow IMF and low SFR of clouds in the CMZ.

We use recent microlensing observations toward the central bulge of the Galaxy to probe the overall stellar plus brown dwarf initial mass function (IMF) in these regions well within the brown dwarf domain. We find that the IMF is consistent with the same Chabrier IMF characteristic of the Galactic disk. In contrast, other IMFs suggested in the literature overpredict the number of short-time events, and thus of very low mass stars and brown dwarfs, compared with observations. This again supports the suggestion that brown dwarfs and stars predominantly form via the same mechanism. We show that claims for different IMFs in the stellar and substellar domains arise from an incorrect parameterization of the IMF. Furthermore, we show that the IMF in the central regions of the bulge seems to be bottom-heavy, as illustrated by the large number of short-time events compared with the other regions. This recalls our previous analysis of the IMF in massive early-type galaxies and suggests the same kind of two-phase formation scenario, with the central bulge initially formed under more violent, burst-like conditions than the rest of the Galaxy.