The Core Mass Function Across Galactic Environments. IV. The Galactic Center

The origin of the stellar Initial Mass Function (IMF) and how it may vary with galactic environment is a matter of debate. Certain star formation theories involve a close connection between the IMF and the Core Mass Function (CMF) so it is important to measure this CMF in a range of Milky Way locations. Here we study the CMF of three Galactic Center clouds: G0.253+0.016 ("The Brick"), Sgr B2 (Deep South field) and Sgr C. We use ALMA 1 mm continuum images and identify cores as peaks in thermal dust emission via the dendrogram algorithm. We develop a completeness correction method via synthetic core insertion, utilizing a realistic mass-dependent size distribution. A power law $\text{d}N/\text{d}\log M \propto M^{-\alpha}$ is fit to the CMFs $>2\:M_\odot$. The Brick has a Salpeter-like index $\alpha=1.28\pm0.09$, while the other regions have shallower indices: Sgr C has $\alpha=0.99\pm0.06$; Sgr B2-DS has $\alpha=0.70\pm0.03$. When smoothed to a common resolution, the differences between the Brick and the others increase as we obtain $\alpha=1.36\pm0.12$, $\alpha=0.66\pm0.06$ and $\alpha=0.62\pm0.04$, respectively, for masses $\gtrsim3\:M_\odot$. Furthermore, we analyze the spatial distribution and mass segregation of cores: Sgr C and Sgr B2-DS show signs of mass segregation, but the Brick does not. We compare our results to several other CMFs from different Galactic regions derived with the same methods. Finally, we discuss how our results may help define an evolutionary sequence of star cluster formation and be used to test star formation theories.