Star Formation Rates of Massive Molecular Clouds in the Central Molecular Zone

We investigate star formation at very early evolutionary phases in five massive clouds in the inner 500 pc of the Galaxy, the Central Molecular Zone. Using interferometer observations of H$_2$O masers and ultra-compact H II regions, we find evidence of ongoing star formation embedded in cores of 0.2 pc scales and $\gtrsim$10$^5$ cm$^{-3}$ densities. Among the five clouds, Sgr C possesses a high (9%) fraction of gas mass in gravitationally bound and/or protostellar cores, and follows the dense ($\gtrsim$10$^4$ cm$^{-3}$) gas star formation relation that is extrapolated from nearby clouds. The other four clouds have less than 1% of their cloud masses in gravitationally bound and/or protostellar cores, and star formation rates 10 times lower than predicted by the dense gas star formation relation. At the spatial scale of these cores, the star formation efficiency is comparable to that in Galactic disk sources. We suggest that the overall inactive star formation in these Central Molecular Zone clouds could be because there is much less gas confined in gravitationally bound cores, which may be a result of the strong turbulence in this region and/or the very early evolutionary stage of the clouds when collapse has only recently started.