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We report a statistical analysis exploring the origin of the overall low starformation efficiency (SFE) of the Galactic central molecular zone (CMZ) and theSFE diversity among the CMZ clouds using a wide-field HCN $J$=4-3 map, whoseoptically thin critical density ($\sim10^7\,\mathrm{cm}^{-3}$) is the highestamong the tracers ever used in CMZ surveys. Logistic regression is performed toempirically formulate star formation probability of 195 HCN clumps, 13 of whichcontain star formation signatures. The explanatory parameters in the best-fitmodel are reduced into the virial parameter $\alpha_{\mathrm{vir}}$ withoutsignificant contribution from other parameters, whereas the performance of themodel without $\alpha_{\mathrm{vir}}$ is no better than that using randomlygenerated data. The threshold $\alpha_{\mathrm{vir}}$ is 6, which translatesinto a volume density ($n_{\mathrm{H_2}}$) of $10^{4.6}\,\mathrm{cm}^{-3}$ withthe $n_{\mathrm{H_2}}$-$\alpha_{\mathrm{vir}}$ correlation. The scarcity of thelow-$\alpha_{\mathrm{vir}}$ clumps, whose fraction to all HCN clumps is 0.1,can be considered as one of the immediate causes of the suppressed SFE. Nocorrelation between the clump size or mass and star formation probability isfound, implying that HCN $J$=4-3 does not immediately trace the mass ofstar-forming gas above a threshold density. Meanwhile, star-forming andnon-star-forming clouds are degenerate in the physical parameters of the CS$\mathit{J}$=1-0 clouds, highlighting the efficacy of the HCN $\mathit{J}$=4-3line to probe star-forming regions in the CMZ. The time scale of thehigh-$\alpha_{\mathrm{vir}}$ to low-$\alpha_{\mathrm{vir}}$ transition is$\lesssim2$ Myr, which is consistent with the tidal compression and X1/X2 orbittransition models but possibly does not fit the cloud-cloud collision picture.

astrophysical journal/the astrophysical journal

HCN $J$=4-3, HNC $J$=1-0, $\mathrm{H^{13}CN}$ $J$=1-0, and  $\mathrm{HC_3N}$ $J$=10-9 Maps of Galactic Center Region II.: Physical  Properties of Dense Gas Clumps and Probability of Star Formation