2025MNRAS.538....1Z

We report the observations of J = 1-0 of HCN, HCO$^+$, H$^{13}$CO$^{+}$, and H$^{13}$CN, HC$_3$N (J = 11-10) emission towards 135 massive star-forming clumps, as part of the ALMA Three-millimeter Observations of Massive Star-forming regions Survey. We present the integrated intensity probability distribution function (I-PDF) for these molecular tracers, modelled as a combination of a lognormal distribution and a power-law tail. The molecular line luminosities for the power-law tail segment, $L_{\rm mol}(p)$, have been calculated. We have investigated the correlation between the bolometric luminosity, $L_{\rm bol}$, and the power-law part of the molecular line luminosity, $L_{\rm mol}(p)$. Our findings suggest that the scaling relationships between $L_{\rm bol}$ and $L_{\rm mol}(p)$ for HCN and HCO$^+$ are sublinear, indicating that these molecules might not be the most effective tracers for the dense gas. In contrast, H$^{13}$CN and HC$_3$N exhibit a nearly linear relationship between $L_{\rm bol}$ and $L_{\rm mol}(p)$, indicating that they can well trace gravitationally bound dense gas. The ratios of $L_{\rm bol}$-to-$L_{\rm mol}(p)$, serving as indicators of star formation efficiency (SFE) within massive star-forming clumps, exhibit a weak anticorrelation with the power-law index in the I-PDF. In addition, the SFE is also weakly anticorrelated with the exponent $\alpha$ of the corresponding equivalent density distribution. Our results implie that clumps with substantial gas accumulation may still display low star formation efficiencies.