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We report studies of the relationships between the total bolometricluminosity ($L_{\rm bol}$ or $L_{\rm TIR}$) and the molecular line luminositiesof $J=1-0$ transitions of H$^{13}$CN, H$^{13}$CO$^+$, HCN, and HCO$^+$ withdata obtained from ACA observations in the "ATOMS" survey of 146 activeGalactic star forming regions. The correlations between $L_{\rm bol}$ andmolecular line luminosities $L'_{\rm mol}$ of the four transitions all appearto be approximately linear. Line emission of isotopologues shows as largescatters in $L_{\rm bol}$-$L'_{\rm mol}$ relations as their main line emission.The log($L_{\rm bol}$/$L'_{\rm mol}$) for different molecular line tracers havesimilar distributions. The $L_{\rm bol}$-to-$L'_{\rm mol}$ ratios do not changewith galactocentric distances ($R_{\rm GC}$) and clump masses ($M_{\rmclump}$). The molecular line luminosity ratios (HCN-to-HCO$^+$,H$^{13}$CN-to-H$^{13}$CO$^+$, HCN-to-H$^{13}$CN and HCO$^+$-to-H$^{13}$CO$^+$)all appear constant against $L_{\rm bol}$, dust temperature ($T_{\rm d}$),$M_{\rm clump}$ and $R_{\rm GC}$. Our studies suggest that both the main linesand isotopologue lines are good tracers of the total masses of dense gas inGalactic molecular clumps. The large optical depths of main lines do not affectthe interpretation of the slopes in star formation relations. We find that themean star formation efficiency (SFE) of massive Galactic clumps in the "ATOMS"survey is reasonably consistent with other measures of the SFE for dense gas,even those using very different tracers or examining very different spatialscales.

monthly notices of the royal astronomical society

ATOMS: ALMA Three-millimeter Observations of Massive Star-forming  regions -- II. Compact objects in ACA observations and star formation scaling  relations