ATOMS: ALMA Three-millimeter Observations of Massive Star-forming
  regions -- II. Compact objects in ACA observations and star formation scaling
  relations
  We report studies of the relationships between the total bolometric
luminosity ($L_{\rm bol}$ or $L_{\rm TIR}$) and the molecular line luminosities
of $J=1-0$ transitions of H$^{13}$CN, H$^{13}$CO$^+$, HCN, and HCO$^+$ with
data obtained from ACA observations in the "ATOMS" survey of 146 active
Galactic star forming regions. The correlations between $L_{\rm bol}$ and
molecular line luminosities $L'_{\rm mol}$ of the four transitions all appear
to be approximately linear. Line emission of isotopologues shows as large
scatters 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 have
similar distributions. The $L_{\rm bol}$-to-$L'_{\rm mol}$ ratios do not change
with galactocentric distances ($R_{\rm GC}$) and clump masses ($M_{\rm
clump}$). 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 lines
and isotopologue lines are good tracers of the total masses of dense gas in
Galactic molecular clumps. The large optical depths of main lines do not affect
the interpretation of the slopes in star formation relations. We find that the
mean 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 spatial
scales.
