  Recent studies have suggested that star formation (SF) in dense gas may be
governed by essentially the same law in Galactic clouds and external galaxies.
This conclusion remains controversial, however, because different tracers have
been used to probe the dense gas mass in Galactic and extragalactic studies. We
conducted observations of Aquila, Oph., and Orion B in HCN(1-0), HCO$^+$(1-0),
and their isotopomers to calibrate the HCN and HCO$^+$ lines used as dense gas
tracers in extragalactic studies and to test the possible universality of the
star formation efficiency in dense gas, SFE$_{dense}$. H$^{13}$CO$^+$ and
H$^{13}$CN were observed to be good tracers of the filaments detected with
Herschel. Comparing the luminosities $L_{HCN}$ and $L_{HCO^+}$ with the
reference masses $M_{Herschel}^{Av>8}$, the empirical conversion factors
$\alpha_{Herschel-HCN}$ and $\alpha_{Herschel-HCO^+}$ were found to be
anti-correlated with the local FUV strength. In agreement with Pety et al.
(2017), HCN and HCO$^+$ were also found to trace gas down to Av>2. As a result,
published extragalactic HCN studies must be tracing all of the moderate density
gas. Estimating the contribution of this moderate density gas from the typical
column density PDFs in nearby clouds, we obtained the following $G_0$-dependent
HCN conversion factor for external
galaxies:$\alpha_{Herschel-HCN}^{fit'}=64\times G_0^{-0.34}$. Re-estimating the
dense gas masses in external galaxies with $\alpha_{Herschel-HCN}^{fit'}$, we
found that SFE$_{dense}$ is remarkably constant over 8 orders of magnitude in
dense gas mass. Our results confirm that SFE$_{dense}$ of galaxies is
quasi-universal on a wide range of scales from ~1-10pc to >10kpc. Based on the
tight link between SF and filamentary structure found in Herschel studies of
nearby clouds, we argue that SFE$_{dense}$ is primarily set by the microphysics
of SF in filaments.
