a) SFR against Mdense and b) SFE against Mdense. Blue filled squares indicate the SFR–Mdense(=) and SFE(=SFR/Mdense) – Mdense relations for the regions observed in this paper. Black open circles indicate the relation between SFR and Mdense in nearby star-forming clouds (Lada et al. 2010). Red filled circles indicate the SFR-Mdense and SFE – Mdense relations obtained for external galaxies (Gao & Solomon 2004b), assuming Mdense = αHCN × LHCN with the corrected αHCN values from our Eq. (17). Green, brown, pink, purple, magenta, and orange filled circles indicate the SFR-Mdense and SFE – Mdense relations in the SMC, LMC, M31, M33, and M51 galaxies (Chin et al. 1997, 1998; Brouillet et al. 2005; Buchbender et al. 2013; Chen et al. 2015, 2017) using our relation of Eq. (17). The uncertainties in the extragalactic SFR values are a factor of ~2 (cf. Bell 2003). The black triangle indicates the position of the central molecular zone (CMZ: |l| < 1 deg, |b| < 0.5 deg) in each plot, where SFR and Mdense were estimated from the number count of massive YSOs and Herschel column density, respectively (Longmore et al. 2013). In both panels, the black solid line and black dashed lines display the simple empirical relation expected from the “microphysics” of prestellar core formation within filaments described in Sect. 4.3 (see also André et al. 2014; Könyves et al. 2015): SFR = (4.5 ± 2.5) × 10-8M⊙ yr-1 × (Mdense/M⊙), i.e., SFE = (4.5 ± 2.5) × 10-8 yr-1.
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