tokens: of the CCH/HC 5 N ratio between the observed values and the model calculations (Taniguchi et al. 2019a ). The red and black curves show the modeled CCH/HC 5 N ratio and temperature, respectively, in (a) the slow warm-up period model with ζ = 1.3 × 10 −17 s −1 , (b) the fast warm-up period (5 × 10 4 yr) model with ζ = 1.3 × 10 −17 s −1 , and (c) the fast warm-up period model with ζ = 4.0 × 10 −14 s −1 . The orange line indicates the observed value in G28.28–0.36 and the yellow range covers the observed values in the three MYSOs including the standard deviation. The blue line in panel (a) indicates the observed value in L1527 and the blue range covers the error in L1527. Figure 6. Production fraction of formation pathways of HC 3 N during the warm-up period (Taniguchi et al. 2019a ). JHC 3 N denotes molecules on the dust surface. As discussed in Section 4.2 , the observed CCH/HC 5 N ratios in MYSOs agree with the model at a temperature of ∼85 K. This temperature corresponds to 1.08 × 10 6 yr, 16 16 This age does not mean a physical age of an MYSO, because we derive the age from the chemical network simulations and the age will change by the assumed warm-up timescales. as shown in panel (a) of Figure 5 . Just before this time ( t 1.07 × 10 6 yr), the main formation pathway of HC 3 N is the reaction between C 2 H 2 and CN (panel (a) of Figure 6 ). This is consistent with the reaction proposed based on the 13 C isotopic fractionation in G28.28–0.36. The electron recombination reaction of HC 3 NH + is dominant in the model with the high cosmic-ray ionization rate during the whole warm-up period (panel (b) of Figure 6 ). Thus, the 13 C isotopic fractionation of HC 3 N in G12.89+0.49 and G16.86–2.16 can be explained by this high cosmic-ray ionization rate model. These results suggest that the cosmic-ray ionization rates in G12.89+0.49 and G16.86–2.16 may be higher than that in G28.28–0.36 or physical structures in G12.89+0.49 and G16.86–2.16 allow cosmic rays to penetrate into regions where carbon-chain species are formed. The observed CCH/HC 5 N ratios in MYSOs agree with the age of (4.7–4.86)×10 5 yr as indicated in panel (c) of Figure 5 . In summary, the observed CCH/HC 5 N ratios around MYSOs can be reproduced in the chemical network simulations at a given temperature and time. Taking the 13 C isotopic fractionation of HC 3 N into consideration, G12.89+0.49 and G16.86–2.16 may prefer the model with the high cosmic-ray ionization rate ( ζ = 4 × 10 −14 s −1 ), while G28.28–0.36 agrees with the model with the standard cosmic-ray ionization rate ( ζ = 1.3 × 10 −17 s −1 ). These results imply that carbon-chain chemistry in G12.89+0.49 and G16.86–2.16 may resemble that in the OMC-2 FIR 4 young intermediate-mass protoclusters (Fontani et al. 2017 ; Favre et al. 2018 ), but that in G28.28–0.36 is different from the other MYSOs and OMC-2 FIR 4. The clear 13 C isotopic fractionation of HC 3 N in G28.28–0.36 supports its bottom-up formation during the
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