A Possible Chemical Clock in High-mass Star-forming Regions: N(HC3N)/N(N2H+)?

We conducted observations of multiple HC3N (J = 10-9, 12-11, and 16-15) lines and the N2H+ (J = 1-0) line toward a large sample of 61 ultracompact (UC) H II regions, through the Institutde Radioastronomie Millmetrique 30 m and the Arizona Radio Observatory 12 m telescopes. The N2H+ J = 1-0 line is detected in 60 sources and HC3N is detected in 59 sources, including 40 sources with three lines, 9 sources with two lines, and 10 sources with one line. Using the rotational diagram, the rotational temperature and column density of HC3N were estimated toward sources with at least two HC3N lines. For 10 sources with only one HC3N line, their parameters were estimated, taking one average value of Trot. For N2H+, we estimated the optical depth of the N2H+ J = 1-0 line, based on the line intensity ratio of its hyperfine structure lines. Then the excitation temperature and column density were calculated. When combining our results in UC H II regions and previous observation results on high-mass starless cores and high-mass protostellar cores, the N(HC3N)/N(N2H+) ratio clearly increases from the region stage. This means that the abundance ratio changes with the evolution of high-mass star-forming regions (HMSFRs). Moreover, positive correlations between the ratio and other evolutionary indicators (dust temperature, bolometric luminosity, and luminosity-to-mass ratio) are found. Thus we propose the ratio of N(HC3N)/N(N2H+) as a reliable chemical clock of HMSFRs.


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We set the criteria for line detection as a signal-to-noise ratio (S/N) above 5 (T mb /rms > 5). Out of 61 UC Hii 133 regions observed by the IRAM 30 m telescope, N 2 H + (J = 1−0) is detected in all sources, except G060.57−00.18. 134 Forty-nine sources among them were detected in both HC 3 N J = 10−9 and J = 16−15 lines and 10 sources among 135 them were detected in HC 3 N J = 10−9. Our complementary observations by the ARO 12 m telescope detected the 136 HC 3 N (J = 12−11) line in 40 sources out of those 49 sources. 137 For our sources, we fitted the spectra of HC 3 N with a single Gaussian profile to obtain their spectral parameters, 138 which are summarized in Table 3. The HC 3 N J = 16−15 line in G033.39+00.00 and the HC 3 N J = 10−9 line in 139 G097.53+03.18 show a large velocity distribution that deviates from the Gaussian profile, so we use the "Print area" 140 command in CLASS to obtain the total integrated intensity. The spectra of HC 3 N lines of all 61 sources are shown in 141 Figure 1. Our ARO 12 m observations also detected HC 3 N (J = 10−9) in 33 sources. For comparison, their HC 3 N J 142 = 10−9 spectra from the IRAM 30 m telescope and the ARO 12 m telescope are displayed in Figure 2. 143 Although N 2 H + (J = 1−0) theoretically has seven hyperfine transitions at different frequencies, the relatively broad 144 line width (≥ 2 km s −1 ) observed toward HMSFRs results in the seven components blending into three groups with 145 roughly Gaussian shapes (e.g. Purcell et al. 2009). Thus we tried to fit the spectra of N 2 H + (J = 1−0) with three Gaus-146 sian profiles. For seven sources (G001.00−00.23, G028.39+00.08, G030.70−00.06, G030.81−00.05, G032.79+00.19, 147 G045.49+00.12, and G097.53+03.18) with blending velocity components, the total integrated intensity of them was 148 obtained by the "Print area" method. The N 2 H + J = 1−0 spectra of our sample are presented in Figure 3 and the 149 fitting results are summarized in Table 4. Line wing features can be found clearly in the HC 3 N spectra of 23 sources and most of them show both blue and red 153 wings (for more details see Table 5). We crossmatched them with the outflow catalogs identified by the CO molecule 154 (Wu et al. 2004;Cyganowski et al. 2008;Maud et al. 2015;Li et al. 2016;Yang et al. 2018;Li et al. 2018;Yang et al. 155 2022) and found that 20 out of 23 sources show CO molecular outflows. The detailed outflow information for these 156 sources is also shown in Table 5.
the circumstellar disk, is caused by shocks from molecular outflows and stellar winds from young stars in HMSFRs 161 (Torrelles et al. 2005). The Class I CH 3 OH maser, associated with shocks, is known to be collision pumped (e.g. 162 Leurini et al. 2016). We find that these sources mostly (19 of 23) show Class I CH 3 OH (methanol) maser emission 163 (e.g. Yang et al. 2017;Kim et al. 2019) and all of them are associated with H 2 O maser emission except G034.79−01.38 164 (e.g. Breen et al. 2010;Titmarsh et al. 2014;Ladeyschikov et al. 2022;Breen & Ellingsen 2011;Xi et al. 2015;Szymczak 165 et al. 2005;Kim et al. 2019;Cyganowski et al. 2013). Therefore, we proposed the existence of shock activities in these 166 sources (Table 5), which needs further mapping observations with high resolution.
where m is the molecular mass of the gas with a value of 51 amu and 29 amu for HC 3 N and N 2 H + , respectively, k is 173 the boltzmann constant, and T is the gas temperature. Then the nonthermal line width can be obtained by 174 ∆V non−thermal = (∆V 2 F W HM − ∆V 2 thermal ) 1/2 , where ∆V F W HM is the observed line width.

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Our calculated results show that the thermal line width can be negligible, with a maximum value of 0.17 km s −1 176 for HC 3 N and 0.19 km s −1 for N 2 H + , which is less than 10% of the total line width of our sources. Figure 4 shows 177 plots of the comparison of the line width between HC 3 N lines (J = 10−9, 12−11 and 16−15) and N 2 H + (J = 1−0) line. We used the FWHM of N 2 H + J = 1−0, F 1 = 0−1 as the intrinsic FWHM of N 2 H + , since this group spectra 179 consists of only one component, without blending. It shows clearly that the line width of HC 3 N tend to be larger than 180 that of N 2 H + toward our UC Hii region sample. Feng et al. (2021) argued that the inner dense warm regions have 181 more turbulence than the outer regions, by comparing the linewidths of the different transitions of HC 3 N. Therefore, 182 our results reflect that HC 3 N is more likely to exist in inner and more active star-forming regions compared to N 2 H + , where η BD is the beam-filling factor and θ s and θ beam are the source size and the HPBW, respectively (Zhang et al. larger than the HPBW of ARO 12 m, may be nonuniform with a clumpy structure). The results show that the sizes of 203 the sources are larger than the HPBW of the IRAM 30 m telescope and smaller than that of the ARO 12 m telescope.

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Thus our ARO 12 m HC 3 N (J = 12−11) data needs to be corrected for the beam dilution effect. According to Equation

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(4), T B for our sample is derived from T mb divided by the beam-filling factor, which can be determined from the source 206 size.

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For 49 sources that have at least two HC 3 N line detections, the rotational temperature and column density of HC 3 N 208 of them are derived by Equation (3) Table 6. For 10 sources with only HC 3 N (J = 10−9) detection, the average 211 T rot value is used as their T rot values. Then the column density of HC 3 N is estimated by Equation (3) (see Table 6). We used the line intensity ratio method to estimate the optical depth of N 2 H + , following the procedure described 214 by Purcell et al. (2009). The theoretical line-integrated intensity of Group 1/Group 2 (see details in Table 2) should 215 be 1:5 under an optically thin condition, assuming equal line width for all individual hyperfine components. Assuming 216 the beam-filling factor is 1, the optical depth of N 2 H + can be determined with the following formula: where τ 2 is the optical depth of N 2 H + group 2. We then calculated the excitation temperature of N 2 H + with the 218 following equation:
where T bg (= 2.73 K) and W are the background brightness temperature and the integrated intensity of N 2 H + group 221 2, respectively. The partition function Q(T ex ) for N 2 H + used in our calculations is Q(T ex ) = 4.198T ex (Purcell et al.

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2009). The derived parameters of N 2 H + , including the optical depth, the excitation temperature, and the column 223 density, are also summarized in Table 6. We find that the excitation temperature of N 2 H + is much lower than the 224 rotational temperature of HC 3 N. This indicates that N 2 H + exists in outer and colder regions, while HC 3 N traces inner 225 and hotter ones, which is consistent with results in Section 3.2. However, N 2 H + emission with a clumpy structure 226 (B eff < 1) cannot be ruled out. In this case, the derived T ex is just a lower limit to the real one. in Section 3.3.2, we recalculated N (N 2 H + ) of HMSCs and HMPOs (see details in Table 7). Then we compared the found, which is supported by Kolmogorov-Smirnov (K-S) test statistical results (see details in Table 8). This is also 243 supported by the values of the mean N (N 2 H + ) within uncertainty ranges and corresponding t-test statistical results

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( from dust grains and reacts with C + to produce C 2 H 2 when the kinetic temperature reaches 25 K. It then reacts 249 with CN in the gas phase through the following neutral-neutral reaction C 2 H 2 + CN → HC 3 N + H, resulting in the 250 formation of HC 3 N (e.g. Hassel et al. 2008). As the temperature reaches T ∼ 55 K, C 2 H 2 in the dust-grain surface 251 can sublimate and further react with CN, leading to an increase in the abundance of HC 3 N in the gas phase. When 252 the temperature is greater than 90 K (above the sublimation temperature of HC 3 N), HC 3 N evaporates directly from  Table 8). The 259 difference in the mean value of HC 3 N between three samples in different evolutionary stages is also significant, with a 260 chance probability of less than 0.05 from the t-tests (Table 8). These results reflect that the column density of HC 3 N 261 gradually increases with evolution, i.e., from HMSCs to HMPOs to UC Hii regions.  (Table   270 8). All chance probabilities of tests (K-S test for distributions and t-test for the mean values) are less than 0.05 (Table   271 8), supporting a statistically significant difference in the HC 3 N/N 2 H + ratio among these three samples. It indicates 272 that the ratio of N (HC 3 N)/N (N 2 H + ) increases in those three evolutionary stages and thus it could be adopted as a 273 chemical clock in HMSFRs.

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The linear beam size is different for sources at different distances. A larger beam size of sources at larger distances 275 may include more relatively diffused low-density gas, which could affect the N (HC 3 N)/N (N 2 H + ) ratio results. To dependence between the ratio and the distance, which means that any observational bias related to the beam dilution 281 is not significant for our ratio results. can be negligible in both HC 3 N and N 2 H + lines. Comparisons show that the line width of HC 3 N is larger than 307 that of N 2 H + , suggesting that HC 3 N is more likely from inner and more active star-forming regions compared 308 to N 2 H + . the column density of HC 3 N increases from HMSCs to HMPOs, and then to UC Hii regions, while that of N 2 H + 316 stays basically stable. And the column density ratio of HC 3 N and N 2 H + was confirmed to increase with HMSFR 317 evolution. Moreover, positive correlations were found between the ratio and other evolutionary indicators (the 318 dust temperature, bolometric luminosity, and luminosity-to-mass ratio). This supports the proposal that the 319 ratio of N (HC 3 N) and N (N 2 H + ) can be a reliable chemical clock for HMSFRs.

ACKNOWLEDGMENTS
This work is supported by the Natural Science Foundation of China (Nos. 12041302, 11590782). We thank the operators and staff at the IRAM 30 m and ARO 12 m telescopes for their assistance during our observations. We also thank Dr. J.Z. Wang, and Dr. X. Chen for their nice comments and suggestions. Y.T.Y. is a member of the International Max Planck Research School (IMPRS) for Astronomy and Astrophysics at the Universities of Bonn and Cologne. Y.T.Y. would like to thank the China Scholarship Council (CSC) for support.                      Note-K-S test and t-est chance probabilities for comparison between: a HMSC and HMPO; b HMPO and UC Hii region; c HMSC and UC Hii region.       Figure 8. The correlations between N (HC3N)/N (N2H + ) and other evolutionary indicators, including dust temperature, bolometric luminosity, and luminosity-to-mass ratio.