We investigate the molecular gas properties of galaxies across the main sequence of star-forming (SF) galaxies in the local Universe using $^{12}$CO($J=1-0$) (hereafter $^{12}$CO) and $^{13}$CO($J=1-0$) ($^{13}$CO) mapping data of 147 nearby galaxies obtained in the COMING project, a legacy project of the Nobeyama Radio Observatory. In order to improve signal-to-noise ratios of both lines, we stack all the pixels where $^{12}$CO emission is detected after aligning the line center expected from the first-moment map of $^{12}$CO. As a result, $^{13}$CO emission is successfully detected in 80 galaxies with a signal-to-noise ratio larger than three. The error-weighted mean of integrated-intensity ratio of $^{12}$CO to $^{13}$CO lines ($R_{1213}$) of the 80 galaxies is $10.9$ with a standard deviation of $7.0$. We find that (1) $R_{1213}$ positively correlates to specific star-formation rate (sSFR) with a correlation coefficient of $0.46$, and (2) both flux ratio of IRAS 60~$\mu$m to 100~$\mu$m ($f_{60}/f_{100}$) and inclination-corrected linewidth of $^{12}$CO stacked spectra ($\sigma_{{\rm ^{12}CO},i}$) also correlate with sSFR for galaxies with the $R_{1213}$ measurement. Our results support the scenario where $R_{1213}$ variation is mainly caused by the changes in molecular-gas properties such as temperature and turbulence. The consequent variation of CO-to-H$_2$ conversion factor across the SF main sequence is not large enough to completely extinguish the known correlations between sSFR and $M_{\rm mol}/M_{\rm star}$ ($\mu_{\rm mol}$) or star-formation efficiency (SFE) reported in previous studies, while this variation would strengthen (weaken) the sSFR-SFE (sSFR-$\mu_{\rm mol}$) correlation.

中文翻译：

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附近星系的 CO 多线成像 (COMING)。十、分子气体的物理条件与局域恒星形成率-质量关系

我们使用 $^{12}$CO($J=1-0$)（以下简称 $^{12}$CO ) 和 $^{13}$CO($J=1-0$) ($^{13}$CO) 在 COMING 项目中获得的 147 个附近星系的映射数据，这是野边山无线电天文台的一个遗留项目。为了提高两条线的信噪比，我们在对齐 $^{12}$CO 的第一时刻图预期的线中心后，堆叠检测到 $^{12}$CO 排放的所有像素. 结果，在 80 个信噪比大于 3 的星系中成功检测到 $^{13}$CO 排放。80 个星系的 $^{12}$CO 与 $^{13}$CO 线 ($R_{1213}$) 的积分强度比的误差加权平均值为 $10.9$，标准差为 $7.0$。我们发现 (1) $R_{1213}$ 与特定恒星形成率 (sSFR) 呈正相关，相关系数为 $0.46$，以及 (2) IRAS 60~$\mu$m 与 100~ $\mu$m ($f_{60}/f_{100}$) 和 $^{12}$CO 堆叠光谱的倾角校正线宽 ($\sigma_{{\rm ^{12}CO},i} $) 还与具有 $R_{1213}$ 测量值的星系的 sSFR 相关。我们的结果支持 $R_{1213}$ 变化主要由温度和湍流等分子气体特性的变化引起的情况。CO-to-H$_2$ 转换因子在 SF 主序中的后续变化不足以完全消除 sSFR 和 $M_{\rm mol}/M_{\rm star}$ ($\ mu_{\rm mol}$) 或先前研究中报道的恒星形成效率（SFE），