CO-to-H${}_2$ Conversion and Spectral Column Density in Molecular Clouds: The Vriability of $X_{\mathrm{CO}}$ Factor

Abstract

Analyzing the Galactic plane CO survey with the Nobeyama 45-m telescope, we compared the spectral column density (SCD) of H${}_2$ calculated for ${}^{12}$CO line using the current conversion factor $X_{\mathrm{CO}}$ to that for ${}^{13}$CO line under LTE in M16 and W43 regions. Here, SCD is defined by $d{N}_{{\mathrm{H}}_2}/dv$ with $N_{{\mathrm{H}}_2}$ and $v$ being the column density and radial velocity, respectively. It is found that the $X_{\mathrm{CO}}$ method significantly under-estimates the H${}_2$ density in a cloud or region, where SCD exceeds a critical value ($\sim 3\times 10^{21}[{\mathrm{H}}_2\mathrm{c}{\mathrm{m}}^{-2}(\mathrm{km}{\mathrm{s}}^{-1}{)}^{-1}]$), but over-estimates in lower SCD regions. We point out that the actual CO-to-H${}_2$ conversion factor varies with the H${}_2$ column density or with the CO-line intensity: It increases in the inner and opaque parts of molecular clouds, whereas it decreases in the low-density envelopes. However, in so far as the current $X_{\mathrm{CO}}$ is used combined with the integrated ${}^{12}$CO intensity averaged over an entire cloud, it yields a consistent value with that calculated using the ${}^{13}$CO intensity by LTE. Based on the analysis, we propose a new CO-to-\Htwo conversion relation, $N_{{\mathrm{H}}_2}^{\ast }=\int X_{\mathrm{CO}}^{\ast }(T_{\mathrm{B}})T_{\mathrm{B}}dv$, where $X_{\mathrm{CO}}^{\ast }=(T_{\mathrm{B}}/T_{\mathrm{B}}^{\ast }{)}^{\beta }{X}_{\mathrm{CO}}$ is the modified spectral conversion factor as a function of the brightness temperature, $T_{\mathrm{B}}$, of the $12$CO ($J=1-0$) line, and $\beta \sim 1-2$ and $T_{\mathrm{B}}^{\ast }=12-16$ K are empirical constants obtained by fitting to the observed data. The formula corrects for the over/under estimation of the column density at low/high-CO line intensities, and is applicable to molecular clouds with $T_{\mathrm{B}}\ge 1$ K (rms noise in the data) from envelope to cores at sub-parsec scales (resolution). (Full resolution copy available at http://www.ioa.s.u-tokyo.ac.jp/~sofue/news/2020_mn_Xco12co13_fugin.pdf)

Accepted for MNRAS, 11 pages, 10 figures, 2 tables, Full resolution copy at http://www.ioa.s.u-tokyo.ac.jp/~sofue/news/2020_mn_Xco12co13_fugin.pdf

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