CO-to-H2 conversion and spectral column density in molecular clouds: the variability of the XCO factor

Abstract

Analyzing the Galactic plane CO survey with the Nobeyama 45-m telescope, we compared the spectral column density (SCD) of $N_{\rm H_2}$ calculated for 12CO (J=1-0) line using the current conversion factor $X_{\rm ^{12}CO}$ to that for 13CO (J=1-0) line under LTE (local thermal equilibrium) assumption in M16 and W43 regions. Here, SCD is defined by $dN_{\rm H_2}/dv$ with $N_{\rm H_2}$ and v being the column density and radial velocity, respectively. It is found that the $X_{\rm ^{12}CO}$ method significantly under-estimates the H2 density in a cloud or region, where SCD exceeds a critical value (∼3 × 1021 [H2 cm−2 (km s−1)−1]), but over-estimates in lower SCD regions. We point out that the actual CO-to-H2 conversion factor varies with the H2 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 $X_{^{12}{\rm CO}}$ is used combined with the integrated 12CO intensity averaged over an entire cloud, it yields a consistent value with that calculated using the 13CO intensity by LTE. Based on the analysis, we propose a new CO-to-H2 conversion relation, $N_{\rm H_2}^* = \int X^*_{\rm CO} (T_{\rm B}) T_{\rm B}\ dv$, where $X^*_{\rm CO} (T_{\rm B})=(T_{\rm B}/T_{\rm B}^*)^\beta X_{\rm ^{12}CO}$ is the modified spectral conversion factor as a function of the brightness temperature, TB, of the 12CO (J=1-0) line, and β ∼ 1 − 2 and $T_{\rm B}^*=12-16$ 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 TB ≥ 1 K (12CO (J=1-0) line rms noise in the data) from envelope to cores at sub-parsec scales (spatial resolution).

Nobeyama 45 m Local Spur CO survey. I. Giant molecular filaments and cluster formation in the Vulpecula OB association

“…The peak column densities obtained from 13 CO are > 10 23 cm −2 , which is larger than that estimated from 12 CO. This tendency is consistent with the other GMCs in the Milky Way (e.g., Sofue & Kohno 2020).…”

“…We derived the physical parameters of the molecular clouds in Vul OB1 following a procedure that uses the X-factor and assumes local thermal equilibrium (LTE), which is described by Pineda et al (2008); Wilson et al (2013), and Sofue & Kohno (2020).…”

Dark Supernova Remnants Revealed by CO-Line Bubbles in the W43 Molecular Complex along the 4-kpc Galactic Arm

“…The mean T B of the surrounding gas cloud around the bubble G31.1+0.2+81 is about T B ∼10 K, velocity width is δv∼5 km s −1 . The mean molecular density can be estimated to be n H 2 ∼X CO T B δv/r∼230 cm −3 , where r = 7 pc is the bubble radius and X CO ∼2 × 10 20 H 2 cm −3 (K km s −1 ) −1 is the conversion factor for extended molecular clouds [32]. The total lost mass inside the bubble is then estimated as M∼4π/3µn H 2 m H r 3 ∼2.3 × 10 4 M , where µ = 2.8 is the mean molecular weight and m H is the hydrogen mass.…”

Dark supernova remnant

“…The column density of the molecular gas near the intensity maximum is NH 2 ∼ 7 × 10 21 H2 cm −2 for a conversion factor of 2 × 10 20 H2 (K km s −1 ) −1 for individual molecular clouds (Sofue & Kohno 2020). This yields a volume density of nH 2 ∼ 2 × 10 3 H2 cm −3 , and total molecular mass of the cloud in the mapped area is estimated to be ∼ 2.4 × 10 3 M⊙.…”

“…In this Letter, we report the discovery of an almost perfect round-shaped hole in a medium sized MC during the search for the sites of SNR-MC interaction (Sofue, et al 2020), using the FUGIN (Four-receiver unbiased galactic imaging survey with the Nobeyama 45-m telescope) survey data in the 12 CO, 13 CO, and C 18 O (J = 1 − 0) line emissions (Umemoto et al 2017). The full beam width at half maximum of the telescope was 15 ′′ , the velocity resolution was 1.2 km s −1 .…”