Can We Trust CO as a Probe of the Densities and Temperatures of Molecular Clouds?

Abstract

We select a chemical magnetohydrodynamic simulation of molecular cloud formation and evolution as a typical example of a Galactic molecular cloud. Its analysis helps us understand how to interpret temperatures and densities inferred from CO line emission maps. We find that the kinetic temperature is always underestimated if it is inferred only from the excitation temperature, T _ex, of the¹²CO(1–0) emission line. We find also that CO primarily traces material at densities above the mean cloud density. In addition, we show that if one assumes a fixed value for the CO–H₂ conversion factor, then one will underestimate the density (and hence the mass) of H₂ at low column densities. In this scenario, the total H₂ mass of the cloud inferred from the emission map is only 60 % of the true mass.

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Our simulation considers magnetized turbulent gas in a periodic box, and follows the chemical, thermal and dynamical evolution [1, 2]. It is characterized by a mean number density of 100 cm⁻³, solar metallicity, volume (20 pc)³, and a turbulent RMS velocity of 5 km/s. We present results after three turbulent crossing times, when the turbulence has reached a statistical steady state. We use the Monte Carlo radiative transfer code RADMC-3D¹ to calculate the emergent CO line intensity [3]. Our aim here is to quantify the range of temperatures and densities where CO could be a good tracer of the physical conditions of the cloud.

Figure 1b shows the 2D Probability Density Function (PDF) of the excitation temperature (T _ex) calculated from the¹²CO(1–0) population levels. We see that the excitation temperature increases with increasing column density. On the other hand, the mean kinetic temperature at the CO ($\langle T_{K}\rangle$) starts with a high value but then decreases with increasing column density. The two values approach each other only at high column densities, N ≳ 10²² cm⁻².

Fig. 1

(a) True H₂ column density. (b) 2D PDF of the projected T _ex vs. N, with reference to A _V . Cyan line: average of the T _ex, white line: CO mass weighted average along the LoS of T _K . (c) 2D PDF of the H₂ column density estimated from W _CO vs. the true H₂ column density. Yellow line: one-to-one relation. Red line: best fit to the low density gas. (d) Cumulative mass of H₂ – normalized by the total mass of H₂. Dotted line: inferred from W _CO. Solid line: true H₂ mass fraction

In Fig. 1c, we show the 2D PDF of the H₂ column density ($N_{\mathrm{H2,est}}$), estimated from the integrated emission map (W _CO), with a fixed CO–H₂ conversion factor $X_{\mathrm{CO}} = 2 \times 1{0}^{20}$ cm⁻² K⁻¹ km⁻¹ s, and the true N _H2 (Fig. 1a). The values agree only at high densities, where the gas is optically thick. At low densities, the relationship lies far from the one-to-one relation. The cumulative mass of H₂ – normalized by the total mass of H₂ – as a function of N is shown in Fig. 1d. We compare the mass estimated from the emission map with true mass. The H₂ mass derived from W _CO is an underestimate at all densities. In total, the H₂ mass estimated from the W _CO map, and considering a fixed CO–H₂ conversion factor is only ∼ 60 % of the true value.

These results suggest that CO observations alone give a misleading view of the physical properties of molecular clouds. Complementary observations of the lower density gas using tracers such as C or C⁺, are required.