Rethinking the N ( H 2 ) / I ( CO ) Conversion Factor

An improved formulation for the N(H 2)/I(CO) conversion factor or X-factor is proposed. The statement that the velocity-integrated radiation temperature of the 12 CO J = 1 → 0 line, I(12 CO), " counts " optically thick clumps is quantified using the formalism of Martin et al. (1984) for line emission in a clumpy cloud. Adopting the simplifying assumptions of thermalized 12 CO J = 1 → 0 line emission and isothermal gas, an effective optical depth, τ ef , is defined as the product of the clump filling factor within each velocity interval and the clump effective optical depth as a function of the optical depth on the clump's central sightline, τ 0. The clump effective optical depth is well approximated as a power law in τ 0 with power-law index, ǫ, referred to here as the clump " fluffiness, " and has values between zero and unity. While the 12 CO J = 1 → 0 line is optically thick within each clump (i.e., high τ 0), it is optically thin " to the clumps " (i.e., low τ ef). Thus the dependence of I(CO) on τ ef is linear, resulting in an X-factor that depends only on clump properties and not directly on the entire cloud. Assuming virialization of the clumps yields an expression for the X-factor whose dependence on physical parameters like density and temperature is " softened " by power-law indices of less than unity that depend on the fluffiness parameter, ǫ. The X-factor provides estimates of gas column density because each sightline within the beam has optically thin gas within certain narrow velocity ranges. Determining column density from the optically thin gas is straightforward and parameters like ǫ then allow extrapolation of the column density of the optically thin gas to that of all the gas. Implicit in this formulation is the assumption that fluffiness is, on average, constant from one beam to the next. This is also required to some extent for density and temperature, but the dependence of the X-factor, X f , on these may be weaker. – 2 – One important suggestion of this formulation is that virialization of entire clouds is irrelevant. The densities required to give reasonable values of X f are consistent with those found in cloud clumps (i.e. ∼ 10 3 H 2 cm −3). Thus virial-ization of clumps, rather than of entire clouds, is consistent …