Mass and Physical Conditions of Molecular Gas at Cosmological Distances Probed with CO Lines

Abstract

A new way of estimating molecular gas mass at cosmological distances is proposed. This method utilizes the CO-to-H2 conversion factors for higher J transitions calculated in various combinations of physical conditions and redshifts on the basis of the large-velocity gradient (LVG) approximation. This method (LVG mass) is an extension of the LTE mass, and its application includes not only high-z objects but also Galactic objects such as gravitationally unbound gas. The calculated CO-to-H2 conversion factor of the J = 1-0 transition at z = 0 naturally explains both the absolute value and the narrow range of variation of that measured in Galactic molecular clouds. By contrast, the CO-to-H2 conversion factors for higher J transitions are very sensitive to the physical conditions of molecular gas. Although only lower limits to molecular gas mass may be reliably obtained from the luminosity of the single higher J transition of CO, we may still be able to estimate the plausible value of the conversion factor by specifying the physical conditions of the molecular gas or by multitransition analyses. Dependence of CO line ratios on physical conditions of molecular gas is examined for various pairs of transitions at different redshifts. At high redshifts, ratios of low-J transitions exhibit narrower ranges of variation because of warmer cosmic background radiation and thus are not good probes of the physical conditions of molecular gas. Ratios of higher J transitions may be less affected by the warmer background and may remain good probes of the physical conditions of molecular gas. They may be analyzed in the same framework established in the present-day universe as long as the CO abundance is similar to that in the present day.