2007A&A...472..435J

Little is known about individual molecular clouds at high redshifts. The gravitational lens toward B0218+357 offers the unique possibility to study cool moderately dense gas with high sensitivity and angular resolution in a cloud that existed half a Hubble time ago. This non-CO molecular multi-level study of a significantly redshifted cloud aims at a better definition of the physical properties of molecular gas in a kind of interstellar environment that is rarely studied in the Galaxy or in the nearby extragalactic space. Observations of the radio continuum and six formaldehyde (H₂CO) lines were carried out with the VLA, the Plateau de Bure interferometer and the Effelsberg 100-m telescope. Three radio continuum maps indicate a flux density ratio between the two main images, A and B, of ∼3.4±0.2. Within the errors the ratio is the same at 8.6, 14.1, and 43GHz. The 1₀₁-0₀₀ line of para-H₂CO is shown to absorb the continuum of image A. Large Velocity Gradient radiative transfer calculations are performed to reproduce the optical depths of the observed two cm-wave ``K-doublet'' and four mm-wave rotational lines. These calculations also account for a likely frequency-dependent continuum cloud coverage. Confirming the diffuse nature of the cloud, an n(H₂) density of <1000cm^–3 is derived, with the best fit suggesting n(H₂)∼200cm^–3. The H₂CO column density of the main velocity component is ∼5x10¹³cm^–2, to which about 7.5x10¹²cm^–2 has to be added to also account for a weaker feature on the blue side, 13km/s apart. N(H₂CO)/N(NH₃)∼0.6, which is four times less than the average ratio obtained from a small number of local diffuse (galactic) clouds seen in absorption. The ortho-to-para H₂CO abundance ratio is 2.0-3.0, which is consistent with the kinetic temperature of the molecular gas associated with the lens of B0218+357. With the gas kinetic temperature and density known, it is found that optically thin transitions of CS, HCN, HNC, HCO⁺, and N₂H⁺ (but not CO) will provide excellent probes of the cosmic microwave background at redshift z=0.68.