Constraining the ortho-to-para ratio of H2 with anomalous H2CO absorption

Context. The ortho-to-para ratio (OPR) of molecular hydrogen is a fundamental parameter in understanding the physics and chemistry of molecular clouds. In dark and cold regions, however, H-2 is not directly observable and the OPR of H-2 in these sources has so far remained elusive. Aims. We show that the 6 cm absorption line of ortho-formaldehyde (H2CO) can be employed to constrain both the density and the OPR of H-2 in dark clouds. Methods. Green Bank Telescope (GBT) observations of ortho-H2CO toward the molecular cloud Barnard 68 (B68) are reported. Non-LTE radiative transfer calculations combined with the well-constrained structure of B68 are then employed to derive the physical conditions in the absorption region. Results. We provide the first firm confirmation of the Townes & Cheung mechanism: propensity rules for the collisions of H2CO with H-2 molecules are responsible for the sub-2.7 K cooling of the 6 cm doublet. Non-LTE calculations show that in the absorption region of B68, the kinetic temperature is similar to 10 K, the ortho-H2CO column density amounts to similar to 2.2 x 10(13) cm(-2), the H-2 density is in the range 1.4-2.4 x 10(4) cm(-3), and the OPR of H-2 is close to zero. Our observations thus provide fresh evidence that H-2 is mostly in its para form in the cold gas, as expected from theoretical considerations. Our results also suggest that formaldehyde absorption originates in the edge of B68, at visual extinctions A(V) less than or similar to 0.5 mag.