Formaldehyde Anti-Inversion at z=0.68 in the Gravitational Lens
  B0218+357
  We report new observations of the 110-111 (6 cm) and 211-212 (2 cm)
transitions of ortho-formaldehyde (o-H2CO) in absorption at z=0.68466 toward
the gravitational lens system B0218+357. Radiative transfer modeling indicates
that both transitions are anti-inverted relative to the 4.6 K cosmic microwave
background (CMB), regardless of the source covering factor, with excitation
temperatures of ~1 K and 1.5-2 K for the 110-111 and 211-212 lines,
respectively. Using these observations and a large velocity gradient radiative
transfer model that assumes a gradient of 1 km s^-1 pc^-1, we obtain a
molecular hydrogen number density of 2x10^3 cm^-3 < n(H2) < 1x10^4 cm^-3 and a
column density of 2.5x10^13 cm^-2 < N(o-H2CO) < 8.9x10^13 cm^-2, where the
allowed ranges conservatively include the range of possible source covering
factors in both lines. The measurements suggest that H2CO excitation in the
absorbing clouds in the B0218+357 lens is analogous to that in Galactic
molecular clouds: it would show H2CO absorption against the CMB if it were not
illuminated by the background quasar or if it were viewed from another
direction.
