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A new constraint on the molecular oxygen abundance at $z \sim 0.886$

We report Karl G. Jansky Very Large Array (VLA) and Atacama Large Millimeter Array (ALMA) spectroscopy in the redshifted molecular oxygen (O$_2$) 56.265~GHz and 424.763~GHz transitions from the $z=0.88582$ gravitational lens towards PKS\,1830$-$21. The ALMA non-detection of O$_2$ 424.763~GHz absorption yields the $3σ$ upper limit $N({\rm O}_2) \leq 5.8 \times 10^{17}$~cm$^{-2}$ on the O$_2$ column density, assuming that the O$_2$ level populations are thermalized at the gas kinetic temperature of 80~K. The VLA spectrum shows absorption by the CH$_3$CHO 56.185~GHz and 56.265~GHz lines, with the latter strongly blended with the O$_2$ 56.265~GHz line. Since the two CH$_3$CHO lines have the same equilibrium strength, we used the known CH$_3$CHO 56.185~GHz line profile to subtract out the CH$_3$CHO 56.265~GHz feature from the VLA spectrum, and then carried out a search for O$_2$ 56.265~GHz absorption in the residual spectrum. The non-detection of redshifted O$_2$ 56.265~GHz absorption in the CH$_3$CHO-subtracted VLA spectrum yields $N({\rm O}_2) \leq 2.3 \times 10^{17}$~cm$^{-2}$. Our $3σ$ limits on the O$_2$ abundance relative to H$_2$ are then $X({\rm O}_2) \leq 9.1 \times 10^{-6}$ (VLA) and $X({\rm O}_2) \leq 2.3 \times 10^{-5}$ (ALMA). These are $5-15$ times lower than the best previous constraint on the O$_2$ abundance in an external galaxy. The low O$_2$ abundance in the $z= 0.88582$ absorber may arise due to its high neutral carbon abundance and the fact that its molecular clouds appear to be diffuse or translucent clouds with low number density and high kinetic temperature.