Neutral chlorine and molecular hydrogen at high redshift

Chlorine and molecular hydrogen are known to be tightly linked together in the cold phase of the local interstellar medium through rapid chemical reactions. We present here the first systematic study of this relation at high redshifts using H$_2$-bearing damped Ly$\alpha$ systems (DLAs) detected along quasar lines of sight. Using high-resolution spectroscopic data from VLT/UVES and Keck/HIRES, we report the detection of Cl$\,$I in 9 DLAs (including 5 new detections) out of 18 high-$z$ DLAs with $N($H$_2) \ge 10^{17.3}\,$cm$^{-2}$ (including a new H$_2$ detection at $z=3.09145$ towards J$\,$2100$-$0641) and present upper limits for the remaining 9 systems. We find a $\sim$5$\,\sigma$ correlation between $N$(Cl$\,$I) and $N$(H$_2$) with only $\sim$0.2$\,$dex dispersion over the range 18.1$\,<\,$log$\,N$(H$_2$)$\,<\,$20.1, thus probing column densities 10 times lower those seen towards nearby stars, roughly following the relation $N$(Cl$\,$I$) \approx 1.5\times10^{-6} \times N($H$_2)$. This relation between column densities is surprisingly the same at low and high redshift suggesting that the physical and chemical conditions are similar for a given H$_2$ (or Cl$\,$I) column density. In turn, the N({Cl\,I})/N({\rm H_2}) ratio is found to be uncorrelated with the overall metallicity in the DLA. Our results confirm that neutral chlorine is an excellent tracer of molecule-rich gas and show that the molecular fraction or/and metallicity in the H$_2$-bearing component of DLA could possibly be much higher than the line-of-sight average values usually measured in DLAs.