HD molecules at high redshift: cosmic ray ionization rate in the diffuse interstellar medium

We present a systematic study of deuterated molecular hydrogen (HD) at high redshift, detected in absorption the spectra quasars. four new identifications HD lines associated with known $\rm H_2$-bearing Damped Lyman-$\alpha$ systems. In addition, we measure upper limits on HD$ column density twelve recently identified DLAs. find that detections have similar $N({\rm HD})/N(\rm H_2)$ ratios as previously found, further strengthening marked difference measurements through Galaxy. This is likely due to differences physical conditions and metallicity between local high-redshift interstellar media. Using measured HD})/N({\rm H_2})$ together priors UV flux ($\chi$) number densities ($n$), obtained from analysis H_2$ CI lines, are able constrain cosmic-ray ionization rate (CRIR, $\zeta$) for eight HD-bearing systems where $n$ $\chi$ available. significant dispersion $\zeta$, few $\times 10^{-18}$ s$^{-1}$ 10^{-15}$ s$^{-1}$. also $\zeta$ strongly correlates -- showing almost quadratic dependence, slightly $Z$, does not correlate $n$, which probably reflects connection cosmic rays star-forming regions.