In this work, we study argon abundances in the interstellar medium of high-redshift galaxies (2<z(abs)<4.2) detected as Damped Lya absorbers (DLA) in the spectra of background quasars. We use high-resolution quasar spectra obtained from the ESO-UVES advanced data products (EUADP) database. We present 3 new measurements and 5 upper limits of ArI. We further compiled DLAs/sub-DLA data from the literature with measurements available of argon and alpha-capture elements (S or Si), making up a total of 37 systems, i.e. the largest DLA argon sample investigated so far. We confirm that argon is generally deficient in DLAs, with a mean value [Ar/alpha]= -0.4+/-0.06dex (standard error of the mean). The [Ar/alpha] ratios show a weak, positive trend with increasing NHI and increasing absorption redshift, and a weak, negative trend with dust-free metallicity, [S/H]. Detailed analysis of the abundance ratios indicates that ArI ionisation, rather than dust depletion or nucleosynthetic evolution, is responsible for the argon deficiency. Altogether, the observational evidence is consistent with a scenario of argon ionisation dominated by quasar metagalactic radiation modulated by local HI self-shielding inside the DLA host galaxies. Our measurements and limits of argon abundances suggest that the cosmic reionisation of HeII is completed above z=3, but more measurements at z(abs)>3.5 are required to probe the final stages of this process of cosmic reionisation.
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