CaII 3934,3969 absorbers, which are likely to be a subset of damped Lyman alpha systems, are the most dusty quasar absorbers known, with an order of magnitude more extinction in E(B-V) than other absorption systems. There is also evidence that CaII absorbers trace galaxies with more ongoing star-formation than the average quasar absorber. Despite this, relatively little is known in detail about these unusual absorption systems. Here we present the first high resolution spectroscopic study of 19 CaII quasar absorbers, in the range 0.6<= z_abs<=1.2, with W3934>=0.2A. Their general depletion patterns are similar to measurements in the warm halo phase of the Milky Way and Magellanic Clouds ISM. Dust depletions and alpha-enrichments profiles of sub-samples of 7 and 3 absorbers, respectively, are measured using a combination of Voigt profile fitting and apparent optical depth techniques. Deviations in [Cr/Zn]~0.3+-0.1dex and in [Si/Fe]>~0.8+-0.1dex are detected across the profile of one absorber, which we attribute to differential dust depletion. The remaining absorbers have <0.3dex (3sigma limit) variation in [Cr/Zn], much like the general DLA population, though the dustiest CaII absorbers remain relatively unprobed in our sample. A limit on electron densities in CaII absorbers, n_e<0.1cm^-3, is derived using the ratio of neutral and singly ionised species, assuming a MW-like radiation field. These electron densities may imply hydrogen densities sufficient for the presence of molecular hydrogen in the absorbers. The CaII absorber sample comprises a wide range of velocity widths, v_90=50-470km/s, and velocity structures, thus a range of physical models for their origin, from simple discs to galactic outflows and mergers, would be required to explain the observations.
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