Every star-forming galaxy has a halo of metal-enriched gas extending out to at least 100 kpc, as revealed by the absorption lines this gas imprints on the spectra of background quasars. However, quasars are sparse and typically probe only one narrow pencil beam through the intervening galaxy. Close quasar pairs and gravitationally lensed quasars have been used to circumvent this inherently one-dimensional technique, but these objects are rare and the structure of the circum-galactic medium remains poorly constrained. As a result, our understanding of the physical processes that drive the re-cycling of baryons across the lifetime of a galaxy is limited. Here we report integral-field (tomographic) spectroscopy of an extended background source -a bright giant gravitational arc. We can thus coherently map the spatial and kinematic distribution of Mg II absorption -a standard tracer of enriched gas- in an intervening galaxy system at redshift 0.98 (i.e., ~8 Gyr ago). Our gravitational-arc tomography unveils a clumpy medium in which the absorption-strength decreases with increasing impact parameter, in good agreement with the statistics towards quasars; furthermore, we find strong evidence that the gas is not distributed isotropically. Interestingly, we detect little kinematic variation over a projected area of ~600 kpc squared, with all line-of-sight velocities confined to within a few tens of km/s of each other. These results suggest that the detected absorption originates from entrained recycled material, rather than in a galactic outflow.
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