Rapid Response Mode Observations of GRB 160203A: Looking for Fine-Structure Line Variability at Z=3.52

Gamma-ray bursts are the most energetic known explosions. Despite fading rapidly, they allow to measure redshift and important properties of their host-galaxies. We report the photometric and spectroscopic study of GRB 160203A and its host-galaxy. Fine-structure absorption lines, detected in the afterglow at different epochs, allow us to investigate variability due to the strong fading background source. We obtained two optical to near-infrared spectra of the afterglow with X-shooter on ESO/VLT, 18 min and 5.7 hrs after the burst, allowing us to investigate temporal changes of fine-structure absorption lines. We measured HI column density log N(HI/cm-2)=21.75+/-0.10, and several heavy-element ions along the GRB sight-line in the host-galaxy: SiII,AlII,AlIII,CII,NiII,SiIV,CIV,ZnII,FeII, and FeII and SiII fine structure transitions from energetic levels excited by the afterglow, at a redshift z=3.518. We measured [M/H]TOT=-0.78+/-0.13 and [Zn/Fe]FIT=0.69+/-0.15, representing the total(dust-corrected) metallicity and dust depletion, respectively. We detected additional intervening systems along the line of sight at z=1.03,z=1.26,z=1.98,z=1.99,z=2.20 and z=2.83. We could not measure significant variability in the fine-structure lines throughout all the observations and determined an upper limit for the GRB distance from the absorber of d<300 pc, adopting the canonical UV pumping scenario. However, we note that the quality of our data is not sufficient to conclusively rule out collisions as an alternative mechanism. GRB 160203A belongs to a growing sample of GRBs with medium resolution spectroscopy, provided by the Swift/X-shooter legacy program, which enables detailed investigation of the interstellar medium in high-redshift GRB host-galaxies. In particular, this host galaxy shows relatively high metal enrichment and dust depletion already in place when the universe was only 1.8 Gyr old.