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. Although they fade rapidly, they give us the opportunity to measure redshift and important properties of their host galaxies. We report the photometric and spectroscopic study of the Swift GRB\,160203A at $z = 3.518$, 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 GRB afterglow with X-shooter on ESO/VLT, 18 minutes and 5.7 hours after the burst, allowing us to investigate temporal changes of fine-structure absorption lines. We measured column density $ 0.10$, and several heavy-element ions along the GRB sightline in the host galaxy, among which \, and and feii $^*$ and siii $^*$ fine-structure transitions from energetic levels excited by the afterglow, at the common redshift $z = 3.518$. We measured $ M/H TOT and a Zn/Fe FIT 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 strength of 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 programme, which enables a 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.