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We present spectroscopic observations obtained with the FORS1 instrument onthe ESO VLT under good seeing conditions of the radio-quiet z_em = 3.04 quasarQ1205-30 and its associated extended Lyman-alpha emission. The extendedLyman-alpha emission was originally found in a deep narrow band image targetinga z_abs = z_em Lyman-limit system in the spectrum of the QSO. Using spectralpoint-spread function fitting to subtract the QSO spectrum, we clearly detectthe extended Lyman-alpha emission as well as two foreground galaxies at smallimpact parameters (2.12 +- 0.04 and 2.77 +- 0.07 arcsec). The redshifts of thetwo foreground galaxies are found to be z = 0.4732 and z = 0.865. We determinethe redshift and velocity profile for the extended Lyman-alpha emission, andanalyzing the velocity offsets between eight QSO emission lines we refine thequasar redshift determination. We use the new redshifts to infer the geometryof the complex. We find that the extended Lyman-alpha emission is clearlyassociated with the quasar. A Lyman-alpha luminosity of 5.6 x 10^43 erg s^-1places this extended emission at the high luminosity end of the few previousdetections around radio-quiet quasars. The extended Lyman-alpha emission isbest explained by hydrogen falling into the dark matter halo inhabited by thequasar.Comment: 13 pages, 11 figures. Accepted for publication in A&

The extended Lyman-αemission surrounding thez= 3.04 radio-quiet QSO1205-30: Primordial infalling gas illuminated by the quasar?