We present spectroscopic observations obtained with the FORS1 instrument on the ESO VLT under good seeing conditions of the radio-quiet z _ { em } = 3.04 quasar Q1205-30 and its associated extended Ly \alpha emission .
The extended Ly \alpha emission was originally found in a deep narrow band image targeting a z _ { abs } \approx z _ { em } Lyman-limit system in the spectrum of the QSO .
Using spectral point-spread function fitting to subtract the QSO spectrum , we clearly detect the extended Ly \alpha emission as well as two foreground galaxies at small impact parameters ( 2.12 \pm 0.04 and 2.77 \pm 0.07 arcsec ) .
The redshifts of the two foreground galaxies are found to be z = 0.4732 and z = 0.865 .
We determine the redshift and velocity profile for the extended Ly \alpha emission , and analyzing the velocity offsets between eight QSO emission lines we refine the quasar redshift determination .
We use the new redshifts to infer the geometry of the complex .
We find that the extended Ly \alpha emission is clearly associated with the quasar .
A Ly \alpha luminosity of 5.6 \times 10 ^ { 43 } \text { ~ { } erg~ { } s } ^ { -1 } places this extended emission at the high luminosity end of the few previous detections around radio-quiet quasars .
The extended Ly \alpha emission is best explained by hydrogen falling into the dark matter halo inhabited by the quasar .