Proof of the existence of a significant population of normal disk galaxies at redshift z > 2 would have profound implications for theories of structure formation and evolution. We present evidence based on Keck HIRES spectra that the damped Lyα absorber at z = 3.15 toward the quasar Q2233+1310 may well be such an example. Djorgovski et al. have recently detected the Lyα emission from the absorber, which we assume is at the systemic redshift of the absorbing galaxy. By examining the profiles of the metal absorption lines arising from the absorbing galaxy in relation to its systemic redshift, we find strong kinematical evidence for rotation. Therefore the absorber is likely to be a disk galaxy. The inferred circular velocity for the galaxy is greater than or equal to 200 km s-1. With a separation of 17 kpc (q0 = 0.1, H0 = 75) between the galaxy and the quasar sight line, the implied dynamic mass for the galaxy is greater than or equal to 1.6 × 1011 M☉. The metallicity of the galaxy is found to be [Fe/H] = -1.4, typical of damped Lyα galaxies at such redshifts. However, in another damped Lyα absorber at z = 2.81 toward Q0528-2505, no kinematical evidence for galactic rotation is evident. In the latter case, the damped Lyα absorber occurs near the background quasar in redshift, so its properties may be influenced by the background quasar. These represent the only two cases at present for which the technique used here may be applied. Future applications of the same technique to a large sample of damped Lyα galaxies may allow us to determine if a significant population of disk galaxies already existed only a few billion years after the big bang.
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