Small Scale Structure at High Redshift: III. The Clumpiness of the Intergalactic Medium on Sub-kpc Scales

Spectra from the Keck HIRES instrument of the Lyman alpha forests in the lines of sight to the A and C components of the gravitationally lensed QSO Q1422+231 were used to investigate the structure of the intergalactic medium at mean redshift z = 3.3 on sub-kpc scales. We measured the cross-correlation amplitude between the two Lyman alpha forests for a mean transverse separation of 120 pc, and computed the RMS column density and velocity differences between individual absorption systems seen in both lines of sight. The RMS differences between the velocity centroids of the Lyman alpha forest lines were found to be less than about 400 m/s, for unsaturated absorption lines with column densities in the range 12<log N(HI)