  Massive galaxies in the distant Universe form stars at much higher rates than
today. Although direct resolution of the star forming regions of these galaxies
is still a challenge, recent molecular gas observations at the IRAM Plateau de
Bure interferometer enable us to study the star formation efficiency on
subgalactic scales around redshift z = 1.2. We present a method for obtaining
the gas and star formation rate (SFR) surface densities of ensembles of clumps
composing galaxies at this redshift, even though the corresponding scales are
not resolved. This method is based on identifying these structures in
position-velocity diagrams corresponding to slices within the galaxies. We use
unique IRAM observations of the CO(3-2) rotational line and DEEP2 spectra of
four massive star forming distant galaxies - EGS13003805, EGS13004291,
EGS12007881, and EGS13019128 in the AEGIS terminology - to determine the gas
and SFR surface densities of the identifiable ensembles of clumps that
constitute them. The integrated CO line luminosity is assumed to be directly
proportional to the total gas mass, and the SFR is deduced from the [OII] line.
We identify the ensembles of clumps with the angular resolution available in
both CO and [OII] spectroscopy; i.e., 1-1.5". SFR and gas surface densities are
averaged in areas of this size, which is also the thickness of the DEEP2 slits
and of the extracted IRAM slices, and we derive a spatially resolved
Kennicutt-Schmidt (KS) relation on a scale of ~8 kpc. The data generally
indicates an average depletion time of 1.9 Gyr, but with significant variations
from point to point within the galaxies.
