We have modelled Atacama Large Millimeter/sub-millimeter Array (ALMA) long baseline imaging of the strong gravitational lens system H-ATLAS J090311.6+003906 (SDP.81). We have reconstructed the distribution of band 6 and 7 continuum emission in the z=3.042 source and we have determined its kinematic properties by reconstructing CO(5-4) and CO(8-7) line emission in bands 4 and 6. The continuum imaging reveals a highly non-uniform distribution of dust with clumps on scales of 200 pc. In contrast, the CO line emission shows a relatively smooth, disk-like velocity field which is well fit by a rotating disk model with an inclination angle of 40+/-5 degrees and an asymptotic rotation velocity of 320 km/s. The inferred dynamical mass within 1.5kpc is (3.5+/-0.5)x10^{10} M_sol which is comparable to the total molecular gas masses of (2.7+/-0.5)x10^{10} M_sol and (3.5+/-0.6)x10^{10} M_sol from the dust continuum emission and CO emission respectively. Our new reconstruction of the lensed HST near-infrared emission shows two objects which appear to be interacting, with the rotating disk of gas and dust revealed by ALMA distinctly offset from the near-infrared emission. The clumpy nature of the dust and a low value of the Toomre parameter of Q=0.3 suggest that the disk is in a state of collapse. We estimate a star formation rate in the disk of 470+/-80 M_sol/yr with an efficiency 65 times greater than typical low-redshift galaxies. Our findings add to the growing body of evidence that the most infra-red luminous, dust obscured galaxies in the high redshift Universe represent a population of merger induced starbursts.
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