ALMA imaging of SDP.81 - I. A pixelated reconstruction of the far-infrared continuum emission.

We present a sub-50 parsec scale analysis of the gravitational lens system SDP.81 at redshift 3.042 using Atacama Large Millimetre/submillimetre Array science verification data. We model both the mass distribution of the gravitational lensing galaxy and the pixelated surface brightness distribution of the background source using a novel Bayesian technique that fits the data directly in visibility space. We find the 1 and 1.3 mm dust emission to be magnified by a factor of μ_tot = 17.6 ± 0.4, giving an intrinsic total star formation rate of 315 ± 60 M_⊙ yr^-1 and a dust mass of 6.4 ± 1.5 × 10⁸ M_⊙. The reconstructed dust emission is found to be non-uniform, but composed of multiple regions that are heated by both diffuse and strongly clumped star formation. The highest surface brightness region is a ∼1.9 × 0.7 kpc disc-like structure, whose small extent is consistent with a potential size-bias in gravitationally lensed starbursts. Although surrounded by extended star formation, with a density of 20-30 ± 10 M_⊙ yr^-1 kpc^-2, the disc contains three compact regions with densities that peak between 120 and 190 ± 20 M_⊙ yr^-1 kpc^-2. Such star formation rate densities are below what is expected for Eddington-limited star formation by a radiation pressure supported starburst. There is also a tentative variation in the spectral slope of the different star-forming regions, which is likely due to a change in the dust temperature and/or opacity across the source.