Estimating sizes of faint, distant galaxies in the submillimetre regime

We measure the sizes of redshift ˜2 star-forming galaxies by stacking data from the Atacama Large Millimeter/submillimeter Array (ALMA). We use a uv-stacking algorithm in combination with model fitting in the uv-domain and show that this allows for robust measures of the sizes of marginally resolved sources. The analysis is primarily based on the 344 GHz ALMA continuum observations centred on 88 submillimetre galaxies in the LABOCA ECDFS Submillimeter Survey (ALESS). We study several samples of galaxies at z ≈ 2 with M* ≈ 5 × 1010 M⊙, selected using near-infrared photometry (distant red galaxies, extremely red objects, sBzK-galaxies, and galaxies selected on photometric redshift). We find that the typical sizes of these galaxies are ˜0.6 arcsec which corresponds to ˜5 kpc at z = 2, this agrees well with the median sizes measured in the near-infrared z band (˜0.6 arcsec). We find errors on our size estimates of ˜0.1-0.2 arcsec, which agree well with the expected errors for model fitting at the given signal-to-noise ratio. With the uv-coverage of our observations (18-160 m), the size and flux density measurements are sensitive to scales out to 2 arcsec. We compare this to a simulated ALMA Cycle 3 data set with intermediate length baseline coverage, and we find that, using only these baselines, the measured stacked flux density would be an order of magnitude fainter. This highlights the importance of short baselines to recover the full flux density of high-redshift galaxies.