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Resolved images of self-gravitating circumstellar discs with ALMA

In this paper we present simulated observations of massive self-gravitating circumstellar discs using the Atacama Large Millimetre/sub-millimetre Array (ALMA). Using a smoothed particle hydrodynamics model of a $0.2M_{\odot}$ disc orbiting a $1M_{\odot}$ protostar, with a cooling model appropriate for discs at temperatures below $\sim 160$K and representative dust opacities, we have constructed maps of the expected emission at sub-mm wavelengths. We have then used the CASA ALMA simulator to generate simulated images and visibilities with various array configurations and observation frequencies, taking into account the expected thermal noise and atmospheric opacities. We find that at 345 GHz (870 $μ$m) spiral structures at a resolution of a few AU should be readily detectable in approximately face-on discs out to distances of the Taurus-Auriga star-forming complex.