Dust trapping by spiral arms in gravitationally unstable protostellar discs

In this paper, we discuss the influence of gravitational instabilities in massive protostellar discs on the dynamics of dust grains. Starting from a smoothed particle hydrodynamics simulation, we have computed the evolution of the dust in a quasi-static gas density structure typical of self-gravitating disc. For different grain size distributions, we have investigated the capability of spiral arms to trap particles. We have run 3D radiative transfer simulations in order to construct maps of the expected emission at (sub-)millimetre and near-infrared wavelengths. Finally, we have simulated realistic observations of our disc models at (sub-)millimetre and near-infrared wavelengths as they may appear with the Atacama Large Millimetre/submillimetre Array (ALMA) and the High-Contrast Coronographic Imager for Adaptive Optics (HiCIAO) in order to investigate whether there are observational signatures of the spiral structure. We find that the pressure inhomogeneities induced by gravitational instabilities produce a non-negligible dynamical effect on centimetre-sized particles leading to significant overdensities in spiral arms. We also find that the spiral structure is readily detectable by ALMA over a wide range of (sub-)millimetre wavelengths and by HiCIAO in near-infrared scattered light for non-face-on discs located in the Ophiuchus star-forming region. In addition, we find clear spatial spectral index variations across the disc, revealing that the dust trapping produces a migration of large grains that can be potentially investigated through multiwavelength observations in the (sub-)millimetric. Therefore, the spiral arms observed to date in protoplanetary disc might be interpreted as density waves induced by the development of gravitational instabilities.