<div>Large scale vortices are thought to be natural outcomes of hydrodynamic instabilities in protoplanetary discs, as for instance the Rossby wave instability <b>[1]</b> or Baroclinic instability. Analytical and numerical studies showed that they can be long-lived and catalyze efficiently dust material concentration <b>[2]</b> and encourage to think they could play a role in protoplanetary-disc evolution and planetesimal formation. Their presence in the outer regions of circumstellar disks is possibly betrayed by recent observations of lopsided structures with ALMA and VLT <b>[3, 4]</b>. Self-gravity (SG) plays a key role in this scenario, particularly when high dust density clumps are trapped in the vortex core. <br></div><div><br></div><div>The constant smoothing length (CSL) formalism is a widely used approach for mimicking the 3D vertically averaged SG which is then used in monophasic, thin-disc (2D) simulations. <b>[5]</b> proposed a substantial correction to the standard CSL formalism that does not underestimate SG at short mutual distances and reliably accounts for (1) the dust phase and (2) its gravitational interaction with gas. In particular, dust SG is proportional to the gas-to-dust scale height, and three space varying smoothing lengths (SVSLs) are necessary for computing SG in 2D, bi-fluid hydrodynamical simulations. For all SG interactions, their rectification decreases SG error to less than 2%.
We propose to show our early numerical results on the capture of dust material by self-gravitating vortices. <br></div><div><br></div><div>This problem was addressed using high-resolution, bi-fluid, 2D simulations thanks to the RoSSBi3D <b>[6]</b> code which was modified for accounting the SVSL correction. <br></div><div><b><br></b></div><div><b><u>References:</u></b> <br></div><div><b>1.</b> Lovelace et al. 1999, ApJ, 513, 805 <br></div><div><b>2.</b> Barge, P. & Sommeria, J. 1995, A&A, 295, L1 <br></div><div><b>3.</b> Tsukagoshi, T. et al. 2019, ApJ, 878, L8 <br></div><div><b>4.</b> Dong, R. et al. 2018, ApJ, 860, 124 <br></div><div><b>5.</b> Rendon Restrepo, S., Barge, P, unpublished <br></div><div><b>6.</b> Rendon Restrepo, S. et al. 2022, arXiv:2207.04252
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