Dust and Gas in the disc of HL Tauri: Surface density, dust settling, and dust-to-gas ratio

The recent ALMA observations of the disc surrounding HL Tau reveal a very complex dust spatial distribution. We present a radiative transfer model accounting for the observed gaps and bright rings as well as radial changes of the emissivity index. We find that the dust density is depleted by at least a factor 10 in the main gaps compared to the surrounding rings. Ring masses range from 10-100 M$_{\oplus}$ in dust, and, we find that each of the deepest gaps is consistent with the removal of up to 40 M$_{\oplus}$ of dust. If this material has accumulated into rocky bodies, these would be close to the point of runaway gas accretion. Our model indicates that the outermost ring is depleted in millimetre grains compared to the central rings. This suggests faster grain growth in the central regions and/or radial migration of the larger grains. The morphology of the gaps observed by ALMA - well separated and showing a high degree of contrast with the bright rings over all azimuths - indicates that the millimetre dust disc is geometrically thin (scale height $\approx$ 1 au at 100 au) and that a large amount of settling of large grains has already occurred. Assuming a standard dust settling model, we find that the observations are consistent with a turbulent viscosity coefficient of a few $10^{-4}$. We estimate the gas/dust ratio in this thin layer to be of the order of 5 if the initial ratio is 100. The HCO$^+$ and CO emission is consistent with gas in Keplerian motion around a 1.7 $M_\odot$ star at radii from $\leq 10 - 120\,$au.