Abstract
ABSTRACT When imaged at high resolution, many protoplanetary discs show gaps and rings in their dust sub-mm continuum emission profile. These structures are widely considered to originate from local maxima in the gas pressure profile. The properties of the underlying gas structures are however unknown. In this paper, we present a method to measure the dust–gas coupling α/St and the width of the gas pressure bumps affecting the dust distribution, applying high-precision techniques to extract the gas rotation curve from emission line data cubes. As a proof of concept, we then apply the method to two discs with prominent substructure, HD 163296 and AS 209. We find that in all cases the gas structures are larger than in the dust, confirming that the rings are pressure traps. Although the grains are sufficiently decoupled from the gas to be radially concentrated, we find that the degree of coupling of the dust is relatively good (α/St ∼ 0.1). We can therefore reject scenarios in which the disc turbulence is very low and the dust has grown significantly. If we further assume that the dust grain sizes are set by turbulent fragmentation, we find high values of the α turbulent parameter (α ∼ 10−2). Alternatively, solutions with smaller turbulence are still compatible with our analysis if another process is limiting grain growth. For HD 163296, recent measurements of the disc mass suggest that this is the case if the grain size is 1 mm. Future constraints on the dust spectral indices will help to discriminate between the two alternatives.
Highlights
The Atacama Large Millimeter/submillimeter Array (ALMA) is revolutionising our understanding of protoplanetary discs thanks to its unprecedented angular resolution
If we further assume that the dust grain sizes are set by turbulent fragmentation, we find high values of the α turbulent parameter (α ∼ 10−2)
Because St is linked to the grain size, it is worth asking what values are compatible with the well known results of dust grain growth in proto-planetary discs; in turn, this sets a constraint on α given the measurements of α/St that we present in this paper
Summary
The Atacama Large Millimeter/submillimeter Array (ALMA) is revolutionising our understanding of protoplanetary discs thanks to its unprecedented angular resolution. When imaged at high resolution, most (though not all, Facchini et al 2019; Long et al 2019) discs show a rich morphology of structures, in terms of crescents (van der Marel et al 2013), spirals (Perez et al 2016) and rings (ALMA Partnership et al 2015; van der Plas et al 2017; Fedele et al 2017, 2018; Dipierro et al 2018; Clarke et al 2018). This latter category in particular is the one occurring most frequently, as shown spectacularly by the high-resolution DSHARP campaign (Andrews et al 2018). The most likely interpretation for the origin of these rings is that a population of young planets is already present at these early stages; the rings are a tool to study the masses and locations of these young planets (Rosotti et al 2016; Bae et al 2018; Zhang et al 2018; Lodato et al 2019)
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