On the millimetre continuum flux-radius correlation of proto-planetary discs

Abstract

A correlation between proto-planetary disc radii and sub-mm fluxes has been recently reported. In this Letter we show that the correlation is a sensitive probe of grain growth processes. Using models of grain growth and drift, we have shown in a companion paper that the observed disc radii trace where the dust grains are large enough to have a significant sub-mm opacity. We show that the observed correlation emerges naturally if the maximum grain size is set by radial drift, implying relatively low values of the viscous $\alpha$ parameter $\lesssim 0.001$. In this case the relation has an almost universal normalisation, while if the grain size is set by fragmentation the flux at a given radius depends on the dust-to-gas ratio. We highlight two observational consequences of the fact that radial drift limits the grain size. The first is that the dust masses measured from the sub-mm could be overestimated by a factor of a few. The second is that the correlation should be present also at longer wavelengths (e.g. 3mm), with a normalisation factor that scales as the square of the observing frequency as in the optically thick case.

6 pages, 3 figures; accepted on MNRAS letters

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Cited by in corpus (34)

• Observations of Protoplanetary Disk Structures
• Dust depleted inner disks in a large sample of transition disks through long-baseline ALMA observations
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• Empirical constraints on turbulence in proto-planetary discs
• Hints for icy pebble migration feeding an oxygen-rich chemistry in the inner planet-forming region of disks
• The efficiency of dust trapping in ringed proto-planetary discs
• The evolution of dust in discs influenced by external photoevaporation
• Multi-wavelength continuum sizes of protoplanetary discs: scaling relations and implications for grain growth and radial drift
• Planet formation and migration near the silicate sublimation front in protoplanetary disks
• Hints on the origins of particle traps in protoplanetary disks given by the $M_{\mathrm{dust}}-M_{\star }$ relation
• Protoplanetary disk masses in NGC 2024: Evidence for two populations
• On the secular evolution of the ratio between gas and dust radii in protoplanetary discs
• Predicting the observational signature of migrating Neptune-sized planets in low-viscosity disks
• A dusty origin for the correlation between protoplanetary disc accretion rates and dust masses
• The evolution of protoplanetary discs in star formation and feedback simulations
• On dust evolution in planet-forming discs in binary systems. I -- Theoretical and numerical modelling: radial drift is faster in binary discs
• A large population study of protoplanetary disks: Explaining the millimeter size-luminosity relation with or without sub-structure
• Dual-Wavelength ALMA Observations of Dust Rings in Protoplanetary Disks
• Population Synthesis Models Indicate a Need for Early and Ubiquitous Disk Substructures
• ALMA 870 $\mu$m continuum observations of HD 100546. Evidence of a giant planet on a wide orbit
• A high-resolution survey of protoplanetary disks in Lupus and the nature of compact disks
• Massive compact dust disk with a gap around CW Tau revealed by ALMA multi-band observations
• Stellar multiplicity affects the correlation between proto-planetary disc masses and accretion rates: binaries explain high-accretors in Upper Sco
• Constraining the turbulence and the dust disk in IM Lup: onset of planetesimal formation
• On the time evolution of the $M_{\mathrm{d}}-M_{\star }$ and $\dot{M}-M_{\star }$ correlations for protoplanetary discs: the viscous timescale increases with stellar mass
• ALMA Observations of Young Eruptive Stars: continuum disk sizes and molecular outflows
• The time evolution of $M_{\mathrm{d}}/\dot{M}$ in protoplanetary discs as a way to disentangle between viscosity and MHD winds
• On dust evolution in planet-forming discs in binary systems. II -- Comparison with Taurus and $\rho$ Ophiuchus (sub-)millimetre observations: discs in binaries have small dust sizes
• Multi-frequency analysis of the ALMA and VLA high resolution continuum observations of the substructured disc around CI Tau. Preference for sub-mm-sized low-porosity amorphous carbon grains
• The evolution of the flux-size relationship in protoplanetary discs by viscous evolution and radial pebble drift
• A tension between dust and gas radii: the role of substructures and external photoevaporation in protoplanetary disks
• Linking Outer Disk Pebble Dynamics and Gaps to Inner Disk Water Enrichment
• Modelling the secular evolution of proto-planetary disc dust sizes -- A comparison between the viscous and magnetic wind case