Multiwavelength analysis for interferometric (sub-)mm observations of protoplanetary disks

Abstract

Context. The growth of dust grains from sub-µm to mm and cm sizes is the first step towards the formation of planetesimals. Theoretical models of grain growth predict that dust properties change as a function of disk radius, mass, age, and other physical conditions. High angular resolution observations at several (sub-)mm wavelengths constitute the ideal tool with which to directly probe the bulk of dust grains and to investigate the radial distribution of their properties. Aims. We lay down the methodology for a multiwavelength analysis of (sub-)mm and cm continuum interferometric observations to self-consistently constrain the disk structure and the radial variation of the dust properties. The computational architecture is massively parallel and highly modular. Methods. The analysis is based on the simultaneous fit in the uv-plane of observations at several wavelengths with a model for the disk thermal emission and for the dust opacity. The observed flux density at the different wavelengths is fitted by posing constraints on the disk structure and on the radial variation of the grain size distribution. Results. We apply the analysis to observations of three protoplanetary disks (AS 209, FT Tau, DR Tau) for which a combination of spatially resolved observations in the range ∼0.88 mm to ∼10 mm is available from SMA, CARMA, and VLA. In these disks we find evidence of a decrease in the maximum dust grain size, a max , with radius. We derive large a max values up to 1 cm in the inner disk 15 AU ≤ R ≤ 30 AU and smaller grains with a max ∼ 1 mm in the outer disk (R 80 AU). Our analysis of the AS 209 protoplanetary disk confirms previous literature results showing a max decreasing with radius. Conclusions. Theoretical studies of planetary formation through grain growth are plagued by the lack of direct information on the radial distribution of the dust grain size. In this paper we develop a multiwavelength analysis that will allow this missing quantity to be constrained for statistically relevant samples of disks and to investigate possible correlations with disk or stellar parameters.

Dust properties across the CO snowline in the HD 163296 disk from ALMA and VLA observations

“…The β(r) profiles are qualitatively consistent with the results of similar analyses performed in other classical smooth disks (Guilloteau et al 2011;Banzatti et al 2011;Pérez et al 2012Pérez et al , 2015Trotta et al 2013;Menu et al 2014;Tazzari et al 2016), with a significant variation of β throughout the disk (∆β > 1), indicating a maximum grain size a max decreasing with the distance from the star. The ALMA and VLA data provide for the first time the combination of signal-to-noise ratio, angular resolution and image fidelity to successfully perform an analysis in the image plane.…”

“…3.4 we have shown that the surface brightness radial profile for the continuum emission at 850 µm is compatible with having an excess peaked around 110 AU, with deconvolved FWHM ≤ 40 AU. To assess the robustness of this result, we performed a direct fit of the interferometric data (i.e., the visibilities) using the fitting scheme described by Tazzari et al (2016) to which we refer for the analysis details. To estimate the disk thermal emission at 850 µm, we used a classical two layer disk model (Chiang & Goldreich 1997) with refinements by (Dullemond et al 2001) and a reduced disk flaring that adequately describes the observed far-infrared flux (from Tilling et al 2012).…”

“…3.6. The modeling methodology is based on a Bayesian approach and employs an affineinvariant Markov chain Monte Carlo (MCMC) ensemble sampler (Foreman-Mackey et al 2013) to explore the parameter space and find the best-fit models (Tazzari et al 2016). In panel (a) of Fig.…”

“…These facilities allow us to obtain sensitive and high angular resolution observations of the dust continuum and gas emission lines from protoplanetary disks and therefore study the radial variations of the physical parameters of the disk. Recent results include the study of the dust properties as a function of radius in disks (e.g., Guilloteau et al 2011;Banzatti et al 2011;Pérez et al 2012Pérez et al , 2015Menu et al 2014;Tazzari et al 2016), and the clear identification of the CO snowline in nearby disks Qi et al 2013Qi et al , 2015, through its effects on DCO + and N 2 H + abundances. It is thus becoming possible to directly investigate the effect of the CO snowline on grain growth observationally.…”

Dust Coagulation with Porosity Evolution

“…Therefore, the radial profile ofˇroughly corresponds to theǎ s a function of different grain sizes. There have been some observational constraints on the radial profile by using interferometric observations at radio wavelengths, which shows thatˇis small inside the disk and large outside the disk (e.g., Isella et al 2010;Guilloteau et al 2011;Pérez et al 2012Pérez et al , 2015Tazzari et al 2016). …”