---
author:
- 'D. Fedele'
- 'M. Tazzari'
- 'R. Booth'
- 'L. Testi'
- 'C. J. Clarke'
- |
    \
    I. Pascucci
- 'A. Kospal'
- 'D. Semenov'
- 'S. Bruderer'
- 'Th. Henning'
- 'R. Teague'
date: 'Received ...; accepted ...'
subtitle: Evidence of multiple gaps opened by a single planet
title: ALMA continuum observations of the protoplanetary disk AS 209
---

Introduction
============

Axisymmetric gaps and rings such as those seen in the protoplanetary disks around HL Tau, TW Hya, HD163296, HD 169142, AA Tau [e.g. @alma15; @Andrews16; @Isella16; @Fedele17; @Loomis17] can now regularly be unveiled by the extremely high resolution available with ALMA. The formation of gaps and rings in disks can be due to several mechanisms such as: planet formation [e.g., @Papaloizou84]; magneto-rotational instability [@Flock15]; condensation fronts [@Zhang15]; dust sintering [@Okuzumi16]; photoevaporation [@Ercolano17].

The rings observed by ALMA show that the millimeter dust grains are radially confined regions in which inward radial migration is slowed down or stopped and so may be key to explaining the retention of large grains in disks on long ($2-3$Myr) timescales (irrespective of the mechanism producing such “dust traps”). In addition, dust traps provide the ideal environment in which to observationally constrain models of grain growth because – in contrast to other regions of the disk – they are regions in which radial drift is relatively unimportant, allowing dust to grow [*in situ*]{} [@Pinilla12]. Given a measure of the local dust density, the timescale for dust growth to a given size is readily obtained from grain growth models [e.g., @Birnstiel12]. Empirical measurement of the maximum grain size in traps would thus provide the cleanest test of the various assumptions (sticking probability, turbulent velocity, fragmentation threshold) that enter these models.

![image](fig_as209_continuum.jpg){width="18cm"}

This paper presents new ALMA 1.3mm continuum observations of the T Tauri disk AS 209 where axisymmetric gaps and rings are detected. AS 209 ($M_{\star} = 0.9\,M_{\odot}$, spectral type K5, $L_{\star} = 1.5\,L_{\odot}$, @Tazzari16) is part of the young (age $\sim 0.5 - 1.0\,$Myr @Natta06) Ophiuchus star forming region at a distance of 126pc from the Sun [@Brown16]. Multi-frequency continuum observations revealed optically thin emission at millimeter wavelenghts beyond a few 10s of  au from the star [@Perez12; @Tazzari16]. @Huang16 found evidence of an extended gas emission (C$^{18}$O) speculating that it is due to external CO desorption in the outer disk. Interestingly, @Huang17 noticed the presence of a dark lane in the dust 1.1mm continuum emission.

The structure of the paper is the following: observations and data reduction are presented in section \[sec:obs\] and the results are discussed in section \[sec:results\]. The data analysis is described in Section \[sec:analysis\]. Section \[sec:hydro\] provides a comparison to hydrodynamical simulations. Discussion and conclusion are reported in sec. \[sec:conclusion\].

Observations and Data reduction {#sec:obs}
===============================

The ALMA observations of AS 209 (J2000: R.A. = 16$^{\rm{h}}$49$^{\rm{m}}$15.296$^{\rm{s}}$, DEC = –14$^\circ$22$\arcmin$09.02$\arcsec$) have been performed on 2016 September 22 (with 38 antennas) and 26 (41 antennas) in band 6 (211–275GHz) as part of the project ID 2015.1.00486.S (PI: D. Fedele). The correlator setup includes a broad (2GHz bandwidth) spectral window centered at 230GHz.

Visibilities were taken in two execution blocks with a 6.05s integration time per visibility totalling 40 minutes, per block, on-source. System temperatures were between $80-145$K. Weather conditions on the dates of observation gave an average precipitable water vapour of 2.2 and 2.3mm, respectively. Calibration was done with $J1517-2422$ as bandpass calibrator, $J1733-1304$ as phase and flux the flux calibrator. The visibilities were subsequently time binned to 60s integration times per visibility for self-calibration, imaging, and analysis. Self-calibration was performed using the 233 GHz continuum TDM spectral window with DA41 as the reference antenna.

The continuum image was created using <span style="font-variant:small-caps;">casa.clean</span> (<span style="font-variant:small-caps;">casa</span> version 4.7); after trying different weighting schemes, we opted for a uniform weight which yields a synthesised beam of 019 $\times$ 014 (PA = 75.5$^{\circ}$). The peak flux is 13mJybeam$^{-1}$ and the r.m.s. is 0.1mJybeam$^{-1}$.

Results {#sec:results}
=======

The ALMA 1.3mm dust continuum image is shown in Fig. \[fig:continuum\]: the continuum emission is characterized by a bright central emission and two weaker dust rings peaking at $\sim 75\,$au and $130\,$au, respectively. The two rings have a similar peak flux ($\sim 2\,$mJy). The rings are intervaled by two narrow gaps. The two gaps have different widths and depths. The radial intensity profile shows a kink around $20-30\,$au which may be the signature of another (spatially unresolved) dust gap. Finally, the continuum flux does not drop to zero at the edge of the outer ring as there is a tenuous emission extending out to $\sim 170-180\,$au. The different disk substructures are clearly visible in the radial intensity profile shown in Fig. \[fig:radial\].

Characterization of the brightness profile
------------------------------------------

In this section we present here the fit of the observed visibilities, which provides an initial characterization of the disk surface brightness useful for the detailed physical modelling carried out in Section \[sec:analysis\]. We assume an axisymmetric brigthness profile defined as follows:

$$I(R)=\delta(R) \ I_0 \left( \frac{R}{R_c} \right)^{\phi_1} 
\exp \left[ -\left( \frac{R}{R_c} \right)^{\phi_2} \right],$$

where $I_0$ is a normalization, $R_c$ is a scale length and $\delta(R)$ is a scaling factor (by definition $\delta(R)>0$) parametrized as:

$$\delta(R)=
\begin{cases}
\delta_{\rm G1}     & \qquad \text{for  R $\in$ [$R_{\rm G1} - hw_{\rm G1}, R_{\rm G1} + hw_{\rm G1}$]}\\
\delta_{\rm R1}         & \qquad \text{for  R $\in$ [$R_{\rm G1} + hw_{\rm G1}, R_{\rm G2} - hw_{\rm G2}$]}\\
\delta_{\rm G2}         & \qquad \text{for  R $\in$ [$R_{\rm G2} - hw_{\rm G2}, R_{\rm G2} + hw_{\rm G2}$]}\\
\delta_{\rm R2}         & \qquad \text{for  R $\in$ [$R_{\rm G2} + hw_{\rm G2}, R_{\rm R2, out} $] } \\
\delta_{\rm out}        & \qquad \text{for  R $\geq  R_{\rm R2, out}$}\\
1                                & \qquad \text{otherwise}
\end{cases}$$

\[eq:delta\]

where $R_{\rm G}$ and $hw_{\rm G}$ are the center and half width of the dust gaps, respectively. The choice of this particular brightness profile serves as a simple realization of an “unperturbed” profile (an exponentially tapered power law), characterized by a few radial regions that can depart from it either due to an excess ($\delta>1$) or a lack ($\delta<1$) of emission. Following the evidence emerging from the synthesized image (Fig. \[fig:continuum\]), we allow for two rings, two gaps, and an outer disk region, following nomenclature in Fig. \[fig:continuum\]. In this framework, a gap in the disk is naturally modelled with $\delta<1$.

![Radial intensity profile of the 1.3,mm dust continuum emission. The profile is azimuthally averaged after deprojecting for the disk inclination ($i = 36^{\circ}$, Sect. \[sec:results\]). The black line shows the mean profile while the shadowed regions indicate the standard deviation along the azimuth angle.[]{data-label="fig:radial"}](fig_as209_radcut.jpg){width="\columnwidth"}

  Parameter                Min   Max            Best-fit
  ---------------------- ----- ----- -------------------
  I$_0$ \[mJy/beam\]         0   100       7.4 $\pm$ 0.2
  $R_c$ \[au\]              20   150          80 $\pm$ 1
  $\phi_1$                  -4     4    -0.24 $\pm$ 0.01
  $\phi_2$                  -4     4     2.19 $\pm$ 0.02
  $R_{G1}$ \[au\]            0    80      61.7 $\pm$ 0.5
  $hw_{G1}$ \[au\]           0    30       8.0 $\pm$ 0.2
  $\delta_{G1}$              0     1    0.03 $\pm$ 0.005
  $\delta_{R1}$              0     3     0.80 $\pm$ 0.02
  $R_{G2}$ \[au\]           80   110     103.2 $\pm$ 0.4
  $hw_{G2}$ \[au\]           0    30      15.6 $\pm$ 0.2
  $\delta_{G2}$              0     1   0.025 $\pm$ 0.005
  $\delta_{R2}$              0    20       4.8 $\pm$ 0.1
  $R_{R2, out}$ \[au\]     130   180     139.8 $\pm$ 0.8
  $\delta_{out}$             0     2     1.95 $\pm$ 0.03
  $i$ \[$^\circ$\]           0    90      35.3 $\pm$ 0.8
  $PA$ \[$^\circ$\]          0   180      86.0 $\pm$ 0.7

  : Parameter space explored by the Markov chains and best-fit values

\[tab:mcmc\]

We perform the fit of the visibilities with a Bayesian approach using the Monte Carlo Markov chains ensemble sampler [@Goodman10] implemented in the <span style="font-variant:small-caps;">emcee</span> package [@Foreman13]. We assume flat priors for all the free parameters. Table \[tab:mcmc\] reports the ranges explored for each parameter.

![ Dust surface density of the <span style="font-variant:small-caps;">dali</span> fiducial model. The dashed line corresponds to the initial unperturbed profile (power-law with exponential tail).[]{data-label="fig:dali_sd"}](fig_as209_dali_sd.jpg){width="\columnwidth"}

We also fit simultaneously for the disk inclination $i$, the East-of-North position angle $PA$, and phase center offset ($\Delta \alpha$, $\Delta \delta$). For each set of values of the free parameters we compute a synthetic image of the model assuming axisimmetry and we use the <span style="font-variant:small-caps;">galario</span> library [@Tazzari17b] to compute the synthetic visibilities (by sampling the Fourier transform of the model image in all the observed $(u,v)$-points) and the resulting $\chi^2$ as

$$\chi^{2} = \sum_{j=0}^{N}|V_{\mathrm{obs}}(u_{j}, v_{j})-V_{\mathrm{mod}}(u_{j}, v_{j})|^{2} w_{j}\,,$$

\[eq:chi\]

where $w_{j}$ is the weight of the observed $(u_{j},v_{j})$ visibility point. The posterior of each model is then computed as $\exp(-\chi^2/2)$ and sampled with 80 chains for 45000 steps (after 5000 burn-in steps). The chains, which reached a good convergence, are shown in Fig. \[fig:mcmc\_chains\] in Appendix \[ap:mcmc\], in the form of marginalized 1D and 2D distributions. The parameters that we infer from the fit of the visibilities are presented in Table \[tab:mcmc\]: for each parameter, we estimate its value as the median of the marginalized distribution and its uncertainty as half the interval between 16% and 84% percentiles.

We find that the 1.3 mm continuum brightness distribution of AS 209 can be explained very well by a profile with two deep gaps ($\delta_{G1}\sim0.03$, $\delta_{G2}\sim 0.025$) at 62 and 103au, respectively, and an excess ring ($\delta_{R2} \sim 4$) at $\sim$ 130au. The excellent agreement of this profile with the observations is apparent in Fig. \[fig:as209\_mcmc\], where the deprojected synthetic visibilities match the observed ones up to 1500k$\lambda$.

[llllll]{}\
Parameter & & Description\
$M_{\star}$ \[$M_{\odot}$\] & & stellar mass\
T$_{\rm eff}$ \[K\] & & stellar temperature\
$L_{\star}$ \[$L_{\odot}$\] & & stellar luminosity\
$d$ \[pc\] & & stellar distance\
$R_{\rm in}$ \[au\] & & disk inner radius\
$R_{\rm c}$ \[au\] & & disk critical radius\
$R_{\rm G1}$ \[au\] & & Gap 1 center\
$hw_{\rm G1}$ \[au\] & & Gap 1 half width\
$R_{\rm G2}$ \[au\] & & Gap 2 center\
$hw_{\rm G}$ \[au\] & & Gap 2 half width\
$R_{\rm R2, out}$ \[au\] & & Ring 2 outer radius\
$R_{\rm out}$ \[au\] & & disk outer radius\
$i$ \[$^{\circ}$\] & & disk inclination\
$PA$ \[$^{\circ}$\] & & disk position angle\
$\chi$, f$_{\rm large}$ & & settling parameters\
$\psi$ & & flaring exponent\
$h_{\rm c}$ & & scale height at $R_{\rm c}$\
\
Parameter & Min & Max & Step & Fiducial &\
$M_{\rm dust}$ \[$M_{\odot}$\] & $1 \cdot 10^{-4}$ & $5 \cdot 10^{-4}$ & $0.5 \cdot 10^{-4}$ & $3.5 \cdot 10^{-4}$ & Disk dust mass\
$\gamma_1$ & -1.0 & 1.0 & 0.1 & 0.3 & $\Sigma (r)$ power-law exponent\
$\gamma_2$ & 1.0 & 3.0 & 0.1 & 2.0 & $\Sigma (r)$ exponential-tail exponent\
$\tilde{\delta}_{\rm G1}$ & & 0.1 & $\Sigma_{\rm dust, large}$ scale factor in gap 1\
$\tilde{\delta}_{\rm R1}$ & 0.5 & 1.0 & 0.05 & 0.75 & $\Sigma_{\rm dust, large}$ scale factor in ring 1\
$\tilde{\delta}_{\rm G2}$ & & 0.01 & $\Sigma_{\rm dust, large}$ scale factor in gap 2\
$\tilde{\delta}_{\rm R2}$ & 2 & 5 & 0.5 & 4.5 & $\Sigma_{\rm dust, large}$ scale factor in ring 2\
$\tilde{\delta}_{\rm out}$ & 1 & 3 & 0.5 & 1.5 & $\Sigma_{\rm dust, large}$ scale factor in outer disk\

\[tab:dali\]

Analysis with a physical disk model {#sec:analysis}
===================================

In this Section we aim to characterize the structure of AS 209 in physical terms, starting from the observed 1.3mm continuum observation. This step is important to estimate the drop of the dust surface density inside the two gaps. For this purpose we use the dust radiative transfer code implemented into the thermo-chemical disk model <span style="font-variant:small-caps;">dali</span> (Dust and Lines, @Bruderer12 [@Bruderer13]). Starting from an input radiation field and from a disk density structure, <span style="font-variant:small-caps;">dali</span> solves the two dimensional dust continuum radiative transfer and determines the dust temperature and radiation field strength at each disk position.

Model description
-----------------

We adopt the characterization of the surface brightness presented in the previous Section as a first guess for the functional form and the location of the gaps to be used for the surface density of the physical disk model that we use in this Section. The dust surface density is:

$$\label{eq:dali_sd}
\Sigma_{\rm dust}(R) = \tilde{\delta} (R) \ \Sigma_{\rm c}  \ \Bigg(\frac{R}{R_{\rm c}}\Bigg)^{\gamma_1} \ \exp\Bigg[ - \Bigg( \frac{R}{R_{\rm c}} \Bigg)^{\gamma_2} \Bigg]$$

where the surface density scaling factor ($\tilde{\delta}$) is parametrized as in eq. \[eq:delta\].

In the vertical direction, the density follows a Gaussian distribution with scale height $h$ ($=H/R$)

$$h = h_{\rm c} \Bigg( \frac{R}{R_{\rm c}}\Bigg)^{\psi}$$

![image](fig_as209_continuum_dali.jpg){width="18cm"}

with $h_{\rm c}$ the critical scale height and $\psi$ the flaring exponent. The critical scale height ($h_{\rm c}=0.13$) and disk flaring ($\psi=0.1$) are taken from @Andrews11. In the adopted version of <span style="font-variant:small-caps;">dali</span>, dust settling is included following @dAlessio06, i.e., adopting two power-law grain size populations with different scale heights: the small grains have a scale height equal to $h$ (similar to the gas) while the scale height of the large grains is $\chi h$ (with $\chi < 1$) to account for the settling of the large grains. Finally, the total dust mass is distributed between the two populations and it is regulated by the parameter $f_{\rm large}$ (large-to-small mass ratio): thus, the dust surface density is $\Sigma_{\rm dust}  \cdot (1 - f_{\rm large})$ and $\Sigma_{\rm dust} \cdot f_{\rm large}$ for the small and large grains, respectively. The flaring parameters are fixed : $\chi = 0.2$, $f_{\rm large} = 0.85$.

We fixed the grain size populations with a small population of sizes between 0.005 and 1[$\mu$m]{} and a large one of sizes between 0.005 and $s_{\rm max}\,$[$\mu$m]{} with both populations sharing the same power-law exponent ($p=3.5$). The dust mass absorption coefficients are taken from @Andrews11.

The maximum grain size of the large dust population affects the dust opacity at millimeter wavelengths with the opacity decreasing by almost an order of magnitude going from $s_{\rm max}$ = 0.8mm to 1.0cm [e.g., @Tazzari16]. This in turn has an impact the dust temperature and the total dust mass. In this paper we fix $s_{\rm max} = 2000\,$[$\mu$m]{} in agreement with the multi-frequency continuum analysis of AS 209 by @Tazzari16.

Fiducial model
--------------

We built a grid of <span style="font-variant:small-caps;">dali</span> disk models varying the following parameters:

-   total dust mass

-   surface density power-law exponent ($\gamma_1$)

-   exponential tail exponent ($\gamma_2$)

-   dust density scaling factors

The explored range of each variable parameter is listed in Table \[tab:dali\]. The values of $R_{\rm c}$, gaps centers ($R_{\rm G1}, R_{\rm G2}$) and gaps sizes (half width $hw_{\rm G1}, hw_{\rm G2}$) are taken from the best-fist results of the multi-components analysis.

Each model is compared with the ALMA continuum observation with the aim of defining a fiducial model for the dust surface density. The comparison is performed in the $uv$-plane: first we compute the synthetic 1.3mm continuum image with <span style="font-variant:small-caps;">dali</span>, then the tool <span style="font-variant:small-caps;">casa.simobserve</span> is used to convert the image into synthetic visibilities at the same $uv$-positions as the observations. Finally we measure the $\chi^2$ between observation and model after deprojecting and binning the visibilities (bin size of 30k$\lambda$).

The fitting procedure is performed in multiple steps: first we vary the global disk properties, i.e. $M_{\rm dust}, \gamma_1, \gamma_2$ until we find a good agreement with the visibilities at the shortest baselines which provides a constraint to the large scale structure. During this step the dust scaling factors are kept fixed: $\tilde{\delta}_{\rm G1}=0, \tilde{\delta}_{\rm G2}=0, \tilde{\delta}_{\rm R1}=1, \tilde{\delta}_{\rm R2}=1, \tilde{\delta}_{\rm out}=1$. In a second step, we constrain the values of the scaling factors while keeping fixed $M_{\rm dust}, \gamma_1, \gamma_2$. The process is repeated until convergence. This allows us to refine the grid resolution iteratively.

The fiducial model is defined by the set of parameters that minimize the $\chi^2$ between the observed and synthetic visibilities (eq. \[eq:chi\]) within the explored parameter space.

The parameters of the <span style="font-variant:small-caps;">dali</span> fiducial model are listed in Table \[tab:dali\]. Figure \[fig:dali\_sd\] shows the dust surface density of the fiducial model and the model image is shown in Figure \[fig:dali\]. We note that, in order to quantitatively reproduce the disk structure (gaps and rings) with DALI we need to set different dust scaling factors for the two gaps: $\tilde{\delta}_{\rm G1} \sim 0.1$ and $\tilde{\delta}_{\rm G2} \sim 0.01$.

![image](fig_as209_hydro_sd.jpg){width="18cm"}

Comparison to hydrodynamical simulations {#sec:hydro}
========================================

In this section we investigate the possibility that the gaps were produced by planets, as has been suggested for other disks, e.g. HL Tau, TW Hydra, HD 163296, and HD 169142 [@alma15; @Andrews16; @Isella16; @Fedele17]. To do this, we have run 2D simulations of planet-disk interaction using a version of FARGO-3D [@Benitez16] modified to include dust dynamics [@Rosotti16]. The disk parameters were chosen to match the best fit model (see Table \[Tab:SimParams\]). The simulations were run using a logarithmic radial grid, extending from 10 au to 300 au at a resolution of $Nr \times N\phi = 550 \times 1024$. Given the relative expense of the hydrodynamic simulations, we have not conducted an exhaustive fit to the data, instead we investigate the typical planetary properties and disk conditions that produce reasonable gap structures. The key information available for constraining the planets properties are the gap width, depth and location. The position of the two gap centers (62 and 103au) are close enough to the ratio of radii expected for two planets migrating together in 2:1 resonance (with semi-major axis ratio 0.63), which forms the starting point for our investigation.

Starting from the relationship between the width of a gap opened by a planet and its mass derived by @Rosotti16, we already see that the inner planet must be low mass due because the inner gap is narrow (just 16au or approximately 2 – 3 pressure scale-heights). This suggests that the mass of the inner planet is in the Neptune mass regime ($\sim 15\,M_\oplus$, i.e. $0.05\,M_\mathrm{J}$). However, while @Rosotti16 showed that these planets can produce observable features, they found gap depths much smaller than the inner gap in AS 209. Nonetheless, the depth of the gap is senstive to disk viscosity, with planets opening deeper gaps in low viscosity disks [@Crida06; @Zhu13]. Thus together with the gap width, the gap depth places constraints on both the planet mass and disk viscosity. Furthermore, at extremely low viscosity, @Dong17 and @Bae17 showed that planets may open multiple dust gaps in inviscid disks, which raises the interesting possibility that the gaps in AS 209 may be opened by a single planet.

From the right panel of Fig. \[fig:hydro\], we see that even a modest viscosity $\alpha = 10^{-4}$ is too high to produce deep enough gaps to explain the structures in AS 209. While a single $0.2\,M_\mathrm{J}$ planet at 95au matches the width of the outer gap, the drop in dust surface density it is far too shallow compared to what is inferred. Although more massive planets can open deep enough gaps (for $\alpha = 10^{-4}$), they produce structures that are too wide and begin to prevent the inflow of dust entirely. This suggests that the outer gap is consistent with a $0.2\,M_\mathrm{J}$ planet, but requires even lower viscosity.

The inviscid ($\alpha = 0$) simulations produce a much better match to the inferred gap structure (Fig. \[fig:hydro\], left panel). Already a single $0.2\,M_\mathrm{J}$ planet at 95 au is in remarkable agreement with the gap structure, producing a deep outer gap along with a second inner gap at approximately the the right location and with a reasonable width and depth. The depth of the gaps is not only sensitive to viscosity, but in the inviscid case it also increases with time, thus being a much weaker tracer of the planet mass than the position of the peaks (as noted by @Rosotti16). However, the width of the gaps are similar in both the viscous and inviscid cases. Interestingly, the simulations produce an additional gap at around 35au, which coincides with similar, but much smaller amplitude, feature in the radial intensity profile (Fig. \[fig:radial\]). Given that the depth of this feature is dependent on parameters such as viscosity, and optical depth effects may further reduce the amplitude of variation in the observed intensity profile, it is possible that this inner structure is related to the presence of a planet near 100au.

Since low viscosity is required to reproduce the gap structure in AS 209, and in this case a single planet may produce both gaps, it is interesting to consider whether there still could be a second planet present. Thus we have re-run both the viscous and inviscid simulations with an inner planets at 57 au, close to the 2:1 resonance with the outer planet. In both cases the planet mass is consistent with the estimate from the relationship between gap width and planet mass: a $0.05\,M_\mathrm{J}$ planet produces a negligible difference to the structure of the gaps and could thus be easily hidden in the gap. The largest planet mass compatible with the gap widths is roughly $0.1\,M_\mathrm{J}$, with larger planet masses producing a gap that is too wide in the inviscid case. While a slightly more massive planet may be compatible with the inner gap when $\alpha = 10^{-4}$, this is hard to reconcile with the need for a lower $\alpha$ in the outer gap.

  Parameter             Value
  --------------------- ------------------------------------
  Temperature           $190 (R/100\,\mathrm{au})^{-0.55}$
  Gas Surface Density   $ 7.5 (R/100\,\mathrm{au})^{-1}$
  Grain size            1 mm
  Viscous $\alpha$      0, $10^{-4}$

  : Disk model used in the planet disk-interaction simulations[]{data-label="Tab:SimParams"}

Conclusions {#sec:conclusion}
===========

The ringed dust structure of AS 209 revealed by ALMA is consistent with the presence of a Saturn-like ($M_{\rm planet} = 0.2 M_{\rm J} = 0.67\,M_{\rm Saturn}$) planet at $r = 95\,$au. The planetary mass is constrained by the width and depth of the dust gap: for the chosen gas properties, our hydrodynamical simulations indicate that less massive planets ($\lesssim 0.5 \,M_\mathrm{Saturn}$) do not produce a gap that is sufficiently wide, while more massive planets ($\gtrsim 1.0 \,M_\mathrm{Saturn}$) prevent the transport of dust inwards entirely, forming a transition disk (inner hole in large grains). Our radiative transfer calculations (Sect \[sec:analysis\]) show that surface density of the mm grains beyond the planet orbit is enhanced and largely confined in a narrow ring. This may be the signature of dust pile-up due to the planet-induced gas pressure maximum beyond the orbit of the planet. Interestingly, the ALMA C$^{18}$O image presented in @Huang16 shows an extended emission peaking at nearly 130au. This extended emission is co-spatial to the outer dust ring. This is a strong indication that the large scale C$^{18}$O emission follows the actual disk surface density in the outer disk and it points to a gas density drop by a factor of a few inside the outer gap (‘$G2$’).

We have also investigated the existence of a second planet in correspondence of the inner dust gap. We conclude that there could be a second planet present in the inner gap if it is less than about $0.1\,M_\mathrm{J}$. Since the two gaps are close to the 2:1 resonance this raises the possibility that the structure could be caused by a pair of planets migrating in resonance. The 1mm surface density resulting from a pair of 0.05$M_{\rm J}$ - 0.2$M_{\rm J}$ is in remarkable agreement with the observations. Nonetheless, while both scenarios require low disk turbulence, the presence of the inner planet is not needed to explain the observed structures.

The inferred presence of the Saturn-like planet at $r \sim 95\,$au raises new questions about planet formation at such large distance from the star. Gravitational instability can occur on short timescales and is a viable process for the formation of giant planets on wide orbits [e.g, @Kratter16]. An alternative scenario is pebble accretion, in which planets grow through the accretion of cm-sized (or larger) grains that are weakly coupled to the gas [@Lambrechts12]. In this case however planet formation is challenged by dust migration: according to dust evolution models such large dust grains are expected to drift towards the star in much less than a Myr [e.g., @Takeuchi05; @Brauer08], which is difficult to reconcile with disk lifetimes (a few Myr, e.g., @Fedele10).

In the case of AS 209, the dust inward migration is likely to be slowed down by the presence of radial dust traps induced by the presence of a Saturn-like planet. While this can help to reconcile the presence of large dust with the disk’s lifetime, it must hinder pebble accretion in the inner disk, restricting this mode of planet formation to the earliest phases of disk evolution, on timescales $\lesssim 1\,$Myr.

This paper makes use of the following ALMA data: ADS$/$JAO.ALMA$\#$2015.1.00486.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), NSC and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI$/$NRAO and NAOJ. DF acknowledges support from the Italian Ministry of Education, Universities and Research, project SIR (RBSI14ZRHR). MT has been supported by the DISCSIM project, grant agreement 341137 funded by the European Research Council under ERC-2013-ADG.

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MCMC {#ap:mcmc}
====

![ Results of multi-components geometrical fit with MCMC: comparison of the observed (gray dots) and bestfit model (red line) deprojected visibilities.[]{data-label="fig:as209_mcmc"}](fig_as209_mcmc_visbin.jpg){width="9cm"}

![image](fig_as209_triangle.pdf){width="18cm"}
