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Issue
A&A
Volume 610, February 2018
Article Number A24
Number of page(s) 9
Section Planets and planetary systems
DOI https://doi.org/10.1051/0004-6361/201731978
Published online 20 February 2018

© ESO, 2018

1 Introduction

Axisymmetric gaps and rings such as those seen in the protoplanetary disks around HL Tau, TW Hya, HD 163296, HD 169142, AA Tau (e.g., ALMA Partnership et al. 2015; Andrews et al. 2016; Isella et al. 2016; Fedele et al. 2017; Loomis et al. 2017) 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., Papaloizou & Lin 1984); magneto-rotational instability (Flock et al. 2015); condensation fronts (Zhang et al. 2015); dust sintering (Okuzumi et al. 2016); photoevaporation (Ercolano et al. 2017).

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 (Pinilla et al. 2012). 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., Birnstiel et al. 2012). 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.

This paper presents new ALMA 1.3 mm continuum observations of the T Tauri disk AS 209 where axisymmetric gaps and rings are detected. AS 209 (M⋆ = 0 .9 M⊙, spectral type K5, L⋆ = 1 .5 L⊙, Tazzari et al. 2016) is part of the young (age ~ 0.5–1.0 Myr; Natta et al. 2006) Ophiuchus star forming region at a distance of 126 pc from the Sun (Gaia Collaboration 2016). Multi-frequency continuum observations revealed optically thin emission at millimeter wavelengths beyond a few 10 s of au from the star (Pérez et al. 2012; Tazzari et al. 2016). Huang et al. (2016) found evidence of an extended gas emission (C18O) speculating that it is due to external CO desorption in the outer disk. Interestingly, Huang et al. (2017) noticed the presence of a dark lane in the dust 1.1 mm continuum emission.

The structure of the paper is the following: observations and data reduction are presented in Sect. 2 and the results are discussed in Sect. 3. The data analysis is described in Sect. 4. Section 5 provides a comparison to hydrodynamical simulations. Discussion and conclusion are reported in Sect. 6.

2 Observations and data reduction

The ALMAobservations of AS 209 (J2000: RA = 16h49m15.296s, Dec = –14∘ 22′09.02′′) have been performed on 2016 September 22 (with 38 antennas) and 26 (41 antennas) in band 6 (211–275 GHz) as part of the project ID 2015.1.00486.S (PI: D. Fedele). The correlator setup includes a broad (2 GHz bandwidth) spectral window centered at 230 GHz.

Visibilities were taken in two execution blocks with a 6.05 s integration time per visibility totalling 40 min, 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 2.3 mm, 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 60 s 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 CASA.CLEAN (CASA version 4.7); after trying different weighting schemes, we opted for a uniform weight which yields a synthesized beam of 0.′′ 19 × 0.′′ 14 (PA = 75.5∘ ). The peak flux is 13 mJy beam–1 and the rms is 0.1 mJy beam–1.

3 Results

The ALMA 1.3 mm dust continuum image is shown in Fig. 1: the continuum emission is characterized by a bright central emission and two weaker dust rings peaking at ~75 and 130 au, respectively. The two rings have a similar peak flux (~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 ~170–180 au. The different disk substructures are clearly visible in the radial intensity profile shown in Fig. 2.

We fitted of the observed visibilities with the aim to provide an initial characterization of the disk surface brightness useful for the detailed physical modelling carried out in Sect. 4. We assumed an axisymmetric brightness profile defined as follows: I(R)=δ(R)I0(RRc)ϕ1exp[-(RRc)ϕ2],\begin{equation}\label{eq:brightness} I(R)=\delta(R) \ I_0 \left( \frac{R}{R_{\rm c}} \right)^{\phi_1} \exp \left[ -\left( \frac{R}{R_{\rm c}} \right)^{\phi_2} \right]\!, \end{equation}(1) where I0 is a normalization, Rc is a scale length and δ(R) is a scaling factor (by definition δ(R) > 0) parametrized as: δ(R)={ δG1 forR∈[RG1-hwG1,RG1+hwG1], δR1 forR∈[RG1+hwG1,RG2-hwG2], δG2 forR∈[RG2-hwG2,RG2+hwG2], δR2 forR∈[RG2+hwG2,RR2, out], δout forR≥RR2, out, 1 otherwise, \begin{equation} h = h_{\rm c} \Bigg( \frac{R}{R_{\rm c}}\Bigg)^{\psi}, \end{equation}(2)where RG and hwG 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 (δ > 1) or a lack (δ < 1) of emission. Following the evidence emerging from the synthesized image (Fig. 1), we allowed for two rings, two gaps, and an outer disk region, following nomenclature in Fig. 1. In this framework, a gap in the disk is naturally modelled with δ < 1.

We performed the fit of the visibilities with a Bayesian approach using the Monte Carlo Markov chains (MCMCs) ensemble sampler (Goodman & Weare 2010) implemented in the emcee package (Foreman-Mackey et al. 2013). We assumed flat priors for all the free parameters. Table 1 reports the ranges explored for each parameter.

We also fitted simultaneously for the disk inclination i, the east-of-north position angle PA, and phase center offset (Δ α, Δ δ). For each setof values of the free parameters we compute a synthetic image of the model assuming axisymmetry and we use the galario library (Tazzari et al. 2017) to compute the synthetic visibilities (by sampling the Fourier transform of the model image in all the observed (u, v)-points) and the resulting χ2 as χ2=∑j=0N|Vobs(uj,vj)-Vmod(uj,vj)|2wj,\begin{equation}\label{eq:chi} \chi^{2} = \sum_{j=0}^{N}|V_{\mathrm{obs}}(u_{j}, v_{j})-V_{\mathrm{mod}}(u_{j}, v_{j})|^{2} w_{j}, \end{equation}(3) where wj is the weight of the observed (uj, vj) visibility point. The posterior of each model is then computed as exp –13; χ2 ∕ 2) and sampled with 80 chains for 45 000 steps (after 5000 burn-in steps). The chains, which reached a good convergence, are shown in Fig. A.2, in the form of marginalized 1D and 2D distributions. The parameters that we infer from the fit of the visibilities are presented in Table 1: 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 (δG1 ~ 0.03, δG2 ~ 0.025) at 62 and 103 au, respectively, and an excess ring (δR2 ~ 4) at ~130 au. The excellent agreement of this profile with the observations is apparent in Fig. A.1, where the deprojected synthetic visibilities match the observed ones up to 1500 kλ.

thumbnail Fig. 1

ALMA 1.3 mm dust continuum image (uniform weighting). The main substructures are highlighted in the right panel.
thumbnail Fig. 2

Radial intensity profile of the 1.3 mm dust continuum emission. The profile is azimuthally averaged after deprojecting for the disk inclination (i = 36∘, Sect. 3). The black line shows the mean profile while the shadowed regions indicate the standard deviation along the azimuth angle.
Table 1

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

4 Analysis with a physical disk model

In this section we aim to characterize the structure of AS 209 in physical terms, starting from the observed 1.3 mm 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 DALI (Dust And LInes, Bruderer et al. 2012; Bruderer 2013). Starting from an input radiation field and from a disk density structure, DALI solves the two dimensional dust continuum radiative transfer and determines the dust temperatureand radiation field strength at each disk position.

4.1 Model description

We adopted the characterization of the surface brightness presentedinthe previous section as a first guess for the functionalform 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 Σdust(R)=δ̃(R)Σc (RRc )γ1exp [- (RRc )γ2 ],\begin{equation}\label{eq:dali_sd} \mathrm{\Sigma}_{\rm dust}(R) = \tilde{\delta} (R) \ \mathrm{\Sigma}_{\rm c} \ \Bigg(\frac{R}{R_{\rm c}}\Bigg)^{\gamma_1} \ \exp\Bigg[ - \Bigg( \frac{R}{R_{\rm c}} \Bigg)^{\gamma_2} \Bigg], \end{equation}(4) where the surface density scaling factor (δ̃) is parametrized as in Eq. (2).

In the vertical direction, the density follows a Gaussian distribution with scale height h ( = H∕R) h=hc (RRc )ψ,\begin{equation} h = h_{\rm c} \Bigg( \frac{R}{R_{\rm c}}\Bigg)^{\psi}, \end{equation}(5) with hc the critical scale height and ψ the flaring exponent. The critical scale height (hc = 0.13) and disk flaring (ψ = 0.1) are taken from Andrews et al. (2011). In the adopted version of DALI, dust settling is included following D’Alessio et al. (2006), that is, 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 χh (with χ < 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 flarge (large-to-small mass ratio): thus, the dust surface density is Σdust ⋅ (1 − flarge) and Σdust⋅ flarge for the small and large grains, respectively. The flaring parameters are fixed : χ = 0.2, flarge = 0.85.

We fixed the grain size populations with a small population of sizes between 0.005 and 1 μm and a large one of sizes between 0.005 μm and smax with both populations sharing the same power-law exponent (p = 3.5). The dust mass absorption coefficients are taken from Andrews et al. (2011).

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 smax = 0.8 mm to 1.0 cm (e.g., Tazzari et al. 2016). This in turn has an impact the dust temperature and the total dust mass. In this paper we fix smax = 2000 μm in agreement with the multi-frequency continuum analysis of AS 209 by Tazzari et al. (2016).

4.2 Fiducial model

We built a grid of DALI disk models varying the following parameters: the total dust mass, the surface density power-law exponent (γ1 ), the exponential tail exponent (γ2) and the dust density scaling factors. The explored range of each variable parameter is listed in Table 2. The values of Rc , gaps centers (RG1, RG2) and gaps sizes (half width hwG1, hwG2) are taken from the best-fist results of the multi-components analysis.

Each model was compared with the ALMA continuum observation with the aim of defining a fiducial model for the dust surface density. The comparison was performed in the uv-plane: first we computed the synthetic 1.3 mm continuum image with DALI, then the tool CASA.SIMOBSERVE is used to convert the image into synthetic visibilities at the same uv-positions as the observations. Finally we measured the χ2 between observation and model after deprojecting and binning the visibilities (bin size of 30 kλ).

The fitting procedure was performed in multiple steps: first we varied the global disk properties, i.e. Mdust, γ1, γ2 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: δ̃G1 = 0, δ̃G2 = 0, δ̃R1 = 1, δ̃R2 = 1, δ̃out = 1. In a second step, we constrained the values of the scaling factors while keeping fixed Mdust, γ1, γ2. The process was 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 χ2 between the observed and synthetic visibilities (Eq. (3)) within the explored parameter space.

The parameters of the DALI fiducial model are listed in Table 2. Figure 3 shows the dust surface density of the fiducial model and the model image is shown in Fig. 4. 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: δ̃G1 = 0.1 and δ̃G2 = 0.01.

Table 2

DALI fiducial disk model.

thumbnail Fig. 3

Dust surface density of the DALI fiducial model. The dashed line corresponds to the initial unperturbed profile (power-law with exponential tail).
thumbnail Fig. 4

DALI fiducial model, comparison of 1.3 mm continuum image. The model image is produced with CASA.CLEAN starting from the synthetic visibilities and adopting the same clean parameters as the observations.

5 Comparison to hydrodynamical simulations

In this section we investigate the possibility that the gaps were produced byplanets, as has been suggested for other disks, for example HL Tau, TW Hydra, HD 163296, and HD 169142 (ALMA Partnership et al. 2015; Andrews et al. 2016; Isella et al. 2016; Fedele et al. 2017). To do this, we have run 2D simulations of planet-disk interaction using a version of FARGO-3D (Benítez-Llambay & Masset 2016) modified to include dustdynamics (Rosotti et al. 2016). The disk parameters were chosen to match the best fit model (see Table 3). The simulations were run using a logarithmic radial grid, extending from 10 to 300 au at a resolution of Nr × Nϕ = 550 × 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 forconstraining the planets properties are the gap width, depth and location. The position of the two gap centers (62 and 103 au) 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.

Startingfrom the relationship between the width of a gap opened by a planet and its mass derived by Rosotti et al. (2016), we already see that the inner planet must be low mass due because the inner gap is narrow (just 16 au or approximately two to threepressure scale-heights). This suggests that the mass of the inner planet is in the Neptune mass regime (~15M⊕, i.e. 0.05 MJ). However, while Rosotti et al. (2016) 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 sensitive to disk viscosity, with planetsopening deeper gaps in low viscosity disks (Crida et al. 2006; Zhu et al. 2013). Thus together with the gap width, the gap depth places constraints on both the planet mass and disk viscosity. Furthermore, at extremely low viscosity, Dong et al. (2017) and Bae et al. (2017) 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. 5, we see that even a modest viscosity α = 10−4 is too high to produce deep enough gaps to explain the structures in AS 209. While a single 0.2 MJ planet at 95 au 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 α = 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 MJ planet, but requires even lower viscosity. The planet was injected at t = 0 and the simulation was stopped after 0.65 Myr.

The inviscid (α = 0) simulations produce a much better match to the inferred gap structure (Fig. 5, left panel). Already a single 0.2 MJ 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 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 Rosotti et al. 2016). However, the width of the gaps are similar in both the viscous and inviscid cases. Interestingly, the simulations produce an additional gap at around 35 au, which coincides with similar, but much smaller amplitude, feature in the radial intensity profile (Fig. 2). 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 100 au.

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 MJ 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 MJ, 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 α = 10−4, this is hard to reconcile with the need for a lower α in the outer gap.

Table 3

Disk model used in the planet disk-interaction simulations.

thumbnail Fig. 5

Results of hydrodynamical simulations for the inviscid (left) and α = 10−4 (right) case. The black line corresponds to the dust surface density determined with DALI (Sect. 4). The (red) dot-dashed line is the 1 mm grains surface density based on the single planet scenario with 0.2 MJ planet at 95 au after 0.65 Myr (Sect. 5). The (blue) dot-dot-dashed and the (green) dashed curves corresponds to the two planets scenario with an inner planet of mass 0.05 and 0.1 MJ , respectively.

6 Conclusions

The ringed dust structure of AS 209 revealed by ALMA is consistent with the presence of a Saturn-like (Mplanet = 0.2 MJ = 0.67 MSaturn) planet at r = 95 au. The planetary mass is constrained by the width and depth of thedust gap: for the chosen gas properties, our hydrodynamical simulations indicate that less massive planets (≲0.5 MSaturn) do not produce a gap that is sufficiently wide, while more massive planets (≲1.0 MSaturn) prevent the transport of dust inwards entirely, forming a transition disk (inner hole in large grains). Our radiative transfer calculations (Sect. 4) 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 C18O image presented in Huang et al. (2016) shows an extended emission peaking at nearly 130 au. This extended emission is co-spatial to the outer dust ring. This is a strong indication that the large scale C18 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 MJ. 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 1 mm surface density resulting from a pair of 0.05 MJ–0.2 MJ 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 ~ 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., Kratter & Lodato 2016). 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 (Lambrechts & Johansen 2012). 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., Takeuchi et al. 2005; Brauer et al. 2008), which is difficult to reconcile with disk lifetimes (a few Myr, e.g., Fedele et al. 2010).

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 ≲1 Myr.

Acknowledgments

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. D.F. acknowledges support from the Italian Ministry of Education, Universities and Research, project SIR (RBSI14ZRHR). M.T. has been supported by the DISCSIM project, grant agreement 341137 funded by the European Research Council under ERC-2013-ADG.

Appendix A Monte Carlo Markov chain

thumbnail Fig. A.1

Results of multi-components geometrical fit with MCMC: comparison of the observed (gray dots) and bestfit model (red line) deprojected visibilities.
thumbnail Fig. A.2

1D and 2D marginalized distributions of the posterior sampling obtained from MCMC. In the 1D marginalized distributions of each parameter the vertical dashed lines represent the 16th, 50th and 84th percentiles: the median is taken as the bestfit value, and half the interval between 16th and 84th percentiles as the uncertainty.

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All Tables

Table 1

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

In the text
Table 2

DALI fiducial disk model.

In the text
Table 3

Disk model used in the planet disk-interaction simulations.

In the text

All Figures

thumbnail Fig. 1

ALMA 1.3 mm dust continuum image (uniform weighting). The main substructures are highlighted in the right panel.
In the text
thumbnail Fig. 2

Radial intensity profile of the 1.3 mm dust continuum emission. The profile is azimuthally averaged after deprojecting for the disk inclination (i = 36∘, Sect. 3). The black line shows the mean profile while the shadowed regions indicate the standard deviation along the azimuth angle.
In the text
thumbnail Fig. 3

Dust surface density of the DALI fiducial model. The dashed line corresponds to the initial unperturbed profile (power-law with exponential tail).
In the text
thumbnail Fig. 4

DALI fiducial model, comparison of 1.3 mm continuum image. The model image is produced with CASA.CLEAN starting from the synthetic visibilities and adopting the same clean parameters as the observations.

In the text
thumbnail Fig. 5

Results of hydrodynamical simulations for the inviscid (left) and α = 10−4 (right) case. The black line corresponds to the dust surface density determined with DALI (Sect. 4). The (red) dot-dashed line is the 1 mm grains surface density based on the single planet scenario with 0.2 MJ planet at 95 au after 0.65 Myr (Sect. 5). The (blue) dot-dot-dashed and the (green) dashed curves corresponds to the two planets scenario with an inner planet of mass 0.05 and 0.1 MJ , respectively.
In the text
thumbnail Fig. A.1

Results of multi-components geometrical fit with MCMC: comparison of the observed (gray dots) and bestfit model (red line) deprojected visibilities.
In the text
thumbnail Fig. A.2

1D and 2D marginalized distributions of the posterior sampling obtained from MCMC. In the 1D marginalized distributions of each parameter the vertical dashed lines represent the 16th, 50th and 84th percentiles: the median is taken as the bestfit value, and half the interval between 16th and 84th percentiles as the uncertainty.
In the text

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