ALMA OBSERVATIONS OF A GAP AND A RING IN THE PROTOPLANETARY DISK AROUND TW HYA

The observed dust continuum emission maps at 336 GHz are plotted for both the full data (Figure 1(a)) and high spatial frequencies only (>200 kλ, Figure 1(b)). The synthesized beam and rms noise were 037 × 031 (∼20 au, ${\rm{P.A.}}\;=\;55\buildrel{\circ}\over{.} 7$) and 0.23 mJy beam⁻¹. The total and peak flux density were 1.41 Jy and 0.15 Jy beam⁻¹, with signal-to-noise ratios (S/N) of 705 and 652, respectively. The results agree well with the previous SMA observations (Andrews et al. 2012) and ALMA observations (Hogerheijde et al. 2016) with lower spatial resolution and sensitivity. The synthesized beam and rms for the data at high spatial resolution data only were 032 × 026 (∼15 au, ${\rm{P.A.}}\;=\;54\buildrel{\circ}\over{.} 5$) and 0.49 mJy beam⁻¹.

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As shown by the black line in Figure 2(a), the dust continuum emission of the full data has a shallow dip in the radial profile of the surface brightness obtained by deprojecting the observed image data assuming an inclination angle of 7° and a position angle of $-30^\circ$ (Qi et al. 2008). By imaging the data at high spatial frequencies only ($\gt 200$ kλ), we identify a gap and a ring at around 25 and 41 au, respectively (Figure 1(b) and gray line in Figure 2(a)). The uv-coverage of the full data set (from 22 to 580 kλ) is sufficiently high and indeed vital for this analysis. The continuum visibility profile as a function of the deprojected baseline length is plotted in Figure 3. Our result is consistent with the recent ALMA observations with higher spatial resolution and sensitivity (Zhang et al. 2016). Since the high spatial frequency data miss the flux of spatially extended structure, the total flux is lower than that of the full data by an order of magnitude. Artificial structure appears at $R\gt 70$ au in the high spatial frequency data, probably due to a failure to subtract the side lobe pattern of the synthesized beam. Its intensity is less than the 2σ noise level and the structure is masked in Figure 2(a). The location of the gap is similar to that of the axisymmetric depression in polarized intensity of near-infrared scattered light imaging of dust grains recently found by Subaru/HiCIAO and Gemini/GPI (Akiyama et al. 2015; Rapson et al. 2015).

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We extract the radial dust surface density distribution (Figure 2(b)), using the deprojected data of the dust continuum emission and the equation,

$$\begin{eqnarray}&&{I}_{d,\nu }={B}_{\nu }({T}_{d})[1-\mathrm{exp}(-{\tau }_{d,\nu })],\end{eqnarray} \tag{ 1 }$$

where ${I}_{d,\nu }$ is the observed intensity of the dust continuum emission at the frequency ν, and ${B}_{\nu }({T}_{d})$ is the Planck function at the dust temperature, T_d. The optical depth, ${\tau }_{d,\nu }$, is defined as ${\tau }_{d,\nu }={\kappa }_{\nu }{{\rm{\Sigma }}}_{{\rm{dust}}}$, where ${{\rm{\Sigma }}}_{{\rm{dust}}}$ is the dust surface density and the dust opacity, ${\kappa }_{\nu }$, is set as ${\kappa }_{\nu }=3.4$ cm² g⁻¹. We adopt ${T}_{d}=22\;{\rm{K}}{(R/\text{10 au})}^{-0.3}$, where R is the disk radius, by fitting the model result in Andrews et al. (2012) and assume a uniform temperature distribution in the vertical direction. The derived dust optical depth is shown in Figure 2(c). We note that the derived dust surface density distribution is consistent with that derived from SMA observations of dust continuum emission and model calculations (Andrews et al. 2012). Also, the assumed dust temperature is consistent with the color temperature obtained from the spectral index of continuum emission across the observed four basebands between 329 and 343 GHz (Figure 2(d)) in the optically thick regions ($\leqslant 30$ au, Figure 2(c)).

To estimate the gap width, ${{\rm{\Delta }}}_{{\rm{gap}}}$, and depth, $({{\rm{\Sigma }}}_{0}-{\rm{\Sigma }})/{{\rm{\Sigma }}}_{0}$, where ${{\rm{\Sigma }}}_{0}$ and Σ are the basic surface density and the surface density with the gap at the gap center, the intensity at the gap, ${I}_{{\rm{gap}}}$ (red crosses in Figure 2(a)), is derived by completing the missing flux of the high spatial frequency data, ${I}_{{\rm{gap}}}^{{\rm{high}}}$ (gray line in Figure 2(a)), with the full spatial frequency data, ${I}^{{\rm{full}}}$ (black line in Figure 2(a)). The intensity profile across the gap was obtained as follows: (i) fit the high-frequency data without the gap using a power-law profile of ${I}_{0}^{{\rm{high}}}=1.1\ \times {10}^{3}{R}_{{\rm{au}}}^{-1.5}$ mJy beam⁻¹, (ii) fit the gap region in the high-frequency data using a single Gaussian profile of ${\rm{\Delta }}{I}_{{\rm{gap}}}\ ={I}_{0}^{{\rm{high}}}-{I}_{{\rm{gap}}}^{{\rm{high}}}\;$ $=\;7.7\mathrm{exp}(-{({R}_{{\rm{au}}}-24.7{\rm{au}})}^{2}/$ $\{2{(5.9{\rm{au}})}^{2}\})$ mJy beam⁻¹ (whose FWHM is 13.9 ± 1.0 au and depth is 7.7 ± 0.5 mJy) (green line in Figure 2(a)), and (iii) obtain the intensity at the gap as ${I}_{{\rm{gap}}}={I}^{{\rm{full}}}-{\rm{\Delta }}{I}_{{\rm{gap}}}$, where ${I}^{{\rm{full}}}$ is the intensity of the full data. In this fitting, we adopted the edges of the gap at R = 9–13 au (inner edge) and 39–43 au (outer edge) so that ${\rm{\Delta }}{I}_{{\rm{gap}}}$ is overlaid to ${I}^{{\rm{full}}}$ smoothly. The optical depth at the gap is derived using ${I}_{{\rm{gap}}}$ and Equation (1), and then the dust surface density at the gap is derived using the same method mentioned above (red crosses in Figure 2(b)). The resulting gap width is ${{\rm{\Delta }}}_{{\rm{gap}}}\sim 15$ au and the depth is $({{\rm{\Sigma }}}_{0}-{\rm{\Sigma }})/{{\rm{\Sigma }}}_{0}\sim 0.23$. We note that our estimate of the gap width is limited by the angular resolution of the high spatial frequency data. The pattern of the gap and ring is also affected by residual artifacts due to the cutoff at 200 kλ, which introduces uncertainties in the location of the gap center, and the width and depth of the gap.

The observed ¹³CO and C¹⁸O $J=3-2$ rotational line emission maps are plotted in Figures 1(c) and (d). The resulting synthesized beam and the 1σ rms noise level in the 0.03 km s⁻¹ width-channels were 041 × 033 (P.A. = 534), 12.0 mJy beam⁻¹ (¹³CO), and 041 × 033 (P.A. = 538), 13.4 mJy beam⁻¹ (C¹⁸O). The integrated intensity maps were created by integrating from 1.18 to 4.30 km s⁻¹ (¹³CO) and from 1.48 to 4.15 km s⁻¹ (C¹⁸O). The resulting noise levels of the map were 8.4 mJy beam⁻¹ km s⁻¹ (¹³CO) and 6.5 mJy beam⁻¹ km s⁻¹ (C¹⁸O). The deprojected radial profiles of the integrated line emission of the ¹³CO and C¹⁸O following the subtraction of the dust continuum emission are plotted in Figure 4(a). The S/N is not sufficiently high enough to analyze the high spatial resolution data.

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We obtain the CO radial column density distribution, using the deprojected data of the ¹³CO and C¹⁸O line observations (Figure 4(d)). The CO column density, ${N}_{{\rm{CO}}}$, is derived from the integrated line emission of  C¹⁸O $J=3-2$ (Rybicki & Lightman 1979; Turner 1991), assuming abundance ratios of CO:¹³CO = 67:1 and ¹³CO:C¹⁸O = 7:1 (Qi et al. 2011). The optical depth of the C¹⁸O line emission, ${\tau }_{{{\rm{C}}}^{18}{\rm{O}},v}$ (Figure 4(c)), is obtained from the observed line intensity as follows. We assume that the CO line-emitting region is mainly in the surface layer, while the dust continuum-emitting region is near the midplane. Thus, the deprojected intensity of the CO line emission plus dust continuum emission can be approximately derived from the following equation by simply assuming three zones in the vertical direction of the disk,

$$\begin{eqnarray}{I}_{{{\rm{C}}}^{18}{\rm{O}}+{\rm{cont}},v} & = & {B}_{\nu }({T}_{g})(1-{e}^{-{\tau }_{{{\rm{C}}}^{18}{\rm{O}},v}/2})\\ & & +{B}_{\nu }({T}_{d})(1-{e}^{-{\tau }_{d,\nu }}){e}^{-{\tau }_{{{\rm{C}}}^{18}{\rm{O}},v}/2}\\ & & +{B}_{\nu }({T}_{g})(1-{e}^{-{\tau }_{{{\rm{C}}}^{18}{\rm{O}},v}/2}){e}^{-{\tau }_{d,\nu }-{\tau }_{{{\rm{C}}}^{18}{\rm{O}},v}/2},\end{eqnarray} \tag{ 2 }$$

where T_g is the gas temperature of the CO line-emitting region and T_d is the dust temperature near the midplane. The continuum-subtracted data, ${I}_{{{\rm{C}}}^{18}{\rm{O}}+{\rm{cont}},v}-{I}_{d,\nu }$, together with Equation (1) are used for the analysis. Since the observed line ratio of $\int {I}_{{{\rm{C}}}^{18}{\rm{O}},v}{dv}/\int {I}_{{}^{13}\mathrm{CO},v}{dv}$ is larger than 1/7 (Figure 4(b)), the ¹³CO line is optically thick. Therefore, we adopt the brightness temperature at the peak of the ¹³CO line (Figure 5) as the gas temperature, T_g. Also, we adopt a dust temperature of ${T}_{d}=22\;{\rm{K}}{(R/\text{10 au})}^{-0.3}$ and the dust optical depth, ${\tau }_{d,\nu }$, is derived from the dust continuum observations (Figure 2(c)). We note that in the analysis we simply assume that the gas temperature is uniform in the vertical direction, and the gas temperature of the C¹⁸O line-emitting region is the same as that of the ¹³CO line-emitting region, although it could be lower in reality. In addition, C¹⁸O could be depleted due to the effect of isotopologue-dependent photodissociation, and ${N}_{{\rm{CO}}}/{N}_{{{\rm{C}}}^{18}{\rm{O}}}$ is possibly higher than 440 (Miotello et al. 2014). The CO column density will be underestimated due to these effects.

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Using the obtained CO column density and dust surface density (Figures 4(d) and 2(b)), we derive the CO gas-to-dust surface density ratio (Figure 4(e)). If we convert it to the H₂ surface density, assuming an abundance ratio of CO to H₂ of $6\times {10}^{-5}$ (Qi et al. 2011), the estimated H₂ gas mass is orders of magnitude lower than that predicted from the observations of the HD line emission by the Herschel Space Observatory (Bergin et al. 2013). The resulting H₂ gas-to-dust surface density ratio (∼0.1–1) is about two orders of magnitude lower than the typical interstellar value of ∼100, which suggests strong CO depletion throughout the disk down to ∼10 au.

The CO gas-to-dust surface density ratio increases beyond a radius of ∼40 au since the dust surface density drops dramatically in this region. It could be due to the drift of pebbles from the outer disk toward the central star (e.g., Takeuchi et al. 2005; Andrews et al. 2012; Walsh et al. 2014b).

The gap and ring resemble those in the HL Tau system, recently found by the ALMA long baseline campaign (ALMA Partnership et al. 2015). Our result shows that gaps and rings in the (sub)millimeter dust continuum can exist, not only in relatively young disks (0.1–1 Myr) but also in relatively old disks (3–10 Myr). One possible mechanism for opening a gap is the gravitational interaction between a planet and the gas (e.g., Lin & Papaloizou 1979; Goldreich & Tremaine 1980; Fung et al. 2014). Such an interaction may also produce the spiral density waves recently found in optical and near-infrared scattered light imaging of dust grains in protoplanetary disks (e.g., Muto et al. 2012). According to recent theoretical analyses of gap structure around a planet (Kanagawa et al. 2015a, 2015b, 2016), the depth and width of the gap are controlled by the planetary mass, the turbulent viscosity, and the gas temperature. The shape of the gap is strongly influenced by angular momentum transfer via turbulent viscosity and/or instability caused by a steep pressure gradient at the edges of a gap. The observed gap has an apparent width and depth of ${{\rm{\Delta }}}_{{\rm{gap}}}\sim 15$ au and $({{\rm{\Sigma }}}_{0}-{\rm{\Sigma }})/{{\rm{\Sigma }}}_{0}\sim 0.23$, respectively. This is too shallow and too wide compared with that predicted by theory. However, the observations are limited to an angular resolution of ∼15 au, and the depth and width could be deeper and narrower in reality. For instance, if we assume that the gap depth times the gap width retains the value derived from the observations, it is possible for the gap to have a width and depth of ${{\rm{\Delta }}}_{{\rm{gap}}}\;\sim$ 6 au and $({{\rm{\Sigma }}}_{0}-{\rm{\Sigma }})/{{\rm{\Sigma }}}_{0}\sim 0.58$, which is similar to the GPI result (Rapson et al. 2015). Such a gap could be opened by a super-Neptune-mass planet, depending on the parameters of the disk, such as the turbulent viscosity (Kanagawa et al. 2015a, 2015b, 2016). If the gap in the larger dust grains is deeper than that in the gas, the planet could be lighter than super-Neptune mass. We note that a planet of even a few Earth masses, although it cannot open a gap in the gas, can open a gap in the dust distribution if a certain amount of pebble-sized particles, whose motions are not perfectly coupled to that of gas, are scattered by the planet and/or the spiral density waves excited by the planet (Paardekooper & Mellema 2006; Muto & Inutsuka 2009).

Another possible mechanism to form a gap and an associated ring in dust continuum emission is the microscopic process of sintering CO ice on dust aggregates (Sirono 2011; Okuzumi et al. 2016). The gaps and rings observed in the younger and more luminous HL Tau system could be explained by the sintering of various molecular ices in the disk at their distinct snow line locations (Okuzumi et al. 2016). Although our observations indicate that the CO-depleted region is located down to ∼10 au in the TW Hya system, model calculations of the temperature in the disk suggest that the CO snow line is located at ∼30 au. Sintering is a process that renders an aggregate less sticky (Sirono 2011). Just outside the CO snow line where sintering occurs, large aggregates are easily destroyed, becoming small fragments through collisions, and their radial drift motion by the above-mentioned mechanism slows down. Thus, dust grains are stuck just outside the CO snow line, and a bright ring and a dark lane inside the ring is formed in the dust continuum emission. If another sintering region is formed inside the dark lane by, for example, CH₄ sintering, the region between the bright CO and CH₄ sintering regions would look like a gap. According to model calculations (Okuzumi et al. 2016), the CH₄ sintering region is located at ∼10 au in the TW Hya disk.

From the CO line observations, we find a very low column density of CO compared with dust throughout the disk, down to a radius of about 10 au. This CO depletion could indicate a general absence of H₂ gas compared with dust. However, the Herschel HD observations (Bergin et al. 2013) indicates that it is more likely that it is due to CO freeze-out on grains with the possibility that subsequent grain-surface reactions form larger molecules even inside the CO snow line (Favre et al. 2013; Williams & Best 2014). The CO column density derived from our observations, ${N}_{{\rm{CO}}}\sim {10}^{18}$ cm⁻², can be explained by detailed model calculations using a chemical network that includes freeze-out of molecules on grains and grain-surface reactions (Aikawa et al. 2015). The model calculations show that the CO depletion will proceed inside the CO snow line due to the sink effect: conversion of CO to less volatile species on grain surfaces. In the case of TW Hya, it could occur on a timescale shorter than the disk lifetime, depending on the amount of small grains. See Aikawa et al. (2015) for more detailed discussions, including the effect on other species. The CO depletion spread over the disk is inconsistent with the prediction by the previous ALMA N₂H⁺ observations that depletion would be localized beyond the CO snow line (Qi et al. 2013). This could be because the N₂H⁺ line emission traces the disk surface and not the CO-depleted region.

Figure 5 shows the brightness temperature at the peak of the ¹³CO $J=3-2$ line obtained by our observations and the N₂H⁺ $J=4-3$ line at 372.672 GHz obtained by the ALMA archived data (2011.0.00340.S). Since the ¹³CO line is optically thick, the brightness temperature at the peak of the line emission represents the gas temperature of the line-emitting region. If LTE is applicable, the N₂H⁺ brightness temperature is higher than the gas temperature of the ¹³CO line-emitting region at the disk radius of ∼40 au, and higher than the dust temperature near the midplane down to ∼15 au (Figure 5). If the N₂H⁺ line is optically thin, the gas temperature of the line-emitting region is higher than the brightness temperature. Therefore, the N₂H⁺ line should come from the surface layer of the disk. Model calculations also predict that N₂H⁺ exists in the disk surface for the model with (sub)micron-sized grains, similar to radical species abundant in the disk surface, such as CN and C₂H (e.g., Walsh et al. 2010; Aikawa et al. 2015). Our results (Figure 5) and the SMA observations of C₂H (Kastner et al. 2015) show that the radial intensity profiles of these species are similar. They have peaks around the disk radius of 40 au, beyond which the dust surface density drops. The result suggests that in order to trace the CO-depleted region, the C¹⁸O line may be more robust than the N₂H⁺ line.

In the CO-depleted region, complex organic molecules would be produced via grain-surface reactions because hydrogen attachment to CO is thought to produce methanol and more complex species (e.g., Watanabe & Kouchi 2008; Walsh et al. 2014a). Methyl cyanide, which has recently been detected from a protoplanetary disk for the first time by ALMA (Öberg et al. 2015), could be formed through such grain-surface reactions.