A Spatially Resolved AU-scale Inner Disk around DM Tau

We present Atacama Large Millimeter/submillimeter Array (ALMA) observations of the dust continuum emission at 1.3 mm and 12CO J=2-1 line emission of the transitional disk around DM Tau. DM Tau's disk is thought to possess a dust-free inner cavity inside a few au, from the absence of near-infrared excess on its spectral energy distribution (SED). Previous submillimeter observations were, however, unable to detect the cavity; instead, a dust ring ~20 au in radius was seen. The excellent angular resolution achieved in the new ALMA observations, 43 x 31 mas, allows discovery of a 4 au radius inner dust ring, confirming previous SED modeling results. This inner ring is symmetric in continuum emission, but asymmetric in 12CO emission. The known (outer) dust ring at ~20 au is recovered and shows azimuthal asymmetry with a strong-weak side contrast of ~1.3. The gap between these two rings is depleted by a factor of ~40 in dust emission relative to the outer ring. An extended outer dust disk is revealed, separated from the outer ring by another gap. The location of the inner ring is comparable to that of the main asteroid belt in the solar system. As a disk with a"proto-asteroid belt,"the DM Tau system offers valuable clues to disk evolution and planet formation in the terrestrial planet forming region.


INTRODUCTION
An outstanding problem in planetesimal formation from aggregating dust in protoplanetary disks is radial drift of dust (Weidenschilling. 1977;Nakagawa et al. 1986): particles embedded in a gaseous disk with surface density decreasing outwards feel a headwind, lose angular momentum to the gas, and drift towards the central star. One solution to this problem is a dust trap (Rice et al. 2006;Johansen et al. 2009), in which mm-sized particles are trapped and accumulate at a local gas pressure maximum. To facilitate the formation of planetesimals in protoplanetary disks on the scale of the inner solar system, dust traps at a few au from the star are needed. Such structures can be searched for by high angular resolution observations of mm continuum emission.
Many mechanisms have been proposed for producing pressure bumps in disks, such as the edges of gaps opened by planets (Zhu et al. 2012;Dong et al. 2015; note that one planet may produce multiple pressure bumps, Dong et al. 2017a). Magnetohydrodynamic (MHD) effects can also form pressure bumps in disks, generated by zonal flows (e.g., Johansen et al. 2009) or at the boundary of dead zones (e.g., Dzyurkevich et al. 2010). Pressure bumps may form at the locations of snowlines too, due to a change in the activity of the magnetorotational instability (e.g., Kretke & Lin 2007). Dust trapped at radial pressure bumps appears to be annular rings in millimeter continuum observations. Such structures have been found in many objects, such as HL Tau (ALMA Partnership et al. 2015), TW Hya (Andrews et al. 2016;Tsukagoshi et al. 2016), HD 163296 (Isella et al. 2016), and MWC 758 (Dong et al. 2018).
Our target, DM Tau (SpT: M1; Kenyon & Hartmann 1995, T eff : 3705 K; Andrews et al. 2011, M * : 0.53 M ⊙ ; Piétu et al. 2007, distance: 145 pc;Gaia Collaboration et al. 2018), has a known transitional disk (Espaillat et al. 2014). A central dust cavity ∼3 au in radius has been inferred based on its spectral energy distribution (SED) (Bergin et al. 2004;Calvet et al. 2005, shown in Appendix). Previous SMA sub-millimeter continuum observations were not able to resolve the 3 au cavity due to insufficient angular resolution; instead, a dust ring at 19 au was discovered (Andrews et al. 2011). Modeling of previous low resolution ALMA continuum observations (project ID:2013.1.00198.S; resolution ∼0. ′′ 4) suggested the presence of another faint dust ring at ∼80 au (Zhang et al. 2016). DM Tau has also been extensively studied in gas emission observations. Bergin et al. (2016a) resolved a C 2 H emission ring at the edge of the dust continuum disk, and many other molecular species, such as H 2 CO and CS, have been detected (Loomis et al. 2015;Semenov et al. 2018).

OBSERVATIONS
DM Tau was observed with ALMA in band 6 in the C43-9 configuration on October 27, 2017, UT as part of the project 2017.1.01460.S, utilizing 47 antennas with the baseline length extending from 135.1 m to 14.9 km. The observations were conducted in five spectral windows: two with bandwidths 117.188 MHz, velocity resolutions ∼0.166 km s −1 , and centered at 220.39868 GHz for 13 CO (2 → 1) and 219.56035 GHz for C 18 O (2 → 1); one with bandwidth 117.118 MHz, velocity resolution ∼0.079 km s −1 , and centered at 230.53800 GHz for 12 CO (2 → 1); and the last two windows for continuum observations with bandwidth 2.0 GHz. The precipitable water vapor was ∼0.5 mm during observations. The total on-source integration time was 66.1 min. The data were calibrated by the Common Astronomy Software Applications (CASA) package (McMullin et al. 2007) version 5.1.1, following the calibration scripts provided by ALMA. We had experimented with self-calibrating the new, high angular resolution ALMA data. However, in these observations, only 16 antennas were located at 2 km baselines. With the 66.1 min on-source integration of our observations, our uv sampling at long baselines is insufficiently redundant. In addition, the continuum flux of our target source is dominated by structures with relatively extended (∼0.2 ′′ ) angular scales. As a result, the gain phase self-calibration flagged out over 50% of the 2 km baseline data even when using a perscan solution interval and combining all spectral windows. This is unfavorable for our major science case of resolving the innermost region of DM Tau. On the other hand, the phase RMS of the <2 km baseline data is low, and the gain phase self-calibration does not help much. Therefore, we decided not performing self-calibration. We utilized the observations of the check (quasar) source J0449+1121 to assess how much our target source can be attenuated due to phase decoherence. The continuum fluxes of J0449+1121 with and without phase self-calibration are 293 and 255 mJy, respectively. This corresponds to a 13% attenuation, which is much smaller than the uncertainty of the dust mass opacity and the dust opacity depth in general.
We combined our data with another ALMA dataset (project ID: 2013.1.00498.S; Pinilla et al. 2018) to recover the missing flux (∼70 mJy out of a total of ∼110 mJy; Beckwith et al. 1990) due to the sparseness of short baseline data. The phase centers of long and short baseline data were determined separately by ellipse isophoto fitting at 10 σ RMS noise in the dust continuum images synthesized by CASA with the CLEAN task using a multi-scale multi-frequency deconvolution algorithm (Rau & Cornwell 2011), and were shifted by fixvis in the CASA tools. We compared the amplitudes as a function of uv-distance at less than 200 kλ between our long baseline data and archival short baseline data, and confirmed their consistency. The CLEANed dust continuum image was synthesized with a Briggs weighting of 2.0 to maximize the signal-to-noise (S/N) ratio, providing RMS noise levels of 11 µJy beam −1 . The total flux density after combining long and short baseline data is 116.75 ± 0.14 mJy, consistent with previous single dish observations assuming a 10 % uncertainty in absolute flux calibration.
The 12 CO (2 → 1) line data in both long and short baseline data were extracted by subtracting the continuum in the visibility space with uvcontsub in the CASA tools. The combined line cube was generated by the CLEAN algorithm with a velocity resolution of 0.5 km/s, and was spatially smoothed with a circular Gaussian kernel of 75 mas by imsmooth in CASA for presentation purposes. Though the 13 CO and C 18 O (2 → 1) line data were processed with the same procedure as 12 CO, they were not detected significantly.
3. RESULTS Figure 1 shows the 1.3 mm dust continuum image of DM Tau after the CLEANed process. We clearly resolve the dust disk into three components: an inner dust ring, an outer dust ring, and an extended outer disk (Figures 1a to c). The peak flux density at the inner and the outer rings is detected with 24 and 59 σ, respectively. An extended structure beyond r =0. ′′ 4 is also marginally detected with ∼5 σ. To derive the azimuthally averaged radial brightness profile (Figure 1d), we deprojected the dust continuum image in the visibility domain following Zhang et al. (2016). The inclination and the position angle of the disk were derived by fitting an ellipse to the outer ring. The fitting results and derived disk's geometric parameters are shown in Table 1.
An inner dust ring at r ∼ 0. ′′ 03 is discovered in our dust continuum images. The ring is spatially resolved into a north and a south blobs ( Figure 1c); the north blob is 20 ± 8 % (2.5 σ) brighter than the south one. More data are needed to confirm the apparent asymmetry. The total flux density of the inner ring inside 0. ′′ 06 is 1.33 ± 0.03 mJy. The contamination from possible free-free emission is less than 8% (3σ level), determined by extrapolating the flux density measured at 3.4 cm (Zapata et al. 2017) to 1.3 mm assuming a spectral index of +0.6. Assuming a distance of 145 pc, a dust opacity per gas mass κ ν =2.3 cm 2 g −1 at 230 GHz , a temperature of 100 K, and a gas-to-dust mass ratio of 100, the total mass of the inner disk is measured as 0.04 M Jup . Our observations also clearly spatially resolved the outer dust ring and the gap between the two rings at 0. ′′ 18 and r ∼0. ′′ 1, respectively (Figures 1b and 1c). The dust continuum emission is detected with 5 σ in the gap region, suggesting that the gap is not dust free. The outer ring is asymmetric: the brightness contrast between the peak flux density at P.A.=∼270 • and that at the opposite position is 1.28 ± 0.04. The inner edge of the outer ring is steeper (I(r) ∝ r 3.9±0.3 ) than the outer edge (I(r) ∝ r −2.8±0.1 ). Because the outer ring is spatially resolved with a radial width of ∼0. ′′ 1 (15 au), the gradient difference is real. The extended structure beyond the outer ring has a nearly flat radial brightness profile (Figure 1d). A possible shallow gap at r ∼0. ′′ 5 can be seen in this structure as well.
Figures 2(a) and (b) show the integrated intensity (0th moment) map for 12 CO obtained from 1.6 to 11.1 km s −1 with 1σ = 3.5 mJy beam −1 km s −1 . The peak emission is 56.5 mJy beam −1 km s −1 , located at the north blob around the inner dust ring. The total integrated intensity is 185 ± 7 Jy km s −1 inside 0. ′′ 18. The intensity-weighted velocity (1st moment) map is shown in Figures 2(c) and (d). The center of the CO gas motion nearly coincides with the center of the outer dust ring derived from the ellipse fitting, and might be closer to the north than to the south blob. To check whether the center of the outer ring is consistent with the rotational center of the CO gas, we plot loci of the peak emission of a Keplerian disk around a 0.53 M ⊙ star (DM Tau's mass) in the position-velocity diagram (Figure 2e), finding that the outer ring's center is the center of the gas rotation.

MODEL FITTING
To test whether the observed asymmetry in the outer dust ring is significant, we performed fitting for dust continuum emission in the visibility domain using a simple analytic disk model, and then subtracted the modeled disk from the data. Our disk model has a simple power-law radial profile with an exponential taper at the outside (e.g., Lynden-Bell & Pringle 1974;Hartmann et al. 1998): where α i and r c i are a scaling factor and a characteristic scaling radius, respectively. The two global components (i) in the profile are: component 1 for the inner and outer dust rings, and component 2 for the extended outer disk (Figure 3a). The q parameter is introduced to specify the radial dependence of the dust temperature T d , that is T d ∝ r −q . Optically thin emission in the Rayleigh-Jeans regime scales as where B ν and τ are the blackbody intensity at frequency ν and the optical depth (τ = κΣ; where κ and Σ denote the opacity and the surface density, respectively). In the radial direction, we have the following components with their scaling factors: δ 1 for r cav < r < r gap 1 1 for r gap 1 < r < r gap 2 0 for r gap 2 < r, Figure 3. (a): Generic surface brightness model. The red and blue solid lines represent the surface brightness profiles of component 1 (the inner and outer rings at r cav < r < r gap 1 and r gap 1 < r < r gap 2 , respectively) and component 2 (the extended outer disk at r gap 2 < r) scaled down by the scaling factor α i , respectively. At r < r cav , no dust emission is assumed due to absence of NIR excess in the DM Tau's SED.
We normalize the total flux in the model (F total ) to the observed value. The disk inclination (i) and position angle (P.A.) are fixed as in Table 1. There are 11 free parameters in the model (r cav , r gap 1 , r gap 2 , δ 1 , f , q, γ 1 , γ 2 , r c 1 , r c 2 , and F total ). The depletion factor δ 2 at r gap 2 (Figure 3a) is measured after the calculations complete. To convert a modeled disk image to complex visibilities with identical uv-coverages of observations, we utilize the public python code vis sample 1 . The computed visibilities Note-Parentheses describe parameter ranges in our MCMC calculations. The errors in γ i are large due to local maxima in calculations. The depletion factor of δ 2 is measured in Figure 3 Our calculations used flat priors with the parameter ranges summarized in Table 2. The burn-in phase (from initial conditions to reasonable sampling) employs 500 steps, and we run another 500 steps for convergence, totaling 1000 steps with 100 walkers. The fitting result and the best-fit surface brightness profile are shown in Table 2 and Figure 3(b), respectively. The corner plot with the MCMC posteriors is also shown in Appendix. The depletion factor δ 2 at r gap 2 is measured as ∼0.356 using the best-fit brightness profile in Figure 3(b). The reduced-χ 2 calculated with the observed and modeled visibilities in Figure 3(c) is 2.4. The residual map prepared using the residual visibilities (data−model) is shown in Figures 3(d) and (e). The residual map shows a structure at ∼7 σ level to the west in the outer dust ring, indicating a real azimuthal asymmetry.

DISCUSSIONS
The most intriguing result in our continuum observations is the detection of the inner dust ring at r ∼4 au and the cavity inside. Combining the SED and measured accretion rate of the system (Ṁ ∼ 6×10 −9 M ⊙ /yr; Manara et al. 2014, only slightly lower than that of typical T Tauri stars; Najita et al. 2015), we now have a more complete picture of its inner region: the cavity inside r ∼4 au has no detectable dust, consistent with the absence of NIR excess on the SED; however the cavity must have a substantial amount of gas in order to sustain a close-to-normal accretion rate. While dust cavities are commonly found in ALMA continuum observations nowdays (e.g. Hashimoto et al. 2015;Isella et al. 2016;Tang et al. 2017;Dong et al. 2017b, see also van der Marel et al. 2018 for a gallery), the inner cavity in the DM Tau disk, together with the cavity at 2.4 au in the TW Hya disk (Andrews et al. 2016;Tsukagoshi et al. 2016), are among the smallest, visible only in long baseline ALMA observations. The origin of the inner cavity is unclear. The measured close-to-normal accretion rate of DM Tau disfavors photoevaporation (e.g., Alexander et al. 2006). A planet can open a gap in gas (e.g., Lin & Papaloizo 1993), in which case the outer edge of the gap (even a shallow on) acts as a "dust filter", trapping ∼millimeter-sized large dust grains and forming a cavity in them (e.g., Rice et al. 2006;Zhu et al. 2012), consistent with our ALMA dust observations. Note that our gas observations are performed with 12 CO, to which the disk easily becomes optically thick. We therefore cannot detect a possible gas gap inside the edge of the inner dust cavity. Future observations of optically thinner CO isotopologues are needed to probe the gas surface density structure across the inner cavity (e.g., van der Marel et al. 2016). However, as argued in Zhu et al. (2011), disk-planet interactions have difficulties in depleting the small (µm-sized) dust in the inner disk, which tend to flow in with the gas. The DM Tau disk is at the extreme -there is no detectable dust inside the inner cavity based on the SED, while CO emission extends all the way toward the central star.
Alternatively, the presence of gas and the absence of small dust inside the cavity may be explained as icy dust being evaporated inside the cavity, fully or partially replenishing the gas. To produce this scenario, the dust that enters the inner cavity has to comprise fully evaporable volatiles (e.g., water), and the gas inside the cavity must be rich in them. If all small icy grains do not evaporate, however, the decreased grain size inside the evaporation front increases the fragmentation efficiency (e.g., Pinilla et al. 2017), thus enriching the cavity with small grains well coupled to the gas, inconsistent with the SED. Overall, both the planet scenario and the grain evaporation scenario have advantage and disadvantage, and additional observations are needed to determine the origin of the inner cavity.
The inner ring is located at a strikingly similar distance to the main asteroid belt in the solar system between Mars and Jupiter. The main belt, located beyond the water snowline at 2.7 AU (e.g., Abe et al. 2000), is thought to have profoundly impacted water delivery onto Earth (e.g., Morbidelli et al. 2000). A fraction of the water snowballs in the main belt found their way into the inner solar system and bombarded the early Earth, as their orbits were perturbed by Jupiter. The water snowline in the DM Tau system, with a host star less luminous than the proto-Sun, should be located closer to its host star than that in the solar system (see also Martin & Livio 2013;Notsu et al. 2016). Should terrestrial planets be forming inside its snowline, water delivery from the inner ring onto the inner planets might be plausible.
As shown in § 4, an axisymmetric inner dust ring is consistent with the data. On the other hand, 12 CO line emission is clearly non-axisymmetric on an ∼au scale -the peak 12 CO emission is located at the north blob (Figure 2), while the rotational center of CO roughly coincides with the stellar location and the center of the inner cavity. A candidate massive planet with M p ∼3 M Jup (COND model at 1 Myr; Baraffe et al. 2003) at a separation of r ∼6 au was detected by Keck sparse aperture masking interferometric observations (Willson et al. 2016). Whether this candidate planet introduces the asymmetry seen in CO emission is yet to be explored.
The continuum emission in the gap between the inner and outer rings (∼4-20 au) is substantially suppressed by a factor of ∼40 relative to the outer ring. The gap also has a steep inner edge ( Figure 1d). Both features are consistent with predictions of gap opening by planets (Zhu et al. 2011;Dong et al. 2015), but inconsistent with some other gap formation mechanisms such as the secular gravitational instability (SGI; e.g., Takahashi & Inutsuka 2014) and sintering of dust grains (Okuzumi et al. 2016) -the latter is expected to produce shallow gaps with depletion factors less than 10 (Okuzumi et al. 2016), while the formation timescale of the ring at r ∼10-20 au in the former mechanism is much longer than DM Tau's age.
In contrast to the symmetric inner ring, the outer ring has a small azimuthal asymmetry at P.A. ∼270 • , similar to the asymmetries found in a few other disks, but with one of the lowest contrast levels, ∼1.3:1 (cf., ∼130 in Oph IRS 48; van der Marel et al. 2013, ∼30 in HD 142527;Fukagawa et al. 2013). This asymmetry may be caused by a local enhancement in the dust surface density, possibly the remnants of particle trapping in a vortex (Barge et al. 2017), or temperature, if the south-west side is the far side while we observe the inner rim of the outer ring there (see e.g., Muto et al. 2015;Soon et al. 2017, for a discussion of HD 142527). Note that if the outer ring is optically thick and the asymmetry traces dust surface density variations, the small contrast seen in the surface brightness may not trace the contrast in the dust surface density, which can be much bigger than 1.3. Our observations also reveal an extended outer disk beyond the outer ring at r >0. ′′ 4 in the dust continuum, and a shallow gap inside. The presence of these structures has been previously suggested by Zhang et al. (2016) and Bergin et al. (2016b).
Our new ALMA observations reveal exciting new details, and yet raise more questions, in the DM Tau system. With an exo-asteroid belt under formation, the DM Tau disk will continue to offer crucial insights into disk evolution and planet formation in the terrestrial-planet-forming region.
We thanks an anonymous referee for a helpful review of the manuscript. This paper makes use of the following ALMA data: