Compact Disks in a High-resolution ALMA Survey of Dust Structures in the Taurus Molecular Cloud

The goal of our target selection was to obtain a sample that spans the full range of disk types for solar-mass stars, without any bias related to any disk property. Previous measurements of the disks, including disk brightness and inference of substructures from SEDs, were explicitly not used in the target selection, except for a previous identification of a primordial disk.

Our sample selection began with the census of Taurus disks around stars identified by Spitzer (Luhman et al. 2010; Rebull et al. 2010). We selected disks around stars of spectral type earlier than M3 to ensure sufficient signal-to-noise ratio (S/N) to image disks across the full range of disk brightness at our sensitivity. Known binaries with separations between 01 and 05 were excluded to avoid interactions at our spatial resolution. Sources with high extinction (A_V > 3 mag) or consistently faint optical/near-IR emission were excluded to avoid edge-on disks and embedded objects. We also excluded from our sample all disks with existing (or scheduled) ALMA images of dust emission with a spatial resolution better than 025. This avoidance of near-duplications is the most significant bias that introduces uncertainties in making robust generalizations from our current sample. Many of the most well-known disks had existing high-resolution observations at the time of our proposal. The final selection eliminated two isolated targets to optimize the efficiency of the ALMA observing blocks. A more complete description of targets that were excluded from our sample is described in Appendix A.

These selection criteria produced a sample of 32 stellar systems, including 10 systems in wide binaries. The spatial distribution of these systems (Figure 1) shows that the sources are located across the Taurus Molecular Cloud, with the densest parts of the cloud excluded because of criterion that required low extinction.

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Table 1 lists the properties of the host stars in our ALMA sample. Most spectral types and the spectral type-temperature conversion are obtained from the optical spectral survey of Herczeg & Hillenbrand (2014). Luminosities are then calculated from the Two Micron All Sky Survey (2MASS) J-band magnitude (Skrutskie et al. 2006), the extinction measured by Herczeg & Hillenbrand (2014), the J-band bolometric correction for the relevant spectral type calculated by Pecaut & Mamajek (2013), and the distance from Gaia DR2 (Gaia Collaboration et al. 2018). The properties of RY Tau were unclear from literature estimates and are derived in Appendix B.

Table 1.  Host Stellar Properties and Observation Results

Name	2MASS	D	AVa	SpTy	Teff	L*	M*	t*	Multiplicity	Peak Iν	Rms Noise	Beam
		(pc)	(mag)		(K)	(L⊙)	(M⊙)	(Myr)	(arcsec)	(mJy beam−1)	(μJy beam−1)	(arcsec)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)
Disks with substructures
CI Tau	04335200+2250301	158	1.90	K5.5	4277	0.81	${0.89}_{-0.17}^{+0.21}$	${2.50}_{-1.10}^{+2.00}$	⋯	8.55	50	0.13 × 0.11
CIDA 9A	05052286+2531312	171	1.35	M1.8	3589	0.20	${0.43}_{-0.10}^{+0.15}$	${3.20}_{-1.60}^{+3.10}$	2.34 (K11)	2.98	50	0.13 × 0.10
DL Tau	04333906+2520382	159	1.80	K5.5	4277	0.65	${0.98}_{-0.15}^{+0.84}$	${3.50}_{-1.60}^{+2.80}$	⋯	12.27	49	0.14 × 0.11
DN Tau	04352737+2414589	128	0.55	M0.3	3806	0.70	${0.52}_{-0.11}^{+0.14}$	${0.90}_{-0.40}^{+0.60}$	⋯	12.87	51	0.13 × 0.11
DS Tau	04474859+2925112	159	0.25	M0.4	3792	0.25	${0.58}_{-0.13}^{+0.17}$	${4.80}_{-2.30}^{+4.80}$	⋯	3.05	50	0.14 × 0.10
FT Tau	04233919+2456141	127	1.30	M2.8	3444	0.15	${0.34}_{-0.09}^{+0.13}$	${3.20}_{-1.60}^{+3.20}$	⋯	10.76	48	0.12 × 0.11
GO Tau	04430309+2520187	144	1.50	M2.3	3516	0.21	${0.36}_{-0.09}^{+0.13}$	${2.20}_{-1.10}^{+1.90}$	⋯	7.87	49	0.14 × 0.11
IP Tau	04245708+2711565	130	0.75	M0.6	3763	0.34	${0.52}_{-0.13}^{+0.15}$	${2.50}_{-1.20}^{+2.20}$	⋯	1.66	48	0.14 × 0.11
IQ Tau	04295156+2606448	131	0.85	M1.1	3690	0.22	${0.50}_{-0.12}^{+0.16}$	${4.20}_{-2.00}^{+4.10}$	⋯	5.76	78	0.16 × 0.11
MWC 480	04584626+2950370	161	0.10	A4.5	8400	17.38	${1.91}_{-0.13}^{+0.09}$	${6.90}_{-5.80}^{+5.10}$	⋯	31.29	69	0.17 × 0.11
RY Tau	04215740+2826355	128	1.95	F7	6220	12.30	${2.04}_{-0.26}^{+0.30}$	${5.00}_{-1.60}^{+3.10}$	⋯	18.98	51	0.14 × 0.11
UZ Tau Eb	04324303+2552311	131	0.90	M1.9	3574	0.35	1.23 ± 0.07	(1.30${}_{-0.60}^{+1.00}$)	3.54 (KH09)	8.44	49	0.13 × 0.10
Smooth disks in single stars
BP Tau	04191583+2906269	129	0.45	M0.5	3777	0.40	${0.52}_{-0.12}^{+0.15}$	${1.90}_{-0.90}^{+1.50}$	⋯	5.18	45	0.14 × 0.11
DO Tau	04382858+2610494	139	0.75	M0.3	3806	0.23	${0.59}_{-0.13}^{+0.15}$	${5.90}_{-2.80}^{+6.10}$	⋯	22.67	58	0.14 × 0.10
DQ Tauc	04465305+1700001	197	1.40	M0.6	3763	1.17	${1.61}_{-0.34}^{+0.58}$	(0.5)	⋯	23.05	45	0.13 × 0.10
DR Tau	04470620+1658428	195	0.45	K6	4205	0.63	${0.93}_{-0.16}^{+0.85}$	${3.20}_{-1.40}^{+2.70}$	⋯	21.11	51	0.13 × 0.10
GI Tau	04333405+2421170	130	2.05	M0.4	3792	0.49	${0.52}_{-0.12}^{+0.15}$	${1.50}_{-0.70}^{+1.20}$	⋯	4.33	50	0.12 × 0.11
GK Tau	04333456+2421058	129	1.50	K7.5	4007	0.80	${0.63}_{-0.13}^{+0.16}$	${1.20}_{-0.60}^{+0.70}$	⋯	3.26	51	0.12 × 0.11
Haro 6-13	04321540+2428597	130	2.25	K5.5	4277	0.79	${0.91}_{-0.17}^{+0.24}$	${2.60}_{-1.10}^{+2.10}$	⋯	32.63	52	0.14 × 0.11
HO Tau	04352020+2232146	161	1.00	M3.2	3386	0.14	${0.30}_{-0.04}^{+0.05}$	${2.70}_{-1.00}^{+1.50}$	⋯	3.93	46	0.12 × 0.11
HP Tau	04355277+2254231	177	3.15	K4.0	4590	1.30	${1.20}_{-0.18}^{+1.14}$	${2.40}_{-1.00}^{+1.90}$	⋯	22.45	51	0.13 × 0.11
HQ Tau	04354733+2250216	158	2.60	K2.0	4900	4.34	${1.78}_{-0.26}^{+1.69}$	${1.00}_{-0.40}^{+0.60}$	⋯	1.16	46	0.12 × 0.11
V409 Tau	04181078+2519574	131	1.00	M0.6	3763	0.66	${0.50}_{-0.10}^{+0.13}$	${0.90}_{-0.30}^{+0.50}$	⋯	4.48	46	0.13 × 0.11
V836 Tau	05030659+2523197	169	0.60	M0.8	3734	0.44	${0.48}_{-0.12}^{+0.14}$	${1.40}_{-0.70}^{+1.10}$	⋯	7.64	49	0.13 × 0.10
Smooth disks around the primary star in binaries/multiple systems
DH Tau A	04294155+2632582	135	0.65	M2.3	3516	0.20	${0.37}_{-0.10}^{+0.13}$	${2.30}_{-1.20}^{+2.10}$	2.34 (I05)	9.14	44	0.13 × 0.11
DK Tau A	04304425+2601244	128	0.70	K8.5	3902	0.45	${0.60}_{-0.13}^{+0.16}$	${2.30}_{-1.10}^{+1.80}$	2.36 (KH09)	12.73	44	0.13 × 0.11
HK Tau A	04315056+2424180	133	2.40	M1.5	3632	0.27	${0.44}_{-0.11}^{+0.14}$	${2.20}_{-1.10}^{+1.90}$	2.34 (KH09)	11.56	48	0.12 × 0.11
HN Tau Ad	04333935+1751523	136	1.15	K3	4730	0.16	1.53 ± 0.15	(2.0)	3.14 (KH09)	7.0	40	0.14 × 0.10
RW Aur A	05074953+3024050	163	(0)	K0	5250	0.99	${1.20}_{-0.13}^{+0.18}$	${13.50}_{-5.90}^{+11.10}$	1.42 (WG01)	18.34	51	0.16 × 0.10
T Tau N	04215943+1932063	144	1.25	K0	5250	6.82	${2.19}_{-0.24}^{+0.38}$	${1.10}_{-0.40}^{+0.70}$	0.68 (KH09)	64.56	52	0.14 × 0.10
UY Aur A	04514737+3047134	155	1.00	K7.0	4060	1.05	${0.65}_{-0.13}^{+0.17}$	${0.90}_{-0.40}^{+0.40}$	0.88 (KH09)	16.91	48	0.15 × 0.10
V710 Tau Ae	04315779+1821350	142	0.55	M1.7	3603	0.26	${0.42}_{-0.11}^{+0.13}$	${2.20}_{-1.10}^{+1.90}$	3.22 (KH09)	7.52	42	0.14 × 0.10

Notes.  Our sample is divided into three subgroups (as listed in the table with three segments), from top to bottom. The distance for individual star is adopted from the Gaia DR2 parallax (Gaia Collaboration et al. 2018). The spectral type is adopted from Herczeg & Hillenbrand (2014) and stellar luminosity is calculated from J-band magnitude and updated to the new Gaia distance. Stellar mass and age are re-calculated with the stellar luminosity and effective temperature listed here using the same method as that used in Pascucci et al. (2016). The last three columns list the peak intensity in continuum maps, noise level, and synthesized beam FWHM.

^aA_V is listed to nearest 0.05 and has an uncertainty of ∼0.2–0.5 mag; the higher uncertainty applies to stars with high veiling at optical wavelengths. RW Aur has a negative statistical extinction and is treated as A_V = 0 mag here. ^bUZ Tau E is a spectroscopic binary in 0.03 au separation (Mathieu et al. 1996; Prato et al. 2002). We adopt its stellar mass from dynamical measurement (Simon et al. 2000). ^cDQ Tau is a double-lined spectroscopic binary with a period of ∼16 days in an eccentric orbit (e = 0.56, Mathieu et al. 1997; Tofflemire et al. 2017). Its stellar mass is adopted from the dynamical measurement of Czekala et al. (2016). ^dHN Tau A has a high inclination angle and appears too faint to derive the accurate stellar mass and age from the grids, for which we adopt the dynamical mass measurement from Simon et al. (2017). ^eV710 Tau North, see discussion of nomenclature in Manara et al. (2019).

References. The references for the quoted stellar multiplicity: K11 = Kraus et al. (2011), I05 = Itoh et al. (2005), KH09 = Kraus & Hillenbrand (2009a), WG01 = White & Ghez (2001).

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The mass and age of each source in our sample and in the Taurus disk sample of Andrews et al. (2013) are then calculated by comparing the temperature and updated luminosity to Baraffe et al. (2015) and non-magnetic Feiden (2016) models of pre-main sequence stellar evolution (see also Figure 2), as in Pascucci et al. (2016). The combination of both sets of evolutionary tracks cover the full range of spectral types in Taurus disks. For sources that are more luminous than the youngest isochrone, we choose the youngest 0.5 Myr isochrone and then calculate the stellar mass based on the stellar effective temperature. For sources that appear fainter than the main population, we calculate a stellar mass from the isochrone of the average age in the full Taurus sample (∼2 Myr). We adopt the stellar dynamical mass measurements from the CO gas rotation for the two spectroscopic binaries (UZ Tau E, Simon et al. 2000 and DQ Tau, Czekala et al. 2016) and two relatively edge-on disks (HN Tau A and HK Tau B, Simon et al. 2017), all corrected for the Gaia DR2 distance.

In Lodato et al. (2019), we analyzed the putative population of hidden planets in the subset of sources with substructures. Most of those host stars have masses measured from gas rotation in the disk (Simon et al. 2000, 2017; Piétu et al. 2007; Guilloteau et al. 2014), which should be more accurate than masses estimated from Hertzsprung–Russell (H–R) diagrams. The accuracy of the host mass was also important to that paper, so that we could compare disk properties to the exoplanet systems around stars of the same mass. For this paper, the masses are most important as a tool for comparison to the parent sample of Taurus disks, including those disks that were excluded from our sample. These different goals led to different choices in the method to measure stellar mass.

In Appendix B, we discuss some of the uncertainties in assigning stellar masses and ages to each target. Although individual stellar masses estimated from evolutionary tracks are marginally consistent with most dynamical measurements, a global comparison indicates that the masses used here are likely underestimated. The average age of the sample is ∼2.3 Myr, consistent with the approximate age of Taurus, but the age of any individual star is unreliable.

Our ALMA observations were conducted as program 2016.1.01164.S (PI: Herczeg) in 2017 August–September. The Band 6 receivers were used for all measurements with an identical spectral window (SPW) setup. The continuum emission was recorded in two SPWs, which were centered at 218 and 233 GHz, each with a bandwidth of 1.875 GHz. The resulting average observing frequency is 225.5 GHz (wavelength of 1.3 mm). Another SPW covered ¹³CO and C¹⁸O J = 2−1 with a velocity resolution of 0.16 km s⁻¹. The remaining SPW was designed to target ¹²CO J = 2−1 line, but was unfortunately incorrectly tuned during the observation. The ¹³CO emission were detected in about one-third of our sample, which will be presented in a forthcoming paper. We adopted the C40-7 antenna configuration to achieve the desired spatial resolution of ∼01.

The selected sample of 32 Taurus disks were split into four different observing groups mainly based on their locations in the sky. One observing group (2017 August 27, see Table 2) consists of bright disks (millimeter flux >50 mJy obtained from Andrews et al. 2013 and Akeson & Jensen 2014) with ∼4 minutes integration time per source. The other three groups, with mostly faint disks (<50 mJy, with exceptions for a few bright disks for observing efficiency), were observed for ∼8–9 minutes per source. Bandpass and flux calibrators were observed at the beginning of each observing group/block, and a phase calibrator near the science targets was repeatedly recorded every 30–60 s. The observing conditions and calibrators for each observing group are summarized in Table 2.

Data reduction started with the standard ALMA pipeline calibration, with scripts provided by ALMA staff. This calibration procedure was performed with CASA v4.7.2 for the first observing group (2017 August 18) and v5.1.1 for the later three groups. Following the pipeline, initial phase adjustments were made based on the water vapor radiometer measurements. The standard bandpass, flux, and gain calibrations were then applied accordingly for each measurement set (see Table 2). In some observations in the second observing group (2017 August 27), the phase calibrator was recorded at different spectral setups from the science targets. We therefore used the weaker check source for phase corrections (see note in Table 2). Self-calibration was performed for our targets, except for the faint GK Tau and HQ Tau, with the procedures elaborated in Long et al. (2018b). As a result, self-calibration provided a visible improvement in image quality in which the image peak S/N for most disks increased by ∼30% and a factor of 2–3 improvement in image S/N was seen for the brightest disks. After continuum self-calibration, the data visibilities were extracted for further modeling. We then created a continuum image for each target using tclean with Briggs weighting and a robust parameter of +0.5. Our final continuum images have a typical beam size of 014 × 011 and a median continuum rms of 50 μJy beam⁻¹ (see peak intensity and noise level for individual disks in Table 1).

Our model fitting is performed in the visibility plane. The main procedure is summarized as follows: we first take a model intensity profile and Fourier transform it to create the model visibilities; the fitting is then executed by comparing the model visibilities to data visibilities with the Markov chain Monte Carlo (MCMC) method to derive the best-fit model.

The choice of model profile is guided by the appearance of the visibility profile. The oscillation pattern in the real part of the visibility profile is seen for a fraction of disks (see also Figure 11 in Appendix C), which likely indicates a disk with a sharp outer edge in millimeter dust grains (e.g., Hogerheijde et al. 2016; Zhang et al. 2016). We therefore adopt an exponentially tapered power law ($I{(R)=A(R/{R}_{c})}^{-{\gamma }_{1}}\exp [-{(R/{R}_{c})}^{{\gamma }_{2}}]$) as the model intensity profile, in which power-law index γ₁ and taper index γ₂ describe the slope of the emission gradient in the inner disk and the sharpness of the falloff beyond the transition radius (R_c), respectively (see Figure 4). The model is also described by a disk inclination and position angle and phase center offsets. We then apply the Galario code (Tazzari et al. 2018) to Fourier transform the model intensity profile into visibilities sampled with the same uv-coverage. The model visibilities are later compared with data visibilities using the emcee package (Foreman-Mackey et al. 2013). The parameters are explored with 100 walkers and 5000 steps for each walker. The burn-in phase for convergency is typically less than 1000 steps. The posterior medians are obtained using the MCMC chains of the last 1000 steps, with the 1σ uncertainty for each parameter calculated from the 16th and 84th percentiles.

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For single stars in our sample with no detectable substructures, we apply the modeling approach described above to fit the disk dust distribution. For multiple stellar systems (see Table 1), the fitting results are adopted from the companion paper of Manara et al. (2019), which fits multiple disk components simultaneously. Our analysis below only includes the circumprimary disks, which are modeled with the same morphologic function as disks in single stellar systems.

The quality of the best-fit model is checked by inspecting the comparisons of data and model in images, visibility profiles, and radial intensity cuts (see Figure 11 in Appendix C). In most cases, the exponentially tapered power law can well describe the dust emission, with residuals less than 3σ. For DR Tau and DQ Tau, however, the comparisons of the best-fit model to data yield asymmetric residuals of 5–10σ. The residual in the innermost disk of the spectroscopic binary DQ Tau may be associated with the high orbital eccentricity (Mathieu et al. 1997). A check of Haro 6-13 also shows 5–10σ asymmetric residuals in the inner disk, as well as a possible faint (3σ) outer disk. Since large residuals are seen in all bright disks (high peak S/N), we may miss some fine details and faint substructures that would have been detected with greater sensitivity and spatial resolution (see, e.g., Huang et al. 2018b). This is also indicated by the data and model comparison at longer baselines (Figure 11), where our simple model might miss some small-scale structures. For all disks, the exponentially tapered power law fits better than the Gaussian profile, except for the faint and compact GK Tau where both models work similarly well.

3.2.1. Best-fit Profile Parameters

The best-fit model parameters, including power-law and taper indices, inclination, and position angle, are summarized in Table 3. The taper index γ₂ describes the profile of the outer disk (Figure 4). The taper index is generally higher than that of the widely used similarity solution, implying sharp outer edges of dust disks. Most of the disks in binary systems have the sharpest outer disk edges (larger γ₂ index) in our sample, hinting at a higher level of outer disk truncation by close companions (see the detailed discussion in Manara et al. (2019)).

Table 3.  Disk Model Parameters

Name	Fν	Reff,68%	Reff,95%	Rc	γ1	γ2	Incl	PA	Source Center
	(mJy)	(arcsec)	(arcsec)	(arcsec)			(deg)	(deg)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
CI Tau	${142.40}_{-0.81}^{+0.47}$	0.706	1.195	⋯	⋯	⋯	${50.0}_{-0.3}^{+0.3}$	${11.2}_{-0.4}^{+0.4}$	04h33m5203 +22d50m2981
CIDA 9A	${37.10}_{-0.20}^{+0.26}$	0.287	0.371	⋯	⋯	⋯	${45.6}_{-0.5}^{+0.5}$	${102.7}_{-0.7}^{+0.7}$	05h05m2282 +25d31m3050
DL Tau	${170.72}_{-0.43}^{+0.93}$	0.702	1.033	⋯	⋯	⋯	${45.0}_{-0.2}^{+0.2}$	${52.1}_{-0.4}^{+0.4}$	04h33m3909 +25d20m3779
DN Tau	${88.61}_{-0.62}^{+0.25}$	0.313	0.475	⋯	⋯	⋯	${35.2}_{-0.6}^{+0.5}$	${79.2}_{-1.0}^{+1.0}$	04h35m2739 +24d14m5855
DS Tau	${22.24}_{-0.23}^{+0.23}$	0.376	0.446	⋯	⋯	⋯	${65.2}_{-0.3}^{+0.3}$	${159.6}_{-0.4}^{+0.4}$	04h47m4860 +29d25m1076
FT Tau	${89.77}_{-0.25}^{+0.27}$	0.264	0.357	⋯	⋯	⋯	${35.5}_{-0.4}^{+0.4}$	${121.8}_{-0.7}^{+0.7}$	04h23m3920 +24d56m1386
GO Tau	${54.76}_{-0.41}^{+0.85}$	0.698	1.187	⋯	⋯	⋯	${53.9}_{-0.5}^{+0.5}$	${20.9}_{-0.6}^{+0.6}$	04h43m0308 +25d20m1835
IP Tau	${14.53}_{-0.18}^{+0.17}$	0.234	0.280	⋯	⋯	⋯	${45.2}_{-0.9}^{+0.8}$	${173.0}_{-1.1}^{+1.1}$	04h24m5709 +27d11m5607
IQ Tau	${64.11}_{-0.72}^{+0.49}$	0.423	0.838	⋯	⋯	⋯	${62.1}_{-0.5}^{+0.5}$	${42.4}_{-0.6}^{+0.6}$	04h29m5157 +26d06m4445
MWC 480	${267.76}_{-1.07}^{+0.51}$	0.345	0.878	⋯	⋯	⋯	${36.5}_{-0.2}^{+0.2}$	${147.5}_{-0.3}^{+0.3}$	04h58m4627 +29d50m3651
RY Tau	${210.40}_{-0.21}^{+0.21}$	0.378	0.509	⋯	⋯	⋯	${65.0}_{-0.1}^{+0.1}$	${23.1}_{-0.1}^{+0.1}$	04h21m5742 +28d26m3509
UZ Tau E	${129.52}_{-0.79}^{+0.68}$	0.445	0.667	⋯	⋯	⋯	${56.1}_{-0.4}^{+0.4}$	${90.4}_{-0.4}^{+0.4}$	04h32m4308 +25d52m3063
BP Tau	${45.15}_{-0.14}^{+0.19}$	0.226	0.321	0.273	${0.10}_{-0.03}^{+0.03}$	${3.93}_{-0.24}^{+0.24}$	${38.2}_{-0.5}^{+0.5}$	${151.1}_{-1.0}^{+1.0}$	04h19m1585 +29d06m2648
DO Tau	${123.76}_{-0.27}^{+0.17}$	0.183	0.263	0.247	${0.53}_{-0.00}^{+0.00}$	${4.97}_{-0.14}^{+0.14}$	${27.6}_{-0.3}^{+0.3}$	${170.0}_{-0.9}^{+0.9}$	04h38m2860 +26d10m4908
DQ Tau	${69.27}_{-0.19}^{+0.15}$	0.124	0.219	0.166	${0.80}_{-0.03}^{+0.03}$	${2.37}_{-0.12}^{+0.12}$	${16.1}_{-1.2}^{+1.2}$	${20.3}_{-4.3}^{+4.3}$	04h46m5306 +16d59m5989
DR Tau	${127.18}_{-0.22}^{+0.20}$	0.188	0.276	0.267	${0.70}_{-0.00}^{+0.00}$	${5.37}_{-0.16}^{+0.16}$	${5.4}_{-2.6}^{+2.1}$	${3.4}_{-8.0}^{+8.2}$	04h47m0622 +16d58m4255
GI Tau	${17.69}_{-0.07}^{+0.25}$	0.145	0.190	0.193	${0.39}_{-0.05}^{+0.05}$	${9.69}_{-3.66}^{+5.56}$	${43.8}_{-1.1}^{+1.1}$	${143.7}_{-1.6}^{+1.9}$	04h33m3407 +24d21m1670
GK Tau	${5.15}_{-0.11}^{+0.19}$	0.065	0.099	0.085	${0.53}_{-0.91}^{+0.59}$	${3.47}_{-3.25}^{+8.64}$	${40.2}_{-6.2}^{+5.9}$	${119.9}_{-9.1}^{+8.9}$	04h33m3457 +24d21m0549
Haro 6-13	${137.10}_{-0.21}^{+0.24}$	0.185	0.264	0.268	${0.78}_{-0.00}^{+0.00}$	${7.25}_{-0.32}^{+0.32}$	${41.1}_{-0.3}^{+0.3}$	${154.2}_{-0.3}^{+0.3}$	04h32m1542 +24d28m5921
HO Tau	${17.72}_{-0.17}^{+0.20}$	0.183	0.267	0.242	${0.48}_{-0.05}^{+0.05}$	${4.30}_{-0.65}^{+0.76}$	${55.0}_{-0.8}^{+0.8}$	${116.3}_{-1.0}^{+1.0}$	04h35m2022 +22d32m1427
HP Tau	${49.33}_{-0.15}^{+0.16}$	0.090	0.125	0.127	${0.68}_{-0.06}^{+0.06}$	${8.31}_{-2.45}^{+3.12}$	${18.3}_{-1.4}^{+1.2}$	${56.5}_{-4.3}^{+4.6}$	04h35m5279 +22d54m2293
HQ Tau	${3.98}_{-0.17}^{+0.08}$	0.129	0.155	0.158	${-0.21}_{-0.34}^{+0.29}$	${16.40}_{-11.51}^{+6.89}$	${53.8}_{-3.2}^{+3.2}$	${179.1}_{-3.4}^{+3.2}$	04h35m4735 +22d50m2136
V409 Tau	${20.22}_{-0.18}^{+0.12}$	0.239	0.311	0.324	${0.59}_{-0.03}^{+0.03}$	${16.11}_{-5.98}^{+6.25}$	${69.3}_{-0.3}^{+0.3}$	${44.8}_{-0.5}^{+0.5}$	04h18m1079 +25d19m5697
V836 Tau	${26.24}_{-0.12}^{+0.16}$	0.128	0.188	0.156	${0.22}_{-0.10}^{+0.08}$	${3.52}_{-0.52}^{+0.55}$	${43.1}_{-0.8}^{+0.8}$	${117.6}_{-1.3}^{+1.3}$	05h03m0660 +25d23m1929
DH Tau A	${26.68}_{-0.12}^{+0.13}$	0.105	0.146	0.140	${0.38}_{-0.07}^{+0.07}$	${5.73}_{-1.08}^{+1.35}$	${16.9}_{-2.2}^{+2.0}$	${18.8}_{-7.2}^{+7.1}$	04h29m4156 +26d32m5776
DK Tau A	${30.08}_{-0.09}^{+0.14}$	0.092	0.117	0.120	${0.60}_{-0.03}^{+0.03}$	${38.93}_{-20.79}^{+14.57}$	${12.8}_{-2.8}^{+2.5}$	${4.4}_{-9.4}^{+10.1}$	04h30m4425 +26d01m2435
HK Tau A	${33.15}_{-0.13}^{+0.15}$	0.156	0.216	0.230	${0.92}_{-0.01}^{+0.01}$	${21.36}_{-10.06}^{+17.75}$	${56.9}_{-0.5}^{+0.5}$	${174.9}_{-0.5}^{+0.5}$	04h31m5058 +24d24m1737
HN Tau A	${12.30}_{-0.18}^{+0.12}$	0.104	0.136	0.140	${0.65}_{-0.05}^{+0.05}$	${16.19}_{-7.31}^{+4.74}$	${69.8}_{-1.3}^{+1.4}$	${85.3}_{-0.6}^{+0.7}$	04h33m3938 +17d51m5198
RW Aur A	${35.60}_{-0.27}^{+0.28}$	0.101	0.132	0.140	${0.70}_{-0.02}^{+0.02}$	${26.24}_{-12.61}^{+14.96}$	${55.1}_{-0.4}^{+0.5}$	${41.1}_{-0.6}^{+0.6}$	05h07m4957 +30d24m0470
T Tau N	${179.72}_{-0.22}^{+0.22}$	0.111	0.143	0.150	${0.68}_{-0.00}^{+0.00}$	${49.58}_{-1.75}^{+0.78}$	${28.2}_{-0.2}^{+0.2}$	${87.5}_{-0.5}^{+0.5}$	04h21m5945 +19d32m0618
UY Aur A	${19.96}_{-1.06}^{+1.07}$	0.033	0.044	0.040	${0.24}_{-2.05}^{+0.97}$	${7.10}_{-5.55}^{+12.59}$	${23.5}_{-6.6}^{+7.8}$	${125.7}_{-10.9}^{+10.3}$	04h51m4740 +30d47m1310
V710 Tau A	${55.20}_{-0.14}^{+0.19}$	0.238	0.317	0.320	${0.48}_{-0.01}^{+0.01}$	${8.82}_{-0.59}^{+0.62}$	${48.9}_{-0.3}^{+0.3}$	${84.3}_{-0.4}^{+0.4}$	04h31m5781 +18d21m3764

Note. The power-law index γ₁ and taper index γ₂, as well as the disk inclination and PA are parameters fitted with MCMC. Total flux (F_ν) and effective radius (R_eff, with both 68% and 95% flux encircled) are derived from the best-fit intensity profile for each disk. The quoted uncertainties are the interval from the 16th to the 84th percentile of the model chains and scaled by the square root of the reduced χ² of the fit. Uncertainties for all radii are extremely small (at a level of 0002) and thus not showing. The source center is derived by applying the fitted phase center offsets to the image center.

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The distribution of materials in the inner disk is characterized by the power-law index γ₁. The negative γ₁ index of HQ Tau indicates depletion toward the inner region, perhaps indicating the existence of a dust cavity that is not well resolved in our current data. Except for HQ Tau, most smooth disks in our sample have similar inner disk profiles, with the median γ₁ value of 0.56 and a standard deviation of 0.26. BP Tau has a peculiar flat inner disk, with γ₁ of only 0.1.

The listed uncertainties for the fitted parameters are adopted as the 16th to 84th percentile range of the posterior distribution for each parameter, and are then scaled by the square root of the reduced χ² of the fit. These uncertainties correspond to statistical uncertainties and are likely underestimated.

Since some targets were observed in multiple nights and with different beam shapes, differences between separate fits to the sets of observations provide us with an independent estimate for the observational errors. We include the fitting results for a few disks in Table 5 in Appendix C. These fits demonstrate that the inclinations and position angles have a precision of ∼1–2 deg, and the effective radii are precise to ∼3%, fluxes to 5%. The power-law and taper indices have larger uncertainties, although the values are generally similar. The scale of the uncertainty depends on disk brightness and disk size. The two disks without self-calibration, GK Tau and HQ Tau, have larger uncertainties derived from the fitting than the average, likely due both to their faintness and their compactness.

3.2.2. Fluxes and Sizes of Dust Disks

Our high-resolution ALMA Survey consists of 32 disks in the Taurus Clouds, one of the largest samples studied at 01 resolution. In Long et al. (2018b), we described the 12 disks that show prominent disk substructures mainly based on the inspection of radial intensity profiles, for which dust emission could not be fit with a single central component. An exponentially tapered power law provides a good fit to most of the other 20 disks (see Section 3), which confirms the robustness of our previous selection in Long et al. (2018b). These 20 disks are therefore referred as smooth disks for their lack of resolved structures, although these disks might host small-scale substructures that are not yet identified in our data. The 20 smooth disks are further separated into 12 disks around single stars and 8 disks in binary (or multiple) systems that have separations in the range of 07–35 and may be affected by tidal interactions (e.g., Artymowicz & Lubow 1994; Harris et al. 2012; Long et al. 2018a). Based on the dust morphology (and the effect of stellar multiplicity on dust distribution), this division leads to three categories of disks (see also Table 1):

Disks with substructures:  12 disks show remarkable dust substructures, including four disks with inner dust cavities (plus additional rings in two disks), three disks with inner disk encircled by a single ring, and five disks with inner disk encircled by multiple rings. The inner disk is modeled by either a Gaussian profile or an exponentially tapered power law, and each substructure component is modeled by a Gaussian ring to infer to gap and ring properties. The possible formation mechanisms for disk substructures are discussed in Long et al. (2018b) and Lodato et al. (2019) based on the derived gap and ring properties. Two multiple systems, CIDA 9 (separation of 234) and UZ Tau E (separation of 356 from the close binary UZ Tau Wab) are included in this subsample.

Smooth disks around singles: 12 disks around stars in single stellar systems are well described by one model component and do not show apparent substructures at current resolution. Some 5–10σ residuals are seen in three bright disks (DR Tau, Haro 6-13, and DQ Tau), which may host unresolved fine substructures in the inner disks. The spectroscopic binary DQ Tau (separation of <0.1 au) is included in this subsample, since the inner cavity caused by the binary motion remains unresolved in our data. The possibly negative power-law index in the very faint HQ Tau may also suggest dust depletion in the inner disk.

Smooth disks in binaries/multiples:  eight disks around primary stars in multiple stellar systems that appear smooth in our observations. The disks around the additional stellar components are detected in all but two systems (DH Tau and V710 Tau). A detailed discussion about this subsample is presented in Manara et al. (2019).

In this section, we will assess the similarities and diversities in stellar mass, disk brightness, system age, disk radius, and dust profile for our defined subsamples (Section 4.1), to evaluate the general properties for systems with detectable substructures.

4.2.1. Comparison of Stellar Masses

Our ALMA sample covers a wide range in stellar mass, from ∼0.3 M_⊙ (set by the prior selection for stars with SpTy earlier than M3) to ∼2 M_⊙, but populates in the early M and late K type stars. Stellar masses in each of the three subsamples span the full range of our whole sample, as can be seen in Figure 5. By performing the two-sample Kolmogorov-Smirnov (KS) test using the ks_2samp task in the Python scipy package, we find that stellar mass distribution in disks with substructures is indistinguishable from that of the smooth disks (p = 94%, or from that of the smooth disks in singles with p = 98%). The similar stellar mass distribution in the three subsamples is also evident in Figure 6, with most disks clustered around 0.5 M_⊙ and a few disks reaching beyond 1 M_⊙ in all three subsamples.

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4.2.2. Comparison of Disk Continuum Luminosities

4.2.3. Comparison of Stellar Ages

4.2.4. Comparison of Dust Disk Sizes

4.2.5. Comparison of Disk Dust Profiles

As established in the previous subsection, disks with substructures are generally more extended in our sample. In this subsection, we demonstrate that these larger radii are obtained because of the presence of outer rings. As can be seen in Figure 3, the inner emission cores for some of the extended ring disks actually have extents similar to those of the smooth disks. Meanwhile, peak brightness distributions are indistinguishable among the three subsamples, though the T Tau N disk is extremely bright (see Figure 7).

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We further explore the disk profiles for the inner emission cores in the extended ring disks and compact smooth disks. In Long et al. (2018b), we employed models with the fewest number of parameters to describe the dust emission morphologies, therefore the inner cores of some disks were modeled with Gaussian profiles. In the comparison of the disk profile parameters, we thus only include the four disks that were modeled with the tapered power-law profile for their inner emission cores when a Gaussian profile would not work equally well. As seen in Figure 7, the inner cores of the ring disks resemble the smooth disks, with values of disk transition radius (R_c), power-law index (γ₁), and taper index (γ₂) well within the parameter ranges of the smooth disk sample. Another four disks with inner cores modeled with Gaussian profiles also have small sizes, with a Gaussian radius less than 02. The inner cores of the ring disks have a steep outer edge similar to that of smooth disks around single stars, while in general shallower than those in binaries.

Disk substructures are present in disks across a wide range of parameter space. In our Taurus sample, we detect disk substructures in all spectral types from A to M3 (the hard cut of our sample selection). A similar spectral type coverage is found within the DSHARP sample (the 18 disks with annular substructures, Huang et al. 2018a), with disks mainly selected from the Lupus and Ophiuchus star-forming region (Andrews et al. 2018a). Most of the disk substructures are revealed from systems of early-type stars (see also a recent compilation of 16 disks with multi-rings by van der Marel et al. 2019), because (1) any serendipitous discovery more likely comes from the preferentially targeted brighter disks, which are linked to earlier spectral types (the stellar mass–disk mass scaling relation, e.g., Pascucci et al. 2016), (2) specialized substructure surveys (e.g., DSHARP) also selected brighter disks to achieve a sensitivity/contrast criterion (Andrews et al. 2018a), and (3) our survey, though covering fainter disks, only probes down to M3 stars.

The existing observations are largely biased toward brighter disks; even our survey, which is designed to include as broad a range in disk brightness, implies a high occurrence rate of disk substructures among bright disks. Most of the faint disks in our sample have small disk radius (typical R_eff,95% ∼ 30 au, see Figure 5), in which substructures may not be captured by our ∼15 au beam. Given the current observational biases and the observed disk luminosity–size relation (Tazzari et al. 2017; Tripathi et al. 2017), higher resolution ALMA observations for M dwarfs (or even brown dwarfs) and faint disks are needed to build a more complete picture of disk substructures.

Dust rings are detected in both young embedded sources (e.g., HL Tau, ALMA Partnership et al. 2015; GY 91, Sheehan & Eisner 2018) and more evolved disks (e.g., TW Hydra, Andrews et al. 2016). In our Taurus sample, substructures are found in systems across an age range of 1–6 Myr (see Figure 6). Even though the age of individual sources remains poorly determined, the wide age difference is still informative. Disk substructures likely form at a very early stage (e.g., ALMA Partnership et al. 2015; Sheehan & Eisner 2018) and are sustained in some way for at least a few megayears, although at least one Class I disk, that of TMC1A, is smooth at a resolution of ∼8 au (Harsono et al. 2018). Current studies have not yet come to firm conclusions about the origin of disk substructures, as a diverse set of mechanisms are capable of reproducing the observed disk patterns. Analyses show no obvious trend between stellar luminosities and the gap/ring locations (Huang et al. 2018a; Long et al. 2018b; van der Marel et al. 2019), thus discarding snow lines as the universal mechanism for disk gap and ring formation. Though no secure evidence has been found to support hidden planets as the cause of gaps in disks (Testi et al. 2015; Guidi et al. 2018), it remains a promising and intriguing explanation, while it opens the question of how relative high mass planets (≳Neptune-mass) can form at early disk ages, especially at large separations (>50 au). The assembly of planets may be rapid and happens very early on. The Class I disks might be the key for exploring the onset of disk morphological transition and toward the first steps of planet formation.

Our disks with substructures have radial extents similar to those of the DSHARP sample (see R_eff,95% comparison in Figure 5), from ∼30 to ∼200 au. The selection criteria of the DSHARP sample inevitably lead to a strong bias toward larger disks (Andrews et al. 2018a). Our blind search of disk substructures in a sample with diverse brightness (also diverse dust disk radius as expected from the disk luminosity–size relation), however, results in a preference of finding disk substructures in larger disks (regardless of disk brightness). A recent study of 16 multi-ring disks compiled by van der Marel et al. (2019) suggests that the average disk outer radius for the 12 younger disks is a factor of 2 larger than that of the four oldest systems. This trend is not seen in either our Taurus sample or the DSHARP sample, as many young disks have a small radius and the oldest disks (e.g., MWC 480 in our sample) are relatively extended. The small number of older systems observed so far prevents us from drawing any final conclusion.

Spatially extended disks in our sample show gaps and rings, with diversity in the number and location of the rings and their contrast with gaps. The smaller disks, however, appear smooth in their radial brightness profiles (see Figure 8). This raises the questions of whether our observations are missing some very faint rings at large radii, and whether smaller disks are scaled-down versions of substructures seen in the larger disks.

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The comparison of the average disk radial profiles in our defined subsamples (Figure 8) shows that (1) the inner 025 emission core for disks with substructures overlaps with the average profile of the smooth disks in single stars; (2) broader emission appearing as a shoulder spanning from 03–05 followed by a shallow wing extending to 10 is seen in the sample with substructures; (3) disks in binary systems are more compact overall. Some rings in the outer disks are very faint (3–10σ), seen as the wing in the average profile. Given the nearly uniform noise level in the images and similar peak brightness distributions (see Figure 7), substructures with similar/stronger significance (i.e., brightness ratio of the central peak to the ring peak) around the currently observed compact disk would have been detected, if they were present.

A comparison between the GO Tau and V836 Tau disks provides an instructive example of the differences between a compact and large disk. Both disks have inner emission cores with similar size and peak brightness. Any 3–10σ ring, like that seen in GO Tau, would have been easily detected in the outer disk of V836 Tau, if rings were present. If the disk brightness of GO Tau were scaled down by a factor of 2–3 to match the total disk flux of V836 Tau (as opposed to the peak flux), then the innermost bright ring is still detectable when simulated with CASA, while the outer faint ring is barely visible. We cannot reject the possibility of very faint outer rings beyond our observational limit in some compact disks, perhaps especially the faintest disk, HQ Tau.

Our observations are only sensitive to substructures with scales of ∼10 au. The non-detections of substructures in our compact disks (as well as the inner emission cores of ring disks) imply that any hidden substructure should be narrow or have low contrast. The three smallest disks (∼30 au, DoAr 33, WSB 52, and SR 4) in the DSHARP sample (Huang et al. 2018a) have disk sizes that are similar to the radii of our compact disks. With a fine resolution of 5 au, radial profiles for DoAr 33 and WSB 52 show emission bumps instead of distinctive gaps, while SR 4 has a prominent deep gap around 11 au (Huang et al. 2018a). By convolving the DSHARP data with our beam size, the dust disks of DoAr 33 and WSB 52 become smooth, while the deep gap in SR 4 remains visible. In the case of efficient dust trapping, dust rings are expected to have a width equal to or narrower than the pressure scale height (e.g., 0.1, Dullemond et al. 2018), thus substructures in the inner disk should have small characteristic scales. The longest baselines of ALMA are needed to image the compact sources, probing the disk material distribution in the giant-planet-forming region of our solar system.

Disk population studies reveal scaling relations in multiple dimensions (e.g., M_*, M_disk, ${\dot{M}}_{* }$, R_disk), linking disk evolution with the bulk properties of disks (e.g., Ansdell et al. 2016; Manara et al. 2016; Pascucci et al. 2016; Mulders et al. 2017). Recent analysis based on spatially resolved observations of 105 disks demonstrate that disk luminosity scales linearly with the surface area of the emitting materials (Andrews et al. 2018b). With better mapping of the disk material distribution, we revisit this relationship to obtain a better understanding of disk demographics.

Figure 9 shows the resulting disk size–luminosity relation for our sample in the Taurus star-forming region. Assuming a linear relationship in the log–log plane, we employ the Bayesian linear regression method of Kelly (2007) with its python package Linmix²⁸ to determine the correlation, considering uncertainties on both axes (including 10% absolute flux uncertainty for luminosity). With this approach, we find a best-fit relation of log R_eff = (2.15 ± 0.15) + (0.42 ± 0.11)log L_mm, where the disk size is the radius that encircles 95% of flux, and the disk luminosity is scaled as F_ν(d/140)² to a uniform 140 pc. The 1σ dispersion is 0.3 dex and the correlation coefficient is r = 0.58. The slope of the relationship is consistent (1σ) with the finding in Tripathi et al. (2017) and Andrews et al. (2018b) that ${L}_{\mathrm{mm}}\propto {R}_{\mathrm{eff}}^{2}$. We also include the scaling relation from Andrews et al. (2018b) with the same 95% definition for disk size in Figure 9, which shows a larger intercept (by 1–2σ). While our observations are conducted at 225 GHz, Andrews et al. (2018b) used data from the ∼340 GHz band in their work. The lower intercept of our derived correlation might be caused by a more concentrated distribution of larger grains and finer angular resolution in our observations, or by the exclusion of some of the large disks in our analysis. Andrews et al. (2018b) also claims that the slope of the correlation is insensitive to the metrics (50%–95%) used for disk size definition, while we find a slightly flatter slope (0.34 ± 0.11) when using R_eff,68%.

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As seen in Figure 9, disks with substructures mostly sit above the derived relationship. The inclusion of the DSHARP sample (R_eff defined as the radius of 95% encircled), steepens the relation by 1σ (0.53 ± 0.08), while still keeping most of the ring disks in the top right of the plot. Tripathi et al. (2017) and Andrews et al. (2018b) reproduced the scaling relation by considering optically thick disks with fractional regions being depleted (optically thin), and interpreted the spread of the correlation as the varying fraction of the optically thin region. Taking a few disks with identical disk luminosity but different spatial extents, the most compact ones are likely to be optically thick overall, while the most extended ones are expected to contain a large fraction of depleted optically thin regions (e.g., multiple gaps). This picture fits into the spatial segregation in the L_mm–R_eff plane for disks with various morphologies (Rosotti et al. 2019b). Multiwavelength observations would be beneficial to access the spectral index information to provide further evidence for this hypothesis.

The continuum emission at millimeter wavelength is heavily dominated by dust grains at a size of ∼ millimeter. These millimeter-size particles are subject to fast radial drift and are expected to be quickly depleted at large disk radii (Weidenschilling 1977); in contrast, dust disks often have large radii and survive for 1–10 Myr. Disk substructures may resolve this apparent contradiction, serving as the mechanism (e.g., dust traps, Pinilla et al. 2012; Dullemond et al. 2018) to hinder radial drift and preserve the disk materials in wide orbits. Our observations seem to fit this picture, where rings are formed at large radii and are the macroscopic consequence of particle trapping, which helps to maintain a large population of millimeter-size grains in the outer disk. For our compact disks, the outer dust disk could be lost through efficient radial drift as dust rings are somehow not able to exist, as seen in the disk of CX Tau, which is very compact (and also smooth) in millimeter dust emission but has a very extended CO gas disk (Facchini et al. 2019). In addition, the compact disks may suffer from past dynamical interactions of very wide binaries, e.g., GI Tau and GK Tau with a projected separation of 136 (Kraus & Hillenbrand 2009b).

Alternatively, the compact disks could have small sizes initially, closely connected to the disk formation process. Nonideal magnetohydrodynamic (MHD) simulations show that disk size distribution in the early protostellar stage strongly depends on the relative orientation of the rotation vector of the molecular cores and magnetic field (Tsukamoto et al. 2015; Wurster et al. 2016), through which both small and large disks could be formed. However, the disk formation process remains unclear, with complications from initial angular momentum distribution, MHD structure, and turbulence (Li et al. 2014; Bate 2018; Tsukamoto et al. 2018).

The inclusion of disk gas size measurements is crucial for the assessment of the formation and evolution path of our compact disks. If the original outer regions of these compact disks are absent through rapid inward drift of millimeter-size grains, R_gas/R_dust,mm should be higher in smaller disks. Disks that are born small would be expected also with small gas disks.

The stellar properties of RY Tau require a re-evaluation of the observed photospheric emission and the Gaia DR2 distance. Initial spectral types of RY Tau of F8 and G0 were measured by Hubble (1922) and Joy (1945), with independent support from Petrov et al. (1999), Calvet et al. (2004), and Herczeg & Hillenbrand (2014), among others. The spectral type of K1 measured by Herbig (1977) propagated into the Herbig & Bell (1988) catalog of T Tauri stars, and has since been widely adopted by many surveys and compilations (e.g., Kenyon & Hartmann 1995; Luhman et al. 2010; Rebull et al. 2010).

To resolve this discrepancy in SpT, we downloaded (from the CADC archive) and coadded 96 high-resolution ESPaDOnS spectra (Donati et al. 2006) of RY Tau, obtained by PIs H. Takami, J.-F. Donati, and C. Dougados in separate programs, with some data published by Chou et al. (2013). The spectra cover 3800–10000 Å with a resolution of R ∼ 68,000. We use the BT-Settl models (version cifist2011_2015; Allard 2014) with solar metallicity and log g = 4.0 to identify regions at <4300 and 5150–5200 Å that are most sensitive to temperature for FG spectral types. A χ² analysis of seven independent regions yields an effective temperature of 6220 ± 80 K, consistent with a spectral type F6-F8 in the Kenyon & Hartmann (1995) temperature scale. The uncertainty of 80 K is the standard deviation of best-fit temperatures between several different spectral regions. The discrepant spectral type of Herbig (1977) was likely caused by a measurement from a low-resolution red spectrum, which is not very sensitive to FG spectral types. Accounting for the minor change in spectral type from Herczeg & Hillenbrand (2014), the extinction here is increased slightly to A_V = 1.94 mag with an uncertainty estimate of ∼0.2 mag.

The Gaia DR2 parallax leads to a distance of 445 ± 45 pc. The uncertainty in the parallax of 0.24 mas yr⁻¹ is higher than the uncertainty of other nearby sources of similar magnitude, and the excess astrometric noise of 1 mas indicates a poor astrometric fit. Bright nebulosity around RY Tau (e.g., Leavitt & Pickering 1907) introduces additional uncertainty into whether the parallax measurement is reliable and likely causes the high excess noise. For 29 Taurus members³⁰ listed in Esplin et al. (2014) that are within 1 degree of RY Tau, the average distance is 128.5 ± 0.3 pc, with a standard deviation of 5 pc. If we focus on the 11 stars with the smallest uncertainties in parallax, the distance is 128.2 pc with a standard deviation of 4 pc. The distance of 128 ± 4 pc is adopted here as the distance to RY Tau.

These updated parameters and the J-band brightness lead to a luminosity of 12.3 L_⊙ (the luminosity from Herczeg & Hillenbrand 2014 would be adjusted to 11.1 L_⊙). Comparison to the non-magnetic Feiden (2016) yields a mass of 2.0 M_⊙, and an age of 5.2 Myr.

The 2MASS J-band is faint, relative to other Taurus sources of similar spectral type. The V-band emission measured by the ASAS-SN survey (Kochanek et al. 2017) is highly variable, likely indicating extinction events. The luminosity is therefore obtained directly from Herczeg & Hillenbrand (2014).

The dynamical mass of CIDA 9 is 1.32 ± 0.24 M_⊙, as measured from CO rotation (Simon et al. 2017) and updated with Gaia DR2 distance. This mass differs significantly from the mass of 0.43 M_⊙ inferred from the spectral type of M1.8 (Herczeg & Hillenbrand 2014). The inner hole of ∼25 au is suggestive of the higher mass. However, the spectrum has strong TiO absorption and could not be mistaken for a K spectral type. A sensitive search for spatially resolved multiplicity revealed an absence of any close companion of CIDA 9A (Kraus et al. 2011); the secondary is located at 23 and is discussed elsewhere.

We recently obtained a high-resolution IGRINS (Mace et al. 2018) HK spectrum of CIDA 9A to evaluate binarity. The A component (in the SW) was placed on the slit. The lines are single peaked and located at a radial velocity of ∼18.7 km s⁻¹, which corresponds to the expected velocity at that location in Taurus (Kraus et al. 2017). For this one epoch (JD of 2458565.64), we can rule out that the source is a double-lined spectroscopic binary, although a robust test will require several epochs. An initial analysis with a two-temperature fit yields a photospheric temperature of 3800–4000 K, warmer than inferred from the TiO bands in the optical but cool enough to still be discrepant from the dynamical mass.