The Architecture of the V892 Tau System: The Binary and Its Circumbinary Disk

V892 Tau was observed on 2015 September 29 as part of the ALMA program 2013.1.00498.S (PI. L. Pérez), using the Band 6 receivers. These observations included 30 antennas with projected baseline lengths between 36 and 1860 m (27–1400 kλ). Two spectral windows (SPWs) were configured to record the continuum data, centered at 217 and 232.4 GHz, each with 128 channels spanning a bandwidth of 1.875 GHz. The ¹²CO J = 2 − 1 line (rest frequency at 230.538 GHz) was targeted in a separate SPW, with a channel spacing of 244 kHz (velocity spacing of 0.32 km s⁻¹). Two isotopolog lines, ¹³CO and C¹⁸O J = 2 − 1, were covered in the remaining SPW at a channel spacing of 488 kHz (velocity spacing of 0.66 km s⁻¹). The quasar J0510+180 was observed at the start of the observing program, serving as both bandpass and flux calibrator. V892 Tau was then observed interleaving with the gain calibrator J0429+2724, reaching a total on-source time of ∼8 minutes. Only the continuum data were published previously in Pinilla et al. (2018).

The raw visibility data downloaded from the ALMA archive were calibrated following the scripts provided by ALMA staff using the required CASA (McMullin et al. 2007) version of 4.5.0. The bandpass shape and absolute amplitude scale were determined and applied to the science target using the observations of J0510+180. The phase variations were corrected using the repeated observations of J0429+2724. Given the bright continuum emission, we then performed a series of self-calibration iterations on the continuum visibility data (including the line-free channels in the line SPWs) using CASA v.5.6.0. Three rounds of phase-only self-calibration (stepping down the solution interval of 90, 60, and 30 s) provide a peak signal-to-noise ratio (S/N) increase of a factor of ∼3, and one iteration of amplitude self-calibration increases the peak S/N again by 30%. The calibration tables were then applied to the line channels.

The fully calibrated visibility data are used to generate images with the tclean task in CASA. The continuum image was produced using Briggs weighting with robust = 0.5 to optimize the image S/N in the outer disk, which results in a synthesized beam with an FWHM of 023 × 016 and an rms noise level of 76 μJy beam⁻¹ at a central frequency of 224 GHz (1.3 mm). For spectral lines, the continuum baseline was first subtracted from the line visibilities using uvcontsub before making the image cubes. The ¹²CO images were created with Briggs weighting (robust = 0.5) in a velocity resolution of 0.5 km s⁻¹. For the weaker ¹³CO and C¹⁸O emission, we generated the images with a Gaussian uv taper and robust parameter of 2 in 1 km s⁻¹ channels, resulting in a larger beam size of 040 × 0 34. The image details are summarized in Table 1.

Table 1. Observational Results

Line/Cont	Freq.	Beam (PA)	Disk-integrated Flux	Image rms	R90%
	(GHz)		(Jy km s−1) or (mJy)	(mJy/beam)	(arcsec)
(1)	(2)	(3)	(4)	(5)	(6)
12CO J = 2 − 1	230.538	023 × 016(18)	14.7 ± 0.4 a	6.4 (0.5 km s−1 channel)	1.45 ± 0.02
13CO J = 2 − 1	220.399	040 × 034(18)	3.3 ± 0.3	6.3 (1 km s−1 channel)	0.97 ± 0.03
C18O J = 2 − 1	219.560	040 × 034( − 04)	1.1 ± 0.1	5.0 (1 km s−1 channel)	0.68 ± 0.03
continuum-disk	224 (1.3 mm)	023 × 016(18)	290.6 ± 0.2	0.076	0.46 ± 0.01
continuum-disk	37.5 (8.0 mm)	008 × 005( − 607)	3.1 ± 0.4 b	0.035	⋯
continuum-disk	30.5 (9.8 mm)	009 × 006( − 702)	1.8 ± 0.3 b	0.025	⋯

Notes.

^a Disk-integrated line fluxes are measured with the Keplerian mask that encompasses all emission in a velocity range from −7 to 23 km s⁻¹, excluding the cloud-contaminated velocity range from 6.5 to 8 km s⁻¹. The reported line fluxes are therefore lower limits, due to the exclusion of these central channels. Line flux uncertainty is estimated as the rms noise level in the integrated intensity map generated without a sigma clip, multiplied by the square root of beam numbers in a mask size with an approximate radius of 2'' (rms * $\sqrt{\mathrm{Mask}\,\mathrm{area}/\mathrm{beam}\,\mathrm{area}}$). ^b The disk emission fluxes at 8 and 9.8 mm are estimated by subtracting the two point sources as modeled in Section 3.3 from the total flux (4.3 and 3.0 mJy, respectively) measured in the images. The uncertainty includes a 10% systematic flux calibration error.

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V892 Tau was observed with the Karl G. Jansky Very Large Array (VLA) using the Ka-band receivers as part of the "Disks@EVLA" large program (project code AC982, PI. C. Chandler). Two 1 GHz-wide basebands were tuned at central frequencies of 30.5 GHz (9.8 mm) and 37.5 GHz (8.0 mm). Data were collected in the A, B, and C configurations on 2011 July 15, 2011 March 19, and 2010 November 1, respectively. These observations cover projected uv spacings from 10 to 4024 kλ. Frequent monitoring of J0429+2724 was used to track the complex gain variations. The bright quasars 3C 84 and 3C 147 were observed as bandpass and flux calibrators, respectively. These VLA data are presented here for the first time.

The raw visibilities were calibrated in CASA using the pipeline ¹⁴ created by the "Disks@EVLA" team. Because the observations were performed spanning half a year, data from individual configurations were shifted to a common phase center before using concat to account for the source proper motion. The continuum images were then generated with tclean using Briggs weighting with robust = 0 to better resolve the inner emission. We have also created the 30.5 and 37.5 GHz combined continuum image using the multiterm, multifrequency synthesis algorithm (mtmfs) with nterms = 2. The image properties are summarized in Table 1.

The ALMA 1.3 mm and VLA (combined) ¹⁵ 8 mm continuum images, as well as their deprojected and azimuthally averaged radial intensity profiles, are shown in Figure 1. The deprojection adopts an inclination angle (i) of 545 and a position angle (PA) of 521, derived from the uv-plane fitting as described below. Emission at 1.3 mm presents a prominent ring at a radius of ∼02, with an inner disk cavity most likely carved by the binary and disk interaction. Subtle azimuthal asymmetry is seen across the dust ring, such that the northern part along the disk minor axis is about 20% brighter. This asymmetry is reflected in the radial profile as the relatively larger uncertainties around the ring peak regions. The dust disk ring is also detected at the longer 8 mm wavelength at similar radii, but only at 3σ–5σ significance, in which any asymmetry would be difficult to quantify. The clumpy distribution of 8 mm emission along the dust ring is likely associated with noise fluctuations (e.g., Macías et al. 2017). A more striking feature in the 8 mm image is the two bright (∼10σ) emission blobs inside the disk cavity. The flat spectral slopes (α ≈ 0) between 8 and 9.8 mm for these two point sources suggest that the bright emission is dominated by ionized gas emission (e.g., Rodmann et al. 2006; Pascucci et al. 2012). This emission, if present, is largely unresolved in the 1.3 mm image. We measure a dust disk radius of 046 at 1.3 mm (defined as the radius that encircles 90% of the flux; e.g., Tripathi et al. 2017). The dust disk around V892 Tau NE is undetected at 1.3 mm. Taking the 3σ upper limit of 0.2 mJy, it is more than 10 times fainter than typical disks around M3 stars (e.g., Andrews et al. 2013).

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To quantify the structure of the circumbinary disk of V892 Tau, we fit the 1.3 mm dust continuum emission in the visibility domain. As the azimuthal asymmetry is only modest at the resolution of our observation, we adopt a modified Gaussian ring model, which can be expressed as

$$\begin{eqnarray}&&I(r)=A\exp \left[-\displaystyle \frac{{\left(r-{R}_{\mathrm{ring}}\right)}^{2}}{2{\sigma }_{\mathrm{ring}}^{2}}\right],\end{eqnarray} \tag{ 1 }$$

where R_ring is the ring peak location and the Gaussian ring width σ_ring is described as

$$\begin{eqnarray}{\sigma }_{\mathrm{ring}}=\left\{\begin{array}{ll}{\sigma }_{\mathrm{in}}, & \mathrm{if}\quad r\leqslant {R}_{\mathrm{ring}}\\ {\sigma }_{\mathrm{out}}, & \mathrm{if}\quad r\gt {R}_{\mathrm{ring}}.\end{array}\right.\end{eqnarray} \tag{ 2 }$$

This model with different inner and outer ring widths is motivated by the fact that the inner ring edge would be severely truncated by the binary–disk interaction (e.g., Cazzoletti et al. 2017). A local pressure bump is also expected exterior to the binary orbit. In dust evolution models with a local pressure maximum, radial asymmetry in the grain distribution is expected as particles in the outer disk take longer to grow and drift to the pressure peak. Such a modified Gaussian ring model has been successfully applied in interpreting dust emission in transition disks (e.g., Pinilla et al. 2018). Previous observations of the V892 Tau disk suggest that emission even at 2.7 mm has a substantial nondust contribution (Di Francesco et al. 1997). Such an emission component, originating close to the stars, may also be present at 1.3 mm. As the two stars are largely unresolved in the 1.3 mm data, we include one point source (F_p) at the disk center to account for any possible nondust emission, as well as thermal dust emission from unresolved circumstellar disks. We therefore have five parameters in describing the continuum emission distribution: F_p, F_disk, R_ring, σ_in, and σ_out, in which F_disk is the integral of Equation (1). Four additional disk geometry parameters (i, PA, and phase-center offsets in R.A. and decl. as δ_α and δ_β ) are also included in the fit.

The Fourier transform of this azimuthally symmetric brightness distribution (i.e., the model visibilities) is then calculated using the Hankel transformation (Pearson 1999) and sampled at the same observed spatial frequencies. The point-source contribution is directly added as a constant flux in the phase-shifted model visibilities. The comparison of the model and data visibilities adopts a Gaussian likelihood ${ \mathcal L }\propto \exp (-{\chi }^{2}/2)$, where ${\chi }^{2}\,=\sum {\left|{V}_{\mathrm{obs}}({u}_{k},{v}_{k})-{V}_{\mathrm{mod}}({u}_{k},{v}_{k})\right|}^{2}{w}_{k}$, with w_k as the observed visibility weights. Uniform priors are assumed for the fitted parameters, with bounds set based on image inspections (see Table 2). We then explore the parameter space with a Markov Chain Monte Carlo (MCMC) method (emcee; Foreman-Mackey et al. 2013), sampled with 45 walkers and 5000 steps per walker. The autocorrelation length is on the order of 100 steps. The adopted parameters and the associated uncertainties are summarized in Table 2 (Model 1), which are estimated as the peaks and 68% confidence intervals of the posterior distributions, constructed with the last 1000 steps of the chains.

Table 2. Dust Disk Model Results

Parameter	Prior	Model 1	Model 2
(1)	(2)	(3)	(4)
Fp	[0, 100] mJy	4.07 ± 0.10	6.65 ± 0.08
δα,Point	[−02, 02]	⋯	−0.171 ± 0.001
δδ,Point	[−02, 02]	⋯	−0.197 ± 0.001
Fdisk	[0, 1000] mJy	290.59 ± 0.18	288.15 ± 0.16
σin	[0'', 02]	0.034 ± 0.001	0.027 ± 0.001
σout	[0'', 10]	0.077 ± 0.001	0.081 ± 0.001
Rring	[01, 05]	0.209 ± 0.001	0.203 ± 0.001
i	[20°, 90°]	54.51 ± 0.03	54.76 ± 0.03
PA	[10°, 70°]	52.10 ± 0.04	52.16 ± 0.04
δα	[−02,02]	−0.128 ± 0.001	−0.129 ± 0.001
δδ	[−02, 02]	−0.146 ± 0.001	−0.146 ± 0.001

Note. In Model 1, we assume that the point-source emission for any nondust contribution and circumstellar dust emission at 1.3 mm is located at the disk center, while Model 2 includes two additional parameters to account for phase-center offsets of the point source.

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The right panel of Figure 2 shows the adopted model radial brightness profile, with a truncated inner disk described with σ_out/σ_in = 2.26. The analysis by Pinilla et al. (2018) using this same ALMA data set only found a subtle asymmetry, with σ_out/σ_in = 1.06. This difference could be explained by the inclusion of the interior point-source model in our fitting, which, if not properly accounted for, could lead to an overestimation of the ring width. As shown in Figure 2, our model describes the main dust ring reasonably well. The residual image, created using the residual visibilities (${V}_{\mathrm{obs}}-{V}_{\mathrm{mod}}$) with the same tclean parameters as the data and model images, highlights the remaining features that are not reproduced by the simple model. First, the azimuthal asymmetry noted above could not be accounted for with an axisymmetric model; this is seen as positive and negative residuals across the disk. Second, nearly symmetric residual emission is observed in the outer disk, which is offset by ∼10° from the disk major axis as indicated by the black and gray dashed lines in Figure 2. This residual pattern suggests that the outer disk may have a different geometry with respect to the main dust ring; such structure might be expected from the binary–disk dynamical interactions. However, the resolution and sensitivity of the current data preclude us from revealing the precise disk morphology variation of the dust content.

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In the above modeling, we assumed that the point-source contribution is located at the disk center, with the same phase-center offsets as the dust ring. This simple assumption is reasonable given our large beam size. The point-source model is introduced to describe emissions coming from close to the two stars. The emission center therefore depends on the nature of the radiation (relative brightness of the emission from each component) and could be offset from the disk center. We performed another fitting with two additional parameters included to allow the location of the point source to vary within the dust cavity. Following the same modeling procedure as outlined above, the results are derived and summarized in Table 2 (Model 2). This new model provides similar dust ring properties to Model 1 but prefers a brighter point source separated from the disk center by 006. ¹⁶ This offset could be explained if the dust ring is eccentric, a feature naturally produced through binary–disk interaction (e.g., GW Ori; Bi et al. 2020; Kraus et al. 2020). In the 8 mm image, emission from (or close to) the two stars is marginally resolved and well separated from the dust ring. This allows us to investigate the possibility of an eccentric ring, though a direct modeling in the uv plane is hindered by the low S/N. Figure 3 shows our by-eye estimate in the image. Assuming the mass center of the binary is one focus of the ellipse, we find that our data are not able to distinguish a dust ring with low eccentricity (e < 0.15) from a circular ring. Given the brightness (4–6 mJy) of the point-source emission at 1.3 mm, future ALMA observations with resolution better than the binary separation (30–60 mas) could easily constrain the disk eccentricity.

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If we assume the disk millimeter emission is optically thin, the available dust mass can be simply estimated. The observed fluxes in the dust ring translate into dust masses of 97–160 M_⊕ and 207–315 M_⊕ for 1.3 and 8 mm measurements, respectively. The upper-end mass corresponds to T_dust = 20 K, typical of Class II disks, and the lower value assumes a higher dust temperature of T_dust = 30 K, which should be more representative for the warm disk condition of V892 Tau (see Section 3.2.2). In this calculation, we adopt the dust opacity κ_{1.3 mm} = 2.3 cm² g⁻¹ (e.g., Andrews et al. 2013) and an opacity power-law index β = 1, which extrapolates to κ_{8 mm} = 0.37 cm² g⁻¹. We note that a lower β, often observed in dust rings (e.g., Long et al. 2020), will lead to an even higher dust mass at the longer wavelength. The dust mass differences between the two wavelengths should therefore be largely attributed to the high optical depth of the 1.3 mm emission.

The CO emission around V892 Tau is detected and spatially resolved with high significance in all three isotopologs, spanning a very broad LSRK velocity range from −7 to 23 km s⁻¹. The channel maps for the three lines with this full velocity range are shown in Appendix C. Strong cloud absorption is seen near the systemic velocity around 8 km s⁻¹, even in C¹⁸O. All emission is observed within a radius of 2 0, and the C¹⁸O emission only emerges from within 10 in radius. The maximum recoverable scale (MRS) ¹⁷ for this observation is only 17 if defined based on the fifth percentile of the baseline lengths. Interferometric observations tend to filter out emission with scales larger than the MRS, therefore these data are likely insufficient to reveal the full gas distribution in the outer disk. Figure 4 shows the spatially integrated line spectra, extracted using a Keplerian mask ¹⁸ designed to encompass all emission in individual channels. Though the CO emission pattern is dominated by the disk rotation, the brighter blueshifted emission suggests asymmetric features along the disk major axis. We estimate the line fluxes by integrating over the velocity range from −7 to 23 km s⁻¹, excluding the range from 6.5 to 8 km s⁻¹, where the line emission is severely contaminated by cloud absorption. These lower limits to the line fluxes are summarized in Table 1.

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The ¹²CO integrated intensity (moment 0) map is shown in Figure 5, including only pixels in individual channels above the 3σ level. The deprojected and azimuthally averaged radial profile extracted from the moment 0 map exhibits a central dip and reaches its maximum brightness interior to the dust ring peak. Radial profiles for the ¹³CO and C¹⁸O lines show similar morphologies, with a deficit of line emission inside the dust disk cavity but with peak locations slightly shifted outward (Figure 5). These signs of a gas density drop in the inner dust disk cavity have been observed in many transition disks (e.g., van der Marel et al. 2021), usually with a smaller cavity radius and lower degree of depletion when compared to the dust component. In the V892 Tau disk, gas depletion is expected from the binary–disk interaction. However, quantifying the gas depletion level and the gas cavity radius is made challenging by cloud absorption. Other molecules with lower abundances, whose lines are less susceptible to cloud contamination, should be employed to trace the gas structure inside the dust cavity.

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Based on the derived radial intensity profile, we measure the CO gas disk radius using a similar method as for the dust disk size (the radius where 90% of the integrated line flux is encircled). This estimation provides a good approximation of the gas disk extensions and can be directly compared with literature measurements (e.g., Ansdell et al. 2018). The R_90%,gas values are summarized in Table 1.

The intensity-weighted velocity (moment 1) map is also shown in Figure 5. The rotation pattern suggests that the northeast side of the disk is blueshifted with respect to the systemic velocity of 8 km s⁻¹. Irregular emission features are also visible, mostly from the redshifted side of the disk, emerging from the disk edge. In the following subsections, we will first use the main feature of Keplerian rotation to constrain the total mass of the central stars, then explore the thermal and vertical structures of the disk, and finally describe the non-Keplerian features associated with the system by comparing the data images with our established Keplerian model.

3.2.1. Stellar Mass from Gas Disk Rotation

3.2.2. Disk Thermal and Vertical Structure

Optically thick lines emit from elevated layers above the disk midplane and therefore can be employed to explore the disk vertical structure (e.g., de Gregorio-Monsalvo et al. 2013; Rosenfeld et al. 2013). The comparison of predicted isovelocity contours to line emission in Figure 6 suggests that ¹²CO J = 2 − 1 emission in the V892 Tau disk emerges from a surface with an aspect ratio (z/r) of ∼0.1. This is consistent with the fact that emission at ∼1'' is only marginally spatially resolved as seen from the channel maps, given the beam size of 02. The CO-emitting surfaces from previous determinations for both T Tauri and Herbig Ae disks are often found at z/r > 0.3 (e.g., Pinte et al. 2018; Law & MAPS team 2021; Paneque-Carreno et al. 2021). The emission surfaces for small dust grains probed by near-infrared scattered light images are slightly lower than the CO surfaces, with z/r ≈ 0.15−0.3 (e.g., Ginski et al. 2016; Avenhaus et al. 2018). Thus, the disk around V892 Tau is an especially "flat" example. The gas disk vertical extension depends on the balance between disk thermal pressure and stellar gravity, in which the pressure scale height $h\propto {c}_{s}/{\rm{\Omega }}\propto \sqrt{{T}_{\mathrm{gas}}/{M}_{* }}$, where the surface gas temperature could be assumed to scale with ${L}_{* }^{1/4}$. The disk scale height would be 30% lower for a system with two equal-mass, coeval stars compared to a single star. Assuming the CO-emitting height scales with the disk pressure height, the flat disk geometry in V892 Tau therefore seems consistent with its nature as an equal-mass binary.

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The brightness temperatures for spatially resolved, optically thick lines in local thermodynamic equilibrium are roughly equivalent to the gas temperature of the emitting disk layer (e.g., Pinte et al. 2018). Using ¹²CO, we are therefore able to probe the disk surface temperature at z/r ≈ 0.1. As continuum subtraction in optically thick line regions would underestimate the true line fluxes (e.g., Weaver et al. 2018), the peak brightness temperature map (Figure 5) is produced using the ¹²CO image cubes generated from the line+continuum visibilities. Our conversion from peak intensity into brightness temperature adopts the full Planck function. As seen in Figure 5, the CO-emitting gas has temperatures spanning a range of 20–80 K, which reaches its peak value at the dust ring location. The drop in gas temperature inside the dust ring is likely due to the combined effects of gas depletion and beam dilution. The gas disk around V892 Tau is warmer than disks around T Tauri stars (e.g., IM Lup, Pinte et al. 2018; GM Aur, Huang et al. 2020a) but has comparable gas temperatures to the disks around Herbig Ae stars in single stellar systems (e.g., HD 163296, MWC 480, Law & MAPS team 2021). Note that the cloud absorption could lead to an underestimate of the gas temperature.

The radial distribution of the surface temperature is usually approximated by a power law. Our fitting of the azimuthally averaged temperature in the radius range of 28–200 au results in a radial profile of $T(r)=47{\left(r/100\mathrm{au}\right)}^{-0.37}\,{\rm{K}}$. As shown in Figure 5, there are significant brightness temperature variations in the two sides of the disk. The emission profile from the blueshifted side of the disk resembles the fitted averaged profile in a power-law manner within the fitting radial range, which however exhibits a steep drop outside 200 au. The line emission from the redshifted side of the disk is ∼10 K brighter than the blueshifted side at around 100 au and then decreases more sharply when moving outwards to produce up to a 20 K difference in the outer disk. The comparison between these two sides of the disk therefore demonstrates strong azimuthal asymmetries in the V892 Tau gas disk (see also Elias 2–27 in Paneque-Carreno et al. 2021). Such asymmetry is also seen in the mid-infrared image at 10.7 μm, in which the inner disk toward the southwest (redshifted) side is brighter (Monnier et al. 2008).

3.2.3. Non-Keplerian Gas Emission Features

To explore the asymmetric nature of the CO emission, we compare in Figure 7 the observed CO images with the model images (as obtained in Section 3.2.1) channel by channel. This detailed comparison helps us to examine how CO line emission in the V892 Tau system deviates from a symmetric disk model. Excess line emission outside of the Keplerian disk edge is observed between 3–6 km s⁻¹ in the blueshifted disk side, while on the opposite side of the disk with redshifted velocities from 9–12 km s⁻¹, the Keplerian disk model produces more emission than what the data suggest. These reveal two main arcs (at 8σ–10σ significance) along the disk outskirts in the collapsed residual maps (lower panels in Figure 7): one residual arc with positive emission on the northeast (blueshifted) side of the disk, and another arc with negative emission on the southwest (redshifted) side. The northeast (blueshifted) side therefore appears more extended. The two arcs are close to rotational symmetry by an angle of ∼180°. A gas disk with varying geometry where the inner and outer disks have different inclinations and position angles could be one possible explanation for such residual patterns.

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Besides the asymmetry along the disk major axis (between the blue- and redshifted disk sides), we also observe emission asymmetries along the disk minor axis, especially from the redshifted disk side. From the velocity range of 9–11 km s⁻¹, emission from the northern side is more extended compared to its southern counterpart, with faint narrow arcs (3σ–4σ in brightness, spanning ∼05 in length) sticking out from the Keplerian disk edge. In velocity channels covering 11.5–12.5 km s⁻¹, CO emission in the outer disk shows discontinuities and short arcs extending outside the main rotating disk. We also see emission clumps to the southeast from 9–10 km s⁻¹, with higher velocity when moving closer to the disk. These features are only detected at relatively low significance, and might be parts of some larger-scale spiral structures in the outer disk that our current data are not able to probe (e.g., Huang et al. 2020b). Based on visual inspection, we propose three spiral arms that roughly match the emission features described above, as shown in Figure 8. Our spiral identifications here are highly inconclusive given the lack of short spacing data.

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Other non-Keplerian features are also present, including excess line emission around 100 au in the 13–14 km s⁻¹ velocity range, twisted emission in the outer disk edge at 10.5 km s⁻¹, and a possible emission bridge connecting the Keplerian wings across the minor axis at 4.5 km s⁻¹. All of the emission features discussed above could be better identified and characterized by future, deeper observations sensitive to a broader range of spatial scales.

The two bright emission blobs inside the disk cavity at 8 mm are roughly separated by one beam (∼005, Figure 1), which is comparable to previous astrometric measurements of the inner binary (Smith et al. 2005; Monnier et al. 2008). It is therefore reasonable to assume that they trace the locations of the two stars. In this section, we will take this unique opportunity to measure the binary separation and position angle at the epoch of the VLA observations. With the well-established total stellar mass from models of the gas disk rotation and the source distance from Gaia, we then provide an updated binary orbital solution by combining our new astrometric determinations with previous measurements.

The stellar locations are determined by fitting to the VLA visibilities. Given the unresolved nature of the two emission clumps, we employ two point-source models, each with three free parameters (flux, centroid position offsets relative to the observed phase center in RA and dec.). Model visibilities are directly written in the form of a constant flux at the observed spatial frequencies with phase-center offsets accounted for. Following the fitting procedure ²¹ outlined in Section 3.1, the parameter space is sampled with 30 walkers and 10,000 steps per walker with emcee (Foreman-Mackey et al. 2013). The autocorrelation length is on the order of 100 steps. We then use the chains of the last 5000 steps to derive the best-fit parameters. Our fitting only uses the A-array data, as this is the only configuration that separates the two peaks. Meanwhile, because the full VLA data sets, combining A-, B-, and C-array configurations, were taken spanning about half a year, this choice largely reduces the uncertainties of stellar location determinations and the subsequent orbit fitting. The measured phase-center offsets of the two peaks are δ_α,A = −0031, δ_δ,A = −0024, and δ_α,B = 0023, δ_δ,B = 0005, where star A and B are to the west and east, respectively (see the relative location in Figure 1 and discussion below). Uncertainties in each offset direction are ∼0002 (the corner plot of the fitting parameters is shown in Appendix D, Figure 18). The derived binary separation is 61 ± 3 mas, with a position angle of 61° ± 3°, measured from north to east. The 8 mm peak fluxes are 0.566 and 0.606 mJy for stars A and B, respectively, with uncertainties of 0.037 mJy. The 9.8 mm data have slightly worse resolution, and the two emission clumps are less well resolved (see Appendix A). To evaluate the systematic errors on the astrometry, we have fitted the 9.8 mm A-array data in the same way and obtained δ_α,A = −0035, δ_δ,A = −0026 and δ_α,B = 0023, δ_δ,B = 0006 with the same uncertainties of 0 002, and fluxes of 0.569 and 0.695 mJy for stars A and B, respectively. The consistency from both wavelengths indicates that the astrometric measurements are robust.

The binarity of V892 Tau was initially proposed by Smith et al. (2005) based on high-resolution speckle imaging at the K band (λ = 2.2 μm), with observations conducted in 1997 and 2003. The two stars were then resolved by Keck observations using near-infrared aperture masking in 2004 (Monnier et al. 2008). These three epochs of observations consistently found slightly brighter emission (by <20%) at 2.2 μm from the southwest component, which was then assigned as the primary star (star A). The binary separations and position angles from these literature measurements are summarized in Table 3. The consistent astrometric measurements in 2003 and 2011 (the latter from the VLA observations) suggest an orbital period of ∼7–8 yr. This estimate assumes that the primary star is located to the southwest at the time when the VLA data were taken. However, given the similar stellar properties of the two stars, there could be a 180° ambiguity of the position angle for individual measurements. Monnier et al. (2008) preferred a flipped geometry of the earlier 1996 measurement, which resulted in an orbital period of 13.8 ± 1.5 yr and semimajor axis of 72.4 ± 6.3 mas (9.7 au). If we follow this orbital solution, our 2011 measurement should also have a flipped position angle of 61° + 180° so that the primary star is located in the northeast. In either case, orbital fitting with all four measurements would be problematic. As shown in Figure 9, the similar projected distances along the decl. axis in 1996 and 2011 are not compatible with a stationary orbital solution. We decided to exclude the earlier 1996 measurements, in which emission from the two stars was not fully resolved (Smith et al. 2005). Our final orbital fitting therefore uses the latest three measurements and assumes the primary star is always located to the southeast. This decision is supported by long-term monitoring of the V892 Tau system that samples more than one complete orbit (A. Kraus & A. Rizzuto 2021, private communication).

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We derived stellar orbits using the Orbits for the Impatient (OFTI) Bayesian rejection sampling algorithm encoded in the orbitize! software package (Blunt et al. 2017, 2020), which is well suited to constrain orbital elements for systems with data only covering a small fraction of the orbital period. Uniform priors were adopted for the following orbital elements: semimajor axis (a) from 0.001 to 10⁷ au (in log space), eccentricity (e) from 0 to 0.5, inclination (i_b) from 0 to π, argument of periastron (ω_b) from 0 to 2π, position angle of the ascending node (Ω_b) from 0 to 2π (counted from N to E), and time of periastron passage (τ) from 0 to 1. The upper boundary of the prior on e is again suggested by the long-term monitoring of V892 Tau (A. Kraus & A. Rizzuto 2021, private communication). Experimental fitting with e ∈ [0, 1] returns a local peak of low eccentricity and some possible highly eccentric orbits (see Appendix Figure 19). The source distance and total stellar mass are allowed to vary but are set as Gaussian priors with parallax measurements taken from Gaia and the dynamical mass posterior from the modeling of the gas disk rotation in Section 3.2.1.

Using the three astrometric measurements, we run a sample of 10⁵ accepted orbits, which constrain the orbital elements as a = 7.1 ± 0.1 au, e = 0.27 ± 0.1, i_b = 593 ± 27, and P = 7.7 ± 0.2 yr as computed from a and M_tot following Kepler's third law, which is about half of the orbital period reported in Monnier et al. (2008). The lack of radial velocity information introduces an ambiguity of 180° in Ω_b and a coupled degeneracy between ω_b and Ω_b. Therefore, we obtain two families of solutions for ω_b and Ω_b (in units of degree), as (1) ${{\rm{\Omega }}}_{{\rm{b}}}={50.5}_{-8.8}^{+9.6}$, ${\omega }_{{\rm{b}}}={179.9}_{-30.3}^{+44.4}$, and (2) ${{\rm{\Omega }}}_{{\rm{b}}}={230.4}_{-8.9}^{+9.7}$, ${\omega }_{{\rm{b}}}={0.2}_{-33.4}^{+40.8}$ where the negative ω_b values are taken from ω_b − 180°. Random draws of orbital solutions are plotted in Figure 9.

Our observations in Section 3 show that the circumbinary disk around V892 Tau exhibits an inner dust cavity with millimeter emission peaking at a radius of ∼02. This ring of emission is also detected at longer wavelengths of 8 and 9.8 mm. The CO gas observations suggest that the disk motion is dominated by Keplerian rotation, in which emission from the northeast side of the disk is blueshifted. These observations suggest a disk geometry with an inclination angle of i_d = 546 ± 13 and a position angle of Ω_d = 530 ± 07 (these are the averages of the consistent posteriors for the mm continuum and CO gas emission models). Assuming Keplerian disk rotation, modeling of the CO surface brightness distribution enables an independent determination of the total stellar mass of the V892 Tau binary as M_tot = 6.0 ± 0.2 M_⊙, confirming the system is composed of two A-type stars. With the total stellar mass and astrometric measurements, including new constraints from high-resolution VLA observations, we are able to measure the binary orbit.

4.1.1. Interaction between the Inner Binary and the Circumbinary Disk

The mutual inclination between the binary and disk orbital planes (Δ) is an important metric for understanding the effect of binary motion on the disk structure and dynamics. This quantity can be expressed as

$$\begin{eqnarray}&&\cos {\rm{\Delta }}=\cos {i}_{{\rm{d}}}\cos {i}_{{\rm{b}}}+\sin {i}_{{\rm{d}}}\sin {i}_{{\rm{b}}}\cos ({{\rm{\Omega }}}_{{\rm{d}}}-{{\rm{\Omega }}}_{{\rm{b}}}).\end{eqnarray} \tag{ 3 }$$

For an individual plane, the inclination (i) and position angle (Ω) together define its absolute orientation. ²² For both the V892 Tau binary and its circumbinary disk, their true orientations are currently unconstrained. As we are interested in the relative orientation of the two planes, we could fix the disk plane and vary the angular momentum vector of the binary orbit. We assume that the disk with i_d = 546 and Ω_d = 530 has its NW side closer to the observer. Following this definition, due to the 180° ambiguity of Ω_b, we obtain two possible solutions (see Figure 10): (1) the two planes are nearly coplanar with Δ = 80 ± 42 when Ω_b = 505, and (2) the two planes are drastically misaligned by Δ = 1132 ± 30 (more close to polar orientation) when Ω_b = 2304.

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Theoretical models of tidal truncation predict that the inner edges (r_in) of circumbinary disks would be located at 2a–3a for binary orbits with moderate eccentricity and when coplanar with their surrounding disks (Artymowicz & Lubow 1994; Hirsh et al. 2020). In the case of misalignment, r_in/a would however have a complicated dependence on the mutual inclination, orbital eccentricity, and binary mass ratio. Based on the calculations presented in Miranda & Lai (2015) for an equal-mass binary, r_in/a varies between 1.5 and 3 when e and Δ exceed some threshold values that depend on disk viscosity and thickness. For both sets of possible Δ in the V892 Tau system, an e ∼ 0.3 suggests r_in/a close to 2, though other numerical simulations suggest wider cavities than these analytical predictions (e.g., Thun et al. 2017). The ratio between the dust disk cavity size and the binary orbital semimajor axis is estimated to be 3.4–4, with the boundary values given by (R_ring − σ_in)/a and R_ring/a, respectively. The dust distribution does not directly trace the disk truncation radius, as the dust grain locations are further regulated by radial drift toward local pressure bumps (e.g., Andrews et al. 2014; Cazzoletti et al. 2017). The inner edge of the gas disk should be located closer to the binary and is a more appropriate comparison to the model predictions. Indeed, as seen in Figure 5, the ¹²CO emission peaks inside the dust ring, closer to what models predict. However, in order to make direct comparisons with the models, future high-resolution gas observations with high excitation lines are required to minimize cloud contamination.

Initially misaligned (with respect to the binary plane) circumbinary disks orbiting around eccentric binaries will undergo precession and evolve into one of two possible final configurations (e.g., Aly et al. 2015). For systems with small initial mutual inclination angles, tidal torques bring the disk plane into alignment with the binary orbital plane on a timescale usually much shorter than the disk viscous timescale (Foucart & Lai 2014; Smallwood et al. 2019). Otherwise, the two planes would be driven toward a polar configuration, where the disk plane is perpendicular to the binary orbital plane (Martin & Lubow 2017). The detailed evolution process and its final outcome depend on specific system characteristics. For example, for a highly eccentric orbit, a very small initial tilt between the binary and disk planes could lead to polar alignment. Following the criteria provided by Zanazzi & Lai (2018), for a binary orbit with e = 0.27, the mechanism leading to polar alignment will likely operate only when the initial misalignment Δ_init > 66°, whereas the coplanar solution is achievable when Δ_init < 58°. In the presence of eccentricity, Δ oscillates before reaching a steady state, with its amplitude and the duration of oscillations depending on the disk size, viscosity, and binary eccentricity (Martin & Lubow 2018). The two orbital solutions for V892 Tau presented here might both be likely, assuming the system is evolving toward the final configuration (coplanar or polar) in the damping process. However, given the short realignment timescale, we would favor the coplanar solution.

When radial differential precession occurs, as in the case where the internal communication timescale across the disk is longer than the disk precession timescale, the disk can warp or even break into two distinct parts (Facchini et al. 2013; Nixon et al. 2013; Doǧan et al. 2018). The resulting misalignment between the inner and outer disk could sometimes leave detectable imprints, seen as shadows in scattered light images and gas kinematic features deviating from a purely Keplerian velocity field (e.g., Casassus et al. 2015; Juhász & Facchini 2017; Walsh et al. 2017; Pérez et al. 2018; Benisty et al. 2018; Zhu 2019). Stronger disk warps are expected to develop in the cooler and radially more extended disks (Martin & Lubow 2018). In the warm circumbinary disk of V892 Tau, the patterned residuals from both the millimeter continuum emission and CO gas suggest a perturbed disk and the presence of a mild disk warp (e.g., Facchini et al. 2018). The asymmetries in the brightness (and presumably gas) temperatures along the disk major axis could be explained if the disk is warped with a more inclined inner region. The southwest part of the inner disk could appear puffed up and intercept more stellar radiation, resulting in a warm plateau and a cooler outer disk. Meanwhile, due to the warp (the inner–outer disk misalignment), the northeast outer disk is directly exposed to more starlight and is thus warmer than the opposite side of the disk at the same radial distance (see also, e.g., Pérez et al. 2018).

4.1.2. Interaction with the Exterior Companion

4.1.3. A System-level View

Figure 11 shows the stellar and disk architecture of the V892 Tau system that we are proposing. The disk radial extensions and warped morphology are both consistent with binary–disk interactions. The coplanarity of the disk and binary orbits also agrees with theoretical expectations for rapid orbital realignment.

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Because the direct formation of a close binary (a < 10 au) is inhibited by the opacity limit of fragmentation (e.g., Larson 1969), the current stellar configuration of the V892 Tau system must have evolved significantly over the past few Myr. In order to build the inner equal-mass binary, inward migration is expected through the exchange of angular momentum between the binary and the surrounding material, including the gas envelope and the individual circumstellar disks (Bate et al. 2002; Tokovinin & Moe 2020). The low-mass tertiary companion V892 Tau NE at 4'' may have also played a critical role in the reconfiguration process (e.g., through exchange interactions; Bate et al. 2002).

Trapping of large dust grains in the radial direction outside an inner cavity is a universal feature predicted and observed in circumbinary disks. However, along the azimuthal direction, the distributions of millimeter-sized grains appear differently. The circumbinary disks around V892 Tau (this work) and GG Tau A (Andrews et al. 2014) show only marginal azimuthal variations. On the contrary, a horseshoe-shaped dust distribution and a substantial east–west emission contrast are observed in HD 142527 (Casassus et al. 2013; Boehler et al. 2017) and AB Aur ²³ (Tang et al. 2017), respectively. Azimuthal dust trapping in circumbinary disks can occur due to either anticyclonic vortices induced by the Rossby wave instability (e.g., Zhu & Stone 2014) or asymmetric gas accumulation at the cavity edge promoted by a high mass ratio binary (e.g., Shi et al. 2012; Ragusa et al. 2017). In the former case, if the disk of V892 Tau has intermediate-to-high viscosity (α > 10⁻⁴), a long-lived vortex cannot survive. In the latter case, the formation of a long-lasting overdense clump is independent of disk viscosity (Miranda et al. 2017; Alexander et al. 2020). Such a feature constitutes an azimuthal pressure bump that is expected to effectively trap marginally coupled dust grains (van der Marel et al. 2021). Both V892 Tau and GG Tau A (taking GG Tau Ab1/Ab2 as one component) are high mass ratio binaries but lack azimuthal dust trapping in their disks. The dust rings in the two systems might have low Stokes numbers due to high local gas surface densities (see discussions in van der Marel et al. 2021).

Spiral density waves are also common outcomes of binary–disk interactions, especially when the binary has an eccentric orbit (e.g., Price et al. 2018). Such spiral structures have been observed in the inner disk of AB Aur, interior to the millimeter dust ring (Tang et al. 2017) and in the outer disks of GG Tau A (Keppler et al. 2020), HD 142527 (Fukagawa et al. 2006; Christiaens et al. 2014), and possibly in GW Ori (Kraus et al. 2020). The orbital solutions derived here for the V892 Tau binary prefer a nonzero eccentricity. While a disk warp is suggested by the CO gas emission, spiral structures are not clearly identified. Faint spirals in the V892 Tau disk are difficult to identify from the bright Keplerian-dominated disk with our shallow observations. The exterior stellar companion could also largely complicate the disk kinematics. With the improved stellar and disk properties for the V892 Tau system, future hydrodynamical simulations would be highly desirable to explore the potential distributions of spiral structures and to confirm or rule out the proposed disk warp.

Planets have been found in both circumstellar and circumbinary configurations (Martin 2018). If they formed early, such planets may not survive the binary orbital decay process expected for close pairs (e.g., Muñoz & Lai 2015). However, once a stable stellar configuration is reached, subsequent planet formation can proceed if there is still sufficient disk material. The dust disk of V892 Tau is among the most massive Class II disks, with dust mass (see Section 3.1) comparable to Class 0/I disks and sufficient to account for the mass of solids in most exoplanetary systems (Tychoniec et al. 2020). The total disk mass, as high as ∼ 0.06 M_⊙, if assuming a gas-to-dust ratio of 100, is however only ∼1% of the central stellar mass. Therefore, gravitational instability may not be a feasible mechanism to form planets. Nevertheless, the abundant pebble mass and high dust density around the pressure bump make the conditions in the disk ring favorable of planet formation.