Sites of Planet Formation in Binary Systems. II. Double the Disks in DF Tau

Sites of Planet Formation in Binary Systems. II. Double the Disks in DF Tau

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  Draft version November11, 2024 Typeset using L A TEX twocolumn style in AASTeX631 Sites of Planet Formation in Binary Systems. II. Double the Disks in DF Tau Taylor Kutra ,1 Lisa Prato ,1 Benjamin M Tofflemire ,2, ∗ Rachel Akeson ,3 G. H. Schaefer ,4 Shih-Yun Tang ,5, 1 Dominique Segura-Cox ,2 Christopher M. Johns-Krull ,5 Adam Kraus ,2 Sean Andrews ,6 and Eric L. N. Jensen 7 1Lowell Observatory, Flagstaff, AZ 86001 USA 2Department of Astronomy, The University of Texas at Austin, Austin, TX 78712, USA 3IPAC/Caltech, Pasadena, CA, 91125, USA 4The CHARA Array of Georgia State University, Mount Wilson Observatory, Mount Wilson, CA 91023, USA 5Physics & Astronomy Department, Rice University, 6100 Main St., Houston, TX 77005, USA 6Center for Astrophysics, Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA 7Dept. of Physics & Astronomy, Swarthmore College, 500 College Ave., Swarthmore, PA 19081, USA ABSTRACT This article presents the latest results of our ALMA program to study circumstellar disk character- istics as a function of orbital and stellar properties in a sample of young binary star systems known to host at least one disk. Optical and infrared observations of the eccentric, ∼48-year period binary DF Tau indicated the presence of only one disk around the brighter component. However, our 1.3mm ALMA thermal continuum maps show two nearly-equal brightness components in this system. We present these observations within the context of updated stellar and orbital properties which indicate that the inner disk of the secondary is absent. Because the two stars likely formed together, with the same composition, in the same environment, and at the same time, we expect their disks to be co-eval. However the absence of an inner disk around the secondary suggests uneven dissipation. We consider several processes which have the potential to accelerate inner disk evolution. Rapid inner disk dissi- pation has important implications for planet formation, particularly in the terrestrial-planet-forming region. 1. INTRODUCTION A comprehensive paradigm for planet formation re- quires a fundamental understanding of the conditions, process, and timescale for circumstellar disk evolution. Although advancements in theory (see review by Pas- cucci et al. 2023) and observations, such as ALMA (Barenfeld et al. 2016; Güdel et al. 2018) or JWST (Ba- jaj et al. 2024), have brought about new insights, puz- zling challenges remain. For example, what triggers the onset of disk dissipation, what is the source of the α viscosity in the disk, and what sustains the persistence of some primordial disks for 5–10 Myr (Herczeg et al. 2023)? Young binary systems offer a unique opportunity to study both the fragility and robustness of circumstel- lar disks because membership in a binary system dic- Corresponding author: Taylor Kutra tkutra@lowell.edu ∗ 51 Pegasi b Fellow tates that tidal truncation by the companion (e.g., Arty- mowicz & Lubow 1994) limits the disk’s outer radii. Thus disks in binaries have determinate maximum sizes. Given the dynamical complexity, it is unsurprising that circumstellar disks in binaries with orbital separations of ≲ 100 AU are smaller, less massive (Jensen et al. 1996; Harris et al. 2012; Barenfeld et al. 2019), and shorter- lived (Cieza et al. 2009; Kraus et al. 2012; Cheetham et al. 2015; Barenfeld et al. 2019) than disks around more widely spaced or single stars (e.g., Akeson et al. 2019). Yet despite these seemingly bleak prospects for disk longevity and potential planet formation, in some cases the circumstellar disks in close binary systems persist. Furthermore, planet formation can proceed in close bi- nary systems, as exemplified by γ Cephei b (Hatzes et al. 2003), GJ 86b (Queloz et al. 2000) and HD 196885 Ab (Correia et al. 2008), albeit less frequently (Kraus et al. 2016). Clearly circumstellar disk evolution is not reg- ulated entirely by membership in a close binary; other processes and influences are at work. This is demon- arXiv:2411.05203v1 [astro-ph.SR] 7 Nov 2024
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  2 Kutra etal. strated by the large range in age at which circumstellar disks dissipate (e.g., Haisch et al. 2001; Williams & Cieza 2011). In addition to the binary environment, other fac- tors drive disk dissipation: by studying the stellar, or- bital, and disk properties in young binaries, we can use these nominally coeval systems to explore these factors, interpreting the evolution of all primordial disks through this lens. Using this paradigm, we investigate the young (1-2 Myr) visual binary, DF Tau. It is composed of two roughly equal mass M2 stars on a 48 year orbit in the Taurus star forming region (Allen et al. 2017). The pro- jected orbital separation is only ∼ 100 mas, correspond- ing to a physical separation of ∼ 14 AU at a distance of 142 pc (Krolikowski et al. 2021). Both the A and B components were designated as classical T Tauri stars (CTTSs) by Hartigan & Kenyon (2003) and White & Ghez (2001) based on accretion signatures (i.e., the Hα equivalent width, UV excess, [O I] molecular emission, and veiling at 6100Ȧ). White & Ghez (2001) found a much weaker ultraviolet (UV) excess for the DF Tau secondary, ∆U = 0.85 mag, compared to that of the primary, ∆U = 2.43 mag. Their criterion for the presence of a disk is ∆U = 0.8 mag; however, the uncertainty in the U-band magnitude is ∼ 30% (0.29 mag), indicating a marginal UV CTTS assignation for DF Tau B. Allen et al. (2017) presented component-resolved, near-infrared (NIR) spectroscopy and photometry of the DF Tau binary and concluded that for DF Tau A, the NIR colors, IR veiling, and optical/NIR colors were all consistent with the presence of an accreting circum- stellar disk. However, they found little variability and no indication of accretion or significant amounts of cir- cumstellar material around the secondary and cautioned that the disk signatures seen for DF Tau B in Hartigan & Kenyon (2003) could have been the result of contamina- tion from the disk of DF Tau A, given that the angular separation at the time of observation was close to the resolution limit of the Hartigan & Kenyon (2003) HST STIS observations. DF Tau is part of our young, small-separation binary sample observed with ALMA in Cycle 7 (PI Tofflemire). Targets were selected for this program on the basis of their relatively complete orbital solutions. As demon- strated in our recent study of the FO Tau binary (Tof- flemire et al. 2024), our goal is to understand the disk dissipation process in the context of the binaries’ stellar and orbital properties. This work is also a component of our larger exploration of the spectroscopic and pho- tometric properties of the individual components in a sample of close to 100 young binary systems (e.g., Kel- logg et al. 2017; Allen et al. 2017; Sullivan et al. 2019; Prato 2023). In this contribution we focus on our new ALMA obser- vations, reanalyze the DF Tau NIR component spectra, including measurements of the stars’ surface averaged magnetic fields, and update the orbital solution with our most recent adaptive optics (AO) observations. Given the precise orbital solution, stellar parameters that sug- gest similar component temperatures and masses, and clear evidence for an inner disk around the primary with only marginal evidence for an inner disk surrounding the secondary star, DF Tau is a key target for understanding the onset of disk dissipation. In section 2 we describe our observations and data re- duction from ALMA, Keck, TESS/K2, and the Lowell 0.7-m and 1.1m telescopes and we present our analysis of the multi-wavelength dataset in Section 3. In Section 4 we discuss our results in terms of the disk and binary interaction, the stellar spin and obliquity and possible origins for the differences contributing to disk dissipa- tion in DF Tau. We summarise our work and list main conclusions in Section 5. 2. OBSERVATIONS AND DATA REDUCTION 2.1. ALMA Our Cycle 7 observations of DF Tau (project code 2019.1.01739.S) mirror those of Tofflemire et al. (2024). We used Band 6 receivers in dual polarization mode and sampled continuum emission over three spectral win- dows centered on 231.6, 244.0, and 245.9 GHz each with a bandwidth of 1.875 GHz and 31.25 MHz resolution. In order to resolve the Keplerian rotation profile of the disk, we chose a fourth spectral window that covers the 12 CO J = 2−1 transition at 230.538 GHz for the source’s heliocentric velocity (16.4 km/s, Kounkel et al. 2019) Observations were taken in compact (short baselines, SB) and extended (long baselines, LB) array configura- tions to ensure both high angular resolution and sensi- tivity to extended emission. The compact configuration (∼C6 configuration), with baselines between 14 m and 3.6 km, achieved an angular resolution and maximum recoverable scale of 0.1” and 2.1”, respectively. Observa- tions took place on 18 July 2021 UTC for 332.640 s using the compact configuration. The extended configuration (∼ C8 configuration), with baselines between 40m and 11.6 km, achieved an angular resolution of 0.031” and a maximum recoverable scale of 0.67”. The observations for this configuration took place on 24 August 2021 UTC for 2830.464 s in the extended configuration. The mini- mum and maximum angular scales covered by both the compact and extended configuration translate to ∼ 4.6 to 100 AU at the distance of Taurus (∼ 140 pc Kenyon
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  Double the Disksin DF Tau 3 et al. 1994; Krolikowski et al. 2021). Given this reso- lution, we were able to separate the emission from the two components and marginally resolve the individual disks. The angular separation between the components is ∼ 0.1” which corresponds to a physical separation of 14 AU and a tidal truncation radius of ≲ 5 AU (0.04”) for a binary of roughly equal mass in a circular orbit (Artymowicz & Lubow 1994). 2.1.1. Calibration and Imaging The extended and compact configurations were both calibrated by the standard ALMA pipeline (CASA v6.1.15, McMullin et al. 2007). The compact config- uration was provided as a fully calibrated measurement set by the North American ALMA Science Center. The extended configuration, however, had several antennae with poor responses to the calibrator in the QA0 report. To ensure these antennae did not introduce any anoma- lous correlated noise features, we flagged these 4 addi- tional antennae from the long baseline measurement set before rerunning the calibration and imaging pipelines. After the raw data was appropriately calibrated, we followed post-processing procedures developed for the DSHARP large ALMA program and focused on combin- ing array configurations and self-calibrating (Andrews et al. 2018). A full description of this approach with ac- companying scripts can be found on the program’s data release web page1 . We first created a continuum data set for each config- uration by excluding channels within ±25 km/ s of the 12 CO J = 2 − 1 transition at the DF Tau systematic velocity. We then imaged each data set using tclean (briggs weighting, robust= 0) to test the astrometric alignment and shift both measurement sets to align the phase centers on the DF Tau A continuum source. Fi- nally, we re-scaled the compact configuration measure- ment set’s flux to match that of the extended measure- ment set. Then we began to iterate on the phase-only self- calibrations for the compact configuration. After using tclean without a mask to create an initial image, we be- gan the self-calibrations with a mask which encompasses only the largest flux in the dirty map so as to not give legitimacy to any spurious correlated noise signals. This created a source model which we used to calibrate the visibilities. We then used two large circular apertures centered on the sources to calculate the signal-to-noise ratio (SNR) for a measure of the strength of the signal before self-calibration. We successively iterated on the 1 https://almascience.eso.org/almadata/lp/DSHARP/ mask for each round of self-calibration, ensuring that only regions with high fluxes were masked. We continued to image, adjust the mask, and self- calibrate until either the SNR did not improve from the previous iteration, the number of flagged solutions for any time interval exceeded 20% (to avoid models which insufficiently describe the data), or we reached the native integration step (6s). For the compact con- figuration, solution intervals of the total duration and of 8000s increased the SNR from an initial value of 41 to a pleateau of ∼ 73. These solution intervals use the entire integration time to compute the gain. Amplitude-only self calibration did not improve the SNR and therefore we continued without it. We then combined the self-calibrated compact mea- surement set with the data from the extended config- uration and repeated the same process as above. Es- tablishing the initial mask for the combined measure- ment set after the initial cleaning was less straightfor- ward than for the compact measurement set because the correlated noise in the beam falls along the same posi- tion angle as the anticipated location of the secondary star’s disk. To avoid including any spurious signal in our masks, we experimented with masking only the sig- nal at the expected position of the primary and then masking the signal at the expected positions of both the primary and secondary during the first round of phase- only self calibration. The correlated noise features were significantly reduced with masks on the primary and secondary. Therefore we continued the phase-only self- calibrations using an initial mask which encompassed only the areas with the highest flux and centered on the predicted locations of the primary and secondary stars. Applying self-calibration for the full duration and for 8000 s increased the SNR from 29 to 117. Shorter inter- vals and amplitude-only self calibration did not signif- icantly improve the data quality, therefore we stopped iterating. The final continuum imaging, Figure 1, was performed with fully interactive masking using Briggs weighting (robust = 0) with a three sigma cleaning threshold. The synthesized continuum beam was 0.054” × 0.025” with a position angle of 16.02◦ . The root-mean-square devi- ation (RMS) of the final image was 0.013 mJy/beam. We also created 12 CO J = 2 − 1 data cubes, using channels within ±15 km/ s of DF Tau’s systemic veloc- ity, for the compact and extended configurations from the initial measurement sets. We then applied the self- calibration steps described above and subtracted the continuum emission. We used a 2-channel spacing of 0.635 km/ s. The final cube was imaged with interactive masking, using Briggs robust= 1 weighting. The synthe-
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  4 Kutra etal. Figure 1. Continuum intensity (left), 12 CO line integrated intensity (moment-0; middle, RMS of 0.8 mJy/beam) and 12 CO first moment maps (right) show detections of circumstellar dust and gas orbiting both the primary and secondary stars of DF Tau. In the left and middle panels, the relative binary orbit of the secondary around the primary is overplotted in white and the centers of the continuum emission, determined using imfit, are shown as white stars, confirming alignment with the binary orbit. The first-moment map (right, continuum emission and beam size are shown with overplotted white contours, hatched region in the color bar indicates velocities which are highly obscured by molecular cloud absorption) shows rough agreement in the direction of rotation of the disks. Beam sizes are shown for all panels in bottom left. sized CO beam is 0.066” × 0.033” mas with a position angle of 19.84◦ . The CO detection is marginal and the RMS of the channel maps is ∼ 1 mJy/beam. There- fore we only present the integrated intensity and first moment maps in Figure 1. The RMS for the integrated intensity map is 0.8 mJy/beam. Cloud absorption is ap- parent in both moment maps, particularly for the north- west (red-shifted) side of the secondary disk. The veloc- ity channels which are most affected have LSRK radio velocities between 5-10 km/s (denoted in Figure 1 with hatched region in the right-most panel’s velocity color bar). The LSRK velocity of the Taurus molecular cloud (∼ 5-8 km/s Narayanan et al. 2008) lies within this same range. 2.2. Keck – AO Imaging We obtained spatially resolved images of DF Tau on three nights between 2019 through 2022 using the NIRC2 camera and the adaptive optics (AO) system on the Keck II Telescope (Wizinowich et al. 2000). On each night we obtained 9−12 images, dithered by 2. ′′ , in each of the narrow-band Hcont (central wavelength 1.5804 µm) and Kcont (2.2706 µm) filters. Additional images were obtained using the Jcont (1.2132 µm) and Lp (3.776 µm) filters on UT 2022 December 29, however, the Lp images were saturated. Each image consisted of 10 coadded exposures of 0.2−0.8 sec. We flat fielded the images using dark-subtracted dome flats and removed the sky background by subtracting pairs of dithered im- ages. We used the single star DN Tau as a point-spread function reference (PSF) observed with the same AO frame-rate immediately before or after the observations of DF Tau. DN Tau has been used as a PSF refer- ence in earlier AO studies (Schaefer et al. 2006) and no companion was detected in prior multiplicity surveys (Simon et al. 1995; Kraus et al. 2011). We constructed binary models using the PSF grid search procedure de- scribed by Schaefer et al. (2014) to measure the sepa- ration (ρ), position angle (P.A.) east of north, and flux ratio (fB/fA) of the components in DF Tau. We applied the geometric distortion solution computed by Service et al. (2016) and used a plate scale of 9.971 ± 0.004 mas pixel−1 and subtracted 0. ◦ 262±0. ◦ 020 from the mea- sured position angles to correct for the orientation of the camera relative to true north. The binary positions and flux ratios are presented in Table 1. 2.3. Keck Spectroscopy: NIRSPEC Behind AO The spectra presented here were also published in Allen et al. (2017) but we include a description of the observations here for completeness and because some
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  Double the Disksin DF Tau 5 steps in the processing were updated (e.g., continuum normalization). We used the cross-dispersed, cryogenic, NIR spectrograph NIRSPEC (McLean et al. 1998), de- ployed behind the Keck II AO system (as NIRSPAO), to obtain angularly-resolved spectra of DF Tau on UT 2009 December 6. In high-spectral resolution mode, we achieved R=30,000 using the two-pixel slit (reimaged by the AO system to a width of 0. ′′ 027 × 2. ′′ 26 arcseconds) oriented to the position angle of the binary at the epoch of our observations, ∼224◦ . Natural seeing at the time of observation was better than 0. ′′ 6; The AO frame rate was ∼438 s−1 with about 500 Wave Front Sensor counts. Four 300 s exposures were taken in an ABBA pattern with a ∼1′′ nod; the airmass was 1.03. The central or- der 49 of the N5 filter, with echelle and cross disperser settings of 63.04 and 36.3, respectively, yielded a wave- length range of 1.5448–1.5675 µm. This order is par- ticularly fortuitous as no significant telluric absorption is present at the high altitude, dry site on Mauna Kea, and the combination of atomic and molecular lines pro- vide for the characterization of a range of spectral types and other stellar properties Tang et al. (2024). Seven other full orders are obtained at our H-band setting; three of these are saturated by the atmosphere and the other four (orders 46, 47, 48, and 50) contain numerous telluric lines. All data reduction was accomplished with the RED- SPEC package2 , which executes both a spatial and spec- tral rectification (Kim et al. 2015). We differenced the pairs of A-B exposures and divided by a dark- subtracted flat field. A byproduct of this software is a two-dimensional, rectified, wavelength-calibrated spec- trum that includes the spectral traces of both binary components. We used custom code to fit a native point spread function to each stellar trace across the detec- tor for order 49 and extract the individual component spectra. The individual PSFs used for the fit to the bi- nary had a FWHM of ∼0.05′′ . The spectra were then flattened, normalized, and corrected for barycentric mo- tion. These 2009 DF Tau A and B NIRSPAO spec- tra were previously published in Allen et al. (2017) and Prato (2023); here we reanalyzed them after performing an improved continuum fit using division by a 5th or- der polynomial and a 1% renormalization. Additional details regarding the observations and extraction of our NIRSPAO spectra are available in Kellogg et al. (2017). 2 https://www2.keck.hawaii.edu/inst/nirspec/redspec.html 2.4. Time-series Photometry DF Tau was observed by both the Transiting Ex- oplanet Survey Satellite (TESS; Ricker et al. 2014; STScI 2018) during sectors 43 and 44 (from 16 Septem- ber through 6 November, 2021 UTC) and K2 (Howell et al. 2014; STScI 2011) during Campaign 13 (between 8 March and 27 May, 2017 UTC). We obtained unre- solved time-series photometry of DF Tau from these mis- sions using lightkurve (Lightkurve Collaboration et al. 2018) from the Mikulski Archive for Space Telescopes3 . From the TESS mission, we acquired the 120 s cadence light curve processed by the Science Processing Opera- tions Center (SPOC Jenkins et al. 2016). From K2, we obtained the 1800 s cadence photometry, which was ex- tracted using the technique described in Vanderburg & Johnson (2014) that accounts for the systematic errors and mechanical failures of the Kepler spacecraft. These lightcurves, and their corresponding Lomb-Scargle peri- odograms (Lomb 1976; Scargle 1982), computed using astropy (Astropy Collaboration et al. 2013, 2018, 2022), are presented in Figure 2. Ground-based photometry of DF Tau continued fol- lowing the publication of results from an initial season in Allen et al. (2017). We continued to use the Low- ell robotic 0.7-m telescope + CCD and V-band filter through the 2019-2020 observing season. Following clo- sure of that telescope, monitoring was resumed in 2022 Nov using the Lowell Hall 1.1-m telescope + CCD and V-band filter. The data were reduced in the same way as in Allen et al. (2017) using conventional differen- tial aperture photometry and the same three compar- ison stars throughout: HD 283654 (K2III), GSC 1820- 0482 (reddened F5/8V), and GSC 1820-0950 (reddened K0:III). While the 0.7-m data usually involved mul- tiple visits each night, the 1.1-m data generally were taken during a single nightly visit that included three to five images. Nightly per-observation uncertainties were ∼ 0.007 mag for the 0.7-m and slightly lower for the 1.1-m telescope. 3. ANALYSIS 3.1. Disk Properties from ALMA The 1.3 mm continuum image in Figure 1 clearly shows circumstellar disks associated with each stellar component. We fit the continuum map for each compo- nent using imfit in CASA, which provides the peak and integrated fluxes presented in Table 2. The total inte- grated flux (from both disks, 4.4 ± 0.26 mJy) is consis- tent with lower angular resolution observations for the 3 https://archive.stsci.edu
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  6 Kutra etal. Table 1. Keck NIRC2 Adaptive Optics Measurements of DF Tau UT Date UT Time Julian Year ρ (mas) P.A. (◦ ) Filter Flux Ratio 2019Jan20 06:40 2019.0521 75.27 ± 0.59 164.05 ± 0.45 Hcont 0.809 ± 0.035 Kcont 0.517 ± 0.021 2022Oct19 11:46 2022.7981 65.39 ± 1.14 119.53 ± 1.00 Hcont 0.700 ± 0.020 Kcont 0.484 ± 0.022 2022Dec29 07:09 2022.9919 65.73 ± 0.90 116.68 ± 0.78 Jcont 0.854 ± 0.069 Hcont 0.762 ± 0.039 Kcont 0.507 ± 0.019 blended system (3.4 ± 1.7mJy, Andrews et al. 2013). Assuming the dust emission is optically thin, we can compute a dust mass: Mdust = Fνd2 κνBν(Tdust) (1) where Fν is the integrated 230 GHz flux, d is the distance to the source, κν is the dust opacity, (2.3 cm2 g−1 at 230 GHz, Andrews et al. 2013) and Bν(Tdust) is the Planck function evaluated at the dust temperature, Tdust, which is computed as Tdust ∼ 25(L/L⊙)1/4 K (Andrews et al. 2013, also assuming optically thin dust emission). This yields an estimate of the dust mass of 4.1±0.3×10−6 M⊙ and 3.5 ± 0.3 × 10−6 M⊙ for the primary and secondary, respectively. These are lower limit estimates of the over- all dust mass contained in the disk because the inner disks are likely optically thick (Huang et al. 2018; Dulle- mond et al. 2018) and may contain up to an order of magnitude more dust hidden below the optical surface (Zhu et al. 2019). To measure the disk parameters (namely inclination, position angle, and effective radius), we forward model the continuum visibilities with an exponentially tapered power-law intensity profile, I(r) = I0 r Rc −γ1 e−(r/Rc)γ2 . (2) Here, γ1 is power-law index and the disk intensity drops exponentially as e−rγ2 (γ2 is the exponential-taper in- dex) outside of the cutoff radius, Rc. This model de- scribes disks with sharply decreasing outer profiles, char- acteristic of disks in close binaries (Manara et al. 2019; Tofflemire et al. 2024) and compact disks (Long et al. 2019). The on-sky model image modifies this radial in- tensity profile with an inclination, position angle, and positional offset. We then compute the complex visibil- ities for the model at the observed uv baselines using the galario package (Tazzari et al. 2018) and fit them to each of the three high bandwidth spectral windows independently in an MCMC framework using emcee (Foreman-Mackey et al. 2013). The high resolution CO spectral window is excluded from our fit given its lower bandwidth and SNR. Our fit employs 400 walkers to fit the 12 parameter model: I0, Rc, i, PA, and positions for each disk. The remaining radial profile indices are fixed at values char- acteristic of truncated binary disks (γ1 = 0.8 and γ2 = 5; based on estimates in Tofflemire et al. 2024; Manara et al. 2019). The convergence of the fit is measured from the chain auto-correlation time. The first 5 auto correlation times are removed as burn in. We fit each of the three continuum spectral windows separately and combined the results in order to cap- ture uncertainties beyond the instrumental measure- ment precision (e.g., Long et al. 2019). Individual fit posteriors are broad and generally overlap. Conserva- tively, we combined the last 5000 steps from each spec- tral window fit and take the median and 95% confidence interval as our adopted value and uncertainty. For DF Tau A, the fit returns iA =41+13 −7 ◦ , PAA = 40+20 −10 ◦ , and Rc,A =3.7+0.3 −0.2AU. For DF Tau B, we find iB =46±9◦ , PAB = 40+8 −14 ◦ , and Rc,B =3.6+0.8 −0.6AU. Since our ex- ponential cutoff is sharp (because γ2 is large), the ra- dius containing 95% of the total flux is ≃ Rc. Figure 3 presents a representative fit for one of the continuum spectral windows. We did not detect any dust emission that would indicate the presence of a circumbinary disk. The 12 CO maps show a weak detection around the primary and the secondary as well. Overall, the in- ferred position angle from the CO Maps (approx 120- 155◦ ) is consistent with that from our visibility mod- eling. The 12 CO emission in the north-west portion of the secondary (i.e., the would-be red-shifted emission from the companion) is absent from both the intensity and first moment maps. This is likely due to molecular cloud absorption, and is consistent with the velocity of the Taurus molecular cloud. 3.2. Orbital Properties from AO Imaging
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  Double the Disksin DF Tau 7 59480 59490 59500 59510 59520 0.75 1.00 1.25 Normalized Flux TESS 57820 57840 57860 57880 57900 0.75 1.00 1.25 1.50 Normalized Flux K2 58000 58500 59000 59500 60000 MJD [JD - 2400000.5] 1.0 2.0 3.0 Normalized Flux Lowell 0 5 10 15 20 25 Period [days] 0.0 0.1 0.2 Power Figure 2. Lightcurves from TESS, K2 and the Lowell 0.7/1.1 m telescopes (top three panels, respectively) and re- sulting periodograms (bottom panel) for the blended DF Tau system. Maximum rotation periods for the observed v sin i, assuming alignment between stellar obliquity and disk incli- nation, and theoretical predictions of stellar radii (the 2 Myr tracks from Feiden 2016), are indicated by shaded regions in red and yellow for the primary and secondary, respectively. There is no significant power at these periods and therefore the variability in the light curve is dominated by stochastic accretion and/or other processes in the inner disk of the pri- mary. The orbital coverage of DF Tau now spans over 36 years. We computed an updated orbital fit by combin- ing the binary positions in Table 1 with measurements previously published in the literature (Chen et al. 1990; Ghez et al. 1995; Simon et al. 1996; Thiebaut et al. 1995; White Ghez 2001; Balega et al. 2002, 2004, 2007; Shakhovskoj et al. 2006; Schaefer et al. 2003, 2006, 2014; Table 2. Derived Properties for DF Tau Parameter DF Tau A DF Tau B Orbital Parameters P [yr] 48.1 ± 2.1 T0 [JY] 1977.7 ± 2.7 e 0.196 ± 0.024 a [mas] 97.0 ± 3.2 i [◦ ] 54.3 ± 2.4 Ω [◦ ] 38.4 ± 2.5 ω [◦ ] 310.6 ± 9.2 Mtot ( d D )3 M⊙ 1.15 ± 0.03 ± 0.48a Stellar Properties Teff [K] 3638 ± 109 3433 ± 84 log g 3.7 ± 0.2 3.9 ± 0.2 v sin i[ km/ s] 16.4 ± 2.1 46.2 ± 2.8 Veiling at 15600Å 1.4 ± 0.2 0.3 ± 0.2 RV [ km/ s] 19.9 ± 1.1 15.5 ± 2.0 B[kG] 2.5 ± 0.7 2.6 ± 0.9 JD 2455171.91488 Disk Properties 1.3mm F [mJy] 2.5 ± 0.19 1.9 ± 0.18 1.3mm Peak I [mJy/beam] 1.5 ± 0.08 1.3 ± 0.08 Mdust[M⊕] 1.4 ± 0.10 1.17 ± 1.11 idisk[◦ ] 41+13 −7 46±9 PAdisk[◦ ] 40+20 −10 40+8 −14 Rc[ AU] 3.7+0.3 −0.2 3.6+0.8 −0.6 a Based on a distance estimate of 142.68 pc to the D4-North subgroup in Taurus (Krolikowski et al. 2021). The first uncertainty in Mtot is propagated from the uncertainties in the orbital parameters P and a while the second sys- tematic uncertainty is derived from propagating the ± 20 pc standard deviation of distances to individual stars in the subgroup. Allen et al. 2017). We used the IDL orbit fitting library4 to compute a visual orbit using the Newton-Raphson method to linearize the equations of orbital motion and minimize the χ2 . The period (P), time of periastron passage (T0), eccentricity (e), angular semimajor axis (a), inclination (i), position angle of the line of nodes (Ω), and the angle between the node and periastron (ω) are fitted for and results are presented in Table 2. The uncertainties in the orbital parameters were computed from a Monte Carlo bootstrap technique. This process involved randomly selecting position measurements from the sample with repetition (some measurements were repeated, others were left out), adding Gaussian uncer- tainties to the selected sample, and re-fitting orbit. We performed 1,000 bootstrap iterations and computed un- certainties in the orbital parameters from the standard deviation of the resulting distributions. The orbital mo- 4 http://www.chara.gsu.edu/analysis-software/orbfit-lib
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  8 Kutra etal. 0 5000 10000 uv Distance (k ) 0 2 4 Vis (mJy) Real 0 5000 10000 uv Distance (k ) 2 1 0 1 Imaginary Model Data 0.2 0.0 0.2 Data 0.2 0.0 0.2 Model 0.2 0.0 0.2 [-3,3] Residual Figure 3. Continuum visibility fitting. Results are shown for spectral window 1. Left Panels: Data and model for the real and imaginary visibilities as a function of uv-distance. Right Panels: Maps of the data, model, and residuals. Contours in the residual image are set at −3σ and 3σ in dashed and solid lines, respectively. The residuals are largely ±3σ. tion of DF Tau B relative to A and the best fitting orbit are plotted in Figure 4. The total system mass can be computed from Ke- pler’s Third Law, assuming that the distance is known. For example, the Gaia distance changed from 124.5 pc in DR2 to 182.4 pc in DR3 with a Renormalized Unit Weight Error (RUWE) of 21.9 (Bailer-Jones et al. 2018, 2021). The high RUWE is likely due to the binarity of the source and a more reliable distance will be obtained when the final solution that includes the astrometric or- bital motion is available. However, the variability of DF Tau A (Allen et al. 2017) might impact the interpreta- tion of the photo-center motion. In the meantime, we adopted the distance of 142.68 ± 20 pc to the D4-North subgroup where DF Tau resides (Krolikowski et al. 2021) to derive a total mass of MA+B = 1.15±0.48M⊙, where uncertainties propagated from the orbital parameters P and a (±0.03M⊙) and the distance (±0.48M⊙) are added in quadrature. 3.3. Stellar Properties from NIR Component Spectroscopy We used the NextGen atmospheric models (Allard Hauschildt 1995) with the Synthmag spectral synthe- sis code of Kochukhov et al. (2010) to produce a grid of H-band order 49 (1.5440 − 1.5675 µm) model spec- tra at solar metallicity that encompasses a large range of late-type dwarf star properties: Teff of 3000–6000 K, surface-averaged magnetic field strength, B, of 0–6 kG, and surface gravity, log(g), of 3.0−5.5. Models are com- puted at intervals of 100 K in Teff and 0.5 dex in log(g) for magnetic field strengths of 0, 2, 4, and 6 kG. Labo- ratory atomic transition data from the Vienna Atomic Line Database 3 (VALD 3, Ryabchikova et al. 2015) were calibrated against the spectrum of 61 Cyg B and the Solar spectrum (Livingston Wallace 1991) and used to synthesize the model spectra following the pro- cedure of Johns-Krull et al. (1999); Johns-Krull (2007). We excluded lines which appeared in the solar and 61 Figure 4. Orbital motion of DF Tau B relative to A based on the AO imaging and measurements from the literature. The solid blue line shows the best fitting orbit while the grey lines show 100 orbits selected at random from the posterior distribution. Cyg B calibration spectra but not in the VALD list, and vice versa. Furthermore, we adjusted the van der Waals broadening constants and line oscillator strengths in the model spectra to best match the observed cali- brator lines in the Sun and 61 Cyg B to improve the accuracy of the synthesized spectra. From this grid of model spectra, we can linearly inter- polate to create model spectra with any desired stellar parameters spanned by the grid. We determined the best-fit stellar parameters using the emcee implementa- tion of the MCMC method. To identify an appropriate initial guess, we used the stellar parameters estimated by Prato (2023). We also applied the line equivalent width ratio method of Tang et al. (2024) to obtain ini- tial temperature estimates of ∼3690 K and ∼3630 K for
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  Double the Disksin DF Tau 9 the primary and secondary, respectively. However, we suspect this is a temperature overestimate for the sec- ondary, given the line blending that results from this star’s high v sin i. Finally, we adopt a wide range of uniform priors for all stellar parameters. With our set of initial guesses and priors, we ran emcee with 32 walkers and iterated for 8000 steps, which allows for a chain length that is sufficiently longer than the autocorrelation time. We then trimmed the first 2000 steps before extracting model parameters. Our best-fit models are shown in Figure 5 and the associated model parameters are listed in Table 2. The primary and secondary of DF Tau are almost stel- lar twins, with similar effective temperatures, surface gravities, and surface-averaged magnetic field strengths. The large differences for the two stars lie in their veiling and v sin i values. The lack of veiling led Allen et al. (2017) to conclude that either the disk around the sec- ondary had dissipated or the inner disk was absent. This is supported by the lack of accretion signatures in Fig- ure 5, e.g., Br 16 H line emission. Examination of other H-band spectral orders shows no trace of other Brackett series lines (e.g., Br 11 in order 45 or Br 13 in order 47). Given our independent measurements for stellar effec- tive temperatures from the spectra and a combined dy- namical mass from the orbit, we can also compare mass estimates from evolutionary models. Using the (Feiden 2016) stellar evolution models, the stellar masses which correspond to stellar effective temperatures of 3638 K and 3433 K are 0.56M⊙ and 0.42M⊙, respectively. This is consistent with our estimate measured total mass of the system, 1.15 ± 0.48M⊕. We can also compare the model-derived flux ratio to that determined in Table 1. Feiden (2016) models give logarithmic luminosities of −0.33 and −0.48, for the primary and secondary respec- tively, which corresponds to a flux ratio of 0.69, in rough agreement with the ratios in Table 1. 3.4. Stellar Variability and Rotation Properties from Time Series Photometry Peaks with significant power in periodograms are used to determine stellar rotation periods, leveraging the light curve modulation caused by spots rotating in and out of view (e.g., Rebull et al. 2020). For DF Tau, both the space-based and ground-based lightcurves appear to be dominated by stochastic variability (Figure 2). The pe- riodogram of the TESS lightcurve reveals two significant peaks at 10.4 and 5.5 days. The periodogram of the K2 lightcurve has peaks at 10.3 and 6.6 days; however there is significantly more power at 15.2 and 21.8 days. The periodogram of six seasons’ worth of ground-based pho- 15450 15500 15550 15600 15650 Wavelength [Ȧ] 0.0 0.2 0.4 0.6 0.8 1.0 Normalized Flux Figure 5. Spatially resolved and continuum normalized spectra of DF Tau A (top) and B (bottom, separated by an offset) in black. 50 randomly selected model spectra from the trimmed MCMC chain are overplotted in blue. tometry has low power peaks at approximately 8 and 14 days. Allen et al. (2017) analyzed one season of ground- based photometry and found a peak in the periodogram at 10.4 days, but they did not find significant power at periods of 5.5 or greater than 10.4 days. It is not clear that any of these light curves are reliably tracking the stellar rotation period, given the implied stellar radius. For example, when a suspected rotation period, iden- tified in the periodograms derived from TESS, K2, or ground-based light curves, is combined with a v sin i, de- termined from the primary star H-band spectrum (e.g., Section 2.2), we can obtain a lower bound on the stellar radius: R∗ ≥ 0.0196 Prot 1 day ! v sin i 1 km/s ! R⊙. (3) For a measured v sin i of 13 ± 4km/s and Prot = 10.4 days, Allen et al. (2017) found a stellar radius limit for the primary star of ≥ 2.68±0.82R⊙. Using our updated v sin i of 16.4 ± 2.1 km/ s, a 10.4 day period implies a radius of ≥ 3.4 ± 0.4R⊙, implying an age well below 1 Myr for the models of Feiden (2016). For the secondary star with v sin i of 46.2 ± 2.8km/s, the derived radii are unphysically large for rotation periods greater than ∼3 days. To estimate these limits on the radii above, Equation 3 assumed a maximum stellar rotation axis inclination of 90 degrees. Another estimate of the stellar radii can be achieved by assuming the star is aligned with the disks or the orbit of the binary (i.e., an inclination of i = 34 − 55◦ ). For DF Tau A, with assumed age of ∼2 Myr and Teff ∼ 3650 K, models of Feiden (2016, which include stellar magntic fields) predict a stellar radius of
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  10 Kutra etal. 100 101 Wavelength (µm) 10−12 10−11 10−10 10−9 10−8 νF ν (erg s −1 cm −2 ) Primary Secondary Figure 6. Angularly resolved photometry of DF Tau A (squares) shows a clear UV Excess when compared with DF Tau B (circles) and an appropriate BT-Settl (CIFIST) stellar photosphere model (grey). Yellow and orange regions denote the Kepler and TESS bandpasses, respectively. Photometry is reproduced from Allen et al. (2017), error bars are smaller than the markers. ∼ 1.8R⊙. With v sin i of 16.4 ± 2.1 km/ s, these param- eters imply a rotation period range from 3.1 to 4.5 days for the primary star. For DF Tau B, with assumed age of ∼2 Myr and Teff ∼ 3450 K, models predict a stellar ra- dius of ∼ 1.6R⊙. With v sin i of 46.2 ± 2.8 km/ s, these parameters imply a rotation period range from 1.0 to 1.4 days for the secondary star for the inclination range of i = 34 − 55◦ . We find no significant power at pre- dicted periods of 5 days in the periodogram for any of the light curves shown in Figure 3. Stellar evolu- tion tracks which do not include stellar magnetic fields, such as Baraffe et al. (2015) or Feiden (2016)’s non- magnetic tracks, have smaller radii on average, which further broadens these discrepancies. It is therefore unlikely that the periodic signals seen in the TESS, K2 and ground-based light curves consis- tently trace stellar rotation. Instead, it is more probable that these lightcurves are dominated by stochastic ac- cretion events onto the primary star. In the TESS and K2 bandpasses, shown in Figure 6, the flux ratios of the primary to the secondary are ∼ 1.2 and ∼ 1.9. This sug- gests that the light curves are indeed dominated by the actively-accreting primary. This conclusion is also sup- ported by seasonal variation of the lightcurve, as seen in our ground-based data presented in Appendix A. 4. DISCUSSION We discuss our measurements of the components of DF Tau and their protoplanetary disks in the context of both the binary-disk interaction as well as possible origins for the missing inner disk of the secondary. 4.1. Binary-Disk and Disk-Disk Interactions As in Tofflemire et al. (2024), our finding of (rough) agreement in the projected inclinations (41 ± 10◦ and 46±9◦ for the primary and secondary, respectively) and position angles (40+20 −10 ◦ and 40+8 −14 ◦ ) of the circumstellar disks and the orbit of this young binary (i = 54.3±1.2◦ , Ω = 38.4±2.5◦ ) does not distinguish between formation mechanisms. Quantatively, we compute the disk-orbit obliquity (Θ) for this system: cosΘ = cos idisk cos iorbit + sin idisk sin iorbit cos(Ωdisk − Ωorbit), (4) where Ωdisk is the position angle of the disk. We find the disk-orbit obliquity to be consistent with zero for both components: the obliquities are 13 ± 13◦ and 8 ± 9◦ for the primary and secondary disk and binary orbit. We can also use Equation 4 to compute the disk-disk obliquity, which is also consistent with zero (Θ = 5 ± 16◦ ). Disk-orbit alignment can be achieved from either for- mation due to fragmentation of a gravitationally unsta- ble disk (e.g. Bate Bonnell 1997; Ochi et al. 2005; Young et al. 2015) or from an initially misaligned sys- tem, formed from core fragmentation (e.g. Zhao Li 2013; Lee et al. 2019; Guszejnov et al. 2023), which has undergone significant damping from various phys- ical mechanisms (see Offner et al. 2023, and references therein for details). The damping mechanism that is relevant on the scales of the binary orbit of DF Tau is viscous warped disk torques (e.g. Bate 2000; Lubow Ogilvie 2000). The damping timescales for these torques are short and decrease ∝ a6 r 9/2 out (Zanazzi Lai 2018). The small disk radii, rout, and semi-major axis of the binary orbit, a, in the DF Tau system makes a damping timescale smaller than the age of the system (∼ 2 Myr from Krolikowski et al. 2021). Given the tight orbital separation of DF Tau, another meaningful comparison is with theoretical predictions of the truncation radius (Artymowicz Lubow 1994; Lubow et al. 2015; Miranda Lai 2015), beyond the first order approximation of Rtrunc ≃ a/3. Following Artymowicz Lubow (1994), Manara et al. (2019) de- rive the truncation radius as: Rtrun = 0.49 a q−2/3 0.6q−2/3 + ln(1 + q−1/3) × bec + 0.88µ0.01 , (5) where a is the semi-major axis, q is the stellar mass ra- tio (MB/MA), e is the orbital eccentricity, and µ is the secondary to total mass ratio (MB/(MA+B)). The pa- rameters b and c depend on µ and the disk Reynolds number. Assuming the stars are of equal mass, and us- ing b = −0.78 to −0.82 and c = 0.66 to 0.94, the ranges
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  Double the Disksin DF Tau 11 in Appendix C1 of Manara et al. (2019), we obtain trun- cation radii estimates of 3.1–3.6 AU for DF Tau’s orbital parameters. Dust disk radii that are smaller than this dynami- cal prediction are likely the result of dust drift (Ansdell et al. 2018). The effects of dust drift on disks in bi- naries are further enhanced because the outer reservoir of dust particles is lost during disk truncation (Zagaria et al. 2021; Rota et al. 2022). Compared to the radii we measure of 3.7 and 3.6 AU (i.e. the 95% effective radius in Table 2) for the primary and secondary re- spectively, there is little evidence of radial drift. How- ever, since our disks are only marginally resolved it is possible that the disks are slightly misaligned from the binary orbit, allowing for larger gaseous extents. But since CO maps are of poor quality, we cannot assess whether the gas disk sizes are consistent with theoret- ical predictions. Higher angular resolution continuum observations or higher SNR CO maps would make this measurement more robust. 4.2. Stellar Obliquity and Rotation The large v sin i of the secondary is also consistent with our picture of DF Tau B lacking an inner disk. The effects of disk locking (Shu et al. 1994), which slows the rotation of stars with strong magnetic fields frozen in to the inner disks, have weakened or dispersed for the secondary but modulate the slow rotation of the primary. Our best-fit for the disk inclinations (41 ± 10◦ and 46 ± 9◦ for the primary and secondary, respectively) is consistent with alignment to the binary orbit (54.3 ± 1.2◦ ). Given this relative co-planarity, it is not improb- able that the binary orbit, the circumstellar disks, and the stellar obliquity are all aligned. If this is the case, and we assume a stellar spin axis that is aligned with the orbital angular momentum vector of the binary or- bit, we can estimate a rotation period for the secondary star, assuming an age ∼2 Myr, of ≲ 1.4 days. For this orientation, we also estimate that the velocity at the surface of the secondary is only ∼ 20% of the breakup velocity. Comparing to the rotation periods of disk-hosting and disk-less single stars in Taurus obtained by (Rebull et al. 2020), this estimate is on the shorter side of the distribu- tion but it is not implausibly fast. Furthermore, there are significantly more stars with rotation periods 2 days that do not have disks than those that do (e.g. those in Figure 8 of Rebull et al. 2020). This is most likely because the stars have spun up after the loss of their disks. Finding DF Tau B in this region of pa- rameter space that bridges the gap between disked and disk-less systems is sensible considering that it appears to be in the early stages of disk dissipation. 4.3. Circumbinary Disk Given the accretion rate of the primary star, the lack of a circumbinary disk in this system is also puzzling. Hartigan Kenyon (2003) measure an accretion rate to be ∼ 10−7 M⊙/year. First, we assume this accretion is entirely due to the primary because the secondary does not show a UV excess. For a dust to gas ratio of 1%, and assuming a constant accretion rate, the circumstel- lar disk around the primary should disappear in ∼ 3000 years. This dissipation timescale is orders of magnitude smaller than the current age of the system(∼ 2 Myr) and therefore in order for the circumstellar disk around the primary star to remain, another mass reservoir is nec- essary. This problem is not resolved if the circumstellar disk is significantly optically thick, which only adds a factor of up to 10 to the estimated lifetime. Can this timescale be extended significantly if the circumstellar disks are supplemented by an outer circumbinary disk? This question prompts us to determine how much dust could be hidden below our detection limit in a circumbi- nary disk. In order to place an upper limit on the amount of dust contained in the inner region of a circumbinary disk, we first calculated the predicted radius of the inner edge of the circumbinary disk. This can be estimated using the orbital parameters and a semi-major axis 3 times that of the binary orbit. Figure 7 shows the expected loca- tion of the circumbinary disk. We estimated the flux around the circumbinary disk in two ways. First, we arranged ellipses which have sizes and orientations the same as the beam in order to determine that approxi- mately 50 beams are required to cover the inner edge of the circumbinary disk. Using the RMS of the continuum image of 0.013 mJy/beam, we estimate the noise in this region as RMS √ Nbeams = 0.09 mJy. To check this result, we summed the integrated flux for each of the beams in Figure 7 to get an estimate of the integrated flux for a donut-shaped region encom- passing the potential circumbinary disk. We found the integrated flux in this region to be 0.27 mJy. When combined with our integrated fluxes for the two disks, this estimate is still consistent with previous measure- ments of the unresolved system(Andrews et al. 2013). This flux corresponds to a dust mass of 1.5 × 10−7 M⊙ (0.15M⊕) for the circumbinary disk. If all this dust fed only the primary disk, the expected lifetime would still be only hundreds of years. We only measured the dust emission in a narrow ring near the expected inner edge of the binary disk because
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  12 Kutra etal. Figure 7. The expected location of the inner edge of a potential circumbinary disk (white dashed line) lies at ap- proximately 3 times the semi-major axis of the binary orbit and is centered on the approximate center of mass of the binary. This does not show significant emission in our final continuum map. However, we place an upper limit on the amount of dust hidden in the circumbinary disk by tracing its inner edge with 48 beams (overplotted grey ovals). that is where the dust will be most concentrated. With an estimated projected separation for the inner disk edge of 0.3” and a maximum recoverable scale of 0.67”, our observations have the capability to detect a circumbi- nary disk at this distance if it is present. However, the lack of a detection suggests that the dust may be in a more diffuse and extended disk which our observations are less sensitive to. Therefore the dust estimates above are likely underestimates of the total dust mass con- tained in the circumbinary disk. Now, we return to our lifetime problem for the cir- cumstellar disk. If all the material in the circumbinary disk is directed to only the circumstellar disk of the pri- mary, the expected lifetime would only increase by an additional ∼ 450 years. Therefore it is unlikely that the circumbinary disk is a significant additional mass reser- voir for the circumstellar disks. 4.4. Twin Stars, Mismatched Disks Central to the puzzle of DF Tau is the question of why the inner disk of the secondary has dissipated when the stars should be coeval. One possibility is that these disks are at different stages of dissipation. Here, we entertain possible origins for such physical differences, in terms of the initial mass of the disk and the viscosity, and discuss whether making the necessary measurements is feasible. The initial mass of circumstellar disks is roughly pro- portional to the stellar mass (Andrews et al. 2013) with a large variance. Perhaps if the disk around the pri- mary initially held significantly more mass, equal accre- tion and thus dissipation rates might have produced the mismatched disks. Although our estimates of the disk dust mass are roughly the same for both outer disks, optically thick emission can hide a significant amount additional mass and the true masses of the disks may be significantly different (Zhu et al. 2019). Other meth- ods to determine the masses of the disks face similar dif- ficulty. For example, kinematic determinations of disk mass, which assume the self gravity of the disk is sig- nificant (e.g. Veronesi et al. 2021), may allow for more accurate estimates. Unfortunately these estimates are only accurate for disks with masses 5% of the stel- lar mass, and require high spatial resolution molecular maps (e.g., Andrews et al. 2024, demonstrate that 20 beams across the disk are needed for an accurate esti- mate). Given the truncation of both disks in DF Tau, the disks are not likely to be a substantial fraction of the stellar mass and the disks are too small to achieve the necessary spatial resolution (∼0.002”) for even the most extended ALMA configuration (0.01”). Therefore it is unlikely this method can give an insightful deter- mination of the true disk mass. Another method by which we might determine the ori- gin of the uneven dissipation between the disks in DF Tau is by determining the disks’ viscosity, as parameter- ized by the dimensionless Shakura-Sunyaev α parameter (Shakura Sunyaev 1973). During early disk dissipa- tion, the accretion rate is determined by the gas viscos- ity: increased viscosities correspond to more accretion, leading to a depleted inner disk. However, determining whether the viscosity of the two disks is significantly different is not an easy task. Direct determinations of α require spatially and spec- trally resolved line emission (e.g., Flaherty et al. 2015; Teague et al. 2016) in order to disentangle thermal and turbulent line broadening. For the dim and compact disks in DF Tau, observations of this sort will have prohibitively long integration times and therefore are unlikely to be performed. Common model-dependent measurements of α require either resolved annular sub- structures (e.g., Dullemond et al. 2018) or constraints on the dust’s vertical scale height (e.g. Villenave et al. 2020; Doi Kataoka 2021). Because our current obser- vations do not reveal evidence for annular substructures in the image or visibility planes, and our disks are not edge on, these methods also will not allow for a deter- mination of the disk viscosity. However, interferometric observations that resolve the inner cavity of DF Tau B, which may be possible with the most extended ALMA configurations, could allow for an indirect measurement
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  Double the Disksin DF Tau 13 of the disk viscosity using methods similar to Dullemond et al. (2018). Another possibility which could clear out the inner disk of the secondary is an unknown (sub-)stellar com- panion. Although the presence of an undetected com- panion is possible, it may be unlikely in this system. Super-Earth-like planets may be able to carve gaps in low viscosity disks (Dong et al. 2017, 2018), but the solid core mass required to form a super-Earth is substantial (∼ 5 − 10M⊕). Although the measured dust masses of the circumstellar disks are small (1.4 and 1.2 M⊕ for the primary and secondary, respectively), perhaps a disk which is optically thick, and thus contains substantially more dust which is hidden, could supply the material required to build these cores. If a planet has already formed in the circumstellar disk of the secondary, per- haps that is the cause of the difference in observed dust masses between the two disks. A planet with a mass of only 0.2M⊕ likely will not have a large impact on the shape of the circumstellar disk. However if the disk were optically thick, then perhaps the missing mass in the secondary, compared to the primary, can be more similar to that of a super-Earth. Because there may be enough solid material in the secondary’s small circumstellar disk to form a planet capable of altering the shape of an inner disk, we do not rule out this possibility. However, we also do not favor this interpretation because of the need for a significant amount of additional dust mass in the disk for previous or ongoing planet formation. Planets are rare in the closest binary systems (Kraus et al. 2016) and a planet embedded in the circumstellar disk around DF Tau B would certainly make this system uncommon. However, clearer and more direct evidence is certainly needed to substantiate such a proposal for this disk. Although it is challenging to determine why the evo- lution of DF Tau’s disks is not the same, it is possible to continue to characterize the physical differences of the disks. For example, the 3.5µm magnitude places a lower limit on the possible inner edge of the secondary: dust grains that have λpeak = 3.5µm must be heated to ∼ 800 K. Since these temperatures will occur in the disk midplane interior to 1 AU (T(r = 1 AU) = 150 K for a passively heated disk Chiang Goldreich 1997), the dominant heat source is accretion (D’Alessio et al. 1998). Therefore we determine the radius of dust which would dominate emission at this wavelength, and constrain the inner edge of the secondary’s disk to be ≳ 0.25 AU. Spatially resolved imaging of the secondary at 10µm will better constrain the inner edge of its disk. Fur- thermore, the peculiarities of DF Tau make it an ex- cellent candidate to test theories of disk dissipation. Angularly-resolved spectroscopic observations of wind- sensitive lines, like the He i 1083 nm line, provide a sen- sitive probe of stellar and inner disk winds, which can be compared to those predicted from theory (e.g., Pascucci et al. 2023). In connection with our results, we note that another study of DF Tau by Grant et al. (2024); their preprint appeared while we were completing this manuscript. In- dependently, Grant et al. (2024) used data from our ALMA program to identify the disk around the sec- ondary and came to the conclusion that the inner disk of DF Tau B is absent. 5. CONCLUSIONS SUMMARY We analyzed the orbital, stellar, and protoplanetary disk properties of the puzzling young binary system, DF Tau, using decades of high angular resolution imaging, angularly-resolved NIR spectra and (sub-)mm interfer- ometry. With the expectation of co-evolution for the disks in young binary systems, we discuss how DF Tau may be a prime target to begin to test disk dissipation theory. The main conclusions of our work are as follows: 1. DF Tau is a young binary system with a semi- major axis of ∼ 14 AU. Its components are twin stars with a dynamically-determined total mass of ∼ 1.1M⊙ and similar effective temperatures. 2. Our ALMA observations in Band 6 detect con- tinuum and 12 CO J = 2 − 1 line emission from each component. The disks have maximum radii 4 AU, the result of tidal truncation. The inte- grated 1.3mm fluxes are 2.5 ± 0.19 and 1.9 ± 0.18 mJy, which allow for a lower estimate of the dust masses of 1.4 ± 0.10M⊕ and 1.2 ± 0.11M⊕ for the primary and secondary, respectively. These low dust masses offer little support to any ongoing planet formation. 3. The inclinations and position angles of the dust disks, measured by directly fitting the visibilities, point to mutual alignment between the binary or- bit and the circumstellar disks. 4. We do not find evidence for a circumbinary disk or extended emission in dust or CO above an RMS of 0.013 and 1 mJy/beam, respectively. We con- strain the upper limit of the dust emission from the circumbinary disk to be 0.27 mJy. The accelerated dissipation of the inner, terrestrial planet-forming zone in the DF Tau B circumstellar disk has important implications for planet formation. This system merits intensive future scrutiny in order to bet- ter understand the conditions that disrupt, in the case of
• 14.
  14 Kutra etal. DF Tau B, and sustain, for DF Tau A, the circumstellar disks over a timescale relevant for planet formation. 6. ACKNOWLEDGEMENTS The authors thank Feng Long, Mike Simon, J.J. Zanazzi, Peter Knowlton, Meghan Speckert, and Jacob Hyden for helpful discussions. We are also grateful to Joe Llama and Cho Robie, who generously shared their computational resources. Funding for this research was provided in part by NSF awards AST-1313399 and AST-2109179 to L. Prato. G. Schaefer and L. Prato were also supported by NASA Keck PI Data Awards, administered by the NASA Ex- oplanet Science Institute. Some of the data presented herein were obtained at the W. M. Keck Observatory from telescope time allo- cated to the National Aeronautics and Space Adminis- tration through the agency’s scientific partnership with the California Institute of Technology and the University of California. Additional telescope time was awarded by NOIRLab (NOAO and NOIRLab PropIDs: 2009B- 0040 and 2022B-970020; PI: G. Schaefer) through NSF’s Telescope System Instrumentation and Mid-Scale Inno- vations Programs. The Keck Observatory is a private 501(c)3 non-profit organization operated as a scientific partnership among the California Institute of Technol- ogy, the University of California, and the National Aero- nautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. The authors wish to rec- ognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct ob- servations from this mountain. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2019.1.01739.S ALMA is a part- nership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI (Re- public of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. The National Radio As- tronomy Observatory is a facility of the National Sci- ence Foundation operated under cooperative agreement by Associated Universities, Inc. Facility: ALMA, Texas Advanced Computing Cen- ter (TACC), Keck:II (NIRSPEC) Software: emcee (Foreman-Mackey et al. 2013), lightkurve (Lightkurve Collaboration et al. 2018), astropy (Astropy Collaboration et al. 2013, 2018, 2022), galario(Tazzari et al. 2018), casa (CASA Team et al. 2022) REFERENCES Akeson, R. L., Jensen, E. L. N., Carpenter, J., et al. 2019, ApJ, 872, 158, doi: 10.3847/1538-4357/aaff6a Allard, F., Hauschildt, P. H. 1995, ApJ, 445, 433, doi: 10.1086/175708 Allen, T. S., Prato, L., Wright-Garba, N., et al. 2017, ApJ, 845, 161, doi: 10.3847/1538-4357/aa8094 Andrews, S. M., Rosenfeld, K. A., Kraus, A. L., Wilner, D. J. 2013, ApJ, 771, 129, doi: 10.1088/0004-637X/771/2/129 Andrews, S. M., Teague, R., Wirth, C. P., Huang, J., Zhu, Z. 2024, arXiv e-prints, arXiv:2405.19574, doi: 10.48550/arXiv.2405.19574 Andrews, S. M., Huang, J., Pérez, L. M., et al. 2018, ApJL, 869, L41, doi: 10.3847/2041-8213/aaf741 Ansdell, M., Williams, J. P., Trapman, L., et al. 2018, ApJ, 859, 21, doi: 10.3847/1538-4357/aab890 Artymowicz, P., Lubow, S. H. 1994, ApJ, 421, 651, doi: 10.1086/173679 Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, AA, 558, A33, doi: 10.1051/0004-6361/201322068 Astropy Collaboration, Price-Whelan, A. M., Sipőcz, B. M., et al. 2018, AJ, 156, 123, doi: 10.3847/1538-3881/aabc4f Astropy Collaboration, Price-Whelan, A. M., Lim, P. L., et al. 2022, ApJ, 935, 167, doi: 10.3847/1538-4357/ac7c74 Bailer-Jones, C. A. L., Rybizki, J., Fouesneau, M., Demleitner, M., Andrae, R. 2021, AJ, 161, 147, doi: 10.3847/1538-3881/abd806 Bailer-Jones, C. A. L., Rybizki, J., Fouesneau, M., Mantelet, G., Andrae, R. 2018, AJ, 156, 58, doi: 10.3847/1538-3881/aacb21 Bajaj, N. S., Pascucci, I., Gorti, U., et al. 2024, AJ, 167, 127, doi: 10.3847/1538-3881/ad22e1 Balega, I., Balega, Y. Y., Maksimov, A. F., et al. 2004, AA, 422, 627, doi: 10.1051/0004-6361:20035705 Balega, I. I., Balega, Y. Y., Hofmann, K.-H., et al. 2002, AA, 385, 87, doi: 10.1051/0004-6361:20020005
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  18 Kutra etal. 58000 58500 59000 59500 60000 MJD [JD - 2400000.5] 1 2 3 Normalized Flux 0.0 0.5 Power 0.0 0.5 Power 5 10 15 20 25 Period [days] 0.0 0.5 Power 5 10 15 20 25 Period [days] Figure 8. Seasonal variation of the DF Tau periodogram using ground-based photometry obtained with the Lowell robotic 0.7m telescope and the Lowell Hall 1.1m telescope. APPENDIX A. SEASONAL VARIATION OF THE PERIODOGRAM To support our claim that the variation in the light curves of DF Tau is dominated by stochastic accretion, we analyzed the 7-year-long ground-based light curve of DF Tau separated by year (Figure 8). The strength of the ∼ 10- and ∼ 5-day signals varies, and at some epochs disappears entirely (e.g., in the periodograms from the seasons around 58000 and 60000 MJD).