11institutetext: Univ. Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France.
11email<EMAIL_ADDRESS>22institutetext: Department of
Astronomy, University of California, Berkeley CA, 94720, USA. 33institutetext:
European Southern Observatory (ESO), Karl-Schwarzschild-Strasse 2, 85748
Garching bei Munchen, Germany. 44institutetext: CRAL, UMR 5574, CNRS,
Université de Lyon, ENS, 9 avenue Charles André, 69561 Saint Genis Laval
Cedex, France.

# Full orbital solutions in pre-main sequence high-order multiple systems: GG
Tau Ab and UX Tau B

Gaspard Duchêne 1122 Jean-Baptiste LeBouquin 11 François Ménard 11 Nicolás
Cuello 11 Claudia Toci 33 Maud Langlois 44

(Received 28/11/2023; accepted 01/04/2024)

###### Abstract

Context. High-order multiple (triple and beyond) systems are relatively
common. Their interaction with circumstellar and circumbinary material can
have a large impact on the formation and evolution of planetary systems and
depends on their orbital properties.

Aims. GG Tau and UX Tau are two pre-main sequence high-order multiple systems
in which the tightest pair has a projected separation of $\approx 5$–20 au.
Characterizing precisely their orbits is crucial to establish their long-term
stability, to predict the dynamics and evolution of circumstellar matter, and
to evaluate the potential for planet formation in such systems.

Methods. We combine existing astrometric measurements with previously
unpublished high-resolution observations of the GG Tau Ab and UX Tau B pairs
and perform Keplerian orbital fits.

Results. For GG Tau Ab the data presented here represent the first detection
of orbital motion. For both systems they yield dramatic increases in orbital
coverage ($\gtrsim 60\%$ and $\approx 100\%$ for UX Tau B and GG Tau Ab, for
orbital periods of $\approx 32$ and $\approx 8$ yr, respectively) and allow us
to obtain well-constrained orbital fits, including dynamical masses with
$\lesssim 10\%$ and $\lesssim 7\%$ random and systematic uncertainties. We
find that both GG Tau A and UX Tau A–B likely form stable hierarchical
systems, although one possible deprojection solution for GG Tau is strongly
misaligned and could experience von Zeipel-Lidov-Kozai oscillations. We
further find that the UX Tau B orbit is much more eccentric than the GG Tau Ab
one, possibly explaining the lack of circumstellar material in the former.

Conclusions. The newly-determined orbits revive the question of the dynamical
fate of gas and dust in these two hierarchical systems and should spur new
dedicated simulations to assess the long-term evolution of the systems and the
dynamical perturbations imposed by the close binaries they host.

###### Key Words.:

Stars: binaries – Stars: individual (GG Tau A) – Stars: individual (UX Tau B)

##  1 Introduction

Stellar multiplicity is ubiquitous in the Galaxy, and even more so among pre-
main sequence stars (Duchêne & Kraus, 2013; Offner et al., 2023). Since the
latter also host planet-forming disks, the influence of stellar companions on
planet formation must be studied theoretically, numerically, and empirically.
For instance, a long-established prediction is that the orbit of binary stars
should severely truncate disks, leading to small circumstellar disks and/or
large cavities interior to circumbinary disks (e.g., Artymowicz & Lubow,
1994). A direct implication of the former is that circumstellar disks in close
binaries should be rare, since small disks have a short (viscous) dissipation
timescale, and compact in size. This has been extensively borne out by
observations of young binary systems (e.g., Harris et al., 2012; Kraus et al.,
2012; Akeson et al., 2019; Manara et al., 2019). Similarly, cavities carved
out by central binaries have been observed in a number of systems (e.g.,
Dutrey et al., 1994; Monnier et al., 2019; Ragusa et al., 2021). Dynamical
perturbations of disks by stellar companions have also been documented in
multiple cases (e.g., Kurtovic et al., 2018; Cuello et al., 2023).

Among multiple systems, triple and higher-order systems are of particular
interest. First of all, such high-order systems represent a sizable fraction
of all systems: among field solar-type and low-mass stars, a quarter to a
third of all non-single systems contain three or more stars (Hirsch et al.,
2021; Reylé et al., 2021). Furthermore, the growing population of known
exoplanets in triple and quadruple systems emphasizes the importance of
understanding planet formation in this context (Cuntz et al., 2022). High-
order systems are generally hierarchical in nature because these are
inherently more stable (Tokovinin, 2021, and references therein). Depending on
the relative orientation of the inner and outer orbital planes, they can
experience von Zeipel-Lidov-Kozai oscillations, through which orbital
eccentricity and the relative alignment angle can vary over broad ranges on
secular timescales (von Zeipel, 1910; Lidov, 1962; Kozai, 1962). Most
importantly, their dynamical influence on surrounding gas and dust is
necessarily more complex than that of a binary system, potentially leading to
different disk truncation thresholds, complex variability of accretion onto
the individual stars, and multiple precession timescales and axes (e.g.,
Martin et al., 2022; Ceppi et al., 2022, 2023). GW Ori is a well-studied
example of a triple-lined spectroscopic system that contains a circumtriple
disk whose dynamics is strongly affected by its orbital configuration (Czekala
et al., 2017; Bi et al., 2020; Kraus et al., 2020). In this study, we focus on
wider, visual binaries, which also offer stable locations for individual,
circumstellar disks.

GG Tau and UX Tau are two hierarchical high-order systems in the L1551 cloud
in the Taurus star-forming region. Since they both host multiple disk
components, they are ideal test-beds to assess the dynamical effects of
multiple systems on their surrounding material. GG Tau is composed of a
hierarchical triple system, GG Tau A, separated by 10″ from a binary system,
GG Tau B (Leinert et al., 1993). The close binarity of GG Tau Ab was
discovered by Di Folco et al. (2014) and its projected separation of $\approx
4$ au suggested an orbital period of a few years. A massive gas and dust disk
surrounds GG Tau A (Guilloteau et al., 1999; Phuong et al., 2020) and several
streamers of material connect it to small circumstellar disks associated with
both GG Tau Aa and Ab (Roddier et al., 1996; Silber et al., 2000; Beck et al.,
2012; Keppler et al., 2020). While it is expected that the orbital motion of
the GG Tau Aa–Ab pair is responsible for carving the cavity inside of the
massive disk, there remains some tension between the cavity size and binary
orbit, and it is likely that the orbit and disk are not in a coplanar
configuration (Beust & Dutrey, 2006; Köhler, 2011; Nelson & Marzari, 2016; Aly
et al., 2018; Keppler et al., 2020; Toci et al., 2024).

UX Tau is a quadruple system (Reipurth & Zinnecker, 1993), with the close
binarity of UX Tau B first reported by Duchêne (1999). Subsequent monitoring
revealed significant orbital motion, although it remained insufficient for
precise orbital fitting (Schaefer et al., 2014). While UX Tau B does not host
circumstellar matter, UX Tau A harbors a well-studied transitional disk (e.g.,
Andrews et al., 2011; Akeson et al., 2019). UX Tau C represents a more complex
case: despite a lack of near-infrared excess (White & Ghez, 2001; McCabe et
al., 2006), it was found to be associated with both gas and dust (Zapata et
al., 2020; Ménard et al., 2020). Most strikingly, these studies identified
tidal trails extending from the UX Tau A disk that suggest a direct dynamical
interaction between the two components. Considering hydrodynamical simulations
of different configurations, Ménard et al. (2020) concluded that the pair
recently underwent an inclined prograde flyby, during which UX Tau C may have
captured material from the UX Tau A disk.

In this paper, we present new high-resolution observations of the close GG Tau
Ab and UX Tau B subsystems (Section 2), revealing (nearly) full orbital
coverage and enabling precise orbital fits (Section 3.1). From these, we
derive dynamical masses for the systems (Section 3.2) and constrain their
geometry relative to the other components of the systems and to the various
disks they host (Section 3.3). In Section 4, we discuss the implications of
our findings on the stellar properties, the survival of compact circumstellar
disks in close binaries, and the overall stability and dynamics of the
systems.

##  2 Observations and detection of the companions

For both systems, our analysis combines published astrometry with new analysis
of archival data. In this section, we describe how we processed the latter to
determine the relative astrometry at new epochs.

###  2.1 GG Tau Ab

GG Tau has been imaged at 2 $\mu$m with the NIRC2 instrument behind the Keck
II adaptive optics system at five epochs from 2010 to 2019 (PIs: A. Ghez,
J.-L. Margot, J. Lu). In all cases, a number of short exposures were used to
avoid saturation on the bright GG Tau A. We retrieved the pipeline-calibrated
data, subtracted a global frame median to remove any residual background, and
performed image alignment and median combination to produce ”epoch average”
frames. Because the separation of the GG Tau Aa–Ab pair is only
$\approx$0$\aas@@fstack{\prime\prime}$25, much smaller than the atmospheric
anisoplanetism angle, and assuming that it is a point source, we can consider
GG Tau Aa as a perfectly matched PSF that can be used to test whether the Ab
component is itself resolved as a close pair. In 2010, we do not see any
evidence that GG Tau Ab is resolved, indicating that its separation and/or
flux ratio was too small. In all other epochs, there is evidence for deviation
from a single point source. The presence of the Ab2 component is most
conspicuous in the 2019 data at a position angle of $\approx 250$° but is also
perceivable in the other epochs (see Figure 1).

Figure 1: Thumbnails of Keck/NIRC2 images in the GG Tau system. The first and
second columns represent GG Tau Aa and GG Tau Ab, normalized to their peak
values, respectively. The third column is the best-fit model of GG Tau Ab
created by shifting and scaling two copies of GG Tau Aa, and the fourth column
is the residuals from this model. Red and blue regions are negative and
positive residuals, respectively, with the color map saturating at $\pm$3% of
the peak pixel in the image of GG Tau Ab. The fifth column shows the result of
subtracting the model of GG Tau Ab1 (centered on the black cross) from the
image of GG Tau Ab, revealing GG Tau Ab2, which is scaled up by a factor of
four for visual purposes. The last column shows the residuals of fitting GG
Tau Ab as a single star instead; they are displayed with the same saturation
levels as in the fourth column for direct comparison.

Figure 2: Reduced $\chi^{2}$ maps for the location of GG Tau Ab2 in the new
PIONIER observations presented here. In the 2013 epoch, solution ”a” is both
the most likely from a pure likelihood perspective, and it is also the most
plausible based on the motion observed between the 2012 and 2014 Keck
observations (see Section 2.1). The second and third highest likelihood
solutions (labelled ”b” and ”c”), located to the West-Southwest of the primary
solution, are also illustrated in Figure 4.

To estimate the relative astrometry of the system, we performed a non-linear
least square fit using the Levenberg-Marquart algorithm as implemented in
lmfit in which we modeled GG Tau Ab as the linear combination of two
translated and scaled copies of GG Tau Aa. While the quality of the adaptive
optics correction varies from epoch to epoch, and the fit is consequently
sensitive to the initial guesses, we find that this approach is robust by
performing the fit at the individual frame level (rather than on the epoch
average frame) and use the standard deviation of the mean of these individual
fits as an estimate of the random errors. Furthermore, we ran the binary fit
with a range of initial parameters and used the range of resulting parameter
values to evaluate the systematic uncertainties. In most cases, the latter
dominate over the random uncertainties, and we consistently adopted the
largest of the random and systematic uncertainties. This fitting process also
yields the flux ratio of the system. In the case of a close asymmetric pair,
however, the flux ratio and separation are generally correlated. This source
of uncertainty is encapsulated in the methodology described above. As a
consistency check, we also fitted the image of GG Tau Ab as a single star; the
resulting residuals are shown in the last column of Figure 1. As expected from
fitting a binary system as a single star, they contain a strong positive-
negative-positive pattern along the binary position angle, further confirming
the binary nature of the system.

Interferometric $H$-band observations with PIONIER were obtained in 2013 and
2015 (PI: E. Di Folco) to follow up on the 2012 discovery observations. Two
datasets were obtained in 2015, but only the 2015/12/21 was of sufficient
quality. The data were reduced using the PIONIER pipeline, similar to the
results presented in Di Folco et al. (2014). We then fitted a model consisting
of two point sources to the calibrated visibilities and phases. The resulting
$\chi^{2}$ maps are shown in Figure 2. We note that the fits are imperfect in
both epochs ($\chi^{2}_{\mathrm{red}}>1$) due to contamination from the nearby
GG Tau Aa, but we consider that the relative astrometry of the close GG Tau Ab
pair is well determined nonetheless. In both the published 2012 and the new
2013 observations, PIONIER was set in its broadband mode, resulting in a very
sparse sampling of the (u,v) plane and, consequently, in ambiguous results.
Two possible solutions from the 2012 data were reported by Di Folco et al.
(2014) and we find three plausible solutions in 2013. In 2012, we could
resolve the ambiguity by comparison with the nearly contemporaneous (2 d
difference) Keck observations. We find that the slightly less likely ”second”
solution matches very well with our Keck result whereas the most likely
solution differs in position angle by 10° (see Figure 4), a large enough
deviation that we can confidently rule it out. In 2013, two of the three
possible solutions have a separation of
$\approx$0$\aas@@fstack{\prime\prime}$039 while the third has a separation of
0$\aas@@fstack{\prime\prime}$031\. The latter is visually much more consistent
with the orbital motion observed in the Keck images between 2012 and
2014111Both of the alternative solutions are also readily excluded by orbit
fits that includes either of them instead of the nominal solution that we
adopt here (see Section 3.1).. We therefore adopted the latter solution. In
2015, PIONIER was used in its spectrally dispersed mode, producing a
significantly improved (u,v) coverage and there is only one possible binary
solution, which we adopt. We assigned the same astrometric uncertainties to
both new PIONIER epochs, as systematic uncertainties are likely to dominate
the error budget of such measurements. In principle, this analysis also yields
an estimate of the binary flux ratio. Unfortunately, the presence of the
nearby GG Tau Aa components introduces a systematic offset in the measured
correlated fluxes, which translates to a large systematic error on flux ratio.
We could not properly assess this effect without independent simultaneous
measurement of the GG Tau Aa–Ab flux ratio and, therefore, could not reliably
determine the flux ratio of GG Tau Ab itself from the PIONIER data.

###  2.2 UX Tau B

The projected separation of the UX Tau B pair was
$\approx$0$\aas@@fstack{\prime\prime}$14 in its 1997 discovery epoch (Duchêne,
1999), enabling multiple follow-up observations up to 2013 (Correia et al.,
2006; Schaefer et al., 2014). We found two unpublished observations of the
system in that same period in which the pair is clearly resolved, using
HST/WFPC2 and Gemini/NIRI in 1997 and 2009, respectively (PIs: K. Stapelfeldt
and P. Allen). We performed a similar analysis to the Keck/NIRC2 images of GG
Tau discussed above to estimate the relative astrometry of the UX Tau B pair.
Results are illustrated in the top two rows of Figure 3). The HST/WFPC2
observations were obtained with two filters, which provide consistent
estimates of the binary astrometry, but find that the flux ratio is
wavelength-dependent: it rises from 0.5 to 0.64 between 0.6 and 0.8 $\mu$m.

More recently, UX Tau was observed at multiple epochs in 2015–17 with the
VLT/SPHERE adaptive optic systems using the IRDIS dual-channel mode (PIs:
J.-L. Beuzit, M. Benisty). We discarded one epoch in which the quality of the
observations were of insufficient quality and again performed a similar binary
fit as above. In most SPHERE observations UX Tau A is either saturated or
placed behind a coronagraphic mask and we therefore used UX Tau C as estimate
of the contemporaneous PSF. As shown in Figure 3, the model residuals in some
epochs are not negligible and elongated. We interpret this as evidence that
the distance between the UX Tau C and UX Tau B is sufficient for deviations in
the PSF to be present. Indeed, the position angle of the B–C pair is $\approx
115\degr$, roughly aligned with the PSF elongation. Another possibility is
that the UX Tau C is marginally resolved due to scattering off its
circumstellar dust, which was found to be elongated roughly along the North-
South direction (Ménard et al., 2020). Either way, as UX Tau B is generally
well-resolved, we trust that the binary astrometry is well determined with the
systematic uncertainties that we estimated using the same method as for GG Tau
Ab.

Figure 3: Thumbnails of HST/WFCP2, Gemini/NIRI and VLT/SPHERE images in the UX Tau system. The columns are similar to those in Figure 1, except that no flux scaling is applied to UX Tau Bb in the last column. Table 1: Astrometry of the GG Tau Ab and UX Tau B systems. † Only the most plausible solutions from these epochs are listed here (see Section 2.2). The flux ratio of the GG Tau Ab pair could not be determined in the new PIONIER data due to the contamination by the nearby GG Tau Aa component. Date | Instrument | Filter | Sep. (″) | PA (°) | Flux Ratio | Ref.
---|---|---|---|---|---|---
GG Tau Ab
2011/12/16 | Keck/NIRC2 | Br$\gamma$ | 0.0305$\pm$0.0015 | 246.8$\pm$1.5 | 0.21$\pm$0.04 | This work
2012/10/29 | Keck/NIRC2 | $K^{\prime}$ | 0.0347$\pm$0.0015 | 232.1$\pm$1.5 | 0.17$\pm$0.04 | This work
2012/10/31 | VLTI/PIONIER | $H$ | 0.0325$\pm$0.0004 | 230.0$\pm$0.4 | 0.23$\pm$0.10 |  Di Folco et al. (2014)†
2013/10/18 | VLTI/PIONIER | $H$ | 0.0312$\pm$0.0004 | 213.2$\pm$0.4 | (…) | This work†
2014/12/11 | Keck/NIRC2 | $K^{\prime}$ | 0.0274$\pm$0.0020 | 181.5$\pm$2.0 | 0.15$\pm$0.03 | This work
2015/12/21 | VLTI/PIONIER | $H$ | 0.0227$\pm$0.0003 | 157.3$\pm$0.4 | (…) | This work
2019/10/13 | Keck/NIRC2 | Br$\gamma$ | 0.0315$\pm$0.0010 | 252.3$\pm$1.0 | 0.22$\pm$0.03 | This work
UX Tau B
1997/12/12 | CFHT/AOBIR | $K$ | 0.138$\pm$0.002 | 303.9$\pm$1.0 | 0.78$\pm$0.05 | Duchêne (1999)
1998/11/19 | HST/WFPC2 | F606W | 0.142$\pm$0.002 | 302.1$\pm$1.0 | 0.50$\pm$0.02 | This work
2002/10/22 | VLT/NACO | $K$ | 0.136$\pm$0.002 | 309.0$\pm$1.0 | 0.81$\pm$0.02 | Correia et al. (2006)
2009/10/25 | Keck/NIRC2 | $K_{c}$ | 0.084$\pm$0.002 | 326.9$\pm$1.0 | 0.81$\pm$0.02 | Schaefer et al. (2014)
2009/12/25 | Gemini/NIRI | $K_{c}$ | 0.085$\pm$0.002 | 327.4$\pm$1.0 | 0.78$\pm$0.01 | This work
2011/10/12 | Keck/NIRC2 | $K_{c}$ | 0.056$\pm$0.002 | 339.7$\pm$1.0 | 0.80$\pm$0.01 | Schaefer et al. (2014)
2013/01/27 | Keck/NIRC2 | $K_{c}$ | 0.032$\pm$0.005 | 359.5$\pm$8.7 | 0.9$\pm$0.4 | Schaefer et al. (2014)
2015/10/25 | VLT/SPHERE | $H$ | 0.047$\pm$0.002 | 259.4$\pm$1.0 | 0.82$\pm$0.03 | This work
2016/01/01 | VLT/SPHERE | $H$ | 0.046$\pm$0.002 | 259.1$\pm$1.0 | 0.83$\pm$0.04 | This work
2016/09/17 | VLT/SPHERE | $H$ | 0.057$\pm$0.002 | 264.9$\pm$1.0 | 0.82$\pm$0.02 | This work
2016/10/15 | VLT/SPHERE | $K_{c}$ | 0.061$\pm$0.003 | 269.0$\pm$1.0 | 0.83$\pm$0.01 | This work
2017/10/12 | VLT/SPHERE | $H$ | 0.070$\pm$0.002 | 272.8$\pm$1.0 | 0.79$\pm$0.03 | This work

##  3 Results

###  3.1 Relative astrometry and orbital fits

All published and new astrometric results are represented in Table 1 and
illustrated in Figure 4. In both cases, the new observations presented here
represent a significant improvement in the orbital coverage of both systems.
For GG Tau Ab, not only do we present the first observation of orbital motion,
but the system has nearly completed a full orbit between 2011 and 2019.
Indeed, this $\approx$8 yr period further confirms the tentative ”a posteriori
detection” in 2003 discussed by Di Folco et al. (2014) if we adopt a position
angle of $\approx$245° for that epoch. In the case of UX Tau B, while the
position angle of the system had changed by $\approx$60° between 1998 and
2013, the new SPHERE observations represent a change of $\approx$270° in the
subsequent 2 yr, and rapid year-by-year motion is evident between 2015 and
2017. These most recent observations lie at intermediate position between the
25 and 40 yr-period orbits presented by Schaefer et al. (2014). This improved
coverage invites orbital fits, which we expect to be well constrained by
existing observations.

Figure 4: Relative orbit of the GG Tau Ab and UX Tau B binaries. In both
panels, orange symbols represent published astrometric datapoints whereas blue
symbols indicate new adaptive optics or HST observations that are presented
here for the first time. In 2012 and 2013 (orange and red symbols,
respectively), the PIONIER observations of GG Tau Ab allowed two and three
possible solutions, respectively. Based on the Keck observations, solutions
”a” in both epochs are the most plausible ones.

To perform the orbital fit, we used the orbitize! package (Blunt et al., 2020)
in combination with the parallel-tempered package ptemcee (Vousden et al.,
2016). Given the tentative nature of the 2003 detection from Di Folco et al.
(2014), and our lack of success in detecting GG Tau Ab2 in VLT/NaCo images at
any epoch, we decided against using it in the fit. We nonetheless verified
that, given its poor astrometric precision, including it would not
significantly alter the fit. The free parameters used in orbitize! are the
eccentricity ($e$), inclination ($i$), phase of periastron ($\tau_{0}$,
measured relative to the earliest data point), position angle of the line of
nodes ($\Omega$), argument of periastron ($\omega$), semi-major axis ($a$),
and total system mass ($M_{sys}$). During the fit, we fixed the parallax of
the system to $\pi=6.91$ mas (the median L1551 estimate from Galli et al.,
2019, see Section 3.2) to convert from angular to physical separations, and we
further converted $M_{sys}$ into the orbital period ($P$) and $\tau_{0}$ into
the time of passage at periastron, $T_{0}$. These three quantities are those
readily constrained by the data. Uniform priors are used for $e$, $\omega$,
$\Omega$ and $\tau_{0}$, log-uniform and sine-uniform are used for $a$ and
$i$, respectively, and a Gaussian prior is used for $M_{sys}$. In the absence
of radial velocity measurements, solutions defined by ($\omega$, $\Omega$) and
($\omega+180\degr$, $\Omega+180\degr$) are degenerate; when extracting the
MCMC chains, we solve the ambiguity by enforcing that
$0\degr\leq\Omega<180\degr$. We applied broad priors on $M_{sys}$ that were
informed by preliminary estimates of the semi-major axis and orbital period.
Specifically, we used 1.0$\pm$0.5 $M_{\odot}$ and 2$\pm$1 $M_{\odot}$ for GG
Tau Ab and UX Tau B, respectively. We performed each fit with ten temperatures
and 100 walkers per temperature, and advanced the chains 40000 steps past an
initial 1000 steps of burn-in, and only kept every tenth walker position to
remove correlations in the chains. Inspection of the chain evolution confirms
that they have reached convergence. The resulting cornerplots are presented in
Appendix A and 68-percentile for all parameters are listed in Table 2. We note
that the large orbital coverage is such that there is no strong correlation
between orbital parameters, with the exception of $\Omega$ and $\omega$. The
location of the periastron is nonetheless well constrained in both cases (see
Figure 5). Finally, we note that we have adopted the astrometric solution with
$i\leq 90\degr$ instead of the solution with $i>90\degr$, as justified in
Section 3.3, even though the data at hand do not allow to solve that
ambiguity.

Figure 5: Random set of 100 orbital solutions selected form the converged part
of the MCMC chain for the GG Tau Ab and UX Tau B binaries (considering the
”trimmed” dataset, see Section 3.1). Black $+$ symbols indicate the periastron
of each plotted orbit.

The orbital fits for both systems are reasonable but, as indicated in Table 5,
neither of the best orbital fit reaches
$\mathrm{min}(\chi^{2}_{\mathrm{red}})=1$, suggesting some underestimates of
the astrometric uncertainties and/or the presence of outliers. We inspected
the fit residuals and determined that the 2014 measurement of GG Tau Ab and
the 1997, 1998 and 2015 measurements of UX Tau B were the most discrepant (at
the $\approx 2.5-3\sigma$ level). We therefore repeated the orbital fit with
”trimmed” datasets, namely excluding the 2014 measurement of GG Tau Ab, and
the 1998222We consider the 1997 HST datapoint more robust than the discovery
1998 CFHT measurement from Duchêne (1999) as precise astrometry was not a
priority in that study. and 2015 measurements of UX Tau B. In both cases, the
fits to the ”trimmed” dataset produces a much better fit, with
$\mathrm{min}(\chi^{2}_{\mathrm{red}})\approx 1.0-1.3$. The confidence
intervals for the ”complete” and ”trimmed” dataset overlap at the $1\sigma$
level, confirming that no datapoint biases the fit significantly. In most
cases, the resulting uncertainties on orbital parameters are comparable for
both fits, with the main exception being the semi-major axis and,
consequently, system mass for GG Tau Ab. We conservatively adopt the ”trimmed”
dataset fit for the subsequent analysis.

Table 2: Orbital parameters of the GG Tau Ab and UX Tau B systems. Parameters listed in the lower part of the table (periastron and apastron distances, and total system masses) are derived from the seven free parameters of the orbital fit in combination with the estimate of the distance to the system. Consequently, two uncertainties are listed, respectively the random (resulting from the orbit fit) and systematic (driven by the distance estimate) uncertainties. “Trimmed” datasets are those in which the most discrepant astrometric points from the fit to “Complete” dataset are discarded prior to the orbital fit (see Section 3.1). | GG Tau Ab | UX Tau B
---|---|---
| ”Complete” dataset | ”Trimmed” dataset | ”Complete” dataset | ”Trimmed” dataset
$P$ (yr) | 8.16 ${}^{+0.08}_{-0.07}$ | 8.13 ${}^{+0.08}_{-0.07}$ | 32.0 ${}^{+0.9}_{-0.8}$ | 31.9 ${}^{+1.0}_{-0.9}$
$T_{0}$ | 2017.59 ${}^{+0.28}_{-0.25}$ | 2017.14 ${}^{+0.24}_{-0.21}$ | 2013.89 ${}^{+0.14}_{-0.13}$ | 2013.95 ${}^{+0.16}_{-0.14}$
$e$ | 0.539 ${}^{+0.033}_{-0.027}$ | 0.574 ${}^{+0.048}_{-0.040}$ | 0.870 ${}^{+0.010}_{-0.009}$ | 0.863 $\pm$ 0.011
$a$ (mas) | 25.7 ${}^{+1.0}_{-0.8}$ | 26.2 ${}^{+2.1}_{-1.4}$ | 79.1 ${}^{+2.4}_{-2.2}$ | 78.8 ${}^{+2.6}_{-2.1}$
$i$ (°) | 40.1 ${}^{+4.4}_{-4.5}$ | 39.9 ${}^{+6.0}_{-5.6}$ | 32.2 ${}^{+5.0}_{-7.2}$ | 33.5 ${}^{+4.9}_{-6.8}$
$\Omega$ (°) | 100.8 ${}^{+14.4}_{-11.2}$ | 125.9 ${}^{+9.4}_{-15.3}$ | 155.1 ${}^{+8.1}_{-9.2}$ | 152.0 ${}^{+8.7}_{-10.4}$
$\omega$ (°) | 292.7 ${}^{+5.0}_{-7.8}$ | 277.7 ${}^{+9.3}_{-5.1}$ | 321.8 ${}^{+9.8}_{-9.2}$ | 325.2 ${}^{+11.3}_{-10.1}$
$d_{\mathrm{peri}}$ (au) | 1.70 ${}^{+0.09}_{-0.08}\,\pm\,0.04$ | 1.62 ${}^{+0.06}_{-0.08}\,\pm\,0.04$ | 1.49 $\pm\,0.11\,\pm$ 0.03 | 1.56$\,\pm\,$0.12$\,\pm\,$0.04
$d_{\mathrm{apo}}$ (au) | 5.73 ${}^{+0.31}_{-0.26}\,\pm\,0.13$ | 5.97 ${}^{+0.68}_{-0.45}\,\pm\,0.14$ | 21.4 ${}^{+0.7}_{-0.6}$$\,\pm$ 0.5 | 21.2 ${}^{+0.8}_{-0.6}$$\,\pm$ 0.5
$M_{sys}(M_{\odot})$ | 0.77 ${}^{+0.09}_{-0.07}\,\pm\,0.05$ | 0.82 ${}^{+0.22}_{-0.12}\,\pm\,0.06$ | 1.47 ${}^{+0.15}_{-0.14}\,\pm\,$0.10 | 1.47 ${}^{+0.15}_{-0.14}\,\pm\,$0.10
min($\chi^{2}_{\mathrm{red}}$) | 2.40 | 1.26 | 1.75 | 1.03

###  3.2 Dynamical masses

We then proceeded to convert the orbital solutions in terms of angular scale
to physical scale, which requires determining the distance to the two systems.
Specifically, $M_{sys}=a^{3}\,P^{-2}\,D^{3}\,M_{\odot}$, where $a$, $P$ and
$D$ are expressed in arcsec, yr and pc, respectively. GG Tau A is included in
the GAIA DR3 catalog (Gaia Collaboration et al., 2016, 2023) but with a very
poor RUWE parameter, most likely because of the internal orbital motion of the
Aa–Ab pair. GG Tau Ba and GG Tau Bb are in the GAIA DR3 catalog with good RUWE
parameters, however. Their parallaxes are 6.87$\pm$0.04 and 6.75$\pm$0.15 mas,
respectively. Similarly, UX Tau B has a bad RUWE parameter and its GAIA DR3
parallax cannot be trusted but UX Tau A and C have good measurements, with
parallaxes of 7.03$\pm$0.03 and 6.92$\pm$0.07 mas, respectively. In both cases
the available measurements are marginally consistent with each other. We also
note that both GG Tau and UX Tau are part of the L1551 group, for which the
mean parallax and associated dispersion is 6.91$\pm$0.16 mas (Galli et al.,
2019). Since the latter is consistent with all individual estimates and is
more conservative, we adopted the L1551 parallax to determine the dynamical
mass of both systems and consider that its associated uncertainty represents a
systematic uncertainty, which we carry separately in Table 2 and illustrate in
Figure 6. For both systems, the systematic uncertainty is commensurate with,
but smaller than, the random uncertainty.

Figure 6: Posterior distribution for the dynamical mass of the GG Tau Ab and
UX Tau B systems. In both cases, dashed and solid histograms represent the
distributions using ”complete” and ”trimmed” astrometric datasets,
respectively. The black horizontal bars represent the systematic error
introduced by the uncertainty on the distance to each system.

###  3.3 System architectures

Since the orbit properties of both systems are well constrained, we can
compare the relative orientation of their orbital plane with other relevant
planes in each system (see Table 3 and Figure 7), as this is relevant to the
stability and dynamical evolution of multiple systems and their associated
disks. We computed the angle between two (orbital or disk) angular momentum
vectors, $\Delta\theta$, following Equation 1 in Czekala et al. (2019), using
Monte Carlo method to sample the input posterior distributions. We note that
for visual orbits, there is an inclination ambiguity whereby orbits with $i$
and $180\degr-i$ inclinations (and, conjointly, $\omega$ and $360\degr-\omega$
argument of periastron) are indistinguishable in the plane of the sky. When
comparing with other planes, we must therefore consider two alternative
deprojection solutions. In the case of GG Tau, we note that with inclinations
of $\approx 35-40\degr$, adopting the alternative inclination leads to orbits
that are nearly perpendicular to each other. Similarly, the wider GG Tau Aa–Ab
orbit is either close to coplanar or nearly perpendicular to the outer ring.
While circumbinary disk in a polar configuration and highly misaligned
hierarchical triple systems exist (e.g., Tokovinin, 2017; Czekala et al.,
2019), we focus here on the configurations that are close to coplanar. We also
note that the relative orientation of the tighter orbit with respect to the
circumtriple disk does not significantly affect the evolution of the system
(Ceppi et al., 2023).

Table 3: Angles defining key planes in the GG Tau and UX Tau systems. System | Plane | $i\,(\degr)$ | $\Omega\,(\degr)$ | Reference
---|---|---|---|---
GG Tau | Ab1–Ab2 orbit | 39.9 ${}^{+6.0}_{-5.6}$ | 125.9 ${}^{+9.4}_{-15.3}$ | This work
| Aa–Ab orbit | 36.2 ${}^{+6.4}_{-5.3}$ | 99.7 ${}^{+19.2}_{-39.9}$ | Toci et al. (2024)
| Circumtriple ring | 35$\pm$2 | 97$\pm$1 | Phuong et al. (2020)
UX Tau | B orbit | 33.5 ${}^{+4.9}_{-6.8}$ | 152.0 ${}^{+8.7}_{-10.4}$ | This work
| A disk | 32$\pm$8 | 164$\pm$8 | Zapata et al. (2020)

In the GG Tau A system, we can compare the Ab1–Ab2 orbital solution we have
obtained to the updated Aa–Ab orbit presented in Toci et al. (2024). Because
the latter is only modestly constrained, the resulting misalignment angle is
only loosely constrained. The most plausible value is $\sim 12\degr$,
suggesting only a modest degree of misalignment between the two orbits. It is
worth noting that the Aa–Ab pair has a distribution of periastron distances
($a(1-e)$) of $31^{+4}_{-5}$ au, which is about five times larger than the
apoastron distance of the Ab1–Ab2 pair. This ratio is relevant in the context
of the dynamical stability of the system (see Section 4.3). Another well-
characterized plane in the GG Tau A system is that of the massive dust ring
that surrounds it. Excluding the near polar configurations, we find that both
orbits have low relative inclinations to the ring, with peaks in the
posteriors of $\Delta\theta\approx 7\degr$ and 20° for the Aa–Ab and Ab1–Ab2
orbits, respectively.

Figure 7: Angle between the orbital and ring angular momentum vectors in the
GG Tausystem. In all cases, we solve the orbital inclination ambiguity by
assuming that the planes are close to coplanar.

Prior to this study, no orbit had been estimated in the UX Tau system due to
the long orbital period associated with the large projected separations, and
correspondingly long orbital periods, of the A–C and A–B pairs. It has not
even been demonstrated whether they are physically bound, although it is
statistically likely (e.g., Leinert et al., 1993). The apoastron distance of
the Ba–Bb pair we find, $\approx 20$ au, is $\approx 40$ times smaller than
the A–B projected separations. Regarding the orbital plane, the only other
plane that is well determined in the system is that of the UX Tau A disk
(Francis & van der Marel, 2020; Zapata et al., 2020; Ménard et al., 2020).
Considering the two ambiguous solutions, we find that the UX Tau Ba–Bb orbit
is either mildly misaligned ($\Delta\theta\lesssim 25\degr$ with a peak in the
posterior at $\Delta\theta\approx 10\degr$) with, or highly tilted
($\Delta\theta=115\pm 25\degr$) relative to the UX Tau A disk.

##  4 Discussion

###  4.1 Stellar properties

The dynamical masses derived in this study must be interpreted in light of
past studies of both systems. Here we consider how our results modify our
understanding of the stellar properties in these systems.

GG Tau is among the best-studied T Tauri multiple systems, in large part
because of the massive dust ring and gaseous disk that surrounds GG Tau A. Its
gas dynamics has allowed for precise estimates of the total dynamical mass of
GG Tau A (e.g., Guilloteau et al., 1999). Most recently, Phuong et al. (2020)
derived a total system mass of 1.41$\pm$0.08 $M_{\odot}$ (scaled to a distance
of 145 pc adopted here). Combined with our GG Tau Ab dynamical mass, this
implies that the mass of GG Tau Aa is 0.59${}^{+0.14}_{-0.22}\,M_{\odot}$,
with the GG Tau Ab subsystem being at least as massive as, and up to $\sim
60\%$ more massive than, GG Tau Aa. The spectral types for GG Tau Aa and Ab
have been estimated at K7–M0 and M0.5–M2, respectively (White et al., 1999;
Hartigan & Kenyon, 2003). Based on the observed range of dynamical masses for
single stars in Taurus (Simon et al., 2019; Braun et al., 2021; Flores et al.,
2022), we estimate that GG Tau Aa is most consistent with a $\approx
0.6\,M_{\odot}$ mass. Similarly, we propose that GG Tau Ab1 and Ab2 have
masses of $\approx 0.5-0.6\,M_{\odot}$ and $\approx 0.2-0.3\,M_{\odot}$,
respectively. The observed $K$ band flux ratio of the Ab1–Ab2 pair, if
interpreted as representative of the stellar photospheres, would be most
consistent a 1:3 mass ratio based on the BT-Setll models (Allard et al.,
2012), but we caution that the presence of continuum emission from
circumstellar material precludes reaching a definitive conclusion without
spatially resolved spectroscopy.

In the absence of a circumstellar disk whose Keplerian motion could be used
(e.g., Akeson et al., 2019), the dynamical mass estimate we obtained for UX
Tau B is the first for this component. Spectroscopic observations have led to
a spectral type estimate of M1–M2 (Hartigan et al., 1994; White & Ghez, 2001;
Luhman, 2018). Based on the compilation of Taurus dynamical masses mentioned
above, this would suggest a 0.5–0.7 $M_{\odot}$ mass for the individual
masses, somewhat in tension with the dynamical mass of $\approx$1.5
$M_{\odot}$ that we obtain. The systematic uncertainty introduced by the
distance to the system does not appear large enough to account for this
mismatch. We note, however, that the mass ratio of the close pair appears
close to unity based on flux ratio measurements (Duchêne, 1999; Correia et
al., 2006; Schaefer et al., 2014) and it is possible that a slightly earlier
spectral type ($\approx$M0.5) for both stars would be consistent with the
derived dynamical mass.

###  4.2 Orbital properties and circumstellar matter

We now consider the implications of the orbital properties we have inferred
for the two systems. We first note that, while GG Tau Ab has a moderate
eccentricity, UX Tau B is among the highest eccentricity systems known among
pre-main sequence visual binaries (see Figure 8). Among main sequence binary
systems, such a high eccentricity is also close to the maximum observed for
this range of orbital periods (Raghavan et al., 2010). This limit is set by
the onset of (partial) tidal circularization over the lifetime of the system.
Therefore, the system could survive if its current configuration as far as
interactions between individual stars are concerned.

The complete orbital solutions we have found place stringent constraints on
where gas and dust can be maintained in a stable configuration. In particular,
the similar $\approx$1.6 au periastron distances for both systems imply that
circumstellar disks around each star can be no larger than $\lesssim 1$ au. No
infrared excess is detected in UX Tau B but there is one in GG Tau Ab, which
is also found to be accreting (White & Ghez, 2001; McCabe et al., 2006).
Irrespective of which of the two components hosts this material, this proves
that it is possible for extremely compact disks to survive in close binaries,
despite the general tendency against it (Cieza et al., 2009; Kraus et al.,
2012, see also Figure 8) or the expectation of a very short viscous timescale
($\lesssim 0.05$ Myr, Cieza et al., 2009). Indeed, there is at least one
system with an even smaller periastron distance, similar eccentricity, and
confirmed infrared excess (ROXs 47, Rizzuto et al., 2016). The presence of
streamers from the massive outer ring onto both GG Tau Aa and Ab (Keppler et
al., 2020) confirms that continuous feeding of (small) circumstellar disks is
likely ongoing, providing a possible explanation to the disk survival and on-
going accretion. We speculate that the lack of circumstellar material around
either component of UX Tau B is due to a lack of outer reservoir that can feed
the system, possibly compounded by its high eccentricity. Indeed, the higher
binary eccentricity leads to regions of stable orbits around either component
that are simply too small to sustain long-lived disks.

Figure 8: Orbital properties of T Tauri visual binaries. In both panels, black
diamonds and green crosses represent $\lesssim 3$ Myr-old systems with and
without circumstellar material, respectively, while yellow crosses are $\sim
10$–20 Myr-old disk-free systems in Upper Scorpius and the TW Hya association.
The two red stars mark the systems studied here. Left: Comparison of orbital
period and eccentricity based on literature results listed in Appendix B.
Right: Comparison of periastron distances and dynamical masses for the same
systems.

We find that the two orbital planes in the GG Tau system have a modest degree
of misalignment ($\Delta\theta\sim 5-20\degr$) with each other and with the
circumtriple ring, in line with a scenario in which the entire system formed
from a single core undergoing collapse and fragmentation (Offner et al.,
2023). It is worth pointing out that the naive expectation would be for the
circumtriple ring to be coplanar with the invariable plane of the triple
system, which is distinct from the two orbital plane themselves, especially so
since the Ab subsystem is somewhat more massive than the Aa component. We also
stress that without radial velocity measurements or additional dynamical
considerations (size of the circumtriple ring, three-body stability), we
cannot exclude the orbital solutions in which the ring is on a roughly polar
orbit around the Aa–Ab system.

###  4.3 System stability and dynamics

Hierarchical triple systems are prone to disruptive instability if their
orbital properties are such that all three star-star separations become
commensurable at some point along the orbits. In order to remain stable, it is
therefore necessary that the tightest pair be much more compact than the
separation to the outer third component. This has been extensively empirically
verified for main sequence systems (e.g., Tokovinin, 2014, 2021). Furthermore,
numerical studies have explored this boundary, taking into account orbital
eccentricity and deviation from coplanarity and over a broad range of mass
ratios (Eggleton & Kiseleva, 1995; Mardling & Aarseth, 2001; He & Petrovich,
2018). With its large projected separation relative to the semi-major axis of
the close binary, the UX Tau A–B system is comfortably in a stable
configuration. The case of GG Tau A is not as extreme, yet both its ratio of
orbital periods ($\gtrsim 25$) and the ratio of periastron of the outer orbit
to periastron of the inner orbit (see Section 3.3) place it in the stable
regime (He & Petrovich, 2018) and among “typical” systems (Tokovinin, 2021).
We note, however, that this assessment assumes that the evolution of the
system is driven exclusively by $N$-body dynamics, whereas continued accretion
of gas and the interaction with the massive outer ring could further modify
either orbits. Therefore, the long-term stability of the system cannot be
definitively confirmed yet.

Beyond the simple ratio of orbital periods, the stability of the system could
be affected by the interplay of von Zeipel-Lidov-Kozai oscillations in the
triple system with the presence and dynamics of circumstellar disks. In order
for these oscillations to take place, the misalignment angle between the two
orbital planes must be $\Delta\theta\gtrsim 40\degr$. One of the two possible
deprojection solutions has a modest misalignment angle ($\Delta\theta\approx
15\degr$), lower than the threshold for the von Zeipel-Lidov-Kozai mechanism
to be triggered. This solution is broadly consistent with the statement that
triple systems are generally mildly misaligned when the outer orbit is wider
than $\approx 50$ au (Tokovinin, 2017). We also note that in this situation,
the ratio of $\sim 25-100$ between the inner and outer orbital periods favors
a low-to-moderate eccentricity for the outer GG Tau Aa–Ab system (Sterzik &
Tokovinin, 2002), which is independently more plausible to account for the
inner radius of the circumtriple ring (Toci et al., 2024). In the alternative
deprojection solution, however, von Zeipel-Lidov-Kozai mechanism would be
triggered and both the misalignment angles and the orbital eccentricities
should go through large oscillations. Given an orbital period of a few
centuries and a moderate eccentricity for the GG Tau Aa-Ab orbit (Köhler,
2011; Toci et al., 2024), the timescale of these oscillations should be
$\lesssim 10^{5}$ yr (Hamers, 2021), significantly shorter than the age of the
system but still much longer than the current orbital coverage.

Finally, we note that we have so far mostly considered UX Tau as a triple
system containing the A and B components. As noted by Zapata et al. (2020) and
Ménard et al. (2020), the morphology of extended spiral arms in the UX Tau A
disk and the presence of circumstellar dust and gas associated with UX Tau C
point to the strong dynamical influence of the latter. However, considering
that UX Tau B system is an order of magnitude more massive than UX Tau C
(Kraus & Hillenbrand, 2009), it is possible that the close binary could also
have a significant dynamical influence on the UX Tau A disk. Conversely, it is
also possible that UX Tau C will alter the orbit of UX Tau B in case a
reasonably close fly-by. The relative astrometry between the two components is
not currently known sufficiently well to explore this possibility at this
stage, however.

##  5 Conclusion

We have presented new adaptive optics and interferometric observations of the
close binary systems GG Tau Ab and UX Tau B, which are both part of higher
order multiple pre-main sequence systems. In both cases, the observations
provide sufficient orbital coverage ($\approx 60-100\%$) to tightly constrain
the Keplerian orbits, with orbital periods of $\approx 8$ and 32 yr for GG Tau
Ab and UX Tau B, respectively.

Deriving dynamical masses for both systems, we find that GG Tau Aa and the
combined Ab subsystem have similar masses, $\approx 0.6-0.8\,M_{\odot}$,
consistent with the known spectral types of the two components and the near-
infrared flux ratio of the Ab subsystem. In the case of UX Tau B, we find its
dynamical mass of 1.5 $M_{\odot}$ to be somewhat higher than expected but
could be reconciled if the two components are of equal mass and of slightly
earlier spectral type than reported in the literature.

The orbital solution we obtain for both systems are eccentric, but markedly
more so for UX Tau B ($e\approx 0.87$). Along with the lack of outer reservoir
that could feed the system, this high eccentricity could explain the lack of
circumstellar dust in the subsystem, as stable orbits are confined to
$\lesssim 1$ au or $\gtrsim 50$ au.

While the orbit of the outer components of the system are moderately
constrained (GG Tau Aa–Ab) or completely unconstrained (UX Tau A–B), we find
it likely that the triple systems are stable on the long term and, thus, that
they could contribute to the growing population of exoplanets in multiple
systems observed in the field. The most important caveats to this assessment
are in the GG Tau system, where 1) ongoing accretion could further alter the
orbits, and 2) one of the possible deprojection solution implies a near-polar
configuration for the triple system in which large von Zeipel-Lidov-Kozai
oscillations would play a major role.

In both systems, new, dedicated hydrodynamical simulations are warranted to
further explore the dynamics of both the stars and the gas+dust components in
both systems. Planet formation in multiple system is an increasingly central
topic is modern astronomy and these systems not only represent arguably
typical systems but their properties are now known with high precision.
Establishing with precision the orbital arrangement of young stars with discs
will be pivotal to understand the long term evolution of discs in multiple
stellar systems. This aspect is crucial to eventually pinpoint the locations
at which planet(esimals) could form in such multiples.

###### Acknowledgements.

We are grateful to an anonymous referee whose comments helped imprve this
manuscript. This project has received funding from the European Research
Council (ERC) under the European Union’s Horizon Europe research and
innovation program (grant agreement No. 101053020, project Dust2Planets; grant
agreement No. 101042275, project Stellar-MADE). This research has made use of
the Keck Observatory Archive (KOA), which is operated by the W. M. Keck
Observatory and the NASA Exoplanet Science Institute (NExScI), under contract
with the National Aeronautics and Space Administration. Some of the data
presented in this paper were obtained from the Mikulski Archive for Space
Telescopes (MAST) at the Space Telescope Science Institute. Some of the data
presented in this paper were obtained as part of ESO programs 096.C-0241,
097.C-0865, 198.C-0209, and 0100.C-0452, and retrieved from the ESO archive.
M. Langlois acknowledge funding from the French National research agency
(grant DDISK, ANR-21-CE31-0015-01).

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##  Appendix A Cornerplots for the orbital fits

In Figures 9 and 10, we present the MCMC cornerplot resulting from the orbital
fits to the GG Tau Ab and UX Tau B systems, respectively. The 180° ambiguity
on $\omega$ and $\Omega$ is inherent to visual orbits and the two families are
collapsed when computing the confidence intervals on all orbital parameters.
We also note that the line of nodes is not defined for $i=0$°, which explains
the wide spread of solutions for $\omega$ and $\Omega$ at the lowest
inclinations for the UX Tau B system.

Figure 9: MCMC cornerplot resulting from the orbital fit to the GG Tau Ab
orbit. While orbitize! converged on the solution with $i>90\degr$, we adopt
the equivalent supplementary angle, which match the convention of the
circumtriple ring. Figure 10: MCMC cornerplot resulting from the orbital fit
to the UX Tau B orbit.

##  Appendix B Orbits of pre-main sequence visual binaries form the literature

Here we compile the visual pre-main sequence binaries with published orbital
solutions. When multiple solutions have been published, we adopted the most
recent solution. Only systems with orbital periods $P<50$ yr are considered
here to ensure good orbital coverage, commensurable with that we obtained for
GG Tau Ab and UX Tau B. We excluded HBC 351 from the sample as it is most
likely to be a member of the 120 Myr-old Plieades open cluster (Luhman et al.,
2009).

Table 4: Orbital solutions for visual pre-main sequence binaries. Systems marked with a $\dagger$ symbols are members of the Upper Scorpius or TW Hydra association, whose age ($\sim 10$–20 Myr) is such that the absence of a disk may no longer be a consequence of multiplicity.  System |  $P$ (yr) | $e$ |  $a$ (au) | Disk? | Reference
---|---|---|---|---|---
DF Tau | 43.7$\pm$3.0 | 0.29$\pm$0.07 | 13.8$\pm$1.0 | Y | Schaefer et al. (2014); Sullivan & Kraus (2022)
DI Tau | 35.1${}^{+36.0}_{-2.9}$ | 0.73${}^{+0.13}_{-0.03}$ | 10.6${}^{+5.5}_{-0.2}$ | Y | Tang et al. (2023); Sullivan & Kraus (2022)
FF Tau | 14.77$\pm$0.18 | 0.634$\pm$0.004 | 6.25$\pm$0.08 | N | Rizzuto et al. (2020); Sullivan & Kraus (2022)
GSC 6209 | 5.52$\pm$0.03 | 0.21$\pm$0.01 | 4.1$\pm$ 0.4 | N† | Rizzuto et al. (2016)
GSC 6794 | 13.28$\pm$0.08 | 0.262$\pm$0.004 | 8.4$\pm$0.8 | N† | Rizzuto et al. (2016)
HP Tau G3 | 27.33${}^{+1.35}_{-1.19}$ | 0.521${}^{+0.009}_{-0.008}$ | 9.07${}^{+0.15}_{-0.12}$ | N | Rizzuto et al. (2020); Kraus et al. (2012)
Hubble 4 | 9.287$\pm$0.004 | 0.680$\pm$0.001 | 5.53$\pm$0.02 | N | Rizzuto et al. (2020); Sullivan & Kraus (2022)
J160517-202420 | 5.88$\pm$0.01 | 0.907$\pm$0.004 | 3.2$\pm$0.3 | N† | Rizzuto et al. (2016)
NTTS 045251 | 6.91$\pm$0.03 | 0.46$\pm$0.02 | 4.8$\pm$0.3 | N | Steffen et al. (2001)
ROXs 47 A | 8.23$\pm$0.12 | 0.82$\pm$0.01 | 4.7$\pm$0.5 | Y | Rizzuto et al. (2016)
RX J1550.0 | 8.74$\pm$0.04 | 0.488$\pm$0.001 | 6.8$\pm$0.7 | N† | Rizzuto et al. (2016)
RX J1601.9 | 8.17$\pm$0.06 | 0.36$\pm$0.01 | 5.3$\pm$0.5 | N† | Rizzuto et al. (2016)
ScoPMS 17 | 14.98$\pm$0.13 | 0.880$\pm$0.002 | 6.9$\pm$0.7 | N† | Rizzuto et al. (2016)
T Tau S | 27.2$\pm$ 0.7 | 0.55$\pm$0.03 | 12.7$\pm$0.1 | Y | Schaefer et al. (2020); White & Ghez (2001)
TWA 5 | 5.94$\pm$0.09 | 0.78$\pm$0.05 | 2.9$\pm$0.3 | N† | Konopacky et al. (2007); Riviere-Marichalar et al. (2013)
V773 Tau A–B | 26.2$\pm$1.1 | 0.10$\pm$0.03 | 15.4$\pm$0.5 | N | Boden et al. (2012); Duchêne et al. (2003)
V807 Tau | 12.0$\pm$0.4 | 0.34$\pm$0.06 | 5.0$\pm$0.3 | Y | Galli et al. (2018); Sullivan & Kraus (2022)
V1000 Tau | 3.6$\pm$0.3 | 0.43$\pm$0.05 | 2.5$\pm$0.1 | Y | Galli et al. (2018); Sullivan & Kraus (2022)
V1023 Tau | 9.30$\pm$0.05 | 0.69$\pm$0.01 | 6.3$\pm$0.1 | N | Galli et al. (2018); White & Ghez (2001)
ZZ Tau | 46.8$\pm$0.8 | 0.58$\pm$0.02 | 11.6$\pm$0.6 | Y | Belinski et al. (2022); Sullivan & Kraus (2022)