Orbital Motion, Variability, and Masses in the T Tauri Triple System (2024)

T Tauri is a young hierarchical triple system in the Taurus star-forming region. The optically dominant component T Tau North (T Tau N) is the prototype for the class of T Tauri objects (Joy 1945) and has a spectral type of K0 (Luhman 2018). The infrared companion, T Tau South (T Tau S), was discovered at a separation of ∼07 (Dyck et al. 1982) and was subsequently revealed to be a close binary with a separation of ∼005 (Koresko 2000). The spectrum of T Tau Sa appears to be relatively featureless while T Tau Sb has the infrared spectrum of an early-M star (Duchêne et al. 2002).

The orbital motion in the T Tau triple has been monitored for almost a complete period (P∼27 yr) over the past two decades (Köhler et al. 2000, 2008, 2016; Koresko 2000; Duchêne et al. 2002, 2005, 2006; Furlan et al. 2003; Beck et al. 2004; Mayama et al. 2006; Schaefer et al. 2006, 2014; Skemer et al. 2008; Ratzka et al. 2009; Csépány et al. 2015). Although T Tau N is one of the most massive and luminous T Tauri stars known and T Tau S is undetected in the optical (Stapelfeldt et al. 1998), modeling the spectral energy distribution of T Tau S (Koresko et al. 1997) and mapping the orbital motion in the triple system (Duchêne et al. 2006; Köhler et al. 2008, 2016; Schaefer et al. 2014) suggest that T Tau Sa is at least as massive as T Tau N.

Along with the positions of the three components, high spatial resolution observations provide measurements of their relative fluxes. According to Beck et al. (2004), the near-infrared flux of T Tau N remained constant from 1994 to 2002. The first spatially resolved observations of T Tau Sa,Sb (Koresko 2000; Duchêne et al. 2006) occurred about a year after the last periastron passage (T∼1996.1). At the time of the discovery, T Tau Sa was about 2 mag brighter than Sb. During 2002–2007, the flux of T Tau Sa entered a highly variable phase where it ranged from ∼2 mag fainter than Sb to 0.8 mag brighter than Sb. The variability of T Tau Sa then appeared to decrease through early 2014, while it remained fainter than Sb (Schaefer et al. 2014). Csépány et al. (2015) and Kasper et al. (2016) reported that T Tau Sa was again brighter than Sb in late 2014 through 2015.

Evidence suggests that T Tau Sa is enshrouded in a small (2–3 au), moderately opaque, edge-on disk (Beck et al. 2004; Duchêne et al. 2005; Skemer et al. 2008; Manara et al. 2019). Beck et al. and Duchêne et al. speculated that changes in the brightness of Sa could be caused by variable extinction, where the starlight intercepts thicker and thinner portions of the circ*mstellar disk as it rotates around the star. Alternatively, van Boekel et al. (2010) argue that the short-term variability is caused by variable accretion. They speculated that the enhanced variability in the early to late 1990s was induced by a tidal perturbation of the disk following periastron passage. Plausibly, both phenomena could contribute to the system's variability.

In this paper we present new adaptive optics (AO) measurements of the relative positions and fluxes of the components in the T Tau triple system obtained in 2015–2019. Based on these data and measurements in the literature, we compute an updated orbit fit to model the motion of T Tau Sb relative to Sa, as well as the motion of their center of mass relative to T Tau N. We derive dynamical masses of T Tau Sa and Sb from the orbital parameters. We also present photometry of the three components sampled at weekly to yearly timescales and discuss the variability of the system.

2.1.Astrometry and Flux Ratios

2.2.Absolute Photometry

We fit the relative orbit of T Tau Sa,Sb to the positions in Table 1 and measurements in the literature (Köhler et al. 2000, 2008, 2016; Koresko 2000; Duchêne et al. 2002, 2005, 2006; Furlan et al. 2003; Beck et al. 2004; Mayama et al. 2006; Schaefer et al. 2006, 2014; Skemer et al. 2008; Ratzka et al. 2009). We used a Newton–Raphson method to minimize χ² by calculating a first-order Taylor expansion for the equations of orbital motion. Table 3 lists the orbital parameters including the period P, time of periastron passage T, eccentricity e, angular semimajor axis a, inclination i, position angle of the line of nodes Ω, and argument of periastron ω. For visual binary orbits, there is a 180° ambiguity in the values of Ω and ω. This ambiguity can be resolved using radial velocity measurements to establish the direction of motion.

With all three components in the AO field of view, T Tau N serves as a reference to map the astrometric center-of-mass motion of the close pair. The astrometric motion provides the mass ratio of the close pair, M_Sb/M_Sa. We fit the astrometric motion by following the same approach outlined in Schaefer et al. (2012). We searched through a range of mass ratios to compute the expected location of the center of mass of T Tau Sa,Sb relative to N. For each trial mass ratio, we fit a representative orbit to the center-of-mass motion of S relative to N and selected the mass ratio that minimized the χ² between the calculated position of the center of mass and the orbit fit. An incorrect mass ratio will produce residual reflex motion that cannot be fit by a simple Keplerian orbit. We found a best-fitting mass ratio of 0.210±0.028 (Table 3). The relative and astrometric orbit fits are shown in Figure 3.

Figure 4 plots the residuals between the measured positions of T Tau Sb relative to Sa compared with the predictions from the orbit fit. There is significant scatter in the recent Gemini observations, especially as the separation of the close pair decreases below 90mas in 2018.8 and later. As a check on the measured flux ratios, we fit a visual orbit for T Tau Sa,Sb to only the Keck observations and earlier measurements in the literature (excluding the Gemini observations reported here). We then computed the expected position of T Tau Sa,Sb at the time of the Gemini observations based on this orbit fit. Fixing the relative separation of the close Sa,Sb pair, we performed another PSF fit to the Gemini images and solved for the component flux ratios and separations relative to T Tau N. The flux ratios derived from the constrained fit are consistent within 1σ with the results reported in Table 1 (except for the Brα flux ratio in 2019.0410 which is discrepant by 1.6σ). This provides confidence that the flux ratios are likely reliable, despite the large scatter in the Gemini positions.

The relative orbit of a binary system provides a measurement of the total mass if the distance is known. To derive masses of the components in T Tau, we used distances of 148.7±1.0 pc measured from the trigonometric parallax with the Very Long Baseline Array (VLBA; Galli et al. 2018) and 143.74± 1.22 pc derived from the Gaia Data Release 2 (DR2; Gaia Collaboration et al. 2018; Bailer-Jones et al. 2018). These two distance measurements are discrepant by 3σ, producing a systematic difference in the total mass derived for T Tau Sa and Sb, as shown in Table 4. Galli et al. (2019) discusses a comparison of several other sources that have both radio and Gaia parallaxes.

Table 4.Dynamical Masses of T Tau Sa and Sb

Parameter	VLBA Parallax	Gaia Parallax
Adopted d (pc)	148.7±1.0	143.74±1.22
Reference	Galli et al. (2018)	Bailer-Jones et al. (2018)
	2.744±0.166	2.479±0.155
MSa (M⊙)	2.268±0.147	2.049±0.137
MSb (M⊙)	0.476±0.060	0.430±0.055

Download table as: ASCIITypeset image

The VLBA parallax is based on mapping the motion of the radio emission from T Tau Sb and must account for the orbital motion of Sb relative to Sa (Loinard et al. 2007; Galli et al. 2018). Galli et al. (2018) attempted to fit an acceleration term caused by the motion relative to T Tau N, but found this contribution to be negligible. Based on the orbit fit for the center-of-mass motion of T Tau S relative to T Tau N (see Section 5), we find a small acceleration term of ∼0.028 mas yr⁻² over the time frame of the VLBA observations. The Gaia parallax is based on the visible light from T Tau N; the measurement has a small amount of excess noise (0.12 mas). In the subsequent discussion we opt to use the masses derived from the Gaia distance because it is less complicated by the orbital motion of the close pair. The accuracy of the parallax should improve in the final Gaia data release.

Combining the mass ratio from the astrometric motion with the total mass from the relative orbit provides individual masses of M_Sa=2.05±0.14 M_⊙ and M_Sb=0.43± 0.06 M_⊙. Currently the masses are measured with a precision of 6.7% and 12.7% for T Tau Sa and Sb, respectively. We expect the precision to improve to 2%–5% by continuing to map the orbital motion for a complete orbital period through the next periastron passage (expected in 2023.3).

While fitting for the astrometric motion, we applied a constraint on the total system mass (N+Sa+Sb) when solving for the representative orbit of T Tau N,S. As discussed by Schaefer et al. (2006), a broad range of orbital parameters can be used to fit an orbit with limited coverage; often with a tail of eccentric solutions that yield very large masses. The constraint on the total mass of the system does not significantly impact the final value of the mass ratio of the close pair, however, it does provide a more realistic set of orbital parameters for the wide pair that can be used to predict and back-track the expected motion in the triple system.

We adopted the combined mass of T Tau Sa+Sb from the visual orbit and the Gaia distance ( =2.48±0.16 M_⊙). We estimated the mass of T Tau N using the magnetic models of stellar evolution computed by Feiden (2016). We used the luminosity derived by Loinard et al. (2007) scaled to the Gaia distance (Bailer-Jones et al. 2018) and assumed an effective temperature of 5280±60 K based on the spectral type of K0 adopted by Luhman (2018) and the temperature scale derived by Pecaut & Mamajek (2013). These stellar parameters correspond to a mass of M_N=2.03±0.12 M_⊙ and an age of 3.8±0.7 MY when compared with the evolutionary tracks, as shown in Figure 5.

High-resolution, infrared spectra of T Tau N in the H band indicate a K5 spectral type for T Tau N (e.g., R. Lopez-Valdivia et al. 2020, in preparation; L. Prato 2020, in preparation). The lower effective temperature, 4200–4400 K, implied by this result may represent the impact of starspots with a large filling factor on the photospheric flux (Gully-Santiago et al. 2017). Discussion of the discrepancy between the K0 spectral type determined at optical wavelengths and the much later K5 type derived from infrared observations is beyond the scope of this paper and will be addressed in a forthcoming paper (L. Prato 2020, in preparation).

When applying the constraint on the wide orbital motion, we limited the total system mass of the three components to be within 4.51±0.59 M_⊙. The uncertainty corresponds to 3σ to provide a broader range of realistic values for the total mass. We also placed an arbitrary upper limit of P<5000 yr on the orbital period. The best fit and range of orbital parameters that represent the motion of the center of mass of T Tau S relative to T Tau N are listed in Table 5 and plotted in Figure 6. These are consistent with the range of orbits for the wide pair found by Köhler et al. (2016).

If the effective temperature of T Tau N is lower than the value implied by the optical spectral type, then this would lead to a smaller mass for T Tau N. However, changing the total mass constraint based on where the effective temperature implied by the infrared spectral type of T Tau N intersects the evolutionary tracks in Figure 5 produces a similar range of possible orbital parameters for the wide N,S orbit. Moreover, the resulting masses of T Tau Sa and Sb change by only 0.003 M_⊙, well within the 1σ uncertainty intervals reported in Table 4.

The absolute photometric measurements from the Gemini observations (Table 2) are plotted in Figure 7. The K-band magnitude of T Tau N remained steady with a range of 5.45–5.65 mag and an average value of K =5.54±0.07 mag. This is consistent with the results reported by Beck et al. (2004) who found that the infrared flux of T Tau N remained constant from 1994 to 2002, with an average magnitude of K=5.53±0.03 mag. The uncertainties at H and L are larger than at K because of the small flux of Sa and Sb in the H band (≳6 mag fainter than T Tau N) and the lower angular resolution in the L band. T Tau N and Sa are similar in brightness in the L band, but Sb is much fainter.

We can expand the time frame of the variability measurements by assuming an average magnitude of K=5.53± 0.03 mag for T Tau N (Beck et al. 2004) and converting the relative flux ratios between the three components into magnitudes. The long-term brightness variations of T Tau Sa and Sb in the K band are plotted in Figure 8. From 2015 to 2019, T Tau Sa experienced a dramatic increase in brightness, becoming ∼2 mag brighter than Sb, continuing the brightening trend reported initially by Csépány et al. (2015) and Kasper et al. (2016). According to the Gemini observations that were taken with higher temporal sampling, the K-band magnitude of T Tau Sa dropped in early 2018 and then began rising again in late 2018 through early 2019. The K-band magnitude of T Tau Sb steadily decreased by ∼2.6 mag over the 2015–2019 interval.

Based on our recent AO imaging of the T Tau triple system, combined with prior measurements in the literature, we fit the orbital motion of T Tau Sb relative to Sa and modeled the astrometric motion of their center of mass relative to T Tau N. Using the distance of 143.74±1.22 pc (Bailer-Jones et al. 2018), we derived dynamical masses of M_Sa=2.05± 0.14 M_⊙ and M_Sb=0.43±0.06 M_⊙. The orbital parameters, mass ratio, and masses are consistent within their uncertainties with the values computed by Köhler et al. (2016). However, the current uncertainties in the orbital parameters are significantly smaller thanks to the improved orbital coverage obtained over the past four years.

The fluxes derived from the AO images show that the K-band flux of T Tau N has remained steady between late 2017 and early 2019, with an average value of K=5.54± 0.07 mag. T Tau Sa is again brighter than Sb, but its K-band brightness varied dramatically in the past four years between 7.0 and 8.8 mag over timescales of a few months. On the other hand, T Tau Sb faded steadily from K =8.5 to 11.1 mag over four years. In a forthcoming paper, T. Beck et al. (2020, in preparation) investigate the link between the variability, orbital motion, circ*mstellar emission, and outflows in the system.

We thank the staff at the Keck and Gemini observatories for their support during the observations. We also thank the referee for providing feedback that improved the paper. G.H.S. and L.P. acknowledge support from NASA Keck PI Data Awards administered by the NASA Exoplanet Science Institute. Additional support was provided through the National Science Foundation (AST-1636624 for G.H.S. and AST-1518081 for L.P.). Some of the data presented herein were obtained at the W. M. Keck Observatory from telescope time allocated to the National Aeronautics and Space Administration through the agency's scientific partnership with the California Institute of Technology and the University of California. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. Some of the observations were obtained at the Gemini Observatory (GN-2017B-Q-29, GN-2018B-Q-137), which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), National Research Council (Canada), CONICYT (Chile), Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina), Ministério da Ciência, Tecnologia e Inovação (Brazil), and Korea Astronomy and Space Science Institute (Republic of Korea). Time at Gemini was granted through the time allocation process at the National Optical Astronomical Observatory (NOAO Prop. ID: 2017B-0280, 2018B-0321; PI: Schaefer). The data were downloaded through the Gemini Observatory Archive. We wish to recognize and acknowledge the significant cultural role that the summit of Maunakea has within the indigenous Hawaiian community. We are sincerely grateful for the opportunity to conduct these observations from the mountain. This research has made use of the SIMBAD database and the VizieR catalog access tool, CDS, Strasbourg, France.

Facilities: Keck:II (NIRC2) - , Gemini:Gillett (NIRI). -