The Gould's Belt Distances Survey (GOBELINS). IV. Distance, Depth, and Kinematics of the Taurus Star-forming Region

The displacement of a single star in the plane of the sky is the combination of its proper motion (μ_α, μ_δ) and the trigonometric parallax (π). In this case, the stellar coordinates as a function of time (t) are given by

$$\begin{eqnarray}&&\alpha (t)={\alpha }_{0}+{\mu }_{\alpha }t+\pi {f}_{\alpha }(t),\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&\delta (t)={\delta }_{0}+{\mu }_{\delta }t+\pi {f}_{\delta }(t),\end{eqnarray} \tag{ 2 }$$

where (α₀, δ₀) are the coordinates of the star at a given epoch (t₀). The projections of the parallactic ellipse (f_α, f_δ) are given by (see, e.g., Seidelmann 1992)

$$\begin{eqnarray}&&{f}_{\alpha }=(X\sin \alpha -Y\cos \alpha )/\cos \delta ,\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&{f}_{\delta }=X\cos \alpha \sin \delta +Y\sin \alpha \sin \delta -Z\cos \delta ,\end{eqnarray} \tag{ 4 }$$

where (X, Y, Z) are the barycentric coordinates of the Earth (in units of au) computed from the planetary ephemerides DE405 using the novas package in Python.

Binaries and multiple systems are very common in the Taurus star-forming region (Duchêne 1999), and our sample contains many such systems that require a dedicated analysis. Since both stars in a binary system move around their common center of gravity, their orbital motion projected onto the plane of the sky has to be taken into account to accurately determine the parallaxes and proper motions of the individual components.

At this stage it is important to distinguish between (i) binaries with orbital periods much longer than the monitoring time of our observing campaign and (ii) binaries with short or intermediate periods where our observations cover a significant fraction of the orbital period. In the first case, it is possible to assume a uniform acceleration (see, e.g., Loinard et al. 2007) leading to

$$\begin{eqnarray}&&\alpha (t)={\alpha }_{0}+{\mu }_{\alpha }t+\displaystyle \frac{1}{2}{a}_{\alpha }{t}^{2}+\pi {f}_{\alpha }(t),\end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray}&&\delta (t)={\delta }_{0}+{\mu }_{\delta }t+\displaystyle \frac{1}{2}{a}_{\delta }{t}^{2}+\pi {f}_{\delta }(t),\end{eqnarray} \tag{ 6 }$$

where a_α and a_δ are the acceleration terms. In the second case, the effects of the binary motion and the existence of a nonuniform acceleration need to be taken into account. It is therefore necessary to fit for the full orbital motion and the astrometric parameters simultaneously. The orbital elements to be considered in this case are the semimajor axis a, the orbital period P, the eccentricity e, the epoch of periastron passage T_p, the argument of the ascending node Ω, the longitude of the periastron ω, and the inclination i of the orbital plane. Thus, the equations for the primary component with semimajor axis a₁ can be written in the form

$$\begin{eqnarray}&&\alpha (t)={\alpha }_{0}+{\mu }_{\alpha }t+\pi {f}_{\alpha }(t)+{a}_{1}{Q}_{\alpha }(t),\end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray}&&\delta (t)={\delta }_{0}+{\mu }_{\delta }t+\pi {f}_{\delta }(t)+{a}_{1}{Q}_{\delta }(t),\end{eqnarray} \tag{ 8 }$$

where Q_α and Q_δ are the orbital factors. They are given by (see, e.g., van de Kamp 1967)

$$\begin{eqnarray}&&{Q}_{\alpha }=B^{\prime} x(t)+G^{\prime} y(t),\end{eqnarray} \tag{ 9 }$$

$$\begin{eqnarray}&&{Q}_{\delta }=A^{\prime} x(t)+F^{\prime} y(t),\end{eqnarray} \tag{ 10 }$$

where the orientation factors B', A', G', F' are related to the Thiele–Innes constants as follows:

$$\begin{eqnarray}&&B^{\prime} =-\cos \omega \sin {\rm{\Omega }}-\sin \omega \cos {\rm{\Omega }}\cos i,\end{eqnarray} \tag{ 11 }$$

$$\begin{eqnarray}&&A^{\prime} =-\cos \omega \cos {\rm{\Omega }}+\sin \omega \sin {\rm{\Omega }}\cos i,\end{eqnarray} \tag{ 12 }$$

$$\begin{eqnarray}&&G^{\prime} =+\sin \omega \sin {\rm{\Omega }}-\cos \omega \cos {\rm{\Omega }}\cos i,\end{eqnarray} \tag{ 13 }$$

$$\begin{eqnarray}&&F^{\prime} =+\sin \omega \cos {\rm{\Omega }}+\cos \omega \sin {\rm{\Omega }}\cos i.\end{eqnarray} \tag{ 14 }$$

The elliptical rectangular coordinates x(t) and y(t) are given by

$$\begin{eqnarray}&&x(t)=\cos E(t)-e,\end{eqnarray} \tag{ 15 }$$

$$\begin{eqnarray}&&y(t)=\sin E(t)\sqrt{1-{e}^{2}},\end{eqnarray} \tag{ 16 }$$

where E(t) is the eccentric anomaly given by Kepler's transcendental equation. Similar equations hold for the secondary component. In this case, we replace a₁ by the semimajor axis a₂ of the secondary, which is scaled by the mass ratio q of the two components.

To simplify the forthcoming discussion, we denote the methodology described above to solve simultaneously for the astrometric parameters and orbital elements of the binary system using absolute positions by the name "full model." Some binaries in our sample also exhibit relative astrometry of the two components from optical and near-infrared (NIR) observations published in previous works that have been incorporated into our study. In this case, our analysis is limited to the right-hand term of Equations (7) and (8) to derive the orbital elements of the binary system. The resulting semimajor axis a refers to the relative orbit of the two components. We denote this solution using relative positions by the name "relative model." Finally, we combine the absolute positions measured in this work and relative positions from the literature to perform a "joint fit" solution.

The source positions obtained from the JMFIT task in AIPS were used to derive the astrometric and orbital parameters of the stars in our sample. Table 4 lists the measured positions for each source in our sample. However, it is important to mention that the positional uncertainties provided by JMFIT, which roughly represent the expected astrometric precision delivered by the VLBA, do not include various systematic errors that may significantly affect the accuracy of the computed astrometric parameters (see, e.g., Pradel et al. 2006). To overcome this problem, additional errors were added quadratically to the positional errors given by JMFIT to adjust the reduced χ² value in the astrometric fit to unity (see also Menten et al. 2007; Ortiz-León et al. 2017b). These additional errors range in most cases from 0.05 to 0.30 mas for both single stars and binaries (the few exceptions are discussed in Section 4).

To solve for the astrometric and orbital elements of the star (or stellar system), we developed our own routine in the Python programming language based on the emcee package (Foreman-Mackey et al. 2013), which implements the Markov chain Monte Carlo (MCMC) method proposed by Goodman & Weare (2010). The algorithm was adapted to our purposes and applied to the general problem of computing the astrometric and orbital parameters from the astrometry fitting. Briefly, the method that we use in this work explores the parameter space using a number of walkers and iteration steps to solve the system of equations presented in Sections 3.1 and 3.2 via Bayesian inference. The walkers move around the n-dimensional parameter space and take tentative steps toward the lowest value of χ². This produces a distribution of the individual solutions given by the ensemble of walkers. We run the MCMC method typically with 200 walkers to sample the distribution of each parameter with a significant number of individual solutions. Then, we take the mean and standard deviation of the distribution of each parameter as our final result.

Our methodology based on the MCMC method was first applied to the sources previously investigated by our team in the Ophiuchus region (Ortiz-León et al. 2017b) for calibration purposes. We varied the number of iterations for each walker from 1 to 2000 steps and verified that convergence of the Markov chains of the ensemble of walkers is attained after ∼100 iterations steps where the mean (and median) of the computed parameters are clearly bounded by the variance of the sample. Figure 3 illustrates the convergence of our results for the Ophiuchus source LFAM 8 as an example. We find a trigonometric parallax of π = 7.242 ± 0.060 mas based on the MCMC methodology described in this section, which is in good agreement with the result of π = 7.246 ± 0.088 mas reported by Ortiz-León et al. (2017b). Thus, the solutions based on the MCMC method presented in this paper are calculated using 500 iteration steps as a conservative threshold to ensure convergence of the Markov chains for both single stars and binaries in our sample.

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V1096 Tau is a binary system that could be resolved in our observations. Both components were simultaneously detected in only one epoch (project BL175IE), where the primary component of the system V1096 Tau A exhibits a flux density of 0.71 ± 0.05 mJy that is almost twice that of the secondary component (V1096 Tau B), with 0.36 ± 0.05 mJy. We detected the primary and secondary, respectively, in a total of four and three epochs. However, our observations cover a small fraction of the orbit so that the fit including the orbital motion of the system does not converge. Hence, we fit the measured positions of the individual components solely for the proper motion and parallax. We included the acceleration term in the astrometry fit for the primary component, which indeed represents a better description to the data, but this was not possible for the secondary due to the limited number of detections available. Our result for the secondary component is only indicative and should be regarded with caution, as it is likely to be biased by the noncorrected orbital motion of the system. The systematic errors that we add to the stellar positions of V1096 Tau A and V1096 Tau B (as described in Section 3.3) reach up to 1 and 3 mas, respectively, and they are significantly larger than the other stars. The weighted mean parallax of the results given in Table 5 for the two components is π = 8.04 ± 0.50 mas. This is consistent with a distance estimate of $d={124.4}_{-7.2}^{+8.2}$ pc. Despite the admittedly large errors on our results, this is the first distance determination for this binary system to date. The weighted mean proper motions of the two components are ${\mu }_{\alpha }\cos \delta =2.612\pm 0.691$ mas yr⁻¹ and μ_δ = −17.372 ± 0.676 mas yr⁻¹. V1096 Tau continues to be monitored by our team, and the results presented in this paper will be refined when more observations become available.

V773 Tau is a well-known quadruple system (see, e.g., Duchêne et al. 2003; Woitas 2003), and the source detected in our observations is the primary component V773 Tau A, which itself is a tight binary. V773 Tau A has been detected in a total of seven epochs during our observing, but a simultaneous detection of both components occurred only in three epochs (see Table 4). Moreover, it has also been observed with the VLBA in 27 additional epochs between 2004 March and 2009 September for projects BM198, BL128, BL146, and BM306 (see Table 3). We note that project BM198 observed J0403+2600 as the main phase calibrator while the other projects (including GOBELINS) used J0408+3032 instead. We corrected the positions measured in BM198 before combining them with the other projects. The mean position of J0403+2600 measured in projects BM198 is α = 04^h03^m05586049 and δ = 26°00'0150275. The mean position of J0403+2600 (relative to J0408+3032) in the other projects is α = 04^h03^m05586052 and δ = 26°00'0150137. Hence, we applied a correction of Δα = 0.000003 s and Δδ = −000138 to the measured positions in project BM198. Another important point to mention about projects BM198 is that these observations include data collected with both the VLBA and the Effelsberg antenna. But for consistency with the rest of the data used in this work, we decided to remove the Effelsberg antenna from the data reduction. The same applies to the BM306 project, which was observed with the High Sensitivity Array (HSA). We removed the external antennae and calibrated the observation using only VLBA data.

The orbital parameters of the short-period binary system V773 Tau Aa–Ab have already been constrained by Torres et al. (2012) based on the past VLBA observations listed in Table 3, supplemented by radial velocity observations from Boden et al. (2007). They derived the dynamical masses of the two components (m_Aa = 1.55 ± 0.11 M_⊙ and m_Ab =1.293 ± 0.068 M_⊙) and a trigonometric parallax of π =7.70 ± 0.19 mas computed from the positions of the barycenter of the system, including a uniformly accelerated proper motion in the analysis. As explained in their study, the model including a uniform acceleration (see Section 3.2) provided a good description to the data, because their observations covered a small fraction of the orbit of the V773 Tau A–B system. However, this not the case when we include the more recent data from the GOBELINS project in this analysis, which increases the time base of collected observations to about 13 yr. We computed the barycentric positions of the V773 Tau Aa–Ab system for the three epochs with simultaneous detections of the two components in our observing campaign and combined them with the recalibrated barycentric positions reported by Torres et al. (2012). We verified that the model assuming a uniform acceleration indeed provides a poor fit to the data with the extended time base of our observations. We thus performed a full fit to the data, including the orbital motion of the V773 Tau A–B in the analysis. Doing so, we derive an orbital period of P = 20.3 ± 0.8 yr that is somewhat shorter than the value of P = 26.2 ± 1.1 yr obtained by Boden et al. (2012) based on relative astrometry and radial velocities. The resulting trigonometric parallax of π = 7.692 ±0.085 mas yields a distance estimate of $d={130.0}_{-1.4}^{+1.5}$ pc for the barycenter of the V773 Tau Aa–Ab system that is more accurate and precise than the result of d = 132.8 ± 2.3 pc obtained by Torres et al. (2012).

V1098 Tau, 2MASS J04182909+2826191, and HD 282630 have been detected in only three epochs of our observing campaign. On the other hand, V999 Tau has been detected in five different projects, but in practice this corresponds to only three epochs owing to the short time interval between projects BL175IC/BL175I7 and BL175JW/BL175JY. As a result, their trigonometric parallaxes are less precise as compared to the other stars in our sample with more detections. Because of the small number of detections, we computed the additional errors on the stellar positions (see Section 3.3) from the methodology outlined in Pradel et al. (2006). The resulting errors reach up to 0.8 mas depending on the position of the source in the sky and the angular separation to the main phase calibrator.

HD 283518 (V410 Tau) was systematically detected in every epoch of our observing campaign. It is known to be a multiple system (see, e.g., Harris et al. 2012), but only one component could be detected in our observations. We do not see the signature of the orbital motion in the stellar positions measured in this work, indicating that the gravitational effects of the secondary on the primary are negligible. Hence, we solved for the astrometric parameters of this source using the methodology described in Section 3.1 for single stars. We also compared our results with the alternative approach outlined in Section 3.2 using a uniform acceleration. Both methods return compatible results (with the same level of accuracy and precision), and the derived acceleration terms in the latter approach are consistent with zero. Thus, the results presented in Table 5 refer to the model without acceleration. The trigonometric parallax that we derive for HD 283518 has a relative error of 0.3%, making it the most precise result in our sample.

V1023 Tau (Hubble 4) is another binary system that was resolved in our observations. The primary component of this system is a weak-line T Tauri star of spectral type K7 (Nguyen et al. 2012), and it has been detected in a total of 14 epochs during our observing campaign. On the other hand, the secondary component could be detected in only two epochs. In addition, the primary has also been observed between 2004 September and 2005 December for projects BL124 and BL136. These data have already been analyzed and published by Torres et al. (2007). We combined these observations with the more recent GOBELINS data to fit the measured positions over a time base of ∼13 yr, which covers one full orbit of the system. Both data sets used the same main phase calibrator so that no correction has to be applied to the measured positions.

First, we performed a full fit of the orbit using only the VLBA observations reported in this paper and in Torres et al. (2007). Then, we combined the VLBA observations of projects BL175J2 and BL175JS where both components were simultaneously detected with the NIR relative astrometry from Rizzuto et al. (2018, submitted) to refine the orbital elements of the binary system. Finally, we combined our VLBA absolute positions with the NIR relative positions to perform a joint fit. Tables 6 and 7 compare our results from the different methods. The distance that we derive here from the full model ($d={130.1}_{-0.5}^{+0.5}$ pc) is somewhat shorter than the value of d = 132.8 ± 0.5 pc obtained by Torres et al. (2007) using VLBA data from projects BL124 and BL136. We argue that the latter result is likely biased by the noncorrected binarity of the source. By combining the VLBA absolute positions with the NIR relative astrometry, we find a distance of $d={129.0}_{-1.9}^{+2.0}$ pc that is less precise but fully consistent with our previous result. The weighted mean of both values yields $d={130.0}_{-0.5}^{+0.5}$ pc, which is the most precise and accurate distance estimate for this source to date. Our analysis also made it possible to determine, for the first time, the dynamical masses of the individual components of this system (m_A = 1.234 ± 0.023 M_⊙ and m_B = 0.730 ± 0.020 M_⊙). This implies a somewhat smaller mass ratio (q = 0.592 ± 0.012) than the value of q = 0.73 previously reported by Harris et al. (2012).

T Tau is a well-known triple system (see, e.g., Duchêne et al. 2002), and the component detected in our observations with the VLBA is T Tau Sb. It has been detected in eight epochs during our observing campaign for the GOBELINS project. In addition, it was also observed by our team between 2003 September and 2005 July for projects BL118 and BL124 (see Table 3). However, we note that projects BL118 and BL128 observed J0428+1732 as the main phase calibrator, while GOBELINS uses it as a secondary calibrator (the main calibrator is J0412+1856). The mean position of J0428+1732 measured for projects BL118 and BL124 is α = 04^h28^m35633679 and δ = 17°32'2358803. In the GOBELINS campaign the mean position of J0428+1732 (relative to J0412+1856) is α =04^h28^m35633685 and δ = 17°32'2358840. Thus, we applied an offset of Δα = 0.000006 s and Δδ = 000037 to the measured positions obtained from projects BL118 and BL124.

We fit the measured positions of T Tau Sb based on the full model to solve for the parallax and orbital motion of the binary system. The orbital elements obtained in this work (see Table 6) refer to the T Tau Sa–Sb system. We attempted to include an additional acceleration term due to the T Tau N component of the system, but the resulting acceleration parameter was consistent with zero. The results presented in Table 5 refer to our first solution (without acceleration). The distance that we derive in this paper for T Tau Sb ($d={148.3}_{-2.1}^{+2.1}$ pc) is in good agreement with the result of d = 147.6 ± 0.6 pc published previously by Loinard et al. (2007) using only data from projects BL118 and BL124. However, we consider our result to be more accurate because it takes into account the binarity/multiplicity of the source. Our solution obtained from the joint fit using the relative astrometry of the T Tau Sa–Sb published in previous studies yields a somewhat more precise distance estimate for this system ($d={148.7}_{-1.0}^{+1.0}$ pc) that confirms our first result. The weighted mean of both results yields a final distance of $d={148.7}_{-0.9}^{+0.9}$ pc.

Other studies have already investigated the orbital motion of the T Tau Sa–Sb system based on relative astrometry and different measurements (Köhler et al. 2008, 2016; Schaefer et al. 2014). As illustrated in Figure 6, we combined the relative positions from previous works to provide a more refined solution for the orbital parameters of the system. This analysis does not include VLBA data since our observations can only detect one component of the system. We note that most of the resulting orbital elements obtained in this paper including all measurements are more precise than the results reported in the individual studies. However, the errors on the individual parameters are still larger as compared to other stars in our sample. One reason for this result is the small coverage of the orbit, which requires further monitoring of the T Tau system.

V1201 Tau and HD 283641 are members of the same hierarchical multiple system, where both sources themselves are binary systems (see Kohler & Leinert 1998; Mason et al. 2001). V1201 Tau and HD 283641 were also identified as wide binaries with a separation of 1323 in a recent study conducted by Andrews et al. (2017) based on data from Gaia-DR1. Indeed, their result is consistent with the mean angular separation of 1453 derived from our observations. The two components of the V1201 Tau system were simultaneously detected in only two epochs (projects BL175I1 and BL175KJ). We measured a flux density of 2.40 ± 0.04 mJy in project BL175I1 (2016 February 28) for the brightest component (hereafter V1201TauA), which significantly decreased to 0.15 ± 0.05 mJy in project BL175KJ (2017 September 18), becoming fainter than the so-defined secondary component V1201 Tau B. We derived a trigonometric parallax only for V1201 Tau B, which was detected in six epochs. We note from Figure 4 that the fit using a uniform acceleration represents a good description to the data, yielding a distance estimate of d = 157.2 ± 1.7 pc. In the case of HD 283641 we detected only one component of the system in our observations. First, we fit the data as described in Section 3.1, and then we introduced the acceleration. We verified that the inclusion of a uniform acceleration in the model increases the errors on the astrometric parameters and that the derived acceleration terms are consistent with zero. As expected, the distance obtained for HD 283641 (d = 159.1 ± 1.8 pc, without acceleration) is compatible within 1σ of the distance derived for V1201 Tau. Both sources are currently being monitored by our team, and we will deliver a more refined solution (including the orbital motion of the system) when these observations become available.

The XZ Tau system is composed of two components (XZ Tau A and XZ Tau B) with angular separation of about 03 (Harris et al. 2012; Joncour et al. 2017). Carrasco-González et al. (2009) report on the detection of a third component (XZ Tau C) in this system separated by 009 from XZ Tau A, making it a triple system. However, a more recent study conducted by Forgan et al. (2014) did not detect XZ Tau C and cast doubt on the existence of the third component. Only one component of this system could be detected in our observations, and we confirm that it corresponds to XZ Tau A. Krist et al. (2008) estimated that the minimum orbital period of the XZ Tau A–B system should be about 99 yr, which greatly exceeds the time base of our observations. Indeed, we see no evidence of binarity in our data, and modeling XZ Tau A as a single star (as described in Section 3.1) provides a good fit to the data (see Figure 4). Finally, it is interesting to note that all components of this system were suggested to be thermal radio sources (see Carrasco-González et al. 2009), but our study shows that XZ Tau A also produces nonthermal emission.

V807 Tau is a hierarchical triple system, and the secondary component was resolved by Simon et al. (1995) into two close companions (V807 Tau Ba/Bb). The secondary has been detected in five epochs during the GOBELINS observing campaign. V807 Tau was also observed with the VLBA in the past (from 2007 March to 2009 March) by Schaefer et al. (2012) for projects BS171 and BS176. They report on three detections of V807 Tau Ba and one detection of V807 Tau Bb. Before combining these data with our own observations, we decided to download the files from the NRAO archive and reduce them by applying the same calibration procedure used in this work. Both data sets observed J0426+2327 as the main phase calibrator, so no correction needs to be applied to the positions measured in projects BS171 and BS176. We found that the source detected in the GOBELINS observations corresponds to V807 Tau Ba.

The model including a uniform acceleration produces a poor fit to the measured positions for V807 Tau Ba, because our observations cover almost one full orbit of the Ba–Bb system. We thus performed a full fit, including the orbital motion of the close pair in our analysis, which indeed represents a better description of the data (see Figure 5). The distance that we derive from VLBA observations is d = 126.6 ± 1.7 pc. Then, we used the NIR relative positions for the Ba–Bb system obtained by Schaefer et al. (2012), together with the VLBA observation from project BS176A, where both components were simultaneously detected to refine the orbital parameters of the system from the relative model (see Figure 6). By combining the VLBA and NIR data, we find a distance of $d={131.8}_{-2.3}^{+2.4}$ pc. The larger discrepancy in the distance estimates delivered by the full model and the joint fit (as compared to the other stars in Table 7) can be explained by the smaller number of data points (i.e., stellar positions) to fit the astrometry. The weighted mean parallax from both methods yields d = 128.5 ± 1.4 pc, which is the first distance estimate for V807 Tau B to date.

The dynamical masses of the individual components (m_Ba = 0.507 ± 0.010 M_⊙ and m_Bb = 0.388 ± 0.013 M_⊙) that we derive in this paper are more precise than the results obtained by Schaefer et al. (2012). As discussed in their study, they used the average distance of 140 ± 10 pc to the Taurus region to compute the stellar masses. We have rescaled the individual masses reported in their work to the distance that we derive in this paper, which gives m_Ba = 0.471 ± 0.018 M_⊙ and m_Bb = 0.397 ± 0.017 M_⊙. However, these numbers are still affected by the systematic error of 0.24 M_⊙, which comes from the ±10 pc uncertainty in the distance used in their analysis. Both results are still in good agreement, but we argue that the dynamical masses derived in this paper are more accurate owing to the improved accuracy and precision of our distance determination.

V1110 Tau has been detected in four epochs during our observing campaign. The trigonometric parallax (π = 11.881 ±0.149 mas) and proper motion (${\mu }_{\alpha }\cos \delta$ = −52.705 ±0.062 mas yr⁻¹, μ_δ = −11.321 ± 0.066 mas yr⁻¹) that we derive here clearly confirm it as a foreground star not related to the Taurus star-forming clouds. This is also shown in Figure 2, where V1110 Tau clearly stands out with a position change rate >50 mas yr⁻¹. In addition, Gaia-DR1 also confirms this finding, yielding a trigonometric parallax of π = 12.53 ± 0.61 mas and proper motion of ${\mu }_{\alpha }\cos \delta$ = −54.471 ± 1.893 mas yr⁻¹, μ_δ =−12.194 ± 1.612 mas yr⁻¹. These values are consistent with but less precise than our results.

Interestingly, Martin et al. (1994) observed V1110 Tau (Wa Tau 1) and did not detect the Li i line in any of the two components of this binary system. Wahhaj et al. (2010) classified V1110 Tau as a weak-line T Tauri star of spectral type K0 and effective temperature of 5250 K. They used the distance of 145 pc to compute the luminosity of the star (3.04 L_⊙) and estimate its age (7.3 Myr) based on the Siess et al. (2000) models. We have rescaled the luminosity of the star to correct for the individual distance ($d={84.2}_{-1.0}^{+1.1}$ pc) that we derived in this paper. This yields a luminosity of 1.03 L_⊙ and an age estimate of 24 Myr, suggesting that it is much older as indicated in previous studies. More recently, Xing (2010) derived a spectral type of K0 and measured the Li equivalent width of only 39 mÅ. In addition, Xing & Xing (2012) detected Hα in absorption, and Rebull et al. (2010) found no significant infrared excess for this source based on Spitzer photometry. Altogether, these properties are consistent with V1110 Tau being a young foreground dwarf not related to the Taurus population of YSOs (see also Briceno et al. 1997).

HP Tau G2 is a weak-line T Tauri star that belongs to a hierarchical triple system with separation of about 10'' from HP Tau G3, which is a tight binary system (see, e.g., Harris et al. 2012; Nguyen et al. 2012). This source has been detected in a total of nine epochs in this work, and it was also observed in the past from 2003 September to 2005 July for projects BL118 and BL124 (see Table 3). We corrected the measured positions in these observations before combining them with the more recent GOBELINS data reported in this work. Projects BL118 and BL124 observed J0426+2327 as the main phase calibrator, while the GOBELINS observations use it as a secondary calibrator and J0438+2153 as the main calibrator. The mean position of J0426+2327 measured between 2003 September and 2005 July is α = 04^h26^m55734795, δ = 23°27'3963371, and the mean position of J0426+2327 (relative to J0438+2153) in the GOBELINS observations is α =04^h26^m55734757, δ = 23°27'3963403. Thus, the corresponding offset to correct the measured positions in projects BL118 and BL124 is Δα = −0.000038 s and Δδ = 000032. After combining the two data sets, we performed a full fit to solve for the parallax, proper motion, and orbital motion of the HP Tau G2–G3 system (see Tables 5 and 6). The distance that we derive in this paper (d = 162.7 ± 0.8 pc) is in good agreement with the result of d = 161.2 ± 0.9 pc obtained by Torres et al. (2009) based only on observations collected for projects BL118 and BL124. This confirms that HP Tau G2 is indeed farther than other Taurus stars.

V1000 Tau has been detected in seven epochs during our observing campaign, and both components were simultaneously detected in five epochs. On 2017 March 14 (project BL175JW) we measured the highest flux density for the primary component (F_ν = 0.96 ± 0.05 mJy). However, both sources appear significantly fainter in the other observations reported in this work, with a flux level below 7σ, which increases the errors on the individual positions of the sources.

During the calibration process of our observations, we noted that two main calibrators have been used for this source during our observing campaign. Projects BL175AE, BL175AO, BL175HD, BL175IC, BL175JW, and BL175KV observed J0438+2153 as the main phase calibrator, while projects BL175D2, BL175I7, BL175IZ, BL175JY, and BL175KS used J0429+2724 in this regard. Thus, we corrected the measured positions in the latter projects before combining the two data sets. J0435+2532 was observed as a secondary calibrator in all projects listed before. The mean position of J0435+2532 (relative to J0438+2153) in the first data set is α =04^h35^m34582910, δ = 25°32'5969919, and the mean position of J0435+2532 (relative to J0429+2724) in the second data set is α = 04^h35^m34582963, δ = 25°32' 5969972. Thus, we applied an offset of Δα = −0.000053 s and Δδ = −000052 to the measured position of the second data set. We applied the same correction to the positions measured for V999 Tau (see Section 4.3) because both sources were observed in the same field and used the same calibrators in all epochs.

We proceeded as follows to calculate the distance to the V1000 Tau system. First, we applied the model with a uniform acceleration to the individual components of the system, but it produced a poor fit to the data. We then considered the model including the orbital motion of the system and solved simultaneously for the proper motion, parallax, and orbital elements. Doing so, we find a distance of $d={136.5}_{-2.4}^{+2.5}$ pc. This approach also allowed us to derive the individual masses of the two components of this system (m_A = 0.663 ±0.101 M_⊙ and m_B = 0.550 ± 0.091 M_⊙). To further investigate our result, we compute the barycenter of the V1000 Tau system using the individual masses derived in this paper and perform a fit including the acceleration terms in our equations. This approach yields a distance estimate of $d={136.4}_{-3.2}^{+3.4}$ pc, which is in good agreement with our previous result and confirms our solution despite the low detection threshold.

V892 Tau is the only source in our sample with a minimum of three detections for which we do not provide a trigonometric parallax. Unlike other stars in our sample, V892 Tau appears as a faint source in our observations, with a detection level of roughly 6σ in the best case. V892 Tau is a Herbig Ae/Be star with a low-mass companion (Leinert et al. 1997), and at this stage it is not clear whether the positions measured in this work refer to the same component of the system since they provide a poor astrometric fit.

HDE 283572 was not included in our target list, but it has been observed by Torres et al. (2007) between 2004 September and 2005 December. We have recalibrated and reanalyzed these data by applying the same methods used for the GOBELINS observations and described throughout this paper. The new distance estimate of $d={129.5}_{-0.9}^{+1.0}$ pc that we derive here is fully consistent with the previous result of d =128.5 ± 0.6 pc obtained by Torres et al. (2007).

The first step in our analysis to compare the results obtained in this paper with Gaia-DR1 is to build a list of Taurus stars that have been previously identified in the literature. In a recent study, Joncour et al. (2017) published an updated census with 338 stars (and stellar systems) in this region. We add V1201 Tau, HD 283641, and V1110 Tau to their list, which have been investigated in this work and were not included in their compilation.

The Gaia satellite observed 204 stars in our list of known YSOs in the Taurus region, but the Tycho-Gaia Astrometric Solution (TGAS; Lindegren et al. 2016) catalog from Gaia-DR1 provides trigonometric parallaxes for only 18 stars (and stellar systems). Eight stars are in common with our sample of 18 stars with measured trigonometric parallaxes (see Table 5), including V1110 Tau, which is more likely a foreground dwarf (see Section 4.10). Figure 7 illustrates the comparison of our results with Gaia-DR1. The rms and mean difference between the trigonometric parallaxes derived in both projects are, respectively, 0.38 and −0.15 mas (in the sense, "GOBELINS" minus "TGAS"). These numbers are smaller than the mean error of σ_π = 0.46 mas on the trigonometric parallaxes from Gaia-DR1 in the Taurus region. Thus, our results are in good agreement with Gaia-DR1, but the trigonometric parallaxes derived in this work are more precise than the ones given in the TGAS catalog. For example, we measured a trigonometric parallax of π = 7.751 ± 0.027 mas for HD 283518 that lies exactly on the equality line (see Figure 7) and is more precise by almost one order of magnitude than the result of π = 7.78 ± 0.29 mas delivered by Gaia-DR1. This confirms the state-of-the-art accuracy and precision that can be obtained from VLBI astrometry and the good complementarity with the Gaia space mission.

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Two points regarding the comparison of our results with Gaia-DR1 are worth mentioning here. First, the trigonometric parallaxes in the TGAS catalog are affected by a systematic error of about 0.30 mas, depending, for example, on the position and color of the stars (Lindegren et al. 2016). Thus, we added the value of 0.30 mas quadratically to the formal errors given in the TGAS catalog. The second and potentially more serious problem is that most of our sources in common with Gaia-DR1 are binaries (or multiple systems). In this context, it is important to mention that all sources in the TGAS catalog were modeled as single stars, so that the orbital motion in binaries is neglected. This explains the most discrepant results obtained for some sources in Figure 7 (e.g., T Tau Sb and V773 Tau A), where this analysis is of ultimate importance and can only be applied with long-term monitoring of the system under investigation. For the reasons mentioned above, we consider the trigonometric parallaxes from the GOBELINS project to be more accurate and precise than the ones given in Gaia-DR1 for the targets in common.

The effective sample of stars that we use in the forthcoming analysis to discuss the distance and kinematics of the Taurus star-forming region consists of 26 stars (or stellar systems). It includes all stars (or stellar systems) listed in Table 5 (excluding V1110 Tau) and the additional 10 sources with trigonometric parallaxes from Gaia-DR1 (see Section 5.1). V1110 Tau is not included in this discussion for the reasons presented in Section 4.10. We use the proper motions and trigonometric parallaxes derived in this work from VLBI observations, and we take the results from the TGAS catalog to complement our sample for stars that were not included in our observing campaign. In the case of V1096 Tau we use the weighted mean parallax and proper motion of the two components given in Section 4.1, which provide a better solution for the system than the individual values listed in Table 5. Figure 8 summarizes the trigonometric parallaxes of the stars in our sample, and Figures 9–12 illustrate the structure in and around the various star-forming clouds investigated in our analysis based on the extinction maps from Dobashi et al. (2005).

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We also searched the literature for the radial velocity of the stars in our sample using the data mining tools available in the CDS databases (Wenger et al. 2000). Our search for radial velocities is based on Hartmann et al. (1986), Herbig & Bell (1988), Gontcharov (2006), Kharchenko et al. (2007), and Nguyen et al. (2012). The properties of GOBELINS and Gaia-DR1 stars in our sample are collectively listed in Table 8. Then, we converted the observed trigonometric parallaxes into distances and used the radial velocities to calculate the three-dimensional Galactic spatial velocities from the procedure described by Johnson & Soderblom (1987). In Table 9 we present the UVW spatial velocity and the peculiar velocity of individual stars in our sample after correcting for the velocity of the Sun with respect to the local standard of rest (LSR). For this correction we use the solar motion obtained by Schönrich et al. (2010). We also present in Table 9 the radial velocities of the stars converted to the LSR, which will be used in the forthcoming discussion to compare with the velocity field of the CO molecular gas in this region produced by the Five College Radio Astronomy Observatory (FCRAO). In this case we used the older IAU standard solar motion to convert the radial velocities to the LSR for consistency with the FCRAO maps (see Jackson et al. 2006). In the following we comment on the distance and kinematics of the individual clouds of the Taurus complex. The properties of the various star-forming clouds discussed below are also summarized in Table 10.

Table 8.  Proper Motions, Trigonometric Parallaxes, Distances, and Radial Velocities of the GOBELINS-Gaia Sample in Taurus

Star	2MASS Identifier	${\mu }_{\alpha }\cos \delta$	μδ	π	d	Reference	Vr	Reference
		(mas yr−1)	(mas yr−1)	(mas)	(pc)		(km s−1)
V1096 Tau	J04132722+2816247	2.612 ± 0.691	−17.372 ± 0.676	8.037 ± 0.497	${124.4}_{-7.2}^{+8.2}$	This work	12.00 ± 5.00	1
V773 Tau A	J04141291+2812124	10.253 ± 0.843	−25.119 ± 0.301	7.692 ± 0.085	${130.0}_{-1.4}^{+1.5}$	This work	16.00 ± 2.50	2
HD 283518	J04183110+2827162	8.703 ± 0.017	−24.985 ± 0.020	7.751 ± 0.027	${129.0}_{-0.4}^{+0.5}$	This work	19.90 ± 0.30	3
V1023 Tau	J04184703+2820073	8.371 ± 0.020	−25.490 ± 0.020	7.686 ± 0.032	${130.1}_{-0.5}^{+0.5}$	This work	15.00 ± 1.70	4
BP Tau	J04191583+2906269	8.683 ± 0.355	−25.846 ± 0.239	7.900 ± 0.492	${126.6}_{-7.4}^{+8.4}$	Gaia-DR1	15.24 ± 0.04	3
RY Tau	J04215740+2826355	9.100 ± 0.140	−25.859 ± 0.091	5.660 ± 0.920	${176.7}_{-24.7}^{+34.3}$	Gaia-DR1	24.30 ± 1.90	2
HDE 283572	J04215884+2818066	8.853 ± 0.096	−26.491 ± 0.113	7.722 ± 0.057	${129.5}_{-0.9}^{+1.0}$	This work	14.22 ± 0.08	3
T Tau Sb	J04215943+1932063	6.790 ± 0.432	−11.131 ± 0.444	6.723 ± 0.046	${148.7}_{-1.0}^{+1.0}$	This work	19.23 ± 0.02	3
HD 283641	J04244904+2643104	10.913 ± 0.037	−16.772 ± 0.044	6.285 ± 0.070	${159.1}_{-1.8}^{+1.8}$	This work	16.23 ± 0.04	3
UX Tau	J04300399+1813493	12.641 ± 0.435	−17.552 ± 0.257	6.330 ± 0.404	${158.0}_{-9.5}^{+10.8}$	Gaia-DR1	15.45 ± 0.02	3
XZ Tau	J04314007+1813571	10.858 ± 0.027	−16.264 ± 0.060	6.793 ± 0.025	${147.2}_{-0.5}^{+0.5}$	This work	18.30 ± 0.04	3
V807 Tau B	J04330664+2409549	8.573 ± 0.068	−28.774 ± 0.201	7.899 ± 0.105	${126.6}_{-1.7}^{+1.7}$	This work	16.85 ± 0.03	3
HD 28867	J04333297+1801004	12.017 ± 0.047	−18.635 ± 0.030	7.580 ± 0.780	${131.9}_{-12.3}^{+15.1}$	Gaia-DR1	−14.70 ± 7.40	5
HP Tau G2	J04355415+2254134	11.248 ± 0.022	−15.686 ± 0.013	6.145 ± 0.029	${162.7}_{-0.8}^{+0.8}$	This work	16.60 ± 1.00	3
V999 Tau	J04420548+2522562	9.533 ± 0.218	−15.684 ± 0.198	6.972 ± 0.197	${143.4}_{-3.9}^{+4.2}$	This work	14.70 ± 2.00	1
HD 30171	J04455129+1555496	9.824 ± 1.675	−24.288 ± 0.994	7.070 ± 0.384	${141.4}_{-7.3}^{+8.1}$	Gaia-DR1	21.13 ± 0.17	3
DR Tau	J04470620+1658428	1.372 ± 2.747	−11.225 ± 1.785	4.820 ± 0.424	${207.5}_{-16.8}^{+20.0}$	Gaia-DR1	21.10 ± 0.04	3
UY Aur	J04514737+3047134	6.099 ± 2.824	−27.027 ± 1.840	6.610 ± 0.508	${151.3}_{-10.8}^{+12.6}$	Gaia-DR1	13.92 ± 0.07	3
HD 282630	J04553695+3017553	3.897 ± 0.113	−24.210 ± 0.132	7.061 ± 0.125	${141.6}_{-2.5}^{+2.6}$	This work	13.58 ± 0.01	3
AB Aur	J04554582+3033043	3.889 ± 0.056	−24.050 ± 0.039	6.550 ± 0.533	${152.7}_{-11.5}^{+13.5}$	Gaia-DR1	8.90 ± 0.90	2
SU Aur	J04555938+3034015	3.857 ± 0.126	−24.367 ± 0.088	7.020 ± 0.671	${142.5}_{-12.4}^{+15.1}$	Gaia-DR1	14.26 ± 0.05	3
V1098 Tau	J04144797+2752346	11.148 ± 0.175	−27.327 ± 0.172	8.070 ± 0.310	${123.9}_{-4.6}^{+5.0}$	This work	⋯	⋯
2MASS J04182909+2826191	J04182909+2826191	8.384 ± 0.195	−19.627 ± 0.217	7.583 ± 0.389	${131.9}_{-6.4}^{+7.1}$	This work	⋯	⋯
V1201 Tau	J04244815+2643161	10.839 ± 0.050	−13.235 ± 0.058	6.363 ± 0.069	${157.2}_{-1.7}^{+1.7}$	This work	⋯	⋯
V1000 Tau	J04420732+2523032	6.010 ± 0.235	−17.720 ± 0.159	7.324 ± 0.132	${136.5}_{-2.4}^{+2.5}$	This work	⋯	⋯
MWC 480	J04584626+2950370	4.790 ± 0.081	−25.044 ± 0.049	7.060 ± 0.476	${141.6}_{-9.0}^{+10.2}$	Gaia-DR1	⋯	⋯

Note. References for radial velocities: (1) Herbig & Bell 1988; (2) Gontcharov 2006; (3) Nguyen et al. 2012; (4) Hartmann et al. 1986; (5) Kharchenko et al. 2007.

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Table 9.  Spatial Velocity for Taurus Stars with Measured Trigonometric Parallaxes and Radial Velocities

Star	2MASS Identifier	U	V	W	Vspace	u	v	w	Vpec	VrLSR
		(km s−1)	(km s−1)	(km s−1)	(km s−1)	(km s−1)	(km s−1)	(km s−1)	(km s−1)	(km s−1)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)
V1096 Tau	J04132722+2816247	$-{11.4}_{-4.9}^{+4.9}$	$-{6.3}_{-2.1}^{+2.0}$	$-{9.1}_{-2.4}^{+2.4}$	${15.9}_{-3.9}^{+3.9}$	$-{0.3}_{-5.0}^{+5.0}$	${6.0}_{-2.2}^{+2.0}$	$-{1.8}_{-2.5}^{+2.4}$	${6.2}_{-2.2}^{+2.1}$	6.29 ± 5.00
V773 Tau A	J04141291+2812124	$-{16.5}_{-2.6}^{+2.6}$	$-{12.5}_{-1.1}^{+1.1}$	$-{10.3}_{-1.3}^{+1.3}$	${23.1}_{-2.0}^{+2.0}$	$-{5.4}_{-2.7}^{+2.7}$	$-{0.3}_{-1.2}^{+1.2}$	$-{3.1}_{-1.4}^{+1.4}$	${6.2}_{-2.4}^{+2.4}$	10.27 ± 2.50
HD 283518	J04183110+2827162	$-{20.0}_{-0.3}^{+0.3}$	$-{11.2}_{-0.1}^{+0.1}$	$-{11.5}_{-0.1}^{+0.1}$	${25.6}_{-0.2}^{+0.2}$	$-{8.9}_{-0.8}^{+0.8}$	${1.1}_{-0.5}^{+0.5}$	$-{4.3}_{-0.4}^{+0.4}$	${9.9}_{-0.7}^{+0.7}$	14.13 ± 0.30
V1023 Tau	J04184703+2820073	$-{15.3}_{-1.6}^{+1.6}$	$-{12.4}_{-0.4}^{+0.4}$	$-{10.6}_{-0.5}^{+0.5}$	${22.3}_{-1.2}^{+1.2}$	$-{4.2}_{-1.8}^{+1.8}$	$-{0.1}_{-0.6}^{+0.6}$	$-{3.4}_{-0.6}^{+0.6}$	${5.4}_{-1.4}^{+1.4}$	9.20 ± 1.70
BP Tau	J04191583+2906269	$-{15.7}_{-0.2}^{+0.2}$	$-{12.0}_{-1.3}^{+1.1}$	$-{10.4}_{-1.2}^{+1.1}$	${22.4}_{-0.9}^{+0.8}$	$-{4.6}_{-0.8}^{+0.7}$	${0.2}_{-1.3}^{+1.2}$	$-{3.2}_{-1.2}^{+1.2}$	${5.6}_{-0.9}^{+0.9}$	9.57 ± 0.04
RY Tau	J04215740+2826355	$-{24.7}_{-2.4}^{+2.3}$	$-{16.9}_{-4.6}^{+3.4}$	$-{14.8}_{-4.1}^{+3.7}$	${33.4}_{-3.5}^{+2.9}$	$-{13.6}_{-2.5}^{+2.4}$	$-{4.7}_{-4.6}^{+3.4}$	$-{7.6}_{-4.1}^{+3.7}$	${16.3}_{-3.2}^{+2.8}$	18.46 ± 1.90
HDE 283572	J04215884+2818066	$-{14.6}_{-0.1}^{+0.1}$	$-{13.2}_{-0.2}^{+0.2}$	$-{10.4}_{-0.2}^{+0.2}$	${22.3}_{-0.2}^{+0.2}$	$-{3.5}_{-0.8}^{+0.7}$	$-{1.0}_{-0.5}^{+0.5}$	$-{3.1}_{-0.4}^{+0.4}$	${4.8}_{-0.6}^{+0.6}$	8.36 ± 0.08
T Tau Sb	J04215943+1932063	$-{18.0}_{-0.2}^{+0.2}$	$-{8.0}_{-0.5}^{+0.5}$	$-{8.1}_{-0.5}^{+0.5}$	${21.3}_{-0.3}^{+0.3}$	$-{6.9}_{-0.8}^{+0.7}$	${4.2}_{-0.7}^{+0.7}$	$-{0.8}_{-0.6}^{+0.6}$	${8.2}_{-0.7}^{+0.7}$	11.83 ± 0.02
HD 283641	J04244904+2643104	$-{17.1}_{-0.1}^{+0.1}$	$-{12.5}_{-0.2}^{+0.2}$	$-{6.5}_{-0.2}^{+0.2}$	${22.2}_{-0.2}^{+0.1}$	$-{6.0}_{-0.8}^{+0.7}$	$-{0.2}_{-0.5}^{+0.5}$	${0.8}_{-0.4}^{+0.4}$	${6.1}_{-0.8}^{+0.7}$	10.02 ± 0.04
UX Tau	J04300399+1813493	$-{14.5}_{-0.5}^{+0.5}$	$-{15.9}_{-1.5}^{+1.3}$	$-{6.1}_{-1.3}^{+1.3}$	${22.4}_{-1.2}^{+1.0}$	$-{3.4}_{-0.9}^{+0.8}$	$-{3.7}_{-1.6}^{+1.4}$	${1.1}_{-1.3}^{+1.4}$	${5.1}_{-1.3}^{+1.2}$	7.68 ± 0.02
XZ Tau	J04314007+1813571	$-{17.0}_{-0.1}^{+0.1}$	$-{13.4}_{-0.1}^{+0.1}$	$-{7.3}_{-0.1}^{+0.1}$	${22.8}_{-0.1}^{+0.1}$	$-{5.9}_{-0.8}^{+0.7}$	$-{1.1}_{-0.5}^{+0.5}$	${0.0}_{-0.4}^{+0.4}$	${6.0}_{-0.7}^{+0.7}$	10.50 ± 0.04
V807 Tau B	J04330664+2409549	$-{15.8}_{-0.1}^{+0.1}$	$-{15.1}_{-0.3}^{+0.3}$	$-{11.4}_{-0.3}^{+0.3}$	${24.7}_{-0.3}^{+0.3}$	$-{4.7}_{-0.8}^{+0.7}$	$-{2.9}_{-0.6}^{+0.6}$	$-{4.2}_{-0.5}^{+0.5}$	${6.9}_{-0.6}^{+0.6}$	10.04 ± 0.03
HD 28867	J04333297+1801004	${14.3}_{-7.4}^{+7.5}$	$-{13.9}_{-1.7}^{+1.4}$	${3.5}_{-3.8}^{+3.7}$	${20.2}_{-5.4}^{+5.4}$	${25.4}_{-7.5}^{+7.5}$	$-{1.6}_{-1.7}^{+1.4}$	${10.7}_{-3.8}^{+3.8}$	${27.6}_{-7.0}^{+7.0}$	−22.57 ± 7.40
HP Tau G2	J04355415+2254134	$-{16.7}_{-1.0}^{+1.0}$	$-{13.8}_{-0.2}^{+0.2}$	$-{5.5}_{-0.4}^{+0.4}$	${22.3}_{-0.7}^{+0.7}$	$-{5.6}_{-1.2}^{+1.2}$	$-{1.5}_{-0.5}^{+0.5}$	${1.8}_{-0.5}^{+0.5}$	${6.1}_{-1.2}^{+1.1}$	9.52 ± 1.00
V999 Tau	J04420548+2522562	$-{15.0}_{-2.1}^{+2.0}$	$-{11.1}_{-0.7}^{+0.7}$	$-{5.0}_{-1.0}^{+1.0}$	${19.3}_{-1.7}^{+1.7}$	$-{3.9}_{-2.2}^{+2.2}$	${1.1}_{-0.9}^{+0.8}$	${2.3}_{-1.0}^{+1.0}$	${4.6}_{-1.9}^{+1.9}$	7.96 ± 2.00
HD 30171	J04455129+1555496	$-{17.7}_{-0.8}^{+0.8}$	$-{18.1}_{-2.3}^{+2.0}$	$-{10.8}_{-2.1}^{+2.1}$	${27.5}_{-1.8}^{+1.7}$	$-{6.6}_{-1.1}^{+1.1}$	$-{5.8}_{-2.3}^{+2.1}$	$-{3.5}_{-2.1}^{+2.1}$	${9.5}_{-1.8}^{+1.7}$	12.71 ± 0.17
DR Tau	J04470620+1658428	$-{18.0}_{-1.2}^{+1.3}$	$-{10.5}_{-4.3}^{+3.7}$	$-{11.5}_{-3.9}^{+3.8}$	${23.9}_{-2.8}^{+2.6}$	$-{6.9}_{-1.4}^{+1.4}$	${1.7}_{-4.3}^{+3.7}$	$-{4.3}_{-3.9}^{+3.8}$	${8.3}_{-2.5}^{+2.4}$	12.83 ± 0.04
UY Aur	J04514737+3047134	$-{14.9}_{-0.6}^{+0.5}$	$-{16.0}_{-3.9}^{+3.4}$	$-{10.5}_{-3.6}^{+3.6}$	${24.3}_{-3.1}^{+2.7}$	$-{3.8}_{-1.0}^{+0.9}$	$-{3.7}_{-4.0}^{+3.4}$	$-{3.3}_{-3.6}^{+3.6}$	${6.3}_{-3.1}^{+2.8}$	8.05 ± 0.07
HD 282630	J04553695+3017553	$-{14.1}_{-0.1}^{+0.1}$	$-{12.8}_{-0.4}^{+0.4}$	$-{9.7}_{-0.3}^{+0.3}$	${21.3}_{-0.3}^{+0.3}$	$-{3.0}_{-0.8}^{+0.7}$	$-{0.6}_{-0.6}^{+0.6}$	$-{2.4}_{-0.5}^{+0.5}$	${3.9}_{-0.7}^{+0.6}$	7.57 ± 0.01
AB Aur	J04554582+3033043	$-{9.6}_{-1.0}^{+1.0}$	$-{14.4}_{-1.5}^{+1.3}$	$-{9.6}_{-1.3}^{+1.2}$	${19.7}_{-1.4}^{+1.2}$	${1.5}_{-1.2}^{+1.2}$	$-{2.1}_{-1.6}^{+1.4}$	$-{2.3}_{-1.3}^{+1.2}$	${3.5}_{-1.4}^{+1.3}$	2.94 ± 0.90
SU Aur	J04555938+3034015	$-{14.8}_{-0.1}^{+0.1}$	$-{12.8}_{-1.7}^{+1.4}$	$-{9.8}_{-1.3}^{+1.2}$	${21.9}_{-1.1}^{+1.0}$	$-{3.7}_{-0.8}^{+0.7}$	$-{0.6}_{-1.7}^{+1.4}$	$-{2.6}_{-1.4}^{+1.3}$	${4.6}_{-1.0}^{+0.9}$	8.30 ± 0.05

Note. Columns (3)–(6) provide the stellar spatial velocity not corrected for the solar motion. The peculiar velocities of the stars after correcting for the velocity of the Sun with respect to the LSR are given in Columns (7)–(10). The radial velocities of the stars (see Table 8) converted to the LSR are given in Column (11).

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Table 10.  Distance and Spatial Velocity of the Various Clouds in Taurus

Cloud	N1	N2	π	d	U	V	W	Vspace
			(mas)	(pc)	(km s−1)	(km s−1)	(km s−1)	(km s−1)
L1495	8	6	7.724 ± 0.019	${129.5}_{-0.3}^{+0.3}$	−15.4 ± 0.1	−11.7 ± 0.1	−11.1 ± 0.1	23.4 ± 0.1
L1495 (B216)	2	1	6.325 ± 0.049	${158.1}_{-1.2}^{+1.2}$	−17.1 ± 0.1	−12.5 ± 0.2	−6.5 ± 0.2	22.2 ± 0.1
L1513	1	1	6.610 ± 0.508	${151}_{-11}^{+13}$	−14.9 ± 0.6	−16.0 ± 3.7	−10.5 ± 3.6	24.3 ± 2.9
L1519	4	3	7.035 ± 0.116	${142.1}_{-2.3}^{+2.4}$	−14.1 ± 0.1	−12.9 ± 0.4	−9.7 ± 0.3	21.3 ± 0.3
L1531	1	1	7.899 ± 0.105	${126.6}_{-1.7}^{+1.7}$	−15.8 ± 0.1	−15.1 ± 0.3	−11.4 ± 0.3	24.7 ± 0.3
L1534	2	1	7.215 ± 0.110	${138.6}_{-2.1}^{+2.1}$	−15.0 ± 2.0	−11.1 ± 0.7	−5.0 ± 1.0	19.3 ± 1.7
L1536	1	1	6.145 ± 0.029	${162.7}_{-0.8}^{+0.8}$	−16.7 ± 1.0	−13.8 ± 0.2	−5.5 ± 0.4	22.3 ± 0.7
L1551	2	2	6.791 ± 0.025	${147.3}_{-0.5}^{+0.5}$	−17.0 ± 0.1	−13.4 ± 0.1	−7.2 ± 0.1	22.8 ± 0.1
L1558	1	1	4.820 ± 0.424	${208}_{-17}^{+20}$	−18.0 ± 1.2	−10.5 ± 4.0	−11.5 ± 3.8	23.9 ± 2.7
Taurus (all stars)	23	18	7.054 ± 0.012	${141.8}_{-0.2}^{+0.2}$	−15.2 ± 0.1	−12.8 ± 0.1	−8.7 ± 0.1	22.8 ± 0.1

Note. We provide for each subgroup the number of stars with known trigonometric parallax (N₁) and radial velocity (N₂), the weighted mean parallax with the corresponding distance, and the weighted mean spatial velocity.

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5.2.1. Lynds 1495

5.2.2. Lynds 1513 and 1519

5.2.3. Lynds 1531, 1534, and 1536

5.2.4. Lynds 1551 and L1558

5.2.5. Taurus (All Stars)

In Table 10 we list the mean distance and spatial velocity derived for all stars in our sample (V1110 Tau, HD 28867, HD 30171, and RY Tau are excluded from this analysis for the reasons discussed before). The mean distance of d = 141.8 ± 0.2 pc that we derive from our analysis is still consistent with the canonical distance estimate of d = 140 ± 10 pc (Kenyon et al. 1994), which is commonly used in the literature for the Taurus region. However, the resulting distance is only representative of a few clouds in the Taurus complex, and it does not reveal the important depth effects that exist in this region as demonstrated in our study. Interestingly, we conclude from Table 10 that the B216 clump in the filamentary structure of L1495 is moving at (ΔU, ΔV, ΔW) = (−1.7, −0.8, 4.9) ± (0.1, 0.2, 0.2) km s⁻¹ with respect to the central part of the cloud, which implies a relative bulk motion of about 5.2 ± 0.2 km s⁻¹ between both structures. It is also interesting to note that L1551, which is the most southern cloud in our sample, is moving at (ΔU, ΔV, ΔW) =(−1.6, −1.7, 4.2) ± (0.1, 0.1, 0.1) km s⁻¹ with respect to L1495 and has a relative motion of 4.8 ± 0.1 km s⁻¹. On the other hand, we see from Table 10 that the spatial velocity for L1519 is fully consistent within 1 km s⁻¹ of the mean spatial velocity computed for all stars in our sample.

We find that the dispersion of the spatial velocities among the various clouds is (σ_U, σ_V, σ_W) = (2.4, 2.5, 2.1) km s⁻¹. For comparison, the velocity dispersions derived from the proper motions converted to tangential velocities in right ascension and declination are 2.4 and 3.1 km s⁻¹, respectively. This implies that the one-dimensional velocity dispersion in Taurus is somewhat higher than the value of 1 km s⁻¹ adopted by Luhman et al. (2009) and smaller than the value of 6 km s⁻¹ estimated by Bertout & Genova (2006). This value is also similar to the one-dimensional velocity dispersion obtained by Dzib et al. (2017) and Kounkel et al. (2017) for YSOs in the Orion Nebula Cluster.

One interesting question that arises from our study is whether the stars and the molecular gas in this region exhibit the same kinematic properties. In this context, Goldsmith et al. (2008) performed a large-scale survey of the ¹²CO and ¹³CO molecular gas in Taurus, which we use here to further discuss our results. Figure 13 summarizes the distance of the various clouds in the central portion of the Taurus complex that we derive in this paper overlaid on the ¹³CO velocity field produced in that survey. We extracted the ¹²CO and ¹³CO spectra at the position of the stars in our sample in a velocity interval from 3 to 13 km s⁻¹, computed the centroid velocity of the molecular gas in each case, and estimated their errors from the rms of the individual spectra. We note that for some stars in our sample there was no apparent signal in one of the two spectra extracted from the ¹²CO and ¹³CO maps. So, we decided to restrict our analysis to the stars with measured centroid velocities from both spectra and took the weighted mean of the computed values as our final estimate for the velocity of the gas at the position of a given star. It is important to mention that this analysis is restricted to only nine stars in our sample with measured radial velocities in the literature (see Table 8) that are included in the region surveyed by Goldsmith et al. (2008) and fulfill this condition.

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In Figure 14 we compare (i) the velocity of the molecular gas with the radial velocity of the stars (both are given with respect to the LSR) and (ii) the distance of the stars with the velocity of the associated gaseous clouds. First, we note that the velocity of the molecular gas (measured at the position of our sources) and the spectroscopic radial velocity of the stars are mostly consistent, confirming that the stars are indeed associated with the underlying gaseous clouds. It is important to mention that most stars used in this analysis are binaries, which explains both the existence of discrepant values (e.g., HD 283518) and the large errors on the radial velocities given in the literature (e.g., V1096 Tau). Second, we note that the velocity of the gas ranges from 6.5 to 7.5 km s⁻¹ for most sources projected toward the central part of the L1495 cloud ($d={129.5}_{-0.3}^{+0.3}$ pc), and it varies from 6.0 to 6.5 km s⁻¹ at the position of the remotest stars in this sample: V999 Tau ($d={143.4}_{-3.9}^{+4.2}$ pc), HD 283641 ($d={159.1}_{-1.8}^{+1.8}$ pc), and HP TauG2 ($d={162.7}_{-0.8}^{+0.8}$ pc). Although a perfect correlation between the distance of the stars and the velocity of the gas is not straightforward from Figure 14 (see, e.g., V773 Tau A and V807 Tau B), we found evidence that the observed velocity of the molecular gas at the position of our targets decreases with increasing distance of the star. This finding and the trigonometric parallaxes derived in this paper support our conclusion that the different structures of the Taurus complex are located at different distances. We will continue to investigate this issue using the upcoming parallaxes from Gaia-DR2 and a more significant number of stars to provide an accurate picture of the gas and stellar kinematics in this region.

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Finally, we note that the angular size of the Taurus complex in the plane of sky is about 12° in both Galactic longitude and Galactic latitude (see, e.g., Figure 1), which roughly corresponds to 30 pc using the mean distance given in Table 10 below. From the closest (L1495) and remotest (L1536) molecular cloud with measured VLBI trigonometric parallaxes in this study (this excludes L1558), we estimate the depth of 33 pc. Thus, we conclude that the distance range in the plane of the sky and that in the line of sight are equivalent.