THE GOULD'S BELT DISTANCES SURVEY (GOBELINS). I. TRIGONOMETRIC PARALLAX DISTANCES AND DEPTH OF THE OPHIUCHUS COMPLEX

The Gould's Belt (see Poppel 1997 for a comprehensive review) is a local Galactic structure containing much of the dense interstellar matter and many of the young stars within a few hundred parsecs of the Sun. It was originally identified by John Herschel (circa 1847) and Benjamin Gould (in the 1870s), who noticed that most of the brightest stars were neither randomly distributed in the sky nor associated with the Galactic plane, but instead concentrated along a great circle tilted by about 18° from the Galactic equator. Modern studies (e.g., Perrot & Grenier 2003) have shown that the Gould's Belt is a broad elliptical ring of young stars and interstellar matter with semimajor and semiminor axes of 375 pc and 235 pc, respectively. The center of the structure is located at about 105 pc from the Sun, in the direction of the Galactic anti-center. There is ample evidence that the Gould's Belt is expanding and has a dynamical age of order 30 Myr; Perrot & Grenier (2003) indicate 26.4 ± 0.4 Myr. The oldest stars associated with the Gould's Belt are also about 30 Myr old (e.g., Stothers & Frogel 1974), but T Tauri stars (age 10⁶–10⁷ years) as well as protostars (≲10⁵ years) and pre-stellar cores are also present, showing that star formation is still ongoing.

The Gould's Belt contains several million solar masses of interstellar material and includes all the nearby sites of active star formation (Orion, Ophiuchus, Perseus, etc.). These have been the benchmarks against which theories of star formation have been tested. Indeed, numerous "Gould's Belt surveys" targeting these regions have been carried out over the years—for instance, the James Clerk Maxwell Telescope Legacy Survey of Nearby Star-forming Regions in the Gould Belt (Ward-Thompson et al. 2007), the Spitzer Gould Belt (Dunham et al. 2015) and c2d (Evans et al. 2009) Legacy Surveys, and the Herschel Gould's Belt Survey (André et al. 2010). To take full advantage of this wealth of high quality information, it is fundamental to have accurate distance measurements to each of the regions in the Gould's Belt. In addition, these regions are a few hundred parsecs away and typically a few tens of parsecs across—and therefore presumably also a few tens of parsecs deep. As a consequence, using a single mean distance (however accurately measured) for all young stellar objects (YSOs) in a given region will result in typical distance errors in excess of 10% for the individual YSOs. A case in point is that of the Taurus star-forming region, which is located at a mean distance of about 145 pc, but is about 30 pc deep (Loinard et al. 2007; Torres et al. 2007, 2009, 2012). Using the mean distance to Taurus to calculate luminosities for YSOs located on the near side of the complex (at 130 pc) results in an error of 25%. Thus it is not sufficient to have an accurate mean distance for each region. Rather, it is highly desirable to have accurate distances to a substantial sample of individual objects within each region. Such detailed information also makes it possible to reconstruct the internal three-dimensional (3D) structure of the clouds.

Recently, Bouy & Alves (2015) used stars from the Hipparcos catalogue to determine the 3D distribution of the spatial density of OB stars within 500 pc from the Sun. They found no evidence for a ring-like structure and claimed that the Gould's Belt is the result of a 2D projection effect. They also proposed that the apparent rotation and expansion of the belt is due to relative motions associated with Galactic dynamics, but this needs to be investigated through accurate measurements of the dynamical state of the Belt.

Understanding the processes of star formation requires accurate observational constraints. The observational signatures predicted by star formation models have to be compared to actual observations, but a direct comparison can only be performed when the stellar properties, such as source size, luminosity, and mass, are well determined. Frequently the distances to star-forming regions are poorly constrained because they are obscured by molecular gas and dust. In such cases, inaccurate distances are often the main source of error in intrinsic parameter determinations.

Numerous indirect methods can be used to estimate the distance to young stars (e.g., de Grijs 2011), but they typically result in systematic uncertainties in excess of 20%. Only trigonometric parallaxes can provide unbiased distance measurements, but they are notoriously challenging to obtain. For instance, the trigonometric parallax of a star at 200 pc is 5 milli-arcseconds (mas), so an astrometric accuracy of 50 micro-arcseconds (μas) on the parallax would be required to measure that distance to 1% accuracy. This is more than one order of magnitude better than the astrometry delivered by the Hipparcos satellite (Perryman et al. 1997). Indeed, Hipparcos did not significantly improve our knowledge of the distance to star-forming regions in the Gould's Belt (e.g., Bertout et al. 1999). Also, the Hipparcos result on the distance to the Pleiades cluster, which is commonly used for testing theoretical stellar models, disagrees with all distance determinations obtained through other methods (Melis et al. 2014; David et al. 2016). The upcoming Gaia astrometric mission (de Bruijne 2012) will likely reach an accuracy of a few tens of μas, sufficient for percent accuracy determinations of distances in the Gould's Belt. However, since it operates at optical wavelengths, Gaia will be limited to stars that have low extinction. This will be an issue in star-forming regions like Orion, Ophiuchus, or Serpens, where values of A_V larger than 10 are common (Cambrésy 1999; Ridge et al. 2006).

For accurate astrometry, an alternative to optical-wavelength space missions is provided by Very Long Baseline Interferometry (VLBI; e.g., Thompson et al. 2007; Reid & Honma 2014). VLBI observations at centimeter wavelengths typically reach an angular resolution of order 1 mas. When VLBI observations are phase-referenced to a bright nearby source, the angular offset between the target and the reference source can be measured to an accuracy of ∼20 to 300 μas, depending on the signal-to-noise ratio of the detection, the declination of the source, and the distance between the target and the reference source (Pradel et al. 2006). The reference sources are usually distant quasars that are very nearly fixed on the celestial sphere. Thus the measured offset between the reference source and the target can be transformed into accurate coordinates for the target. When several such observations collected over 1 year or more are combined, the parallax and proper motion of the target can be measured with high accuracy. Also, the astrometry quality of both VLBI and Gaia observations can be tested by considering objects that both instruments can detect.

Two technical points are worth mentioning here. The first is that a systematic error on the target coordinates will obviously occur if the reference quasar position is not well known. The positional errors of reference calibrators used in VLBI observations are typically between 0.5 and 10 mas, so this is the level of accuracy that can be expected on absolute coordinates derived from VLBI data. However, this additive error will equally affect all observations of a given target (as long as the same calibrator is used), and hence have no measurable effect on the parallax and proper motion measurements obtained from multi-epoch observations. The second, potentially more serious issue is that because of emerging jet components, the photocenter of the quasars may shift with time when accuracies of a few μas on positions and a few μas yr⁻¹ on proper motions are reached (e.g., Reid & Brunthaler 2004). Because our typical positional errors are $100\mbox{--}300\,\mu \mathrm{as}$, this problem will not be relevant for the data presented here, and can be mitigated by including several reference sources in the observations and monitoring their relative positions as a function of time (e.g., Reid & Honma 2014).

VLBI astrometry can only be applied to a specific class of targets if they are detectable in VLBI observations (e.g., Thompson et al. 2007; Reid & Honma 2014). This requires that the potential targets not only be radio sources but also have an average brightness temperature in excess of ∼10⁶ K within the synthesized beam (i.e., be non-thermal sources), as VLBI arrays do not have sufficient sensitivity to detect weaker emission.¹⁷ A summary of the mechanisms that produce non-thermal radio emission in YSOs is provided in Appendix A. VLBI observations of non-thermal continuum emission from young stars have been used to measure very accurate trigonometric parallaxes to individual YSOs and star-forming regions (Loinard et al. 2005, 2007, 2008; Menten et al. 2007; Torres et al. 2007, 2009, 2012; Dzib et al. 2010, 2011, 2016). These observations focus on YSOs that were previously known to be non-thermal radio emitters. Building upon these successes, we have initiated a large project (the Gould's Belt Distances Survey, hereafter GOBELINS¹⁸ ) aimed at measuring the trigonometric parallax and proper motions of a large sample of magnetically active young stars in the Gould's Belt (specifically in Taurus, Ophiuchus, Orion, Perseus, and Serpens) using VLBI observations.

GOBELINS was approved by the Telescope Allocation Committee of the National Radio Astronomy Observatory in the spring of 2010. It followed a two-stage strategy. During the first phase, large maps of each of the regions of interest were obtained, using conventional interferometry observations, with the Karl G. Jansky Very Large Array (VLA; we called this first phase of the project the Gould's Belt Very Large Array Survey). These maps (published by Dzib et al. 2013, 2015; Kounkel et al. 2014; Ortiz-León et al. 2015; and Pech et al. 2016) enabled us to identify radio-bright YSOs in each region and attempt a first separation between thermal and non-thermal sources. For instance, in Ophiuchus, Dzib et al. (2013) identified 56 radio sources associated with YSOs and proposed that for ≳50% of them, the emission is of non-thermal origin. The second stage consists in multi-epoch VLBI observations of the selected targets with the Very Long Baseline Array (VLBA; Napier et al. 1994), to measure the astrometric elements (trigonometric parallax and proper motion) of each target. In this paper, we report on the first VLBI observations of the sources in the Ophiuchus region.

The results from GOBELINS will be used first and foremost to pinpoint the location of the regions of star formation within the Gould's Belt, as well as their internal three-dimensional structure. In addition, since the proper motion of each target will be measured simultaneously with its trigonometric parallax, the transverse component of the velocity vector will be obtained. In many cases, the radial velocity will be available from the literature or could be measured with dedicated optical or near-infrared (NIR) spectroscopy. Thus GOBELINS will also provide the complete velocity vector for many targets. This will enable us to examine both the internal dynamics of each region and the large-scale relative motions of the different clouds in the Gould's Belt (see Rivera et al. 2015 for a preliminary example). In particular, these measurements will help characterize the overall dynamics of the Gould's Belt and will be relevant to the understanding of its very origin.

GOBELINS will also provide radio images of a large sample of YSOs at milli-arcsecond resolution. This is unparalleled at any other wavelength, and will enable us to characterize the population of young, very tight, binary and multiple systems (see Torres et al. 2012 and Dzib et al. 2010 for examples of young multiple systems characterized by VLBI observations), as well as the magnetic structures around young stars (R.M. Torres et al. 2016, in preparation). Finally, these results will enable us to study the physical processes underlying the radio emission. For instance, the Gould's Belt Very Large Array Survey data (Dzib et al. 2013, 2015; Kounkel et al. 2014; Ortiz-León et al. 2015; Pech et al. 2016) have shown that the radio emission from YSOs is reasonably correlated with their X-ray luminosity, following the so-called Güdel-Benz relation (Guedel & Benz 1993; Benz & Guedel 1994). The VLBI observations will enable us to unambiguously separate the thermal and non-thermal components and re-examine this relation in more detail. It will also allow us to examine the prevalence of non-thermal radio emission in young stars as a function of their age and mass, providing clues regarding the magnetic evolution of YSOs.

As mentioned earlier, in the present paper we will focus on the GOBELINS observations of the Ophiuchus region. Ophiuchus is one of the best-studied regions of star formation (see Wilking et al. 2008 for a recent review). It consists of a centrally condensed core associated with the dark cloud Lynds 1688 (where A_V = 50 to 100 magnitudes; Wilking et al. 2008) and several filamentary clouds (collectively known as the "streamers") extending toward the east (Lynds 1689 is a particularly prominent dark cloud associated with the eastern streamer) and the northeast (see Figure 1 in this paper and Figure 1 in Dzib et al. 2013).

The distance to Ophiuchus has been discussed in some detail by Wilking et al. (2008), Lombardi et al. (2008), Loinard et al. (2008), and Mamajek (2008). The canonical value of 160 pc (Bertiau 1958; Whittet 1974; Chini 1981) remained in use until very recently. Evidence for a somewhat shorter distance (120–145 pc) started to emerge from optical photometric and astrometric studies of the nearby Upper Scorpius subgroup (de Geus et al. 1989; de Zeeuw et al. 1999). The implications for Ophiuchus itself, however, were limited by the unclear relation between Upper Scorpius and Ophiuchus (see Wilking et al. 2008 for a discussion of this topic). More recently, Mamajek (2008) used the trigonometric parallaxes of the stars illuminating seven reflection nebulae within 5° of the Ophiuchus core to derive an estimate of 135 ± 8 pc. Both Knude & Hog (1998) and Lombardi et al. (2008) combined Hipparcos parallaxes and extinction measurements to conclude that Ophiuchus is at a distance of about 120 pc. Lombardi et al. (2008), in particular, report a mean distance of 120 ± 6 pc for the entire region, with some evidence that the streamers might be ∼10 pc closer than the core. This would be consistent with the distance of 96 ± 9 pc derived by Le Bouquin et al. (2014; see also Schaefer et al. 2008) for the pre-main sequence binary Haro 1–14c, located in the northeastern streamer.

It is important to note that none of the measurements mentioned so far involve direct trigonometric parallaxes to Ophiuchus cluster members. This is, of course, because the stars in that cluster are too deeply embedded to be detectable with Hipparcos or ground-based optical telescopes. Indeed, to date, there are only two published trigonometric parallaxes for Ophiuchus, and both were obtained through VLBI observations. The first measurement was reported by Imai et al. (2007) and targeted water masers associated with the Class 0 protostar IRAS 16293-2422, located in the northern part of Lynds 1689. They derive a distance of ${178}_{-34}^{+18}$ pc, significantly larger than the 120–140 pc estimates that seem to emerge from the previously described recent studies of the Ophiuchus core. It is not clear if this discrepancy stems from issues with one or more of the distance measurements, or if it is indicative that the eastern streamer is significantly more distant than the core. The second parallax measurement was reported by Loinard et al. (2008), and focused on two young stars (DoAr 21 and S1) located toward the Ophiuchus core. They obtain 120 ± 5 pc for the mean distance to these two stars, and adopt this value as the best estimate of the distance to the Ophiuchus core.

In summary, there is a growing consensus that the Ophiuchus core is at 120–140 pc, but reducing the level of uncertainty regarding the distance has proven difficult. In addition, there are some conflicting results regarding the orientation of the streamers relative to the core. This unsatisfactory state of affairs largely results from the scarcity of direct parallax measurements to Ophiuchus members.

In this paper we present new VLBA observations taken over a period of 4 years as part of GOBELINS, and report on the detection of 26 young stellar systems in the Ophiuchus region (corresponding to 34 individual young stars, as some of the systems are multiple). The target sample and observing strategy are described in Section 2, the detections are described in Section 3, and the properties of the detected radio emission are analyzed in Appendix A.2. Section 4 focuses on a subset of this sample and presents the astrometry of 16 stellar systems. We first analyze single objects in Section 4.1, and then stars in multiple systems in Section 4.2 (other detected sources that are not known young stars are analyzed in Appendix B). Finally, we provide a new improved distance to the core of Ophiuchus, and a description of the cloud depth in Section 5.

Source positions were modeled to derive the trigonometric parallax (ϖ), proper motion (${\mu }_{\alpha }$, ${\mu }_{\delta }$), and mean position (${\alpha }_{0}$, ${\delta }_{0}$). The fits were performed by minimizing the associated ${\chi }^{2}$ (e.g., Loinard et al. 2007) and solving for the five astrometric elements simultaneously. For the errors in the positions at each epoch, we used the statistical errors provided by JMFIT, which roughly represent the expected theoretical precision of VLBA astrometry. However, systematic errors may significantly contribute to the astrometric accuracy (Pradel et al. 2006) and affect the derived astrometric parameters.

We estimate the systematic errors in two different ways: First, we use the empirical relation found by Pradel et al. (2006), according to which the VLBA astrometric accuracy scales linearly with the angular separation between the source and the phase calibrator. In the core, sources are separated from the phase calibrator, J1627-2427, by up to 04. Given this angular separation, and a typical declination of $\sim -25^\circ$, the expected VLBA rms astrometric errors $\sqrt{{({\rm{\Delta }}\alpha \cos \delta )}^{2}+{({\rm{\Delta }}\delta )}^{2}}$ are $\sim 210\,\mu$as. For this calculation, we have assumed that the rms errors for source coordinates, VLBA station coordinates, Earth orientation parameters (EOPs), and wet tropospheric zenith-path delays all contribute together (Tables 3 and 4, and Equation (2) in Pradel et al. 2006).

The systematic errors were also estimated by quadratically adding an error to the statistical errors given by JMFIT until a reduced ${\chi }^{2}$ of 1 was achieved in the astrometric fits. These systematic errors are in general several times larger than those predicted by the empirical relation. We note, however, that in their simulations, Pradel et al. (2006) assumed a full track on the source, while in our observations the source is tracked over less than 4 hr, resulting in a poorer $(u-v)$ coverage. We used the latter approach (based on a measured reduced ${\chi }^{2}$) to deal with systematic errors. As stated previously, these errors were added quadratically to the statistical errors of each individual epoch and used in the last iteration of the fits.

In the following subsections, we will comment separately on a few of the critical sources describing the additional data that were taken from the VLBA archive, when available, and detailing the quality of the fits. In Table 4, we provide the resulting astrometric parameters and distances for the complete sample. The corresponding measured source positions and best fits are shown in Figure 2.

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Table 4.  Parallaxes and Proper Motions

GBS-VLA	Other Identifier	Parallax	${\mu }_{\alpha }\cos \delta$	${\mu }_{\delta }$	${{\rm{a}}}_{\alpha }\cos \delta$	${{\rm{a}}}_{\delta }$	Distance
Name		(mas)	(mas yr−1)	(mas yr−1)	(mas yr−2)	(mas yr−2)	(pc)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
J162556.09-243015.3	WLY2-11	7.330 ± 0.112	−9.78 ± 0.09	−25.11 ± 0.20	0.94 ± 0.38	6.02 ± 0.83	136.4 ± 2.1
J162557.51-243032.1	YLW24	7.404 ± 0.143	−7.26 ± 0.04	−25.29 ± 0.07	⋯	⋯	135.1 ± 2.6
J162603.01-242336.4	DoAr21	7.385 ± 0.234	−19.63 ± 0.19	−26.92 ± 0.13	⋯	⋯	135.4 ± 4.3
J162622.38-242253.3	LFAM2	7.060 ± 0.072	−5.64 ± 0.09	−27.02 ± 0.30	⋯	⋯	141.6 ± 1.5
J162629.67-241905.8	LFAM8	7.246 ± 0.088	−5.89 ± 0.06	−29.54 ± 0.16	⋯	⋯	138.0 ± 1.7
J162634.17-242328.4	S1	7.249 ± 0.091	−2.05 ± 0.02	−26.72 ± 0.04	⋯	⋯	138.0 ± 1.7
J162642.44-242626.1	LFAM15	7.253 ± 0.054	−6.31 ± 0.02	−26.95 ± 0.05	⋯	⋯	137.9 ± 1.0
J162643.76-241633.4	VSSG11	7.160 ± 0.152	−10.48 ± 0.16	−38.99 ± 0.35	0.31 ± 0.65	−1.54 ± 1.09	139.7 ± 3.0
J162649.23-242003.3	LFAM18	7.232 ± 0.068	−11.62 ± 0.06	−18.30 ± 0.15	−0.10 ± 0.32	8.17 ± 0.84	138.3 ± 1.3
J162718.17-242852.9	YLW 12Bab	7.230 ± 0.057	6.56 ± 0.02	−26.26 ± 0.04	−0.62 ± 0.01	−0.17 ± 0.02	138.3 ± 1.1
J162718.17-242852.9	YLW 12Bca	7.230 ± 0.057	−11.23 ± 0.07	−23.10 ± 0.10	0.19 ± 0.03	0.11 ± 0.05	138.3 ± 1.1
J162721.81-244335.9	ROXN39	7.317 ± 0.021	−7.32 ± 0.31	−26.21 ± 0.73	⋯	⋯	136.7 ± 0.4
J162730.82-244727.2	DROXO71	7.327 ± 0.125	−4.41 ± 0.11	−28.79 ± 0.33	⋯	⋯	136.5 ± 2.3
J163035.63-243418.9	SFAM 87	7.206 ± 0.080	−7.69 ± 0.02	−26.04 ± 0.04	⋯	⋯	138.8 ± 1.5
J163152.10-245615.7	LDN1689IRS5	6.676 ± 0.046	−6.38 ± 0.03	−22.74 ± 0.04	⋯	⋯	149.8 ± 1.0
J163200.97-245643.3	WLY2-67	6.616 ± 0.088	−5.94 ± 0.12	−24.08 ± 0.30	⋯	⋯	151.2 ± 2.0
J163211.79-244021.8	DoAr51	6.983 ± 0.050	−4.80 ± 0.08	−23.11 ± 0.11	⋯	⋯	143.2 ± 1.0

Note.

^aParallax is fixed at the value obtained for YLW 12Bab when solving for the other astrometric parameters.

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4.1.1. DROXO 71

4.1.2. DoAr 21

4.1.3. LFAM 18

4.1.4. YLW 24, LFAM 2, LDN 1689 IRS5 and WLY 2-67

Our VLBA observations (combined with past astrometric observations) have detected a total of eight multiple systems (cf. Table 2). In six of them, the individual components have been detected at sufficient epochs such that we can model their orbital motion, in addition to parallax and proper motion. Two different fits were performed as follows. In the first "full model," we use all available absolute VLBA positions of individual components (including data from epochs where a single component is detected), together with relative positions, to solve for the orbital elements, center of mass at first epoch of the GOBELINS observations where the primary is detected (${\alpha }_{\mathrm{CM},0}$, ${\delta }_{\mathrm{CM},0}$), parallax (ϖ), and proper motion (${\mu }_{\alpha }$, ${\mu }_{\delta }$) of the system. The orbital free parameters in this model are period (P), time of periastron passage (T), eccentricity (e), angle of line of nodes (Ω), inclination (i), angle from node to periastron (ω), semimajor axis of primary (a₁), and mass ratio ${m}_{2}/{m}_{1}$. Combining the mass ratio with Kepler's third law (that contains the sum of masses), and because we know the distance to the system from the parallax solution, the masses of each component are also inferred. The orbital solutions are derived by minimizing ${\chi }^{2}$, which is computed for a grid of initial guesses of model parameters. The errors in the parameters were calculated by taking the average, weighted by ${\chi }^{2}$, of the output uncertainties over values across the entire grid.

From the VLBA images, we compute, for each system, the angular separation and position angle of the secondary relative to the primary star. In addition, we have compiled from the literature separations measured with near-infrared (NIR) observations. These data are shown in Figure 3 for each source separately. In the second "relative astrometry model" we only use the separation and position angle of secondary relative to primary, measured at epochs when both components are detected simultaneously. We use the orbital elements determined from the "full model" as initial parameters for the Gudehus (2001) code, the Binary Star Combined Solution Package,¹⁹ to solve for P, T, e, Ω, i, ω, and a. The total mass of the system, M_T, is then obtained from Kepler's law, but we are not able to determine individual masses in this case. For this fit, the uncertainties in the orbital elements are computed from the scatter on model parameters.

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The results from both fits are given in Table 6, and the resulting orbits are shown in Figure 3. We find that both fits are consistent with each other within the errors. We will comment on each system separately in the following subsections.

Table 6.  Orbital Elements

Name	a	P	T0	e	Ω	i	ω	M1	M2	MT
	(mas)	(years)			(°)	(°)	(°)	(M${}_{\odot }$)	(M${}_{\odot }$)	(M${}_{\odot }$)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)
LFAM 15
Full	16.40 ± 0.13	3.591 ± 0.0183	2007.008 ± 0.039	0.528 ± 0.005	337.93 ± 0.81	110.30 ± 0.49	235.54 ± 1.02	0.4687	0.421	0.89
								± 0.0146	± 0.010	± 0.01
Rel. astr.	16.98 ± 0.16	3.598 ± 0.0099	2010.626 ± 0.011	0.561 ± 0.007	340.05 ± 0.49	109.77 ± 0.27	239.60 ± 0.64	⋯	⋯	0.99
										± 0.03
YLW 12Bab
Full	12.70 ± 0.09	1.425 ± 0.0012	2005.174 ± 0.009	0.444 ± 0.003	135.15 ± 1.03	75.60 ± 1.25	158.69 ± 1.47	1.3969	1.258	2.66
								± 0.0194	± 0.006	± 0.02
Rel. astr.	12.54 ± 0.06	1.424 ± 0.0005	2013.720 ± 0.003	0.442 ± 0.003	135.38 ± 0.32	74.32 ± 0.48	160.11 ± 0.99	⋯	⋯	2.58
										± 0.07
SFAM 87
Full	35.58 ± 0.31	7.691 ± 0.007	2023.781 ± 0.006	0.343 ± 0.001	22.36 ± 8.57	−162.66 ± 2.84	346.19 ± 8.83	1.0207	0.999	2.02
								± 0.0224	± 0.038	± 0.04
Rel. astr.	35.79 ± 0.30	7.719 ± 0.019	2008.404 ± 0.015	0.341 ± 0.005	18.62 ± 4.32	−157.95 ± 2.59	344.25 ± 4.91	⋯	⋯	2.06
										± 0.09
DoAr 51
Full	32.83 ± 0.45	8.102 ± 0.063	2012.025 ± 0.044	0.802 ± 0.004	51.56 ± 6.31	18.95 ± 1.75	216.41 ± 6.42	0.7909	0.781	1.57
								± 0.0140	± 0.042	± 0.05
Rel. astr.	32.47 ± 0.39	8.070 ± 0.035	2012.020 ± 0.029	0.801 ± 0.005	51.81 ± 9.66	17.80 ± 4.36	215.81 ± 10.20	⋯	⋯	1.54
										± 0.07
Rizzuto+16	32.69 ± 0.35	8.233 ± 0.117	2012.009 ± 0.010	0.818 ± 0.009	24.1 ± 11.0	16.3 ± 2.0	243.0 ± 10.9	⋯	⋯	1.57
										± 0.03( ± 0.29)
ROXN 39
Full	54.3 ± 3.9	11.2 ± 1.5	2056.1 ± 1.2	0.40 ± 0.12	25.4 ± 2.9	68.4 ± 3.3	120.0 ± 12.9	2.31	0.97	3.3
								± 1.04	± 0.50	± 1.2
S1
Full	19.99 ± 0.20	1.734 ± 0.003	2017.089 ± 0.020	0.745 ± 0.010	118.9 ± 17.7	36.2 ± 6.1	294.6 ± 15.8	5.78	1.18	6.95
								± 0.15	± 0.10	± 0.18

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4.2.1. LFAM 15

The source LFAM 15 has been found to be double in 7 out of our 10 observed epochs. LFAM 15 was also observed in four epochs as part of project BL128 (Table 5), between 2005 June and 2006 March. We have calibrated these additional data and detected the source in three epochs, albeit always as a single component. In Figure 4, we show the measured positions for each component and the resulting best "full model" fit that, as mentioned before, consists of the sum of orbital motion around the center of mass, proper motion, and parallax of the system.

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4.2.2. YLW 12B

YLW 12B is found to be a hierarchical triple source formed by a close binary (separation of 4–17 mas, equivalent to 0.6–2.4 au), detected in nine epochs, and a third component, located a few hundred mas to the southwest of the binary and detected in seven epochs (Figure 5). Hereafter, we call the close binary YLW 12Bab and the third component YLW 12Bc. Six archival VLBA observations, obtained between 2005 and 2006 as part of project BL128, have also been found for this source; they have been calibrated and analyzed (Table 5). One of these older epochs was discarded due to poor weather conditions during the observations. In these archival observations, both components of YLW 12Bab were detected on 2005 June 8 and 2006 June 1, while YLW 12Bc was detected on 2005 June 8 and 2006 March 24.

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Given the distance to the source, the angular separation between YLW 12Bab and YLW 12Bc of ∼140 and ∼320 mas in 2005 and 2016, respectively, corresponds to 20 to 45 au. This suggests that the sources form a bound multiple system, and later in this section we provide stronger evidence that supports this conclusion. To fit the positions of the YLW 12Bab components, and to take the effect of the third companion into account, we add two more free parameters to the "full model." These parameters are the acceleration of the center of mass of YLW 12Bab in each direction, ${a}_{\alpha }$ and ${a}_{\delta }$, which we consider to be uniform. As in the case of LFAM 15, three plots were constructed to visualize the best fit solution. In the first panel of Figure 6, we show the observed positions of the compact binary and the best fit, while in the second panel, we show this fit and source positions with the effect of parallax removed. Using the solution for the mass ratio from the "full model," we now compute the positions of the center of mass of YLW 12Bab, and plot them along with the parallax plus proper motion model in the third panel of Figure 6. It is clear that the compact binary follows a curved motion as a result of the gravitational force exerted by the third companion. Indeed, we find that the acceleration is statistically different from zero at $\gt 8\sigma$ in both directions.

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Let us now discuss the third star of the system. The positions of YLW 12Bab relative to YLW 12Bc, as well as the acceleration vector of YLW 12Bab, are shown in Figure 5. We see that the acceleration vector of YLW 12Bab points toward YLW 12Bc, as would be expected of a gravitationally bound system. This plot also shows that our assumption of a uniform accelerated motion is a reasonable approximation, because our observations cover only a small fraction of the orbit expected for the wider system. We attempted to fit the orbit of this source around the center of mass of the whole system with a simultaneous distance and proper motion fit for the three stars. However, we were not able to constrain most of the orbital parameters because the VLBA detections of the third companion are still insufficient. We only find solutions for the following parameters: Ω ∼ 85°, ϖ = 7.190 ± 0.088 mas, ${\mu }_{\mathrm{CM},\alpha }\cos \delta =-4.55\pm 0.03$ mas yr⁻¹, ${\mu }_{\mathrm{CM},\delta }=-24.27\,\pm 0.06$ mas yr⁻¹; limits on the mass, ${M}_{3}\gt 3\,{M}_{\odot }$, period, $P\sim 300\mbox{--}400\,\mathrm{years}$, and that inclination is consistent with the compact binary. Even though we do not have enough data for modeling the orbit of YLW 12Bc, we can still constrain its proper motion and acceleration using its absolute positions measured with the VLBA. In order to do so, we fit the third star separately using the astrometric code for single sources to solve solely for proper motion and acceleration terms, while fixing the parallax at the value derived for YLW 12Bab. We show this last fit in the fourth panel of Figure 6, and give the solution of the astrometric parameters in Table 4.

As mentioned previously, the trajectory of YLW 12Bab is somewhat curved. That of YLW 12Bc is, on the other hand, more linear. This results in a smaller measured acceleration for YLW 12Bc (∼0.2 mas yr⁻²) than for YLW 12Bab (0.64 mas yr⁻²), and suggests that YLW 12Bc is the most massive member of the system. Indeed, we find that ${M}_{3}\gt 3\,{M}_{\odot }$, while ${M}_{1}=1.26\,{M}_{\odot }$ and ${M}_{2}=1.40\,{M}_{\odot }$. This is the reason why we plot the position of YLW 12Bab relative to YLW 12Bc in Figure 5, rather than the converse. We also see that, as expected, the acceleration of YLW 12Bc points, within the errors, toward YLW 12Bab (see Figure 5).

4.2.3. SFAM 87

SFAM 87 (also called ROX 39) has been detected in four epochs of GOBELINS. This source was also observed in six epochs from March 2008 to May 2009 as part of project BT097, but these data are yet to be published. We calibrated these additional epochs (Table 5) and combined them with our more recent data for the astrometric fits. The source is resolved into two components that are simultaneously detected in 6 out of the 10 total epochs (3 in BT097 and 3 in GOBELINS). We note that Cheetham et al. (2015) identified a companion to SFAM 87 in March 2013, using NIR aperture masking. This source appears to be the counterpart of the secondary source detected in our VLBA images (Figure 3). We used all available VLBA and NIR data to fit jointly orbital and proper motion, as well as parallax. The resulting best fit is shown in Figure 7 in a similar fashion to LFAM 15.

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4.2.4. DoAr 51

DoAr 51 (also called ROXs 47A) is located in the Lynds 1689 eastern streamer, 12 east of the Ophiuchus core. The source has been detected in seven epochs, and was found to be double in all of them. DoAr 51 was identified as a hierarchical triple system composed of a tight binary with separation of about 40 mas and a third component about 0.8 arcsec away by Barsony et al. (2003). Cheetham et al. (2015) confirmed the tight binary using NIR aperture masking observations. They resolved the source into two components, with an angular separation of 51.5 ± 0.20 mas in June 2009 and 43.38 ± 0.18 mas in April 2010. This is to be compared with a separation of 40 ± 30 mas reported by Barsony et al. (2003) in May 2002. More recently, Rizzuto et al. (2016) used the two positions measured by Cheetham et al. (2015) and three new detections in the NIR to model the orbit of the system. These five detections are shown in Figure 3, together with the positional offsets between the components of the system as seen in our VLBA images. It is clear that our radio sources are the counterparts of the NIR sources, as they lie along the orbit derived by Rizzuto et al. (2016). We model all data available from VLBA and NIR observations to better constrain the orbit of the system. The resulting best fit using the "full model" is shown in Figure 8, and the corresponding orbit in Figure 3. For comparison, we also show in this latter figure the orbit derived by Rizzuto et al. (2016).

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4.2.5. ROXN 39

The components of the system ROXN 39 have been detected separately in seven and five epochs, respectively, and simultaneously in only three epochs. The "full model" fit and measured positions of individual components are shown in Figure 9, while Figure 3 shows the same model and relative positions. We did not fit the "relative model" to this system because of the small number of simultaneous detections of both components. Consequently, the orbital parameters are less constrained, compared to the other systems described previously.

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4.2.6. S1

This source has been detected in a total of 8 epochs, and was also observed at 14 epochs as part of projects BL128 and BT093 (Table 5). The distance estimate by Loinard et al. (2008) of $d={116.9}_{-6.4}^{+7.2}$ pc, based on the data from the first six of these old epochs, is significantly different from the distance obtained here for others sources in Lynds 1688 (which range from 130 to 140 pc), and hence requires a careful inspection. We re-calibrated the data used in Loinard et al. (2008), as well as the additional eight unpublished observations obtained as part of BL128 and BT093. Similarly to DoAr 21, source positions measured at these 14 older epochs were corrected before fitting the data, by the positional offset of the calibrator, J1625-2527, relative to its old position.

A second source was detected in four epochs of the archival data, at an angular separation of about 20–30 mas from S1 (Figure 10). The detections are, however, only evident by self-calibrating the images, and the source is not present in the most recent epochs, so they should be taken somewhat cautiously. It is interesting, however, that Richichi et al. (1994) did report on the detection, using the lunar occultation technique in the NIR, of a companion to S1 at about 20 mas. Our detections of a second source in the system would be consistent with that earlier result. If we assume that the source is double, we can fit the orbital motion of the system jointly with the astrometric parameters and use the positions of the putative second component to estimate individual masses. To that end, we discard the BL128 and 2nd BT093 secondary epochs, as well as the second, fourth, and sixth BT093 primary epochs, because their corresponding images are of poor quality due to observing issues (cf. Table 5), and source positions do not match up to the best fit solution. The "full model" fit, shown in Figure 11, yields $\varpi =7.249\pm 0.091$ mas and a distance of 138.0 ± 1.7 pc. The derived mass for the primary component is $5.8\,{M}_{\odot }$, which is consistent with its B4 spectral type, while for the secondary we find a mass of $1.2\,{M}_{\odot }$. When ignoring the secondary component, the purely astrometric fit to all available data of the primary source yields $\varpi =8.335\pm 0.522$ mas, and hence the distance derived by Loinard et al. (2008). It is clear that this discrepancy in the results from the astrometry alone and the "full model" fits is due to the fact that the former does not take into account the multiplicity of the source. In the rest of the paper, we will use the results based on the astrometric plus orbital model, which are consistent with the distances obtained for other sources in Lynds 1688. Since the two components are detected simultaneously in only two epochs, we are not able to fit the "relative model" to relative positions, and only provide the resulting orbital parameters from the "full model" in Table 6.

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4.2.7. VSSG 11

VSSG 11 has been detected in seven observed epochs, and was found to be double in the last three. The second component is separated about 9 mas from the primary source. We perform the fits similarly to the other multiple systems discussed previously. However, because our observations only cover a small fraction of the orbit, the "full model" fit to the secondary source does not converge. This produces considerably larger errors in the astrometric and orbital parameters than those derived for the other multiple systems. Also, we were not able to reproduce the observed separations between the components of the system. We then fit solely parallax and accelerated proper motion. The resulting best fit is shown in Figure 12.

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4.2.8. WLY 2-11

We have observed the Class I protostar YLW 15 at 11 epochs, and clear detections were obtained at five. Only one source is detected in the VLBA images, and since YLW 15 is known to be a binary system (Curiel et al. 2003), it is important to determine which of the two stars is detected in our VLBA data. This can be achieved by comparing the astrometry of the present VLBA observations with that of the VLA data published by Curiel et al. (2003), which were obtained between 1990 and 2002. Such a comparison is shown graphically in Figure 13. The positions of the two sources in the system (VLA 1 and VLA 2) are shown as a function of time as black and red symbols, respectively. We also calibrated and imaged the data from a VLA observation obtained in 2007 as part of project AF455. The VLBA positions are shown as blue symbols. It is clear that the source detected with the VLBA is located very near the expected position of VLA2 at the epochs of the VLBA observations, and more than half an arcsecond away from the expected position of VLA1. We conclude that the source detected with the VLBA is VLA2.

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A marginal (7–9σ) VLBI detection of YLW 15 has been reported in the past (Forbrich et al. 2007). Indeed, the authors themselves mentioned that their detection was difficult to interpret, as the position did not coincide with the expected location of any of the two protostars in the system. This can also be seen in our Figure 13, where the position of the VLBI source reported by Forbrich et al. (2007) is shown as a cyan triangle. Their observations were conducted, under project code BF083, with the High Sensitivity Array (HSA), which for that run consisted of the Green Bank (GBT) 100 m radio telescope, the phased Very Large Array (equivalent in collecting area to a 130 m dish), as well as the VLBA. We calibrated these data following the standard procedures for incorporating non-VLBA antennas. We achieve rms noise levels between 10 and 22 $\mu \mathrm{Jy}\,{\mathrm{beam}}^{-1}$ (depending on the AIPS ROBUST parameter used for imaging), which are consistent with the value reported by Forbrich et al. (2007) of 15.4 $\mu \mathrm{Jy}\,{\mathrm{beam}}^{-1}$. We do not detect the source, and confirm our suspicion that their detection was likely spurious.

Even though five data points are, in principle, enough to perform an astrometric fit, most of our VLBA detections of YLW15 were obtained rather closely in time (two are separated by ∼3 weeks and other two by only ∼3 days). Moreover, the five detections were acquired around successive spring equinoxes, with no detection close to the fall equinox. As a result of this, the astrometric fit produces unreliable results. We will wait until we have more detections for the derivation of the astrometric parameters of this star.

Figure 15 shows the distribution of the 16 individual sources with astrometric parameters measured in this paper. In order to calculate the motion of each source relative to its local environment, we need to remove the contribution of the solar peculiar motion. For this correction, we use the formulation of Abad & Vieira (2005), and the solar motion relative to the LSR derived by Schönrich et al. (2010). They obtained rectangular components of the solar motion (u_⊙, v_⊙, w_⊙) = (11.1 ± 0.7, 12.2 ± 0.47, 7.25 ± 0.37) km s⁻¹, directed toward the Galactic center, the direction of Galactic rotation, and the Galactic north pole, respectively. Corrected proper motions were transformed to tangential velocities (Table 7) and overlaid on Figure 15. It is clear that, with the exception of a few objects that may belong to a different substructure of the complex, all sources share similar motions. The derived one-dimensional velocity dispersion in R.A. and decl. of sources in Lynds 1688 are 2.8 and $3.0\,\mathrm{km}\,{{\rm{s}}}^{-1}$, respectively. These are larger than the values found in other studies, which range from ∼1 to 2 km s⁻¹ (Makarov 2007; Wilking et al. 2015). However, our sample size is small, and our results need to be confirmed with additional proper motions and parallaxes. In addition, we estimate that the associated errors of the velocity dispersions (assumed to be Gaussian distributed) are 1.8 and 2.0 km s⁻¹, in R.A. and decl., respectively. Thus, within the errors, our results are still consistent with past measurements.

Table 7.  Corrected Proper Motions and Tangential Velocities

Name	${\mu }_{\alpha \cos \delta }^{\mathrm{corr}}$	${\mu }_{\delta }^{\mathrm{corr}}$	${v}_{\alpha }^{{\rm{t}}}$	${v}_{\delta }^{{\rm{t}}}$
	(mas yr−1)	(mas yr−1)	(km s−1)	(km s−1)
(1)	(2)	(3)	(4)	(5)
WLY2-11	−1.96 ± 0.72	−4.2 ± 0.75	−1.26 ± 0.46	−2.72 ± 0.49
YLW24	0.63 ± 0.83	−4.17 ± 0.84	0.41 ± 0.53	−2.67 ± 0.54
DoAr21	−11.74 ± 0.89	−5.91 ± 0.86	−7.54 ± 0.57	−3.79 ± 0.55
LFAM2	1.87 ± 0.87	−6.94 ± 0.73	1.26 ± 0.58	−4.66 ± 0.49
LFAM8	1.82 ± 0.83	−8.96 ± 0.76	1.19 ± 0.54	−5.86 ± 0.5
S1	5.65 ± 0.88	−6.1 ± 0.77	3.69 ± 0.57	−3.99 ± 0.51
LFAM15	1.37 ± 0.74	−6.29 ± 0.71	0.9 ± 0.49	−4.11 ± 0.46
VSSG11	−2.88 ± 0.92	−18.67 ± 0.9	−1.9 ± 0.61	−12.36 ± 0.59
LFAM18	−3.96 ± 0.82	2.25 ± 0.71	−2.59 ± 0.53	1.47 ± 0.46
YLW12B	3.05 ± 0.77	−3.66 ± 0.7	2.0 ± 0.5	−2.4 ± 0.46
ROXN39	0.33 ± 0.91	−5.25 ± 0.83	0.21 ± 0.59	−3.4 ± 0.54
DROXO71	3.22 ± 0.81	−7.77 ± 0.72	2.09 ± 0.52	−5.03 ± 0.47
SFAM87	−0.41 ± 0.86	−5.48 ± 0.76	−0.27 ± 0.56	−3.6 ± 0.5
LIRS5	0.21 ± 0.71	−3.55 ± 0.69	0.15 ± 0.5	−2.52 ± 0.49
WLY2-67	0.58 ± 0.79	−5.06 ± 0.67	0.41 ± 0.57	−3.63 ± 0.48
DoAr51	2.1 ± 0.84	−3.15 ± 0.72	1.43 ± 0.57	−2.14 ± 0.49

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YSOs are often detectable radio sources due to a variety of mechanisms. One common radio emission process in YSOs is thermal bremsstrahlung (free–free) continuum emission, either from photo-ionized gas around massive stars (e.g., Churchwell 2002) or from shock-ionized gas in supersonic jets and outflows (e.g., Rodríguez 1997). The brightness temperature corresponding to thermal bremsstrahlung emission, however, is typically only 10⁴ K—much too small to be detectable in VLBI observations. The situation with thermal dust continuum emission, which can be detected up to centimeter wavelengths from circumstellar disks (e.g., Pérez et al. 2015), is even worse, as such emission has brightness temperatures of at most several hundred K. Thermal line emission, from molecules or atoms, is similarly limited to brightness temperatures smaller than several hundred K. Thus to find emission that could be detected in VLBI observations, one must turn to non-thermal mechanisms. For line emission, this implies focusing on strongly amplified maser lines, like those of water (H₂O), methanol (CH₃OH), formaldehyde (H₂CO), silicon monoxide (SiO), or hydroxyl (OH). Those lines (particularly those of water and methanol) are widespread in regions of high-mass star formation, and can be detected and studied with VLBI observations up to distances of several kpc. Indeed, the BeSSeL project (Brunthaler et al. 2009) takes advantage of these lines to measure the parallax and proper motions of high-mass star-forming regions distributed across the entire Milky Way disk. In the Gould's Belt star-forming regions, however, only a handful of maser sources are known (e.g., Moscadelli et al. 2006).

Non-thermal continuum emission also exists, and broadly corresponds to the situation where electrons gyrate in a magnetic field. This type of radiation is called cyclotron, gyro-synchrotron, or synchrotron emission, depending on whether the electrons are non-relativistic (with a γ Lorentz factor of about 1), mildly relativistic (γ of a few), or ultra-relativistic (γ ≫ 1), respectively (Dulk 1985). Such continuum non-thermal emission has been detected around a number of low-mass young stars (e.g., Forbrich et al. 2011, and references therein), and has been interpreted as coronal emission from active stellar magnetospheres. The most common mechanism appears to be gyro-synchrotron, although maser-amplified cyclotron emission (Smith et al. 2003) as well as synchrotron emission (Massi et al. 2006) have also been reported in rare instances. The magnetic field in which the electrons are gyrating is generated through the dynamo mechanism, which requires convection in the outer layers of the stellar interior (e.g., Dormy et al. 2013). As a consequence, non-thermal coronal emission should occur only in low-mass stars, because intermediate and high-mass stars are fully radiative. This is true both for main sequence and pre-main sequence stars: while low-mass T Tauri stars approach the main sequence on fully convective Hayashi tracks, stars more massive than about 3 ${M}_{\odot }$ follow radiative Henyey tracks (e.g., Palla & Stahler 1993). It is noteworthy, however, that a few intermediate-mass young stars have been found to exhibit non-thermal coronal emission (Andre et al. 1991; Dzib et al. 2010). The electrons gyrating in the magnetic field are thought to be accelerated to mildly relativistic speeds during energetic reconnection processes (Parker 1957), so the emission is often produced in flares (e.g., Bower et al. 2003) and is therefore highly variable. Once again, there are some exceptions to this general behavior (e.g., Andre et al. 1991). Finally, it should be mentioned that most of the low-mass young stars where non-thermal emission has been reported are T Tauri stars (particularly Weak Line T Tauri stars), although a few younger Class I protostars have also been detected (Forbrich et al. 2006; Deller et al. 2013).

Coronal non-thermal radio continuum emission usually remains unresolved at the milli-arcsecond resolution of VLBI observations (e.g., Loinard et al. 2007; but see Andre et al. 1991). Theoretically, the emission is expected to be confined to the magnetosphere of the YSO, which extends to only a few stellar radii (Bouvier et al. 2007). This is indeed very small—for instance, 10 ${R}_{\odot }$ corresponds to about 0.5 mas at 100 pc.

As mentioned in the main text, we have firmly detected a total of 26 YSOs, corresponding to roughly half of the 50 YSOs targeted in our observations. This confirms the claim by Dzib et al. (2013) that about 50% of the radio-bright YSOs in Ophiuchus are non-thermal emitters. We searched the literature and found that only six of these YSOs had previously been detected in VLBI experiments. These sources (DoAr 21, S1, LFAM 15, VSSG 11, YLW 12 B, and SFAM 87) were known to be magnetically active stars, with centimetric non-thermal radio emission, before our observations (e.g. Andre et al. 1992; Loinard et al. 2008). We note that Forbrich et al. (2007) reported on the detection, with the HSA, of one of the components of the binary class 0/I source YLW 15 (a target that we also detect here). However, our analysis of the proper motions of the system components (see Section 4.3) suggests that the detection by Forbrich et al. (2007) was likely spurious. The 26 detected YSOs correspond to a total of 34 individual young stars, because five detections are found to be tight binary systems, while one corresponds to a triple system (see Table 2).

Dzib et al. (2013) also published a list of YSOc detected in their VLA observations. They reported as YSOc those radio sources that are not associated with known young stars, but that show high VLA flux variations, a negative spectral index, or circular polarization. Four of these sources were also detected in our VLBA observations, as well as another 27 (presumably background) sources. We analyze the astrometry of these 31 objects in Appendix B and find that, as expected, most of them are extragalactic sources.

In order to establish the nature of the emission, we have measured the brightness temperature (T_b) of the VLBA-detected sources, according to

$$\begin{eqnarray}&&{T}_{b}=\displaystyle \frac{2{c}^{2}}{{k}_{B}{\nu }^{2}}\displaystyle \frac{{S}_{\mathrm{total}}}{\pi {\theta }_{\mathrm{maj}}{\theta }_{\min }},\end{eqnarray} \tag{ 1 }$$

where ${\theta }_{\mathrm{maj}}$ and ${\theta }_{\min }$ are the deconvolved sizes of the major and minor axes diameter, and ${S}_{\mathrm{total}}$ is the total flux density measured in the VLBA images. Since most of the sources have been detected at several epochs, we are reporting the highest measured brightness temperature. For unresolved sources, we give a lower limit to T_b obtained using the corresponding beam size as an upper limit for the source size. Brightness temperatures are given in columns (7) and (5) of Tables 2 and 8, respectively. All of the VLBA-detected YSOs have ${T}_{b}\gt {10}^{6}$ K, which is larger than the brightness temperature expected for thermal bremsstrahlung radiation (${T}_{b}\gtrsim {10}^{4}$ K), and consistent with the brightness temperature expected for non-thermal emission. Our study has, therefore, found a population of non-thermal YSOs larger than previously reported. It is noteworthy that non-thermal emission is detected in sources in the Class I to Class III stages.

In Figure 16, we plot the VLBA flux density at 5 GHz of the detected YSOs as a function of their evolutionary phase, as measured from their infrared/millimeter spectral energy distribution (SED). It appears at first glance that older objects have, on average, stronger non-thermal radio emission. The significance of this correlation can be assessed by a Kolmogorov-Smirnov test on the three YSOs classes. The p values derived from such a test are $\gt 0.08$, so we cannot reject the null hypothesis that different classes are taken from the same distribution function. The relation is, therefore, not statistically significant. We also perform the Wilcoxon rank-sum statistic finding similar results. Thus our conclusion about the significance of the correlation does not depend on the statistical test that we use.

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From Table 2, it is clear that Class II and III sources are the most common types of YSOs with non-thermal radio emission. Past studies had only found two cases of Class I protostars with non-thermal emission detectable in VLBI observations. These sources are CrA IRS 5 (Deller et al. 2013) and EC 95 (Dzib et al. 2010). Here we have detected non-thermal emission from three other Class I objects, namely LFAM 4, YLW 15,²⁰ and WLY 2-67. Therefore we have more than doubled the number of protostars with confirmed non-thermal emission. In a recent study, Heiderman & Evans (2015) investigated whether the Class 0+I and Flat SED sources identified in the c2d (Evans et al. 2009) and Gould Belt (Dunham et al. 2015) surveys are in the embedded phase. These authors used the detection of the ${\mathrm{HCO}}^{+}\,J=3\to 2$ as a good indicator of the Stage 0+1, which corresponds to "a star and a disk embedded in a dense, infalling envelope" (van Kempen et al. 2009). Our three Class I objects with non-thermal radio emission meet the criterion to be in this embedded stage. Non-thermal emission has not been detected in Class 0 sources, and at this point it is unclear if this results from a lack of such emission or if such young systems always contain thermal radio jets that systematically absorb underlying active coronas.

Magnetic activity is known to occur throughout the early evolution of low-mass stars, so protostellar sources could easily produce non-thermal emission. On the other hand, accretion and outflow activity is also present in this protostellar stage. In order for the observer to see the radio emission from the stellar corona, the line of sight cannot cross regions where optically thick radio emission is present (i.e., the central portions of disks or wind/outflow systems). This might occur only for some privileged relative orientation of the system, and naturally explains the low fraction of detected protostars in our observations, in comparison with the larger number of detections of more evolved objects.

There does seem to exist a correlation between non-thermal radio emission in YSOs and multiplicity. Perhaps the best documented case is that of the V773 Tau system (Massi et al. 2002; Torres et al. 2012), where the radio flux increases by more than one order of magnitude when the system passes periastron. We have found here that a significant fraction of the VLBA-detected young stars belong to very tight binary or multiple systems (with a separation of a few tens of mas—a few au; Table 2). Multiplicity may help clear out the surrounding material, and result in non-thermal emission that is statistically less affected by free–free absorption, but the exact mechanisms behind this remain unclear. The flux from thermal jets becomes transparent at frequencies above a few GHz (Reynolds 1986). Thus coronal non-thermal emission from protostars with thermal emission should be detectable at higher frequencies.

In our VLBA observations, we found that seven YSOs form multiple systems, and one more has evidence of multiplicity (see Table 2). This represents $\sim 30 \%$ of the total number of YSOs detected with the VLBA. The angular separations of the components in these systems range from 4 to 315 mas, corresponding to 0.6–44 au at the distance of Ophiuchus. In order to investigate if this fraction is expected from the known population of multiple systems in Ophiuchus, or if it indicates that tight multiple systems are more likely to be non-thermal radio emitters than single stars or wider multiple systems, we compared it with the binary fraction reported in the literature. Recently, Cheetham et al. (2015) compiled high-resolution multiplicity data and combined them with their results from an aperture masking survey; they obtained a binary fraction of 35 ± 6% for spatial scales from 1.3 to 41.6 au. Taken at face value, our VLBA detection of 30% of binaries with separations between 0.6 and 44 au appears to be consistent with the binary fraction derived from the multiplicity survey by Cheetham et al. (2015). However, we still favor the idea that very tight binaries are more often radio sources than single stars or more separated binary systems, because seven of our eight detected binaries have separations of a few au, whereas only one has a separation larger than 10 au. Thus, for separations below 10 au, there does appear to be an excess of radio-bright binaries. Our interpretation will be tested by considering the whole sample of multiple stars seen in the five regions observed by GOBELINS, and comparing with multiplicity studies in the infrared, where aperture masking observations can explore angular separations similar to those attained with the VLBA.

We show in Figure 17 the number of objects versus the radio luminosity at 5 GHz (i.e., the luminosity function) of the 26 YSOs detected with the VLBA. The number of objects appears to decrease with increasing luminosity, following roughly a linear trend (in logarithmic luminosity). Assuming that the trend is valid for lower luminosities, we can infer that deeper observations with an improved sensitivity by an order of magnitude will detect ∼20 more YSOs with non-thermal radio emission, thus doubling the number of sources). It will be interesting to construct the luminosity function for the other regions considered in GOBELINS and see if this is a general trend.

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