IN-SYNC VI. Identification and Radial Velocity Extraction for 100+ Double-Lined Spectroscopic Binaries in the APOGEE/IN-SYNC Fields

We analyze high-resolution (R ∼ 22,500) near-infrared (1.51–1.70 μm) spectra taken with the 300-fiber APOGEE spectrograph (Wilson et al. 2012) on the Sloan 2.5 meter telescope (Gunn et al. 2006) at Apache Point Observatory. During SDSS-III, the APOGEE survey obtained nearly 620,000 spectra of more than 150,000 stars throughout the Milky Way, which were released in the SDSS twelfth data release (DR12; Alam et al. 2015). The vast majority of APOGEE targets are red giants (Zasowski et al. 2013), collected in service of the survey's primary science goal, to dissect the structure, dynamics, chemical evolution, and star formation history of the Milky Way (Majewski et al. 2015). As Alam et al. (2015) describe, several "ancillary science" programs were approved to utilize the unique capabilities of the APOGEE spectrograph and data analysis infrastructure to target complimentary science goals. Our analysis focuses on identifying SB2s within fields observed as part of the IN-SYNC ancillary science program, which targeted regions of recent and current star formation activity.

The primary regions targeted by the IN-SYNC program are IC 348 (Cottaar et al. 2014, 2015) and NGC 1333 (Foster et al. 2015) in the Perseus Molecular Cloud (PMC), the Orion A molecular cloud (Da Rio et al. 2016), and NGC 2264. Here, we summarize the most pertinent details of the target selection and observations in the fields containing these regions; for more details, we refer the reader to the full descriptions given in each of the papers cited above. The highest priority targets in each region were selected from existing catalogs of young stellar objects (YSOs) identified by photometric or spectroscopic signatures of youth, such as infrared excess, emission line activity, and/or low surface gravity. If high-priority targets did not require the full complement of 230 science fibers allocated to each APOGEE field, candidate members selected via color–magnitude or proper motion cuts were allocated fibers at lower priority. In total, nearly 3500 pre-main-sequence stars were observed as part of the IN-SYNC program: 2700 in the Orion A cloud, 380 in IC 348, and 110–120 in NGC 1333 and NGC 2264. For this paper, however, we analyzed all sources in the fields containing the IN-SYNC targets, regardless of how they were originally targeted, as some may provide serendipitous detections of cluster members. Including all targets in each field provides a final sample of 4556 unique sources: 2771 in Orion, 1309 in Perseus (IC 348 and NGC 1333), 100 in Pleiades, and 376 in NGC 2264: for the remainder of this paper, we refer to these objects as the Complete IN-SYNC Sample.

As seen in Figure 1, the observing strategy and schedule achieved in different IN-SYNC target regions resulted in distinct cadences for each of the binaries identified in our sample. Fibers cannot be placed on targets separated by less than 72'' on a single APOGEE plate, such that repeat observations of a given APOGEE field are required to observe targets with nearby neighbors. Fields in Orion, which were limited to a narrow observing window, emphasized using repeat visits to a given field to alleviate crowding and expand the total sample size, such that a typical Orion target was only observed for one epoch. The IC 348 field, by contrast, was observed over a longer window, with visits dedicated to obtaining multiple epochs for sources at intermediate and large cluster radii, to enable the detection and characterization of binaries in the cluster and surrounding field populations. Sources in the IC 348 field were therefore typically observed at least three to four times, with a substantial number having as many as 16 observations.

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The APOGEE pipeline produces reduced spectra for each observation of a target, as well as a combined spectrum co-adding all observations to maximize the resultant signal-to-noise (S/N). We focus our analysis on the individual spectra of each source, typically referred to as "visit spectra" in the APOGEE documentation, as these time-resolved observations are of greater use for identifying and characterizing SB2 systems.

The APOGEE pipeline calculates CCFs for each visit spectrum (see Figure 2 for sample spectra and associated CCFs for a high-visit IN-SYNC target in IC 348). The spectrum is cross correlated against the best-fit synthetic spectrum from the APOGEE RV mini-grid, a set of models sparsely spanning effective temperature, metallicity, and log(g) space. The resulting CCF is computed for 401 lags, with a velocity resolution per lag step of 4.14 km s⁻¹; as Nidever et al. (2015) and Cottaar et al. (2014) demonstrate, however, the stability of the APOGEE spectrograph enables the measurement of RVs at the 0.1–0.2 km s⁻¹ level by centroiding each CCF peak.

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The APOGEE reductions of each visit spectrum provide the lag-to-velocity conversion factor, the heliocentric correction for that epoch, and the radial velocity estimate determined by the APOGEE pipeline. We do not utilize the radial velocity measurements produced by the APOGEE pipeline, as those measurements are derived under the assumption that the source in question is a single star. Instead, we perform a new analysis of the APOGEE-produced cross-correlation functions to identify likely SB2s and determine each component's radial velocity.

To extract radial velocities we begin by converting the APOGEE pipeline CCFs from lag-space to velocity-space, using

$$\begin{eqnarray}&&{v}_{{radial}}=({10}^{\alpha \beta }-1)c+{v}_{{helio}},\end{eqnarray} \tag{ 1 }$$

where c is the speed of light in vacuum, β gives the index for the array of 401 CCF lag steps, v_helio is that star's heliocentric correction at the epoch of observation, and α is the exponential lag-to-velocity conversion factor ($6\times {10}^{-6}$ or 4.14 km s⁻¹ per step) associated with the APOGEE-produced CCFs.

Our dual RV-extraction algorithm first attempts to identify two distinct velocity components in the CCF measured from each visit spectrum. The maximum of each CCF is identified as the primary peak, and the portion of the CCF bounded by the local minima on either side of the primary peak is removed. Once the primary peak has been subtracted from the CCF, the maximum of the remaining portion of the CCF is selected as a candidate secondary peak, and the velocity separation between the primary and putative secondary peak is calculated to characterize the velocity separation at that epoch. Comparing the velocity separations measured between the primary and secondary peaks for all observations of a given source, the epoch with the largest peak separation can be identified; in the discussion that follows, we identify this epoch as the "widest separated CCF". This procedure forces a dual-peak fit to all CCFs, even sources which have only one astrophysically significant peak. The parameter cuts detailed in Section 3.2, however, eliminate most sources with genuinely singly-peaked CCFs from our final sample of candidate SB2s.

Once a source's widest separated CCF has been identified, Lorentzians are fit to all epochs of the source's CCF in three steps. First, the components of the widest separated CCF are fit separately to establish an initial set of parameters (i.e., central velocity, peak height, and width parameter) to describe each peak. Next, using the best-fit parameters for each peak as a starting point, a second fit to the widest separated CCF is then performed, with both peaks fit simultaneously. In the third and final step, the best-fit parameters from the dual fit to the widest separated CCF are used to initiate dual-component fits to all of a source's CCFs. Detailed descriptions of each step follow.

• 1.  
  Individual fits to primary and secondary peaks. The portions of the widest separated CCF masked as containing the CCF's primary and secondary peaks are passed to the IDL routine MPFITFUN, which fits each peak separately with a Lorentzian model ($L=\rho \tfrac{{\gamma }^{2}}{{(x-{x}_{0})}^{2}+{\gamma }^{2}}$, with x₀ the peak center, ρ the peak height, and γ the width parameter). From this fit, we obtain initial values for the width, height, and location of each component's peak profile.
• 2.  
  Dual-component fit to widest separated epoch. Using the initial values determined for the peak parameters in the previous step, the widest separated CCF is refit using MPFITFUN with a dual Lorentzian model (${L}_{{CCF}}\,={L}_{{prim}}+{L}_{{\sec }}$). The peak profile parameters (width, height, and peak center location) derived from this dual, simultaneous fit to a single CCF are used to place constraints on the width, relative peak heights, and maximum peak separation for all epochs for that source. We choose to constrain the width and relative peak height to ±10% of the best-fit values from the individual fits to the widest separated epoch. This step ensures that the peak parameters are fit consistently across all epochs for an individual source.
• 3.  
  Dual-component fits to all epochs. The full suite of CCFs measured for a given source are then fit with dual-peak models. Each fit is initialized with the best-fit parameters from the dual-component fit of the previous step, and variations in peak height and width are limited to ±10% of the best-fit values for the widest separated epoch: the primary degree of freedom at this stage is the peaks' locations, which are allowed to vary between epochs. The dual Lorentzian model is again fit with MPFITFUN, along with the aforementioned constraints. An example of a resulting fit is shown in Figure 3.

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We applied this procedure to all ∼4500 sources in the Complete IN-SYNC sample, producing radial velocity measurements for each component of the putative binary, along with statistics describing the structure of each CCF (i.e., the r statistic, introduced in Equation (2)).

To efficiently and objectively identify likely SB2s in the Complete IN-SYNC sample we identify parameters derived from the sources CCFs which can be used to pre-select likely SB2s for visual confirmation. For this purpose, we use three parameters—two intrinsic and one model-dependent—that can be calculated at each epoch for each source, and then used to eliminate sources with no evidence for a second spectroscopic component.

The two intrinsic properties of each source's CCF that we examine are H, the height of the primary CCF peak, and r, a parameter originally introduced by Tonry & Davis (1979) to describe the strength of a given CCF peak relative to the CCF's anti-symmetric component. H is measured as the maximum value of the CCF; low H value indicates that the observed spectrum has low S/N, or is poorly matched by the APOGEE template spectrum. The second intrinsic property that we measure, r, serves as a convenient tool to identify CCFs which are highly asymmetric due to the presence of a secondary peak. Following Equation (23) by Tonry & Davis (1979), the r parameter can be calculated as

$$\begin{eqnarray}&&r=\displaystyle \frac{H}{\sqrt{2\,}{\sigma }_{a}},\end{eqnarray} \tag{ 2 }$$

where ${\sigma }_{a}$ gives the rms of the anti-symmetric component of the CCF:

$$\begin{eqnarray}&&{\sigma }_{a}=\sqrt{\displaystyle \frac{1}{N}\sum {(c(n+{x}_{0})-c({x}_{0}-n))}^{2}},\end{eqnarray} \tag{ 3 }$$

where N is the number of lag steps in the total range, and $c({x}_{0}\pm n)$ signify the CCF function associated with the two halves of the CCF, divided about x₀, the location of the primary peak. Likely binaries with multiple CCF peaks will have low values of r (high values of ${\sigma }_{a}$ due to a strong asymmetry from the secondary peak) and putatively single stars will have high values of r, due to their single, highly symmetric CCF peaks. To accentuate the asymmetry of the CCF further we calculate $r/{\sigma }_{a}$ for each epoch and retain the minimum value for each source. This minimum value corresponds to the epoch at which the CCF has the least symmetry about the primary peak.

The final parameter we use to identify candidate SB2s is the velocity separation between the primary and secondary peaks identified in the automated process described in Section 3.1. Specifically, we identify candidate SB2s based on their maximum v_sep measured across all epochs. Bona fide SB2s will have moderate maximum velocity separations, neither too large nor too small: too large a ${v}_{{sep},\max }$ indicates that the secondary radial velocity has been measured from a spurious/noisy CCF peak at a non-physical RV, while too small a ${v}_{{sep},\max }$ indicates that the "secondary" CCF peak is not separable from the primary peak itself.

To validate the range of H, r, and v_sep values that can be used to pre-select a sample of likely SB2s, we visually inspected CCFs for hundreds of APOGEE targets to establish validated samples of high-confidence SB2s, and sources with no evidence of binarity. The first classification was performed on a sample of 200 sources: 50 APOGEE targets previously identified by S.D.C. as likely SB2s, to demonstrate the H, r, and v_sep values of high-confidence binaries, and 150 sources drawn randomly from the Complete IN-SYNC sample, to identify the parameter values of SB2s that can be identified with typical IN-SYNC spectra. The CCFs of sources in this semi-random sample were scrutinized carefully to identify less obvious SB2s: sources with subtle, but time-dependent CCF asymmetries that indicate the presence of two components.

Based on the properties of the SB2s we identified in the semi-random sample, we defined criteria which enable the pre-selection of a sample of potential SB2 targets. Specifically, we preserve as viable SB2 candidates those sources that meet the following criteria:

• H > 0.30 across all epochs; sources with low CCF peaks are discarded, as this indicates either a low S/N spectrum or a poor match between the APOGEE template spectrum and observed spectrum, either of which will pose challenges for reliable SB2 identification.
• (r/σ_a)_min < 460; sources that do not meet this criteria are highly symmetric at all epochs, consistent with being a single, RV-stable star.
• 30 < v_sep,max < 220 km s⁻¹; sources with maximum velocity separations above and below this threshold have non-physical putative secondary components, indicating the absence of a physically meaningful secondary component.

Applying these criteria to the Complete IN-SYNC sample identified a set of 533 candidate binaries (∼12% of the Complete IN-SYNC sample).

To evaluate the success and efficiency of these criteria for pre-selecting SB2s, two of us (M.A.F. and K.R.C.) then visually examined and classified all 533 candidate SB2s, along with 10 additional candidates identified by a cursory examination of the CCFs for the Complete IN-SYNC sample. The CCFs of these 543 candidate SB2s were examined and assigned a numerical value to rank the strength of the evidence for their binary status, which could include: at least one visit with fully separated peaks, multiple epochs with merged structures, or a majority of epochs with consistent shoulder behavior (see Figure 3). Sources with fully separated peaks were rated the highest, and are almost certainly binary systems, while sources with either of the other two behaviors were rated lower and categorized as potential binaries. Based on this criteria scores from 1–5 were assigned to candidate SB2s, where 1 indicated low likelihood of binarity and 5 indicated high likelihood of binarity. The two independent scores were then added to give each candidate SB2 a relative likelihood of being a bona fide SB2 on a 10 point scale.

Figure 4 shows the 543 candidate SB2s selected from the Complete IN-SYNC sample, where each source has been color-coded to indicate its visual inspection rating. We retain sources with a combined numerical rating of six or larger as binary candidates: we identify 70 high-confidence binaries and 34 potential binaries. We identify systems with at least one epoch with fully separated peaks as high-confidence binaries, and label as potential binaries those that show consistent merged structures or peak shoulder behavior throughout all epochs. Examples of these three behaviors can be seen in Figure 3. The percentage of visually classified sources retained by the parameter cuts outlined above are listed in the legend of Figure 4; these cuts retain almost all of the visually confirmed high-confidence binaries, and most of the potential binaries.

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It should be noted that the sample returned after the parameter cuts has a majority of false positives (439/533); however, the purpose of the parameter cuts is to reduce the number of sources which are visually inspected without losing likely SB2s. In this respect, the parameter cuts do well, returning >90% of the binaries which can be found by visual inspection of the entire sample, while reducing the number of stars that actually require that visual inspection by ∼90%. There are two primary reasons for these false positives; low S/N epochs leading to poorly fit CCFs, and secondary peaks fit to noise "spikes" in the absence of a true second peak. The former case often gives poorly fit RVs for both the primary and the secondary component, while the latter often gives non-physical secondary RVs.

Sources selected as potential or high-confidence binaries will often have epochs where the primary and secondary components have identical RVs, thus the CCF has only one genuine peak; in this case, our peak fitting algorithm will fit a spurious secondary peak. In these cases and when the object has multiple other well fit epochs, we adopt the primary RV for the secondary component as well. In future work the processes of Sections 3.1 & 3.2 will be swapped, such that candidate binaries will be identified based on direct quantitative measures of CCF structure, rather than fit parameters. This is due to the aforementioned issues of low S/N epochs, spurious secondary fits, and very broad peaked CCFs, all of which can lead to false indicators of binarity in the fit parameters.

The Lorentzians fit to each CCF diagnose the RVs of each component, but do not provide a robust uncertainty estimate for those RVs. For single stars, centroiding techniques can routinely achieve velocity precisions of a few percent, but RVs inferred from multi-component fits such as we adopt here are subject to systematic and random errors that produce non-Gaussian error distributions that are best bounded with empirical error estimates. As an empirical estimate of the precision of our dual-component RV measurements, we report the residuals of our observed component velocities with respect to the best-fit RV_prim versus RV_sec (Wilson plot) for each system; examples of Wilson plots are shown in Figures 5 and 6. Using a simple ${\chi }^{2}$ minimization method, we obtain the best linear fit to the RV_prim vs RV_sec data for each system. For each pair of RV measurements extracted from a given visit spectrum, we calculate the perpendicular distance between the location defined by those empirical measurements and the linear fit to the full ensemble of RV measurements of that system. We use this "perpendicular velocity distance" as a pseudo-measure of the uncertainty in our extracted radial velocities.

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For systems with three or more visits, we calculate the "perpendicular velocity distance" for each epoch and use that value as an estimate of that epoch's velocity precision. For systems with fewer than three epochs, we estimate the global precision of our RV measurements using a distribution fit to the velocity residuals calculated for 3+ epoch systems. Figure 7 shows the distribution of the residuals for systems with three or more epochs, with normal and exponential distributions overlaid. The exponential fit better reproduces the empirical distribution than the normal fit across the range of velocity residuals. We adopt the exponential fit value corresponding to the 68th percentile or pseudo-normal 1σ (1.817 km s⁻¹) as representative of the typical velocity errors for systems in our sample with fewer than three visits. Using this exponential fit to calculate the expected 95th and 99th percentile velocities deviations produces pseudo-normal errors of 2σ = 4.871 and 3σ = 9.190 km s⁻¹, respectively.

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Though absolute masses cannot be determined for non-eclipsing systems from spectroscopy alone, the system's mass ratio can be derived. We infer mass ratios for systems with more than a single epoch from the best linear fit to the system's RV_prim versus RV_sec relationship. Mass ratio estimates are the slope of the linear best fit to the RVs,

$$\begin{eqnarray}&&\displaystyle \frac{{M}_{{\sec }}}{{M}_{{prim}}}=\displaystyle \frac{{{RV}}_{{prim}}}{{{RV}}_{{\sec }}}.\end{eqnarray} \tag{ 4 }$$

The distribution of inferred mass ratios is shown in the inset of Figure 8 for systems with more than one epoch. As expected, the distribution is dominated by sources with mass ratios near one, but there are a number of sources with mass ratios <0.7. A number of these apparently low-mass ratio systems have only a few observations (two to three epochs), such that their inferred mass ratios may be particularly sensitive to errors in the extracted RV values, and/or the association of those RVs with the system's primary and secondary components. Nonetheless, there are several apparently low-mass ratio systems with observations over several epochs and reliable RV_prim versus RV_sec relationships, suggesting that they are bona fide low-mass ratio systems (see Figure 6): three particularly notable examples are 2M03424086+3213347 (16 epochs and q = 0.217), 2M06413207+1001049 (six epochs and q = 0.050), and 2M03430679+3148204 (15 epochs and q = 0.340).

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We used a Kolmogorov-Smirnov test to determine if these low-mass ratio systems were consistent with three prior measurements of the distribution of mass ratios in samples of SB2 systems.¹³ We compare the mass ratios we measure to those measured for (1) 1410 SB2s in the SB9 catalog of spectroscopic binaries (Pourbaix et al. 2004), (2) 32 main-sequence SB2s characterized by Mazeh et al. (2003), who used infrared spectroscopy to detect secondaries for optically identified SB1s, and (3) 15 SB2s identified in the optical by Kounkel et al. (2016). Figure 8 shows the CDFs for these three mass ratio distributions, along with the CDF for the mass ratios that we measure from the APOGEE/IN-SYNC sample.

We find a vanishingly small likelihood (K-S statistic ∼ 10⁻⁴%) that the mass ratios of the IN-SYNC and Mazeh+ SB2s are drawn from the same distribution. This may reflect a bias against equal-mass systems in the Mazeh et al. (2003) sample: since q = 1 systems would be unlikely to appear as an optical SB1, the sample of stars Mazeh et al. (2003) were able to convert into infrared SB2s should have preferentially lower q values than an unbiased sample of SB2s. We find better agreement (K-S statistic ∼ 10%) between the IN-SYNC SB2 and Kounkel+ samples, with the Kounkel+ sample shifted towards higher mass ratio systems than the IN-SYNC SB2 sample. This is consistent with the difference in observations; Kounkel+ used optical spectroscopy, where low-mass secondaries will be difficult to detect, whereas this study used infrared spectroscopy, for which the contrast ratio between a hot primary and a cool secondary is more favorable. Surprisingly, we find our best agreement (K-S statistic ∼16%) between the IN-SYNC SB2 and Pourbaix+ samples. We also note the agreement between our sample and the SB9 sample is especially good for q > 0.4, indicating that the number of low-mass ratio systems in our sample is consistent with this larger sample.

A binary's systemic velocity provides an important constraint on its potential membership in a cluster population. We infer systemic velocities for all systems in our sample with multi-epoch coverage by using the best-fit RV_prim versus RV_sec relationship to identify the point at which RV_prim = RV_sec. As with the mass ratios determined from the same data, we include systemic velocities for binaries with two or three epochs but note that they are significantly more uncertain due to the sparse coverage of the RV_prim versus RV_sec plane. The uncertainties we report for these systemic velocity estimates are propagated from the formal uncertainties in the slope and intercept of the best-fit line.

Table 2 contains the basic properties we have inferred for each system in our sample, including mass ratio and systemic velocity estimates. The table also includes the number of APOGEE spectra obtained for the system, as the reliability of the inferred parameters scale strongly with the temporal coverage. We remind the reader that mass ratios and systemic velocities are impossible to derive for sources with only a single epoch of APOGEE observations, and are highly uncertain for sources with only two or three epochs of observations. The confidence flag encodes the robustness of the binary identification, as outlined in Section 3.2.

Table 2.  Fit Parameters

2Mass ID	Nepochs	γ (km s−1)	q $\left(\tfrac{{M}_{1}}{{M}_{2}}\right)$	Ca
03434101+3237320	16	22.107 ± 1.601	${0.942}_{-0.018}^{+0.018}$	L
03424086+3213347	16	22.743 ± 3.143	${0.217}_{-0.023}^{+0.023}$	P
03450783+3102335	7	−62.974 ± 11.080	${0.788}_{-0.089}^{+0.089}$	L
05342386-0515403	5	34.418 ± 3.170	${0.724}_{-0.024}^{+0.024}$	L
03443444+3206250	2	23.622 ± 6.450	${0.819}_{-0.188}^{+0.181}$	P
03292204+3124153	1	⋯	⋯	L

Note. A sample of the fit parameter table, which is provided in full online. Values for γ and q are not provided for single-visit systems, as they can only be determined from multi-epoch sources.

^aConfidence; L indicates likely binary systems and P indicates potential binary systems. (This table is available in its entirety as supporting data in the online version of this article.)

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4.2.1. Cluster Membership

Binaries that are physically bound to a cluster must have systemic velocities consistent with the cluster's mean velocity and overall velocity dispersion; if not, they would kinematically separate in short order. To evaluate membership status, we compare the systemic velocity measured for each binary in our sample to the radial velocity of the cluster to which it is presumed to belong. Figure 9 shows the velocity offset between the systemic velocities measured for binaries in each IN-SYNC cluster field and that cluster's mean RV. We conservatively adopt a threshold of ±10 km s⁻¹, corresponding to a ∼3σ error for a typical individual velocity measurement in our sample (Section 3.3), to identify systems with systemic velocities consistent with membership in each cluster. Of the 52 systems with more than one epoch of APOGEE spectra, we find 38 have systemic velocities that appear consistent with membership. Specifically, we find 22/26 binaries in the IC 348 field have a systemic velocity consistent with membership; similarly, we find 10/14, 3/6, 3/4, and 0/2 binaries in the Orion A, Pleiades, NGC 2264 and NGC 1333 fields are likely members of the targeted stellar population. We also calculate the velocity dispersion of these likely cluster members and compare with values reported in the literature for each cluster: ${\sigma }_{348}=3.23$ km s⁻¹ (0.72 from Cottaar et al. 2015), ${\sigma }_{{Orion}}=3.46$ km s⁻¹ (2.5 from Da Rio et al. 2017), ${\sigma }_{2264}=6.03$ km s⁻¹ (3.5 from Fűrész et al. 2006), and ${\sigma }_{{Pleiades}}=3.53$ km s⁻¹ (1.02 from Mermilliod et al. 2009). In all cases, the dispersions we measure from the SB2 population exceed those measured previously for the not-obviously-RV variable cluster members. The large velocity dispersions are almost certainly a product of the larger uncertainties associated with the systemic velocities we measure, however; the uncertainties on the systemic velocities are typically at the few-km s⁻¹ level, of the same order as our measured velocity dispersions and significantly larger than the uncertainties associated with the non-variable sources in each cluster.

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In the case of Orion A, we can compare our simple kinematic membership determination with the membership probabilities calculated by Bouy et al. (2014) from astrometric and photometric measurements. Of the 65 binaries we identify in the Orion A fields, 14 have counterparts within 3 arcseconds in the Bouy et al. catalog (note that this is not the same 14 systems as those in the previous paragraph). Only three of these 14, however, have multiple APOGEE observations, as required to estimate their systemic velocities. Of those three, all have systemic velocities that meet our conservative criteria for membership status, although two have relatively large δRV values: 2MJ05345563−0601036 (γ = 26.01 ± 5.06, Bouy probability 12.8%), 2MJ05352989−0512103 (γ = 32.46 ± 4.33, Bouy probability 1.8%), 2MJ05364717−0522500 (γ = 33.42 ± 7.92, Bouy probability 7.1%). The remaining 11 systems are single-epoch sources, so we can do no better than to check if the component RVs bound the mean RV of Orion. In this regard 10/11 of the single-epoch systems are potential Orion members, though Bouy et al. (2014) infer a 0% membership probability for 9/10 of these systems. For the 11th system, 2MJ05341347−0423539, we find component RVs of 38.2 ± 1.8 km s⁻¹, and 56.5 ± 1.8 km s⁻¹, which are both higher than the mean RV of the Orion population, while Bouy et al. (2014) infer a membership probability of 42.7%. Probabilities for all 14 systems can be found in the Appendix.

4.2.2. IC 348 Velocity Dispersion

For the 22 binaries with systemic velocities consistent with membership in IC 348, we can test if the dispersion in our derived systemic velocities is consistent with the value of 0.72 km s⁻¹ measured by Cottaar et al. (2015) from the full APOGEE data set for this cluster. To do so, we compare the dispersion measured from our binary sample with that predicted by simulations incorporating the Cottaar et al. (2015) dispersion and the uncertainties in our measured systemic velocities. This simulation has three steps:

• 1.  
  Initialize a sample of 22 synthetic systemic velocities randomly drawn from a normal distribution with a deviation equal to the dispersion reported in Cottaar et al. (2015).
• 2.  
  To each synthetic systemic velocity, we add a randomly generated velocity error; each source's errors are sampled separately from normal distributions with standard deviations scaled to match the uncertainties associated with our individual systemic velocity measurements.
• 3.  
  We then compute the standard deviation of the "measured" systemic velocities in this synthetic cluster sample.

Given the moderate size of our observed sample (22 binaries), we repeat this simulation 50,000 times to determine the distribution of dispersions we could expect to measure from our sample. We find a mean "measured" dispersion of 2.79 km s⁻¹, with a standard deviation of 0.66 km s⁻¹. The actual systemic velocities we measure for IC 348 members have a standard deviation of 3.23 km s⁻¹, which is well within one standard deviation of the mean of the simulated set. Figure 10 shows the cumulative distribution of the synthetic velocity dispersions measured from all 50,000 simulated systemic velocity samples. Our measured dispersion falls at the 77.8th percentile, such that we could expect to measure a larger dispersion ∼22% of the time. We conclude that the systemic velocities we measure are consistent with the dispersion measured by Cottaar et al. (2015), but note that the width of the velocity dispersion measured from our binary sample is still dominated by our measurement errors; more accurate measurements are required to rule out potential differences in the velocity dispersions of single & multiple cluster members.

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We attempt to fit orbits to systems with at least eight epochs of APOGEE spectra that meet our criteria for RV coverage and period significance. Our criteria for acceptable RV coverage is based on a statistic developed by Troup et al. (2016) to describe the fraction of a star's velocity range which is well sampled by the available RV data,

$$\begin{eqnarray}&&{V}_{{cov}}=\displaystyle \frac{N}{N-1}\left(1-\displaystyle \frac{1}{{{RV}}_{{span}}^{2}}\displaystyle \sum _{i=1}^{N}{({{RV}}_{i+1}-{{RV}}_{i})}^{2}\right),\end{eqnarray} \tag{ 5 }$$

where N is the number of epochs, ${{RV}}_{{span}}={{RV}}_{\max }-{{RV}}_{\min }$, and RV_i are the extracted radial velocities (Equation (23), Troup et al. (2016)). We calculate this statistic using the primary and secondary RVs measured for each system and use the average of these two values to characterize the quality of the system's velocity coverage. The utility of the V_cov velocity coverage parameter can be seen in Figure 6 (${{\rm{V}}}_{{cov}}=66.5$%) and Figure 5 (top panel: ${{\rm{V}}}_{{cov}}=86.5$%; bottom panel: ${{\rm{V}}}_{{cov}}=50.4$%). We only attempt to fit orbits to systems with ${{\rm{V}}}_{{cov}}\gt 80 \%$; systems with less coverage are prone to erroneous fits to an eccentric orbit with a prominent velocity maxima near periastron in the unsampled portion of the orbit.

We also limit our orbit fits to sources whose period determinations have false alarm probabilities <3%. We measure periods by computing a Lomb-Scargle periodogram over a range of periods tuned to the temporal sampling of each system: the periodogram is computed for periods as long as four times the time between the minimum RV and the nearest RV measurement which differs by 80% of the total RV span (${{RV}}_{\max }-{{RV}}_{\min }$). We use this initial periodogram to identify the most likely/significant periods, and recompute their significance with more densely sampled periodograms computed for a narrow period range ($\delta P\pm 2 \%$), and retain the period with the lowest false alarm probability.

Taken together, our criteria for performing a full orbital fit are APOGEE RVs from at least eight epochs (of which there are ten sources), velocity coverage (V_cov) > 80%, and a period with a false alarm probability of 3% or less. Only two systems from our final sample meet all three requirements for a secure orbital fit: 2M03423215+3229291 (N = 16, velocity coverage 87.1%, period significance 97.9%) and 2M03434101+3237320 (16, 86.5%, 98.2%). Two other systems meet our velocity coverage criteria and have periods with significance >90%: 2M03441568+3231282 and 2M03430679+3148204. The first of these suffers from extremely similar primary and secondary peak heights in the CCFs, making the assignment of RVs ambiguous at all epochs. The second system only exhibits shoulder behavior, where the primary and putative secondary CCF peaks are merged at all epochs, such that our RV-extraction method fails to provide robust primary and secondary RVs.

We fit orbital parameters to these two systems using the IDL routine RVfit by Iglesias-Marzoa et al. (2015). RVfit uses a simulated annealing algorithm, which is a Monte-Carlo method relying on random sampling, to fit Keplerian orbits to sets of RVs. The orbital parameters that we determine for these two systems, along with their associated uncertainties, are given in Table 3. Phased orbits are plotted in Figure 11.

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Table 3.  Orbital Parameters

2Mass ID	03423215+3229291	03434101+3237320
Period (days)	2.372 ± 0.001	10.560 ± 0.001
Tp (HJD)	2456169.5 ± 0.1	2456170.7 ± 0.1
Eccentricity	0.006 ± 0.005	0.319 ± 0.001
ω (deg)	252.29 ± 1.36	174.91 ± 0.71
K1 (km s−1)	24.26 ± 0.08	64.42 ± 0.28
K2 (km s−1)	27.25 ± 0.07	68.74 ± 0.28
q (M2/M1)	0.890 ± 0.004	0.937 ± 0.006
Δq	0.007	0.005
γ (km s−1)	−31.10 ± 0.07	21.93 ± 0.07
${\rm{\Delta }}\gamma$	0.05	0.177

Note. Δq and ${\rm{\Delta }}\gamma$ are the difference between the mass ratio and systemic velocity derived using the Wilson plots and those returned from the RVfit routine. All four measures lie within the combined uncertainties.

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Note that RVfit requires the user to define upper and lower bounds for the seven fit parameters (systemic velocity; eccentricity, period; angle and time of periastron; and component velocity amplitudes, K₁ and K₂). and additionally returns an estimate for the mass ratio. The upper and lower bounds for each orbital parameter were

• Eccentricity: zero to one.
• Angle of periastron: zero to $2\pi$ radians.
• Time of periastron: the full time span of the source's observations.
• Systemic velocity: γ ± δ, where γ and δ are our systemic velocity estimate and uncertainty, respectively (Section 4.2).
• Velocity amplitudes: ${{RV}}_{\max }+10$ km s⁻¹ and ${{RV}}_{\min }-10$ km s⁻¹, where RV_min and RV_max are the minimum and maximum RVs measured, regardless of component designation.
• Orbital Period: 0 to 4 times the greater of the primary and secondary time spans computed as the time between the minimum RV and the RV which exceeds the minimum RV by at least 80% of the total RV span (${{RV}}_{\max }-{{RV}}_{\min }$).

Both sources are located in the IC 348 field, however the systemic velocities obtained from the orbit fit (in good agreement with those obtained from the Wilson plot) indicate that neither system is a member of the IC 348 cluster. Both systems have mass ratios implying near equal-mass components, with photometric colors suggesting an early M spectral type for 2M03423215+3229291 (J-K = 0.88), and spectra in the literature indicating a solar-like primary for 2M03434101+3237320 (Nesterov et al. 1995, G0). Both systems also have relatively short periods, but differ in eccentricity; 2M03423215+3229291 is nearly circular whereas 2M03434101+3237320 is decidedly non-circular, with a robust eccentricity of e ∼ 0.3. We note that Cieza & Baliber (2006) measure a 2.3d photometric period for 2M0342315+3229291 which agrees quite well with our spectroscopically determined period, suggesting that the system may be either tidally distorted or eclipsing.