WIYN OPEN CLUSTER STUDY. LIX. RADIAL VELOCITY MEMBERSHIP OF THE EVOLVED POPULATION OF THE OLD OPEN CLUSTER NGC 6791

Our ongoing spectroscopic survey of NGC 6791 has, to date, yielded 1189 RV measurements of 260 stars. Observations utilize the Hydra Multi-Object Spectrograph (MOS) on the WIYN 3.5 m telescope, capable of obtaining ∼70 stellar spectra simultaneously over a 1° field of view. We use 31 diameter fibers along with the bench spectrograph echelle grating, resulting in a spectral resolution of ∼20,000 (15 km s⁻¹). Due to the number of source fibers, the echelle grating is not cross-dispersed and the X14 filter is used to isolate the 11th spectral order. This 250 Å wide region centered at 5125 Å contains many stellar absorption lines including the Mg i b triplet.

To begin our observing program, the catalog is split into bright (12 < g' < 15.9) and faint (12.9 < g' < 16.8) sub-samples to prevent on-chip contamination between source spectra. Bright and faint Hydra configurations generated from these sub-samples are observed for one and two hours, respectively, to ensure a sufficient signal-to-noise ratio (S/N ≃ 18 per resolution element under ideal observing conditions for all targets). Integrations are split into three equal exposures to reduce the impact of cosmic ray contamination. Of the 81 available fibers, each configuration observes a maximum of 71 stellar spectra with 10 fibers reserved for sky sampling. As accurate wavelength calibration is vital to this program's success, comparison ThAr emission lamp spectra are taken before and after each configuration to correct for wavelength shifts during the observing sequence. Dome flat-field images are also taken for each configuration to aid in throughput correction and aperture identification during spectral extraction.

Target prioritization aims to efficiently determine the RV membership of proper-motion-selected stars. Monte Carlo (MC) simulations have shown that three observations over the course of 200 days can determine, to ∼90% confidence, whether a star has a constant or variable RV for binary orbital periods up to 1000 days (following Geller & Mathieu 2012). As such, for a given observing run, we place stars with one observation at the highest priority followed by twice-observed likely members (stars whose first two RV measurements fall within the cluster's RV distribution), twice-observed likely non-members, unobserved stars, and finally, stars with three or more observations over the course of at least 200 days. The 12 blue HB candidates from P11 were given the highest priority until their RV memberships were determined. Unlike previous WOCS RV studies, we have not yet chosen to prioritize binary orbit determinations for velocity-variable stars in favor of maximizing the number of single stars with determined RV memberships. Stars with the highest PM probabilities were also prioritized in our observations.

All WOCS image processing and data reduction are completed using standard IRAF⁵ tasks. Our routine is as follows. Bias subtraction from an overscan region is first applied to raw science and flat-field images. Spectral extraction, flat-field correction, throughput correction, and dispersion solutions are computed and applied with the dohydra reduction task. Remaining sky fibers are visually inspected for quality and median combined to perform sky subtraction. The three fully reduced spectra from each configuration are then median combined to improve S/N and remove cosmic ray contamination.

Fourier cross-correlation functions (CCFs) between stellar spectra and a zero-velocity template are computed using the IRAF task fxcor. A Gaussian fit to the CCF peak provides the relative velocity shift between the two spectra, which is then corrected for the Earth's orbital motion to produce a heliocentric RV. Geller et al. (2008) define a minimum CCF peak height of 0.4 as sufficient correlation for a secure RV measurement utilizing the same observational and data reduction schemes. We adopt this same minimum CCF peak value to identify acceptable RV measurements. Finally, systematic fiber-to-fiber RV offsets derived by Geller et al. (2008) are then applied to the computed heliocentric RV, yielding our final RV measurement.

In the case of double-lined spectroscopic binaries, we are able to retrieve the radial velocities of both stars simultaneously using the two-dimensional correlation routine TODCOR (Zucker & Mazeh 1994). Using a zero-velocity template for each star, we fit a two-dimensional correlation that is able to effectively decompose strongly blended lines. The result of this routine is a heliocentric RV for each star in the system that is then corrected for fiber–fiber variations.

As in previous WOCS surveys, the standard Fourier cross-correlation template is a high-S/N solar spectrum from a sky flat. For most stars in the NGC 6791 sample, a strong correlation peak is found using the solar template. However, a handful of RGs in our sample exhibit the Swan C₂ absorption band near 5165 Å that prevents precise RV measurements against a solar template. For this subset, we use the spectrum of the K1 III star, HD172171, from the publicly available ELODIE Stellar Library (Prugniel & Soubiran 2001) as our template. This spectrum is provided at zero velocity and is set to a zero-heliocentric velocity for cross-correlation. Containing the same C₂ absorption feature and at a spectral resolution of ∼42,000, we retrieve strong correlation peaks for this subset of RGs in our sample. Additionally, the RV zero points for cluster members found using the solar and RG template are consistent.

To assess our measurement precision, we fit the standard deviations of RV measurements with a χ² distribution following Geller et al. (2008). For consistency across our sample, we take only objects with at least three observations and use only the first three RV measurements when calculating standard deviations (σ_obs). The χ² function models the distribution of error for measurements of single (non-velocity-variable) stars. We fit the following form,

$$\begin{equation} \chi ^2(\sigma _{\rm obs})= A\left(\frac{2}{\sigma ^2_i}\right) (\sigma _{{\rm obs}}) {\rm exp} \left(-\frac{\sigma ^2_{\rm obs}}{\sigma ^2_i}\right), \end{equation} \tag{ 1 }$$

with two free parameters: A, the χ² normalization, and σ_i, our RV measurement precision. The velocity variability of binary stars in our sample inflates the tail of our error distribution with sources of high measurement deviation. To account for this, we fit χ² only to data within a σ_max cutoff to limit binary contamination. Varying σ_max at 0.1 km s⁻¹ intervals, we find that a value of σ_max = 0.7 km s⁻¹ produces the lowest residuals in the fit and we adopt this value as our cutoff.

Figure 2 presents our empirical RV standard deviations with the best-fit error distribution over-plotted as a solid line. The dashed vertical line signifies the σ_max cutoff. Contamination from velocity variables can be clearly seen exceeding the χ² fit beyond the cutoff. We find a best-fit precision of σ_i = 0.38 ± 0.02 km s⁻¹ that is insensitive to the value of σ_max chosen, producing a consistent result for σ_max = 0.6–0.8 km s⁻¹. Our best-fit measurement precision is consistent with that found in the Geller et al. (2008) study of NGC 188 (σ_i = 0.4 km s⁻¹).

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From our RV precision, we define a minimum standard deviation in observed RV for a star to be characterized as "velocity variable." As in Geller et al. (2008), we use the quantity e/i to define velocity variables where e is the observed standard deviation of a given star (σ_obs) and i denotes our precision (σ_i). Stars with e/i > 4 are designated as velocity variables. The e/i limit is plotted as the vertical dotted line in Figure 2, where stars falling right of this line are considered to be velocity variable.

The results of our RV survey are summarized in Table 1, where we present 10 lines selected to illustrate the table format and relevant comment and class fields. The full table is available in the online journal. For each star, we include the WOCS ID (ID_W), R.A. and declination (J2000), g' magnitude, and (g'-r') color from the P11 catalog. The succeeding columns present the number of WIYN RV measurements (N_obs), mean RV ($\overline{\rm RV}$), PM membership probability (P_μ), RV membership probability (P_RV), e/i value, membership class (detailed in Section 5.2), and comments. Both the $\overline{\rm RV}$ and e/i value are calculated using an error-weighted mean. RV membership probabilities in parentheses indicate a tentative value for velocity variable stars based on their mean RV ($P_{\overline{\rm RV}}$), which remains uncertain until a binary orbital solution is found. In the comment field, we highlight the following stars: velocity variables as single- or double-lined spectroscopic binaries ("SB1" and "SB2," respectively), RGs containing strong C₂ absorption for which a K iii stellar template was used ("C₂ Band"), BSSs ("BSS"), and finally, rapidly rotating stars ("RR"), defined as having a CCF FWHM ⩾60 km s⁻¹, are presented with their projected v sin i rotational velocity in parentheses.

Table 1. Radial Velocity Summary Table

IDW	R.A.	Decl.	g'	g'-r'	Nobs	$\overline{\rm RV}$	Pμ	PRV a	e/i	Class	Comment
1002	19:20:55.11	37:47:16.3	14.63	1.41	5	−47.51	99	96	0.31	SM
1003	19:20:50.04	37:47:28.2	13.50	0.95	1	−49.49	10	⋅⋅⋅	⋅⋅⋅	U
1004	19:20:58.63	37:47:40.5	11.99	0.88	3	−13.21	10	0	0.70	SN
2003	19:20:47.66	37:47:32.3	15.33	1.23	3	−54.20	99	(0)	53.30	BU	SB1
3006	19:20:49.72	37:43:42.7	14.83	1.50	4	−46.47	99	94	1.30	SM	C2 Band
4003	19:20:59.95	37:46:03.3	15.15	0.28	13	−44.76	99	54	1.62	SM	BSS
6006	19:20:49.65	37:44:07.8	15.18	1.10	3	−49.03	10	(89)	4.26	BLM	SB1
7021	19:20:33.03	37:55:55.9	14.21	1.10	14	−75.11	41	(0)	11.00	BLN	SB1
7045	19:21:22.34	38:07:57.1	14.04	0.39	10	−1.88	37	(0)	3.22	SN	RR (113.1 km s−1)
43033	19:22:15.20	37:48:47.2	15.82	0.55	6	−41.70	6	(0)	79.28	BU	SB2

Notes. Photometry, coordinates, and proper motion membership probabilities come from I. Platais et al (2014, in preparation). ^aRV membership probabilities in parenthesis indicate the probability of the mean RV for velocity variables ($P_{\overline{\rm RV}}$) and remain uncertain until a binary orbital solution is found.

Only a portion of this table is shown here to demonstrate its form and content. Machine-readable and Virtual Observatory (VO) versions of the full table are available.

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Stars designated as RR have reduced RV measurement precision due to their broadened photospheric absorption lines and correspondingly broad CCF peaks. The Geller et al. (2010) study of the young open cluster M35 found that RV measurement precision scaled linearly with the projected vsin i rotational velocity and had the functional form σ_i = 0.38 + 0.012(vsin i) km s⁻¹. We find that 10 stars in our sample (∼4%) are defined as RRs and following Geller et al. (2010), we derive vsin i for these stars from their CCF FWHM. The largest vsin i found is ∼110 km s⁻¹. For these stars, the e/i value and velocity-variable designation are computed based on their vsin i dependent σ_i value. None of the 10 RRs are RGB or RC stars as expected; however, 3 are binary BSS candidates (see Section 6.3).

Table 2 presents every NGC 6791 RV measurement and CCF peak height obtained with the WIYN telescope through 2014 February. We have included only a selection of the table here for brevity. The full table is available in the online journal. The right two columns are reserved for SB2s when a velocity and CCF peak height for each star can be obtained.

Calculations of RV membership require a decomposition of the RV distribution into field star and cluster distributions. To separate these two components, we fit our distribution of RV measurements for the entire sample (P_μ ⩾ 1%) simultaneously with two Gaussians. Figure 4 presents our RV measurement histogram of single, non-rapidly rotating stars with the best-fit field star and cluster population models over-plotted in red and blue, respectively. The fit is made to an 80 km s⁻¹ region centered around the cluster peak. From this procedure, we find a cluster RV of −47.40 ± 0.13 km s⁻¹ and RV standard deviation of σ₆₇₉₁ = 1.1 ± 0.1 km s⁻¹. The true one-dimensional velocity dispersion of the cluster, σ_c, is less than the Gaussian fit σ₆₇₉₁ due to inflation from binary contamination and our measurement precision. These issues are addressed in Section 6.4.

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With a model of the two populations, we define RV membership with the following equation:

$$\begin{equation} P_{\rm RV}(v)=\frac{F_{\rm cluster}(v)}{F_{\rm field}(v) + F_{\rm cluster}(v)}, \end{equation} \tag{ 2 }$$

where F_cluster(v) is the cluster model value for the stellar RV, v, and F_field(v) is the field star model value for the same RV (Vasilevskis et al. 1958). We find the field distribution to be well separated from the field velocity center (−30.85 km s⁻¹), providing a good separation in membership probability between cluster and field stars.

Figure 5 presents a histogram of our RV membership probabilities for single stars. As noted above, a clear separation is found between cluster members and field stars. In keeping with previous WOCS practice, we set our cutoff for RV membership at P_RV = 50%, designated by the vertical dashed line.

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With our membership scheme established, we use the field distribution presented in Figure 4 to estimate the number of field star contaminants expected among our RV members. By integrating the model field distribution over RVs producing P_RV ⩾ 50%, we expect seven of our RV members to be field stars.

From our RV membership determination, we define a star's membership "Class," given in the penultimate column of Table 1, following Geller et al. (2008). As presented in Section 3.1, MC simulations show that three RV measurements over the course of 200 days can detect, to ∼90% confidence, binaries with orbital periods up to 1000 days. This baseline in time and number of observations is required for membership determination and as such, any star not meeting this criterion is given an unknown (U) classification in Table 1. A single star (e/i ⩽ 4) meeting these conditions is designated a single member (SM) if P_RV ⩾ 50% or a single non-member (SN) if its RV probability falls below this criterion. A velocity-variable star (e/i > 4) can fall into three classes: (1) binary likely member (BLM) if the membership probability based on its mean RV ($P_{\overline{\rm RV}}$) exceeds our criterion, (2) binary unknown (BU) if $P_{\overline{\rm RV}}$ falls below 50% but the range of measured RV crosses the cluster mean, or (3) binary likely non-member (BLN) if the range in measured RV does not cross the cluster mean. Once orbital solutions are found for binary systems, P_RV will be computed based on the center-of-mass velocity. At that point, binary stars will be classified as binary members (BM) or binary non-members (BN) with the same criteria as single stars. Table 3 lists the number of stars falling within each membership class.

Of the 280 stars in our sample, 193 are single (non-velocity variable) stars with RV membership determinations. Figure 6 presents the comparison of RV and PM membership probabilities for all single stars. The vertical dashed line marks the RV (50%) membership criterion. All blue HB candidates from P11 are presented as blue diamonds. Note that some blue HB candidates are velocity variables and thus are presented as blue diamonds without central points. Their RV membership positions represent the probabilities of their mean RV ($P_{\overline{\rm RV}}$) and are subject to change until an orbital solution is found (see Section 6.2 for full details). In Figure 6, we also present the marginal distributions along each axis in the top and right panels.

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Integrating the PM membership probabilities of stars with RV membership determinations (193), 106 ± 3 cluster members are predicted, in good agreement with the 101 RV members found. Breaking the stars with RV membership determinations into three subsamples based on their PM membership probabilities we find:

• 1.  
  86 ± 1 cluster members out of 89 are predicted in the P_μ > 80% sample while 81 RV members are found,
• 2.  
  17 ± 2 cluster members out of 37 are predicted from the 19% ⩽ P_μ ⩽ 80% sample while 11 RV members are found,
• 3.  
  3 ± 1 cluster members out of 67 are predicted from the 1% ⩽ P_μ < 19% sample while 9 RV members are found.

Generally, we find fewer RV cluster members than the PM membership probabilities would suggest. However, for stars with 1% ⩽ P_μ < 19%, we find ∼6 more RV members than the PM prediction. Recalling that seven field stars are expected among our RV members (Section 5.2), it is reasonable to suspect that some of our field contaminants are likely to be drawn from the nine RV members with 1% ⩽ P_μ < 19%. As such, we note them in our cleaned CMD (gray points; Figure 7(b)).

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However, of these nine low-P_μ RV members, seven fall on the cluster RGB or RC in the cleaned CMD. Based on the CMD distribution of the 67 stars with 1% ⩽ P_μ < 19% and RV membership determinations, a random draw of nine such stars would predict only one to fall in the RGB/RC region. For this reason we suspect that most of these nine stars are in fact cluster members and include them with equal significance in our analyses below.

Three-dimensional kinematic membership determinations using both PM and RV measurements allow us to construct a cleaned CMD for the evolved population of NGC 6791. Figure 7(a) displays the PM probable members (P_μ ⩾ 19%) within our magnitude limit as black circles, with the 12 blue HB candidates marked in blue diamonds. Stars with P_μ < 19% are shown as light gray points. The addition of RV membership information produces Figure 7(b) and represents the most secure, systematic membership determination to date for this cluster. In this lower panel, single members (SMs) are marked as black points. Circled points signifying binary likely members (BLMs).

In Figure 7(b), we also include three candidate binary members falling near the BSS population as gray "⊗" symbols. Although these stars are currently listed as BUs or BLNs in Table 1, based on their RV measurements to date, we feel they have a high likelihood of becoming members once orbital solutions are found. The two BUs (WOCS 54008 and 62041) have large RV variations and few observations, which we suspect are short-period binaries whose mean RV bears little significance on their RV memberships. The other is a BLN (WOCS 46008) whose mean RV is within 3σ of the cluster mean velocity. Due to the astrophysical significance of binary stars to the formation of BSSs (see Section 6.3), we note them here for completeness but do not include them in the analysis below.

The lower panel of Figure 7 reveals a richly populated RGB and RC with 97 SM and BLM stars. We find an RG/RC binary fraction of 6.2% for orbits up to 1000 days, assuming that all BLMs are indeed members (fraction not corrected for detection incompleteness). This binary fraction is less than the global RG/RC binary fraction due to our insensitivity to long-period binaries. Additionally, it is likely not representative of the main sequence binary population given that the increased radii of post-main-sequence stars will alter or envelop the orbits of close binary companions. (We have not included the three blue HB candidates found just to the blue of the RC in the above analysis, but we comment on them in Section 6.2.)

The width of the RGB is roughly (g'-r') ∼ 0.2 mag, broader than expected for a single-age stellar population. Brogaard et al. (2012) derived a differential reddening map that, when applied on a star-by-star basis, significantly narrowed the RGB.

With the RG/RC and BSS populations well-defined, we empirically classify BSSs within our sample as members falling blue of (g'-r') = 0.7. We designate eight SM and BLM stars as BSSs and find four to be velocity variable. The BSS population is discussed further in Section 6.3.

Three stars in our CMD are assigned to neither the RG/RC nor BSS population. They are the two brightest, WOCS 57012 (SM; P_RV = 55%, P_μ = 91%) and 58012 (RV member only; P_RV = 92%, P_μ = 14%), and the reddest, WOCS 9018 (SM; P_RV = 95%, P_μ = 79%), stars on the cleaned CMD (Figure 7(b)). Their CMD locations are not predicted by any phase of stellar evolution at the age of NGC 6791, nor do we know of similarly located members in other open clusters. Even given our typically high RV membership probabilities, field contamination cannot be ruled out. Indeed, as noted earlier, our membership probability model (Figure 4) predicts seven field contaminants among the RV members.

Table 4 summarizes our RV membership results for the 12 blue HB candidates from P11. Here, we provide the WOCS IDs (ID_W) with a cross-reference to the ID given in P11 (ID_P11) in the first two columns. We find four of these stars to be SMs. Three (WOCS 2001, 23004, 15007) fall just to the blue of the RC (see CMD in Figure 7(b)) and the fourth, WOCS 4003, is the bluest star in the cleaned CMD, lying in the BSS regime.

Table 4. NGC 6791 Blue HB Proper Motion Candidate Members

IDW	IDP11	R.A.	Decl.	g'	g'-r'	Pμ	$\overline{\rm {RV}}$	σRV	PRV a	Comment b
							(km s−1)	(km s−1)
23004	69976	19:20:46.00	37:47:54.8	14.98	1.04	95	−47.04	0.34	96	2–45
2001	65895	19:20:51.37	37:46:30.5	14.79	1.07	99	−47.86	0.34	95	NW-20
15007	60456	19:21:07.20	37:44:34.7	15.19	1.02	99	−44.80	0.51	56	3–27
4003	64589	19:20:59.95	37:46:03.3	15.15	0.28	99	−44.76	0.62	54	2–17
46008	64067	19:20:34.98	37:45:52.3	15.25	0.39	99	−40.89	5.29	(0)	S2746; RR; SB1
7021	89107	19:20:33.03	37:55:55.9	14.21	1.10	41	−75.11	4.18	(0)	S2382; SB1
8031	93625	19:21:42.32	37:58:05.5	15.16	0.59	58	−18.89	4.25	(0)	SB1
18007	58857	19:21:02.55	37:43:59.5	15.19	0.53	99	15.57	0.81	0	3–22
9007	69734	19:21:08.07	37:47:49.4	14.57	1.10	99	−22.84	0.33	0	3–33
21016	82982	19:21:14.70	37:53:07.5	15.28	0.90	53	11.47	0.29	0	S14140
19018	52460	19:20:17.44	37:41:23.9	15.12	0.84	42	10.05	0.29	0	S440
11019	45106	19:20:31.40	37:38:09.7	15.00	0.51	27	−54.49	0.28	0	S2101

Notes. Photometry, coordinates, and proper motion membership probabilities come from I. Platais et al (2014, in preparation). ^aRV membership probabilities in parenthesis indicate the probability of the mean RV for velocity variables ($P_{\overline{\rm RV}}$) and remains uncertain until a binary orbital solution is found. ^bStetson et al. (2003) IDs are preceded by an "S," remaining IDs are from Kinman (1965). SB1 marks single line spectroscopic binaries and RR marks rapid rotators.

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Of the remaining eight blue HB candidates, five are single stars that are RV non-members (P_RV = 0). Two, while velocity variable (BLN), have mean velocities far from the cluster mean; with a minimum of 12 RV measurements for each, we conclude that they are also RV non-members. The last blue HB candidate, WOCS 46008, is a velocity variable, rapid rotator listed as a BLN in Table 1. With a mean RV 2.7σ (6.5 km s⁻¹) from the cluster mean velocity, we consider it a potential binary member and include it in Figure 7 as the brightest gray "⊗" symbol in the BSS region of the CMD. An orbital solution will be required to securely determine this star's RV membership.

The results of our RV membership study do not support the presence of a continuous blue HB population suggested by P11. Instead, we find one SM to reside with BSSs in the CMD and three SMs that fall just blue of the RC. This observational finding is consistent with the Brogaard et al. (2012) theoretical conclusion that a blue HB, if one were to exist, would be more luminous than the P11 proposed candidates.

Even so, the three SMs falling near, but to the blue of, the RC remain puzzling as they cannot be explained by the typical photometric error (∼0.02 mag). Although our field star and cluster population model predicts seven field contaminants in Figure 7(b), these three stars have high PM and RV membership probabilities (Table 4), leaving a small chance that all three are field stars.

We speculate that these three may be evolved descendants of BSSs. If, for simplicity, we model these stars with normal stellar evolutionary tracks, we find that all three lie on the giant branch of a 1.3 Gyr isochrone, implying masses of ∼2 M_☉. (Here, we use a reddening of E(g'-r') = 0.165, an extinction of $A_{g^\prime }=0.65$ mag, an age of 8 Gyr, [Fe/H] = +0.30 (Boesgaard et al. 2009), and a distance of 3.8 kpc, obtained by matching Padova isochrones (Bressan et al. 2012) to the NGC 6791 RC and RGB.) This stellar mass is roughly 75% more massive than a typical NGC 6791 giant (1.2 M_☉; Basu et al. 2011). Such a mass is not unprecedented for a BSS, which in this case would have formed ∼1 Gyr ago. We note that it is surprising that all three stars do not have detected velocity variability given the high BSS binary fraction found in NGC 6791 (Section 6.3) and in other open clusters (Geller & Mathieu 2012). This may point to stellar collisions or mergers as the formation mechanism of our evolved BSSs candidates (Leigh & Sills 2011).

The SM status of our fourth blue HB candidate, WOCS 4003 (2–17; Kinman 1965), confirms the membership first proposed by Green et al. (1996) as a blue HB star. A subsequent analysis of this star by Brogaard et al. (2012), however, found its spectral properties to be most consistent with a mass of 1.9 M_☉, whereas the expected mass of an HB star is ∼0.6 M_☉. The large mass along with low luminosity (for a blue HB star) led these authors to conclude a BSS classification.

Again assuming standard stellar evolutionary tracks, we find this star to lie on a ∼0.9 Gyr isochrone with a mass of ∼2 M_☉. We conclude (in agreement with Brogaard et al. 2012) that WOCS 4003 is a BSS member that formed perhaps ∼1 Gyr ago. Given the large mass and non-varying RV, this BSS may also be a candidate for formation via a merger or collision.

Table 5 presents the membership information for BSS members and candidate members. We break our BSS sample into two groups based on their membership likelihood. First, as ordered in Table 5, are SMs and BLMs, totaling eight stars. The second is comprised of three potential BSS members, all velocity variables (BU and BLN), whose large amplitude of variability (e/i > 4) and small number of RV measurements make their RV memberships uncertain. We suspect these stars may be cluster members. They are plotted as gray "⊗" symbols in the BSS region of Figure 7(b).

Table 5. NGC 6791 Blue Straggler Membership

IDW	R.A.	Decl.	g'	g'-r'	Pμ	$\overline{\rm {RV}}$	σRV	PRV a	Comment b
						(km s−1)	(km s−1)
Single Members & Binary Likely Members
4003	19:20:59.95	37:46:03.3	15.15	0.28	99	−44.76	0.62	54	Blue HB Can.
21028	19:21:56.64	37:52:05.8	15.64	0.51	8	−46.06	1.04	92
33025	19:19:52.07	37:48:31.6	16.34	0.45	60	−45.10	0.97	71
70011	19:21:12.68	37:49:48.7	15.83	0.48	97	−47.02	0.37	96
11003	19:20:58.31	37:47:08.1	16.64	0.50	99	−46.07	1.59	(92)	SB1
22004	19:21:01.05	37:47:34.7	16.68	0.47	99	−48.21	3.77	(95)	SB1
57009	19:20:53.91	37:42:26.0	16.27	0.56	99	−49.62	2.11	(75)	SB1
58008	19:20:10.42	37:47:42.1	16.30	0.39	99	−47.76	5.08	(96)	SB1, RR
Candidates
46008	19:20:34.98	37:45:52.3	15.25	0.39	99	−40.05	4.39	(0)	SB1, RR, Blue HB Can.
54008	19:21:10.71	37:45:31.4	15.83	0.29	99	−55.34	10.99	(0)	SB1, RR
62041	19:21:57.88	37:30:56.9	16.36	0.55	2	−53.01	28.80	(0)	SB1

Notes. Photometry, coordinates, and proper motion membership probabilities come from I. Platais et al (2014, in preparation). ^aRV membership probabilities in parenthesis indicate the probability of the mean RV for velocity variables ($P_{\overline{\rm RV}}$) and remain uncertain until a binary orbital solution is found. ^bSB1 marks single line spectroscopic binaries and RR marks rapid rotators.

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We note that one BLM BSS (WOCS 58008) and two binary BSS candidates (WOCS 46008, 54008) are designated as rapid rotators. While orbital solutions are still required to confirm the membership of these stars, the distribution of BSS rotation rates may prove to be a valuable test of BSS formation theories (Sills et al. 2005).

Observations to date yield an NGC 6791 BSS population of eight stars, four being SMs and four being BLMs. Among the eight BSS SMs and BLMs, we find a binary fraction of 50% for binaries with orbits up to 1000 days, assuming that all the BLMs are indeed members. The three candidate BSSs would only increase this binary frequency. This is higher than both the RG/RC binary frequency found above and the main sequence binary fraction determined by the Janes & Kassis (1997) analysis of the CMD binary main sequence (14%). Although still preliminary, the high binary fraction of NGC 6791 BSSs agrees with the findings of Geller & Mathieu (2012) for NGC 188 BSSs (76 ± 19%). This suggests that binaries may play a key role in the formation of BSSs in NGC 6791. A complete analysis of the binary BSS orbital solutions is required before determining the roles of any specific BSS formation mechanism.

Our systematic RV survey finds σ₆₇₉₁ = 1.1 ± 0.1 km s⁻¹ from our Gaussian fitting procedure (Section 5.2). However, undetected binaries in our sample broaden the wings of the RV distribution and inflate our observed dispersion value. Thus, this Gaussian-fit RV dispersion is an upper limit.

Modeling the effects of binarity on the observed RV dispersion is beyond the scope of this paper. Instead, we use the normal probability plot (Chambers et al. 1983) to derive a measure of the observed RV dispersion that is less sensitive to the wings of the distribution. The normal probability plot in Figure 8 compares our mean RV measurements for single stars (open circles) to a normal distribution. Measurements drawn from a normal distribution map into a straight line whose inverse slope corresponds to the standard deviation of the parent distribution, which in this case is the observed RV dispersion (before correction for measurement errors).

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Using the same RV center from our Gaussian fit (Section 5.2), denoted by the dashed vertical line, we fit a line to the central 1.4 km s⁻¹ (vertical dotted lines). We justify fitting to only this central region because this range of data is normally distributed. Fits to more centralized regions reproduce the same result with larger error. Outside this range, it is clear the RV measurements deviate from Gaussian, possibly from binary contamination. Our best-fit line yields an observed RV dispersion of 0.73 ± 0.09 km s⁻¹. We then deconvolve the best fit RV dispersion with our measurement precision (0.38 km s⁻¹) to obtain a true one-dimensional velocity dispersion of σ_c = 0.62 ± 0.10 km s⁻¹.

We calculate the cluster mass using the equation for dynamical mass in projection from Spitzer (1987),

$$\begin{equation} M=\frac{10 \left\langle \sigma _c^2 \right\rangle R_h}{G}, \end{equation} \tag{ 3 }$$

where σ_c is the one-dimensional velocity dispersion of the cluster and R_h is the projected half-mass radius. Equation (3) assumes a gravitational potential energy prefactor of 0.4, the observed (projected) half-mass radius measured, R_h, is three-fourths of the true half-mass radius, and $\sqrt{3}\sigma _c=\sigma _{\rm 3D}$ (Spitzer 1987).

Using R_h = 5.1 ± 0.2 pc from King model fitting (P11), we find a mass of 4600 ± 1500 M_☉. Current literature values for the mass of NGC 6791 based on photometry range from ⩾4000 M_☉ (Kaluzny & Udalski 1992) to ∼5000 M_☉ (P11), in good agreement with our dynamical mass determination. In the context of other open clusters, our derived mass places NGC 6791 in the top 5% of the Piskunov et al. (2008) open cluster sample, complete to 850 pc.

6.5.1. WOCS 54008

6.5.2. WOCS 43033

6.5.3. WOCS 54034

6.5.4. Kepler Selected Targets