8 Geller et al. Class Number SM 305 SN 452 BM 39 BN 17 BLM 16 BU 16 BLN 68 U 231 Fig. 8.— Color-magnitude diagram of M35 including only cluster members (P $_{RV}$≥ 50%) with photometry from WIYN 0.9m (source 2). We plot the RV variables with orbital so- lutions with circles and without orbital solutions with dia- monds. We show the 180 Myr Padova isochrone as the black line. The solid gray line shows where binaries with mass ra- tios of 1.0 lie on the CMD, and the dashed gray line shows the deviation from the isochrone of twice the photometric error. We follow the same classification system as Geller et al. (2008) and Hole et al. (2009) in order to provide a qualitative guide to a given star’s mem- bership and variability, in addition to the calculated RV memberships and e/i values. We provide these classifications for all observed stars, while the member- ships and e/i values are only provided for a subset of appropriate stars. etry is of higher precision than that taken on the Bur- rell Schmidt (see Section 2.1). We also plot a 180 Myr Padova isochrone using the cluster parameters derived by Kalirai et al. (2003) in the black curve. Binaries with orbital solutions are circled and RV variables without or- bital solutions are marked by diamonds. For stars with e/i< 4, we classify those with P$_{RV}$ ≥ 50% as single members (SM), and those with P$_{RV}$ < 50% as single non-members (SN). If a star has e/i ≥ 4 and enough measurements from which we are able to derive an or- bital solution, we use the γ -RV to compute a secure RV membership. For these binaries, we classify those with P$_{RV}$ ≥ 50% as binary members (BM) and those with P$_{RV}$ < 50% as binary non-members (BN). For RV vari- ables without orbital solutions, we split our classifica- tions into three categories. If the mean RV results in P$_{RV}$ ≥ 50%, we classify the system as a binary likely mem- ber (BLM). If the mean RV results in P$_{RV}$ < 50% but the range of measured RVs includes the cluster mean RV, we classify the system as a binary with unknown member- ship (BU). Finally, if the RV measurements for a given star all lie either at a lower or higher RV than the clus- ter distribution, we classify the system as a binary likely non-member (BLN), since it is unlikely that any orbital solution could place the binary within the cluster distri- bution. We classify stars with < 3 RV measurements as unknown (U), as these stars do not meet our minimum criterion for deriving RV memberships or e/i measure- ments. In the following analysis, we include the SM, BM and BLM stars as cluster members. Including these stars, we find 360 total cluster members in our sample. We list the number of stars within each class in Table 2. Additionally, we use the Padova isochrone to plot the location on the CMD of binaries with mass ratios q = 1, shown as the gray line. We note that there are a number of stars observed brighter and to the red of this line, some that we have not identified as RV variables. In this loca- tion on the CMD one would expect to find either higher- order systems or field stars. There are 33 RV members that lie above the q = 1 line; 22 are single and 11 show RV variability. We expect a 6% field star contamination within the cluster members sample (Section 4.1). If we include only the 309 cluster members that have photom- etry from the WIYN 0.9m (and are therefore shown in Figure 8), this results in 19 possible field stars; including our entire cluster member sample results in 22 possible field stars. Therefore field star contamination cannot ac- count for all of these sources, suggesting that a subset of these stars are indeed higher-order systems. We also note that there are an additional 12 cluster members with photometry from the Burrell Schmidt that lie above the q = 1 line, but recall that this source of photometry is of poorer precision. Finally, for use in Sections 5.2, we follow a similar pro- cedure as Montgomery et al. (1993) to attempt to photo- metrically identify binaries that lie far from the isochrone on the CMD. We derive the distance of each star from the main-sequence isochrone and fit a Gaussian function rep- resenting the photometric error distribution to the dis- tribution of these distances. We notice a clear excess in the observed distribution from the Gaussian fit at 2 σ , shown as the dashed gray line in Figure 8. We attribute this excess to photometric binaries. A 1 M ⊙ star in M35 with the additional light from a companion of mass-ratio q = 0 . 78 would lie on this line. Therefore sources ob- served above this line are likely binaries with larger mass ratios ( q > 0 . 78), or very infrequently, field stars. We observe 42 cluster members above this line that show In the following section, we present a CMD for M35 cleaned of field star contamination (Section 5.1), com- pare the spatial distribution of the single and binary members (Section 5.2), and analyze the RV dispersion of the cluster (Section 5.3). In Figure 8, we show the CMD for all RV cluster mem- bers in M35 from this study for which we have pho- tometry from the WIYN 0.9m, as this set of photom- 5. DISCUSSION 5.1. Color-Magnitude Diagram TABLE 2 Number of Stars or Star Systems Within Each Membership Class 4.3. Membership Classification of Radial-Velocity Variable Stars