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no significant RV variation (and therefore fall into the SM class). Many of these are likely long-period binaries that are outside of our detection limits, as the hard-soft boundary for solar-type stars in M35 is ∼ 10 $^{5}$− 10 6 days, and we only detect binaries with P ≲ 10 4 days (Geller & Mathieu, in preparation). 

## 5.2. Spatial Distribution and Mass Segregation 

In Figure 9 we compare the cumulative projected ra- dial distributions of the single and binary members of M35. We have attempted to reduce the contamination from undetected binaries within our single-star sample by only including stars with no detectable RV variation (SM) that are fainter and bluer than the dashed gray line in Figure 8. This conservative cut removes large- q (i.e., high total mass) binaries that have periods longer than our detection limit. We have not applied any correc- tion for the spatial bias found in our observations (Sec- tion 2.4), because this bias will be present in both the single- and binary-star samples and should therefore not effect this analysis. A Kolmogorov-Smirnov test shows no significant difference between these two populations with a value of 60%. We therefore conclude that the solar-type main-sequence binaries in M35 show no evi- dence for central concentration as compared to the single stars. 

Mathieu (1983) finds a half-mass relaxation time for the cluster of 150 Myr, comparable to the cluster age. This study of the radial spatial distributions for proper- motion-selected member stars in the 8 . 0 < V < 14 . 5 ( ∼ 4.4 - 1.2 M ⊙ ) range revealed mass segregation only among stars more massive than 2 M ⊙ . The degree of seg- regation lessens with decreasing mass, and is largely non- existent among solar-like stars. McNamara & Sekiguchi (1986b) found similar results in their proper-motion se- lected sample, which covered stars down to V = 14 . 5 ( ∼ 1.2 M ⊙ ). We only include primary stars with masses of 1.6 - 0.8 M ⊙ , and therefore most of our binaries have total masses that are lower than the higher-mass stars that have been shown to be mass segregated. Mathieu (1983) found that M35 is fit well with a multi-mass King model. In such models the reduction in mass segregation for lower-mass systems derives from more severe tidal truncation of higher-dispersion velocity distributions in a cluster potential dominated by the solar-like stars. 

To determine the true RV dispersion of the cluster, we follow the procedure of Geller et al. (2008). We first limit our sample to only include SM stars that have v sin i ≤ 10 km s − $^{1}$. We limit the v sin i value to ensure that we only use the highest precision RV measurements for this anal- ysis. These narrow-lined stars have a precision σ$_{i}$ = 0.5 km s − $^{1}$. We will discuss the effect of undetected binaries that likely remain within this sample in Section 5.3.1. 

Using this sample of 67 SM stars, we first derive the ob- served dispersion σ$_{obs}$ by taking the standard deviation of the mean RVs for each star, and we find σ$_{obs}$ = 0 . 86 ± 0 . 07 km s − $^{1}$. This observed dispersion is a function of our measurement precision and is also inflated by undetected binaries. Therefore, in order to derive the true RV dis- persion, we must first account for the precision on these 

## 5.3. Cluster Radial-Velocity Dispersion 

RV measurements. We derive 8 the “combined RV dis- persion” σ$_{cb}$ from : 

Here, n = 67 is the number of stars used in this analysis, and ξ$_{i}$ is the mean error of the RV for the i th star defined as, 

where RV$_{j}$ is one of the m number of RV measurements for a given star i , and RV$_{i}$ is the mean RV for that star. We note that the second term in Equation 3 is very nearly equal to σ 2 i / 3, as we have 3 RVs for most of the stars in this sample, and these narrow-lined stars all have the same precision of σ$_{i}$ = 0 . 5 km s − $^{1}$. Following this proce- dure, we derive a combined dispersion of σ$_{cb}$ = 0 . 81 ± 0 . 08 km s − $^{1}$. The error on this combined dispersion is almost entirely due to the statistical error on σ$_{obs}$ . 

We find no significant difference in the combined RV dispersion of the SM or BM stars. For the BM stars, we use the γ -RVs in place of the mean RVs, and substi- tute the measurement precision for the standard devia- tion portion in Equation 4. There is also no significant variation in the combined RV dispersion as a function of radius, although due to the small sample sizes our binned RV dispersion values have large uncertainties (of 0.1 - 0.15 km s − 1 for bins of 10 arcmin). 

This combined RV dispersion is inflated by undetected binaries. In the following section, we quantify this effect and apply the correction to derive the true RV dispersion of M35, an improvement on the procedure of Geller et al. (2008). 

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