content_image/432104.jpg content_image/432103.jpg content_image/432110.jpg
the single-measurement RV precision for that star. We adopt a floor to our precision at 0.5 km s − $^{1}$, as found for our narrow-lined stars, and shown by the break in the dashed line in Figure 5. 

<img src='content_image/432104.jpg'>

We lack sufficient observations to perform this same analysis using observations in the 637.5 nm region or for observations taken after the spring of 2008 (see Sec- tion 2.2). Therefore, for the 129 stars that do not have any observations in the 512.5 nm region ( ∼ 11% of our ob- served stars), we visually inspect the spectra and CCFs. For narrow-lined stars, we set the precision to 0.5 km s − $^{1}$, and for rotating stars we set the precision to 1.0 km s − $^{1}$. We can then use this RV precision value for a given star to determine whether our observations for this star are constant or variable in velocity (see Section 4.2). We note that only 13 of these stars have sufficient observa- tions for their RVs to be considered final, and only 2 are probable members. 

The full M35 database is available with the electronic version of this paper; here we show a sample of our re- sults in Table 3. The first column in Table 3 contains the WOCS identification number ( ID$_{W}$ ). These num- bers are defined in the same manner as in Hole et al. (2009), with the cluster center set at α = 6 $^{h}$9$^{m}$7 . $^{s}$5 and δ = +24 $^{◦}$20$^{′}$28′′ (J2000). Next we give the corresponding IDs from Meibom et al. (2009), McNamara & Sekiguchi (1986a) and Cudworth (1971) ( ID$_{M}$ , ID$_{Mc}$ and ID$_{C}$ ). The next few columns provide the right ascension ( RA ), declination ( DEC ), the BV photometry and the source number ( S ) for this photometry (see Section 2.1). Next, we show the number of RV measurements ( N ) and the mean and standard error of the RV measurements. For stars with only one RV measurements, we show the single-measurement RV precision instead of the standard error. Next we provide this single-measurement RV pre- cision ( σ$_{i}$ , derived using equation 1), the mean and stan- 

## 4. RESULTS 

dard error of the v sin i measurements $^{6}$, the e/i value (see Section 4.2), the calculated RV membership proba- bility (P$_{RV}$ , see Section 4.1), the proper-motion member- ship probability from McNamara & Sekiguchi (1986a) ( P$_{PM}$ 1 ) and Cudworth (1971) ( P$_{PM}$ 2 ), where available, and then, the classification of the object (see Section 4.3). For RV-variable stars with orbital solutions, we present the center-of-mass ( γ ) RV with the derived error in place of the mean RV and its standard error, and add the com- ment SB1 or SB2 for single- and double-lined binaries, respectively. Additionally, for binaries without orbital solutions that appear to be double-lined, we add the com- ment of SB2. Finally, for purposes of future research we include seven rapid rotators for which we have been un- able to derive RVs from our spectra, and label them with the comment RR. 

The RV distribution of M35 is clearly distinguished from that of the field when we plot a histogram of the mean RVs for the observed stars in our stellar sample. In Figure 6, we show a histogram of the mean RVs for stars with ≥ 3 RV measurements whose standard deviations are < 2 km s − $^{1}$, as well as the γ -RVs for binary stars with orbital solutions, thus excluding from the fit any RV variables whose γ -RVs are unknown. The cluster shows a well-defined peak rising above the broad distribution of the field stars. We simultaneously fit one-dimensional Gaussian functions, F$_{c}$ ( v ) and F$_{f}$ ( v ), to represent the cluster and field RV distributions, respectively, and then use these fits to calculate RV membership probabilities for each individual star. We compute the membership probability P$_{RV}$ ( v ) with the usual formula: 

(Vasilevskis et al. 1958). We plot these Gaussian fits in Figure 6 with the dashed lines, and show the fit param- eters in Table 1. 

For a given single star, we use the mean RV to com- pute the RV membership probability. For a given binary star with an orbital solution, we compute the RV mem- bership probability from the γ -RV. For RV-variable stars without orbital solutions, the γ -RVs are not known, and therefore we cannot calculate RV membership probabil- ities. For these stars, we provide a preliminary member- ship classification, described in Section 4.3. 

<img src='content_image/432103.jpg'>

## 4.1. Membership 

<img src='content_image/432110.jpg'>

