WOCS. RV Measurements in M35 5 Fig. 4.— Histogram of v sin i measurements (left) and v sin i as a function of ( B − V ) 0 (right) for the cluster members of M35. We have removed double-lined binaries and any binaries with known periods less than 10.2 days, the circularization period in M35 (Meibom & Mathieu 2005). We only show stars with mean v sin i values derived from ≥ 3 observations within the 512.5 nm region. Notice that the stars with the largest rotation are generally also the bluest stars in our sample. We create a series of artificially broadened templates by convolving our standard solar template with a series of theoretical rotation profiles of specific v sin i values. We then cross correlate this series of broadened templates with the original narrow-lined template and measure the FWHM of the CCF peak as described above. In Fig- ure 3 we show the results of this analysis along with a polynomial fit to the data. We use this curve to derive v sin i values for all observations of stars in M35 in the 512.5 nm region. We then take the mean v sin i for each star, using only our highest quality (CCF peak height > 0.4) spectra, and provide these values in Table 3. We are unable to reliably measure v sin i values below 10 km s − $^{1}$, due to the spectral resolution; we therefore impose a floor to the v sin i at this value. Kraft 1967; Pleiades, Soderblom et al. 1993; Blanco 1, Mermilliod et al. 2008; IC 2391, Platais et al. 2007). We determine the RV measurement precision following Geller et al. (2008), where a χ 2 distribution is fit to the distribution of the standard deviations of the first three RV measurements for each star in an ensemble of stars. Here we do this operation on samples of stars with dif- fering v sin i . Specifically, we consider stars with v sin i of ≤ 10 km s − $^{1}$, 10 - 20 km s − 1 and 20 - 80 km s − $^{1}$. The bin sizes were chosen arbitrarily in order to pro- vide sufficiently large samples. The first bin contains all narrow-lined stars for which we have imposed a floor to the v sin i (see Section 3.1); these stars have line widths characteristic of the auto-correlation of our spectral reso- lution. The remaining bins contain stars with line widths increased by stellar rotation. 3.2. Radial-Velocity Precision The median FWHM value that we observe is 46.1 km s − 1 which corresponds to v sin i = 10.3 km s − $^{1}$. Exclud- ing stars rotating slower than 10 km s − $^{1}$, we find a preci- sion of 1.4 km s − 1 for individual v sin i values of ≤ 25 km s − $^{1}$, which increases to 1.6 km s − 1 for v sin i > 25 km s − $^{1}$. These precision values were derived in the same manner as for our RV precision, with a fit to a χ 2 function; see Section 3.2 and Geller et al. (2008). Where possible, we derive a mean v sin i for a given star from multiple, gen- erally ≥ 3, observations within the 512.5 nm region. We have compared our v sin i measurements to the rotation periods from Meibom et al. (2009) for stars observed in both studies, and find the v sin i and rotation periods to be consistent. A detailed study of the RV measurement precision of our observation and data-reduction pipeline has been done by Geller et al. (2008) for late-type stars in the old open cluster NGC 188. For the narrow-lined stars in NGC 188 they find a single-measurement precision of 0.4 km s − $^{1}$. This precision is also a function of the S/N of the spectrum, as shown in Geller et al. (2008) by the degrading precision with increasing V magnitude as well as decreasing CCF peak height. The largest S/N effect seen for narrow-lined stars in NGC 188 is to degrade the precision by 0.25 km s − $^{1}$. The effect of rotation is larger than this amount. Here, we derive a relationship be- tween the measurement precision and v sin i and use this relationship in our analysis throughout this paper. In the left panel of Figure 4, we plot a histogram of the mean v sin i measurements for M35 cluster members. (See Section 4.1 for our membership criteria.) In this and the other panel, we have excluded any binaries with periods known to be less than the circularization period in M35 of 10.2 days (Meibom & Mathieu 2005), as the rotation of the stars in these binaries have likely been af- fected by tidal processes. We have also removed any stars that appear to be in double-lined binaries, as the spectral lines in many of these observations are broadened due to the secondary spectrum at similar, though slightly off- set, RV. In the right panel of Figure 4, we plot the mean v sin i as a function of ( B − V ) 0 for M35 cluster mem- bers. We see a clear trend of increasing rotation towards bluer stars, as has also been observed in other young open clusters and the field (e.g., field, Hyades, Pleiades, In Figure 5 we show the RV precision as a function of v sin i in M35 for observations taken in the 512.5 nm region. The narrow-lined stars have a RV precision of 0.5 km s − $^{1}$, similar to that found for the narrow-lined stars in NGC 188 observed with this same setup. As ex- pected, the value of the measurement precision increases with increasing line width. For the most rapidly rotating stars ( v sin i > 50 km s − $^{1}$), the measurement precision degrades to ∼ 1.0 km s − $^{1}$. We fit a linear relationship to the points in Figure 5, shown as the dashed line: where σ$_{i}$ is our precision. We use this equation with the mean measured v sin i for a given star to calculate σ$_{i}$ = 0 . 38 + 0 . 012( v sin i ) km s − $^{1}$, (1)