arXiv:1001.0033v1  [astro-ph.SR]  30 Dec 2009WIYN OPEN CLUSTER STUDY. XXXVIII. STELLAR RADIAL VELOCITIE S IN THE YOUNG OPEN
CLUSTER M35 (NGC 2168)
Aaron M. Geller∗, Robert D. Mathieu∗, Ella K. Braden∗, Søren Meibom∗,†
Department of Astronomy, University of Wisconsin - Madison , WI 53706, USA
and
Imants Platais
Department of Physics and Astronomy, The Johns Hopkins Univ ersity, Baltimore, MD 21218, USA
and
Christopher J. Dolan∗
Department of Astronomy, University of Wisconsin - Madison , WI 53706, USA
ABSTRACT
We present 5201 radial-velocity measurements of 1144 stars, as p art of an ongoing study of the
young (150 Myr) open cluster M35 (NGC 2168). We have observed M 35 since 1997, using the Hydra
Multi-Object Spectrograph on the WIYN 3.5m telescope. Our stellar sample covers main-sequence
stars over a magnitude range of 13.0 ≤V≤16.5 (1.6 - 0.8 M ⊙) and extends spatially to a radius of
30 arcminutes (7 pc in projection at a distance of 805 pc or ∼4 core radii). Due to its youth, M35
provides a sample of late-type stars with a range of rotation period s. Therefore, we analyze the radial-
velocity measurement precision as a function of the projected rot ational velocity. For narrow-lined
stars (vsini≤10 km s−1), the radial velocities have a precision of 0.5 km s−1, which degrades to 1.0
km s−1for stars with vsini= 50 km s−1. The radial-velocitydistribution shows a well-defined cluster
peak with a central velocity of -8.16 ±0.05 km s−1, permitting a clean separation of the cluster and
field stars. For stars with ≥3 measurements, we derive radial-velocity membership probabilities a nd
identify radial-velocity variables, finding 360 cluster members, 55 of which show significant radial-
velocity variability. Using these cluster members, we construct a co lor-magnitude diagram for our
stellar sample cleaned of field star contamination. We also compare th e spatial distribution of the
single and binary cluster members, finding no evidence for mass segr egation in our stellar sample.
Accounting for measurement precision, we place an upper limit on the radial-velocity dispersion of
the cluster of 0 .81±0.08 km s−1. After correction for undetected binaries, we derive a true radia l-
velocity dispersion of 0 .65±0.10 km s−1.
(galaxy:) open clusters and associations: individual (NGC 2168) - (s tars:) binaries: spectroscopic
1.INTRODUCTION
Young open clusters are laboratories for the direct
study of the near-primordial characteristics of stellar
populations. Their properties, and particularly those of
the binary systems, offer unique insights into how stars
arebornand provideessentialguidancefor N-bodystud-
ies of star clusters. Indeed, with sophisticated N-body
simulations now able to model real open clusters (e.g.,
Hurley et al. 2005), knowledge of the correct initial con-
ditions are all the more important. In particular, the ini-
tial binary population has a vast impact on the dynami-
cal evolution of the cluster, and the characteristics of the
initial binary population will affect the overallfrequency,
formation rate and formation mechanisms of anomalous
stars, like blue stragglers, as interactions with binaries
are thought to be catalysts for the formation of these ex-
otic objects (Hurley et al. 2005; Knigge et al. 2009). As
a rich open cluster with an age of ∼150 Myr, M35 is a
prime cluster to define these hitherto poorly known ini-
tial conditions for the binary population required for any
∗Visiting Astronomer, Kitt Peak National Observatory, Nati onal
Optical Astronomy Observatory, which is operated by the Ass o-
ciation of Universities for Research in Astronomy (AURA) un der
cooperative agreement with the National Science Foundatio n.
†Current address: Harvard-Smithsonian Center for Astrophy sics,
60 Garden Street, Cambridge, MA 02138, USAopen cluster simulation.
M35 is a fundamental cluster in the WIYN Open Clus-
ter Study (WOCS; Mathieu 2000), and as such has a
strong base of astrometric and photometric observations
fromboththeWOCScollaborationandothers. Theclus-
ter is centered at α= 6h09m07.s5 andδ= +24◦20′28′′
(J2000),towardstheGalacticanticenter. Numerouspho-
tometric studies have identified the rich main-sequence
population (e.g., Kalirai et al. 2003; von Hippel et al.
2002; Sung & Bessell 1999). WOCS CCD photometry
places the cluster at a distance of 805 ±40 pc, with an
ageof150 ±25Myr, ametallicityof[Fe/H]=-0.18 ±0.05
and a reddening of E(B−V)=0.20±0.01 (C. Deliyan-
nis, private communication). The most recent published
parameters, from Kalirai et al. (2003), place the cluster
at a distance of 912+70
−65pc ((m−M)0= 9.80±0.16)
with an age of 180 Myr, adopting a E(B−V)=0.20 and
[Fe/H] = -0.21. (See Kalirai et al. (2003) for a thorough
review of previous photometry references and their de-
rived cluster parameters). We note that these two recent
studies used different isochrone families.
There have been multiple proper-motion studies
of the cluster (Ebbighausen 1942; Cudworth 1971;
McNamara & Sekiguchi 1986a), although none deter-
mine clustermembership for individual starsfainter than2 Geller et al.
V≈15.0. Using proper motions, Leonard & Merritt
(1989) derive a cluster mass from 1600-3200 M ⊙within
3.75 pc. Detailed observations have also been made
in M35 to study tidal evolution in binary stars
(Meibom & Mathieu 2005; Meibom et al. 2006, 2007),
lithium abundances (Steinhauer & Deliyannis 2004;
Barrado y Navascu´ es et al. 2001), and white dwarfs
(Reimers & Koester 1988; Williams et al. 2004, 2006,
2009).
This is the first paper in a series studying the dy-
namical state of M35 through the use of radial-velocity
(RV) measurements. The data and results presented
in this series will form the largest database of spec-
troscopic cluster membership and variability in M35 to
date. In this paper, we present results from our ongo-
ing radial-velocity study of the cluster, which we began
in September 1997. Our stellar sample includes solar-
type main-sequence stars within the magnitude range of
13.0≤V≤16.5, which corresponds to a mass range1of 1.6
- 0.8 M ⊙. The main-sequence turnoff is at V∼9.5,∼4
M⊙. In Section 2, we describe this stellar sample, ob-
servations and data reduction in detail. We thoroughly
investigate our RV measurement precision and the effect
of stellar rotation in Section 3. Then in Section 4 we de-
rive RV membership probabilities, and use our study of
the RV precision to identify RV variables, which we as-
sume to be binaries or higher-order systems. Within this
mass range, we identify 360 solar-type main-sequence
members; 305 are single2(non-RV-variable) stars while
55 show significant RV variability. We then use these re-
sults to plot a color-magnitude diagram (CMD) cleaned
offield starcontamination, tosearchfor evidenceofmass
segregation and to study the cluster RV dispersion (Sec-
tion5). Finally, inSection6, weprovideabriefsummary.
In future papers, we will study the binary population of
M35in detail, providingobservationsthat will be used to
directly constrain the initial binary population of open
cluster simulations.
2.OBSERVATIONS AND DATA REDUCTION
In the following section, we define our stellar sample,
provide a detailed description of our observations and
data reduction process, and discuss the completeness of
our spectroscopic observations.
2.1.Photometric Target Selection
Initially, we created our M35 target list from the stars
in three wide-field CCD images centered on M35, taken
by T. von Hippel with the Kitt Peak National Observa-
tory (KPNO) Burrell Schmidt telescope on November 18
and 19, 1993. These images have Vexposures of 4 s, 20 s
and 180 s and Bexposures of 4 s, 25 s and 240s covering
a 70′×70′field. We obtained BandVphotometry with
a limiting magnitude of V= 17, denoted as source 1 in
1This mass range is derived from a 180 Myr Padova isochrone
(Marigo et al. 2008) using the distance, reddening and metal licity
from Kalirai et al. (2003).
2In the following, we use the term “single” to identify stars
with no significant RV variation. Certainly, many of these st ars
are also binaries, although generally with longer periods a nd/or
lower mass ratios ( q=m2/m1) than the binaries identified in this
study. When applicable, we have attempted to reduce this bin ary
contamination amongst the single star sample by photometri cally
identifying objects as binaries that lie well above the sing le-star
main-sequence (see Section 4.2).Fig. 1.— Color-magnitude diagram for stars in the field
of M35 highlighting the selected region used in this survey.
We plot all stars in the field with the gray points to show
the location of our selected sample relative to the full clus -
ter. Our stellar sample is bounded by the solid black lines.
Within this region, we plot observed stars in the solid black
points. Additionally, for reference we plot a 180 Myr Padova
isochrone (Marigo et al. 2008) using the distance, reddenin g
and metallicity from Kalirai et al. (2003)
Table 3. Additionally, we derive astrometry from these
plates, tied to the Tycho catalogue.
More recently, we added to our database the BVpho-
tometry of Deliyannis (private communication), taken
on the WIYN30.9m telescope with the S2KB 2K by
2K CCD. This photometry derives from a mosaic of five
fields. Each field has a 20′×20′field-of-view, with one
central field and four tiled around the center, for a total
field-of-view of of 40′×40′. This photometry is denoted
as source 2 in Table 3, and covers 74% of the objects
we have observed in this study. We note that this pho-
tometry is more precise than that of source 1. The star-
by-star difference in Vmagnitudes for the two sources is
roughly Gaussian with σ= 0.06 mag. However there is
a tail that extends beyond three times this sigma value.
Therefore we caution the reader when using magnitudes
from source 1.
We selected stars for the RV master list based on three
constraints. The faintest sources that can be observed
efficiently at echelle resolution using the Hydra Multi-
Object Spectrograph (MOS) on the WIYN 3.5m have
V=16.5; this therefore sets our faint limit for observa-
tions. Stars bluer than ( B−V)∼0.6 ((B−V)0∼0.4)
do not provide precise RV measurementsdue to rapid ro-
tationandpaucityofspectrallines; thisthereforesetsour
blue limit for observations. Finally, we perform a photo-
metric selection of cluster member candidates, shown as
the outlined region4in Figure 1. This region includes a
wide swath above the main sequence so as to not select
against binary stars (e.g. Dabrowski & Beardsley 1977),
yet also removes stars that are very likely cluster non-
members. This photometric selection allows for an effi-
cient survey of the cluster. Our sample extends radially
to 30 arcminutes from the cluster center. At a distance
of 805 pc, this corresponds to the inner ∼7 pc of the
3The WIYN Observatory is a joint facility of the University of
Wisconsin-Madison, Indiana University, Yale University, and the
National Optical Astronomy Observatories.
4Specifically, we select stars with 0 .6<(B−V)<1.5, 13.0<
V <16.5 and between the lines defined by 5 .7(B−V)+8.6< V <
5.7(B−V)+11.0.WOCS. RV Measurements in M35 3
Fig. 2.— Completeness of our observations as a function of Vmagnitude (left) and projected radius (right). We plot the
completeness in stars observed ≥3 times with the dashed line, and stars observed ≥1 time with the solid line.
cluster in projection. Given the core radius derived by
Mathieu (1983) of1.9 ±0.1pc, oursample isdrawn from
the inner ∼4 core radii.
Note that we lack BVphotometry for ∼11% of the
point sources found within 30 arcminutes from the clus-
tercenterin2MASS.Formostoftheseobjects, itislikely
that there is a nearby or overlapping additional object
which has prevented accurate BVphotometric measure-
ments from either of our sources. These objects, by de-
fault, are not included in our stellar sample. In total, our
stellar sample contains 1344 stars.
2.2.Spectroscopic Observations
Since September 1997, we have collected 5201 spec-
tra of 1144 stars within this stellar sample as part of
an ongoing observing program using the WIYN Hydra
MOS. For the majority of these observations, we use Hy-
dra’s blue-sensitive 300 µm fibers, which project to a 3.1′
aperture on the sky. We use the 316 lines mm−1echelle
grating, isolating the 11th order with the X14 filter. The
resulting spectra span a wavelength range of ∼25 nm,
with a dispersion of 0.015 nm pixel−1, centered on 512.5
nm. We have also occasionally centered our observation
on 637.5 nm using a very similar setup. In this region,
we use the same grating, but isolate the 9th order with
the X18 filter. These observations span a slightly larger
wavelength range of ∼30 nm, and have a dispersion of
0.017 nm pixel−1. Due to a broken filter, observations
taken after the spring of 2008 use different observing se-
tups than discussed above; most are centered on 560 nm
and all use the echelle grating. We have not noticed any
decrease in performance from the new wavelength range,
but we caution the reader that we lack sufficient obser-
vations in these setups to reliably determine our RV pre-
cision for these measurements. During this same period
certain upgrades were made to the spectrograph collima-
tor5. All observed regions are rich in metal lines. The
typical velocity resolution is 15 km s−1. In a two-hour
integration, the spectra have signal-to-noise (S/N) ra-
tios ranging from ∼18 per resolution element for V=16.5
stars to∼100 per resolution element for V=13 stars.
We create fiber configurations ( pointings ) for our ob-
servations using a similar method as Geller et al. (2008).
Monte Carlo simulations show that we require at least
5http://www.astro.wisc.edu/ ∼mab/research/bench upgrade/threeobservationsoverthecourseofayearinordertoen-
sure 90% confidence that a star is either constant or vari-
able in RV out to binary periods of 1000 days (Mathieu
1983, Geller & Mathieu, in preparation). Given three
observations with consistent RV measurements over a
timespan of at least a year and typically longer, we clas-
sify a given star as single (strictly, non-RV variable) and
finished, andmoveittothelowestpriority. Ifagivenstar
has three RV measurements with a standard deviation
>2.0 km s−1(four times our precision for narrow-lined
stars; see Section 4.2), we classify the star as RV vari-
able and give it the highest priority for observation on a
schedule appropriate to its timescale of variability. This
prioritization allows us to most efficiently derive orbital
solutions for our detected binaries.
We place our shortest-period binaries at the highest
priority for observations each night, followed by longer-
period binaries to obtain 1-2 observations per run. Be-
low the confirmed binaries we place, in the following or-
der, “candidate binaries” (once-observedstars with a RV
measurement outside the cluster RV distribution or stars
with a few measurements that span only 1.5 - 2.5 km
s−1), once observed and then twice observed non-RV-
variable likely members, twice observed non-RV-variable
likely non-members, unobserved stars, and finally, “fin-
ished” stars. Within each group, we prioritize by dis-
tance from the cluster center, giving those stars nearest
to the center the highest priority. A typical pointing
will contain ∼70 fibers placed on individual stars in our
sample and ∼10 sky fibers.
For a given pointing we obtain three consecutive ex-
posures, each of 40 minutes. In poor transparency or
with a particularly bright sky, we restrict the targets
toV <15.0 and shorten the integration time, gener-
ally to 20 minute exposures. We obtain Thorium-Argon
(ThAr), oroccasionallyCopper-Argon(CuAr), emission-
lamp comparison spectra (300 s integrations) before and
after each set of science integrations for wavelength cal-
ibration and to check for wavelength shifts during the
observing sequence. For each set of integrations we also
obtain one flat-field image (200 s) of a white spot on
the dome illuminated by incandescent lights. Associat-
ing the flat-field images with the science integrations is
particularly critical for calibrating throughput variations
between the fibers in order to apply sky subtractions. In
total, we have observed 106 distinct pointings in M354 Geller et al.
over the roughly 11 years since our survey began.
2.3.Data Reduction
For a thorough description of our data reduction pro-
cess, seeGeller et al.(2008). Inshort, weperformastan-
dard bias and flat-field correction to the images using
the overscan strip and the flat-field images, respectively.
The flat-field spectra are used to trace each aperture in
a given pointing and thereby extract the science spec-
tra. Wavelength solutions derived from the emission-
lamp spectra are applied, followed by sky-subtraction
using sky fibers from each pointing. The three sets of
spectra (one set from each integration in a given con-
figuration) are then combined via a median filter to re-
movecosmicraysignalsandimproveS/N.These reduced
spectra are cross-correlated with a high S/N solar spec-
trum, obtained using a dusk sky exposure taken on the
WIYN 3.5m with the same instrument setup as the given
pointing. A Gaussian fit to the cross-correlation func-
tion (CCF) yields a RV and a full width at half maxi-
mum (FWHM, in km s−1) for each stellar observation.
The mean UT time is used to find and correct each RV
measurement for the Earth’s heliocentric velocity. Fi-
nally we apply the unique fiber-to-fiber RV offsets de-
rived by Geller et al. (2008) for the WIYN-Hydra data
to these RVs. As in Geller et al. (2008), to ensure a
sufficient quality of measurement, we incorporate into
our database only those spectra with a CCF peak height
higher than 0.4. Additionally, we examine the distri-
bution of RVs for each individual star and visually in-
spect any measurements that are outliers in the distri-
bution. Occasionally we remove a measurement whose
CCF, though having a peak height above 0.4, clearly
provides a spurious measurement (e.g., inadequate sky
subtraction).
2.4.Completeness of Spectroscopic Observations
We have at least one observation for 1144 of the
1344 stars in our stellar sample, for a completeness of
85% across our entire sample. 60% of the stars in our
stellar sample have sufficient observations for their RVs
to be considered final (813/1344). For these stars, we ei-
ther have ≥3 RV measurements that show no variation,
or, if we do see RV variability, we have found a binary
orbital solution. (These 813 stars comprise the SM, SN,
BM and BN classes; see Section 4.1). Of those stars not
finalized, 231 have only one or two observations, and an-
other 100stars arevariable but do not yet havedefinitive
orbital solutions.
In Figure 2, we show the completeness of our observa-
tions as functions of Vmagnitude (left) and projected
radius (right). We plot the completeness in stars ob-
served≥3 times with the dashed line and stars observed
≥1 time with the solid line. Our prioritization of stars
by distance from the cluster center is evident by our de-
creasing completeness with cluster radius. The decreas-
ing completeness towards fainter stars reflects the need
for dark skies with minimal sky contamination in order
to obtain sufficient S/N in our spectra to derive reliable
RVsforfaint stars. Thereare37starswith V <15in our
stellar sample that do not have RV measurements, one of
which is a proper-motion member. 15 were observed but
did not yield reliable RVs, mostly due to rapid rotation.22 were not observed, 15 of which are farther than 20
arcminutes in radius from the cluster center.
Thedifferenceincompletenessbetweenbrightstarsob-
served≥1 and≥3 times is also a result of an increas-
ing population of rapidly rotating stars towards bluer
(B−V) color. For many of these stars, we have multi-
ple observations of which only a few, and sometimes one,
exceed this cutoff value of CCF peak height >0.4 and
therefore are included in our database. For purposes of
future research we also include seven rapid rotators in
Table 3 for which we have been unable to derive RVs
from our spectra.
3.EFFECTS OF STELLAR ROTATION ON
MEASUREMENT PRECISION
3.1.Observed Rotation
Because of its youth, M35 provides a sample of
late-type stars with a range of rotational periods
(Meibom et al. 2009); some of these stars have projected
rotational velocities that exceed our spectral resolution.
As such, the cluster presents an opportunity to explore
empiricallythedependence ofourmeasurementprecision
on increasing vsini, whereiis the inclination angle of
the stellar rotation axis to our line of sight.
Fig. 3.— FWHM as a function of vsinifor observations
in the 512.5 nm region. FWHM values are measured from
the CCF peaks derived from a series of artificially broadened
templates, of known vsini, correlated against the original
narrow-lined spectrum. We also show a polynomial fit to the
data, which we then use to derive vsinivalues for observed
stars in M35. Additionally we plot a dashed line at vsini
= 10 km s−1, below which the curve flattens out due to our
spectral resolution. We impose a floor in vsiniat this value
as we are unable to reliably measure slower rotation.
The measured FWHM of the CCF for a given star is
directly related to the vsini(Rhode et al. 2001). Thus
in order to derive a vsinivalue, we first measure the
FWHM of the CCF peak. To do so, we fit a Gaussian
function to the peak, forcing the baseline of the Gaus-
sian to start at the background level of the CCF. Specif-
ically, we subtract from the CCF a polynomial fit to this
backgroundlevel, and then fit the Gaussian to the subse-
quent “continuum subtracted” CCF. We only use spec-
tra from the 512.5 nm region to measure the FWHM, as
the FWHM is dependent on the setup (i.e., the disper-
sion, etc.), and most of our observations were taken in
the 512.5 nm region. We then use a similar technique as
Rhode et al. (2001), to convert this FWHM to a vsini.WOCS. RV Measurements in M35 5
Fig. 4.— Histogram of vsinimeasurements (left) and vsinias 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 peri od in
M35 (Meibom & Mathieu 2005). We only show stars with mean vsinivalues derived from ≥3 observations within the 512.5
nm region. Notice that the stars with the largest rotation ar e 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 vsinivalues. 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
vsinivalues for all observations of stars in M35 in the
512.5 nm region. We then take the mean vsinifor 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 vsinivalues below 10 km
s−1, due to the spectral resolution; we therefore impose
a floor to the vsiniat this value.
The median FWHM value that we observe is 46.1 km
s−1which corresponds to vsini= 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−1for individual vsinivalues of ≤25 km
s−1, which increasesto 1.6km s−1forvsini >25km s−1.
These precision values were derived in the same manner
as for our RV precision, with a fit to a χ2function; see
Section 3.2 and Geller et al. (2008). Where possible, we
derive a mean vsinifor a given star from multiple, gen-
erally≥3, observations within the 512.5 nm region. We
have compared our vsinimeasurements to the rotation
periods from Meibom et al. (2009) for stars observed in
both studies, and find the vsiniand rotation periods to
be consistent.
In the left panel of Figure 4, we plot a histogram of
the mean vsinimeasurements 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-
fectedbytidalprocesses. Wehavealsoremovedanystars
that appearto be indouble-lined binaries, asthe 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
vsinias a function of ( B−V)0for 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,Kraft 1967; Pleiades, Soderblom et al. 1993; Blanco 1,
Mermilliod et al. 2008; IC 2391, Platais et al. 2007).
3.2.Radial-Velocity Precision
We determine the RV measurement precision following
Geller et al. (2008), where a χ2distribution 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-
feringvsini. Specifically, we consider stars with vsini
of≤10 km s−1, 10 - 20 km s−1and 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
thevsini(see Section 3.1); these stars have line widths
characteristicof the auto-correlationof our spectralreso-
lution. The remainingbins containstarswith line widths
increased by stellar rotation.
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 Vmagnitude 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 vsiniand use this
relationship in our analysis throughout this paper.
In Figure 5 we show the RV precision as a function
ofvsiniin 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 (vsini >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:
σi= 0.38+0.012(vsini) km s−1,(1)
whereσiis our precision. We use this equation with
the mean measured vsinifor a given star to calculate6 Geller et al.
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.
Fig. 5.— RV measurement precision as a function of the
averagevsini(in km s−1) for single lined stars with ≥3 ob-
servations. The bins are vsiniof≤10 km s−1, 10 - 20 km
s−1and 20 - 80 km s−1, chosen to provide sufficiently large
samples. The gray horizontal bars indicate the bin sizes for
each point. The black vertical error bars show the one sigma
errors on the precision fit values. The dotted line shows the
fit to these data, and provided in Equation 1; we impose a
floor to our precision at 0.5 km s−1.
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
anyobservationsinthe512.5nmregion( ∼11%ofourob-
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.
4.RESULTS
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 ( IDW). These num-
bers are defined in the same manner as in Hole et al.
(2009), with the cluster center set at α= 6h9m7.s5 and
δ= +24◦20′28′′(J2000). Nextwe givethe corresponding
IDs from Meibom et al. (2009), McNamara & Sekiguchi
(1986a) and Cudworth (1971) ( IDM,IDMcandIDC).
The next few columns provide the right ascension ( RA),
declination ( DEC), theBVphotometry 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-measurementRV precision instead of the standard
error. Next we provide this single-measurement RV pre-
cision (σi, derived using equation 1), the mean and stan-TABLE 1
Gaussian Fit Parameters For Cluster
and Field RV Distributions
Cluster Field
Ampl. (Number) 69.0 ±2.0 2.4 ±0.4
RV(km s−1) -8.17 ±0.05 13 ±4
σ(km s−1) 0.92 ±0.08 34 ±4
dard error of the vsinimeasurements6, thee/ivalue
(see Section 4.2), the calculated RV membership proba-
bility(P RV, seeSection4.1), theproper-motionmember-
ship probability from McNamara & Sekiguchi (1986a)
(PPM1) and Cudworth (1971) ( PPM2), where available,
andthen, theclassificationoftheobject(seeSection4.3).
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
solutionsthatappeartobedouble-lined, weaddthecom-
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.
4.1.Membership
The RV distribution of M35 is clearly distinguished
from that of the field when we plot a histogram of the
mean RVs for the observedstars 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 orbitalsolutions, thus excludingfrom the fit anyRV
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, Fc(v) andFf(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 PRV(v) with the usual formula:
PRV(v) =Fc(v)
Ff(v)+Fc(v)(2)
(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.
6For double-lined binaries and stars with no observation in t he
512.5 nmregion, wedo notderive a vsinivalue. For starswith only
one measurement in the 512.5 nm region, we convert the 1-sigm a
error on the FWHM (derived from the Gaussian fit to the CCF
peak) to an error on the vsiniusing the fit shown in Figure 3. As
this relationship is not linear, we provide the mean of the de rived
upper and lower errors on vsini.WOCS. RV Measurements in M35 7
Fig. 6.— RV histogram for stars in the field of M35. We
include the mean RVs for stars observed ≥3 times with RV
standarddeviations <2kms−1andtheγ-RVsfor binarystars
with orbital solutions, excluding RV variables whose γ-RVs
are unknown. The bin sizes are 0.5 km s−1, equal to our
RV precision for narrow-lined stars, as found in Section 3.
The dashed lines show the simultaneous Gaussian fits to the
cluster and field RV distributions.
Fig. 7.— Histogram of membership probabilities, P RV, for
stars observed ≥3 times with RV standard deviations <2 km
s−1and for binaries whose γ-RVs are known. For the single
stars, we compute P RVusing the mean observed RV; for bi-
naries with orbital solutions, P RVis based on the γ-RV. We
show our membership cutoff of P RV=50% with the dashed
line, above which we classify a star as a cluster member. Note
that we do not show the full height of the bin at lowest mem-
bership probability for clarity.
In Figure 7, we show the distribution of RV member-
ship probabilities, displaying a clean separation between
the cluster members and field stars. In the following
analysis, we use a probability cutoff of P RV≥50 % to
define our cluster member sample. Using the 344 single
clustermembersandbinaryclustermemberswithorbital
solutions, we find a mean cluster RV of -8.16 ±0.05 km
s−1. From the area under the fit to the cluster and field
distributions, we estimate a field contamination of 6%
within our cluster member sample (P RV≥50%). Though
this estimate is derived excluding the RV variables that
do not have orbital solutions, the percent contamination
should be valid for the cluster as a whole.
Our RV membership probabilities agree well with the
proper-motion memberships of Cudworth (1971) and
McNamara & Sekiguchi (1986a). We note that our stel-
lar sample covers only the faintest portion of either
proper-motion study. There are 24 Cudworth (1971)proper-motionmembers within our observed stellar sam-
ple, of which we find 14 (58%) to also have ≥50% RV
membership probabilities. Cudworth (1971) note that
forV >13 they begin to find significant errors in
their photometry and expect many field stars to con-
taminate their proper-motion member sample; this can
likely explain the 10 discrepant stars. There are 70
McNamara & Sekiguchi(1986a)proper-motionmembers
within our observed stellar sample, of which we find 64
(91%) to also have ≥50% RV membership probabilities.
McNamara & Sekiguchi (1986a) expects up to 15 field
stars contaminating their cluster member sample from
13< V <15, which can easily account for the 6 dis-
crepant stars.
We also note that NGC 2158 is only ∼28 arcminutes
away from the center of M35, at α= 6h07m25sandδ=
+24◦05′48′′(J2000), and thus is within the spatialregion
that we have surveyed. Scott et al. (1995) find a mean
RV for NGC 2158 of 28 ±4 km s−1. There are five stars
within our sample that lie within the cluster radius of 2.5
arcminutes Carraro et al. (2002) from the center of NGC
2158 and have RVs within three times the standard error
(12 km s−1) of the mean RV : 125044, 39017, 111050,
57037, 54048. Two of these stars (125044 and 57037)
have less than three observations; the remaining three
have≥3observationsandappeartobenon-RV-variables.
4.2.Radial-Velocity Variability
RV-variable stars are distinguishable by the larger
standard deviations of their RV measurements. Here,
we assume that such velocity variability is the result of
a binary companion, or perhaps multiple companions.
Specifically, we consider a star to be a RV variable if the
ratio of the standard deviation of its RV measurements
to the single-measurement RV precision7(e/i) for that
star is greater than four (Geller et al. 2008). We provide
thee/ivalue for each single-lined star in Table 3; we
label double-lined systems as RV variables directly, and
include the comment of SB2 in Table 3.
MonteCarloanalysishasshownthat, forsimilarobser-
vations ofsolar-typestars in NGC 188, Geller & Mathieu
(in preparation) can detect the majority of binaries with
periods less than 104days and a negligible fraction of
longer-period binaries. Though the slightly poorer preci-
sionforthe M35datawill effect the specific completeness
numbers, we can assume a similarly high completeness in
detected binaries with periods less than 104days and a
corresponding drop in completeness for longer-period bi-
naries. Some of the undetected systems are evident from
their separation from the main sequence (see Figure 8).
We have currently identified 55 RV-variable members
of M35, and have derived orbital solutions for 71%
(39/55) of this sample. In following papers we will pro-
vide the orbital solutions for these systems, including
all derived parameters. We will then perform a detailed
analysis of the distributions of these orbital parameters
as well as the binary frequency of the cluster.
7We use the same nomenclature of “ e/i” as in Geller et al.
(2008), though in other sections, for clarity, we have label ed the
precision as σi, so as not to confuse the precision with an inclina-
tion angle.8 Geller et al.
TABLE 2
Number of Stars
or Star Systems
Within Each
Membership
Class
Class Number
SM 305
SN 452
BM 39
BN 17
BLM 16
BU 16
BLN 68
U 231
4.3.Membership Classification of Radial-Velocity
Variable Stars
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/ivalues. We provide these
classifications for all observed stars, while the member-
ships and e/ivalues are only provided for a subset of
appropriate stars.
For stars with e/i<4, we classify those with P RV≥50%
as single members (SM), and those with P RV<50% as
singlenon-members(SN). Ifa starhas e/i≥4and 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
PRV<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
PRV≥50%,weclassifythesystemasabinarylikelymem-
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/imeasure-
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.
5.DISCUSSION
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).
5.1.Color-Magnitude Diagram
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-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 .
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.
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
ofstarsobservedbrighterandtothe redofthis 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
notethatthereareanadditional12clustermemberswith
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-
metricallyidentify binariesthatlie farfromtheisochrone
ontheCMD. Wederivethedistanceofeachstarfromthe
main-sequenceisochroneand fit a Gaussianfunction 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 showWOCS. RV Measurements in M35 9
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 ∼105−106days,
and we only detect binaries with P/lessorsimilar104days (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 arefainter and bluer than the dashed grayline
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
amongstarsmoremassivethan 2M ⊙. The degreeofseg-
regationlessenswith decreasingmass, and is largelynon-
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.
5.3.Cluster Radial-Velocity Dispersion
To determine the true RV dispersion of the cluster, we
followtheprocedureofGeller et al.(2008). Wefirstlimit
oursampletoonlyincludeSMstarsthathave vsini≤10
km s−1. We limit the vsinivalue to ensure that we only
use the highest precision RV measurements for this anal-
ysis. These narrow-lined stars have a precision σi= 0.5
km s−1. We will discuss the effect of undetected binaries
that likely remain within this sample in Section 5.3.1.
Usingthissampleof67SMstars,wefirstderivetheob-
serveddispersion σobsbytakingthestandarddeviationof
themeanRVsforeachstar,andwefind σobs= 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 theseFig. 9.— Cumulative projected radial spatial distributions
of the M35 single and binary cluster members. We have ex-
cluded any stars from the single-star sample that are bright er
and redder than the dashed grey line in Figure 8, as these
stars are likely long-period binaries that are outside of ou r de-
tection limits. We plot the single stars with the black point s
andtheRVvariables with theopen diamonds. We findnosig-
nificant evidence for central concentration of the RV-varia ble
population.
RV measurements. We derive8the “combined RV dis-
persion” σcbfrom :
σ2
cb=σ2
obs−1
nn/summationdisplay
i=1ξ2
i. (3)
Here,n= 67 is the number of stars used in this analysis,
andξiis the mean errorof the RV for the ith star defined
as,
ξi=
m/summationdisplay
j=1/parenleftbig
RVj−RVi/parenrightbig2
m(m−1)
1/2
(4)
whereRVjis one of the mnumber of RV measurements
for a given star i, andRViis the mean RV for that star.
WenotethatthesecondterminEquation3isverynearly
equal to σ2
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 σi= 0.5 km s−1. Following this proce-
dure, wederiveacombineddispersionof σcb= 0.81±0.08
km s−1. The error on this combined dispersion is almost
entirely due to the statistical error on σobs.
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−1for bins of 10 arcmin).
This combined RV dispersion is inflated by undetected
binaries. In the following section, we quantify this effect
and apply the correctionto derivethe true RV dispersion
ofM35, an improvementon the procedureofGeller et al.
(2008).
8The use of Equations 3 and 4 is an improvement over the pro-
cedure of Geller et al. (2008) adapted from McNamara & Sander s
(1977). The uncertainty on σcbalso follows McNamara & Sanders
(1977).10 Geller et al.
5.3.1.Contribution from Undetected Binaries
The combined RV dispersion defined in Equation 3 is
also described by,
σcb=σc+β (5)
whereσcis the true RV dispersion of the cluster and
βrepresents the contribution from undetected binaries
within our sample. Therefore, in order to derive the true
RV dispersion of the cluster we have performed a Monte
Carlo analysis to determine this contribution from unde-
tected binaries.
We first create a set of simulated binaries with or-
bital parameters distributed according to the Galactic
field solar-type binaries studied by Duquennoy & Mayor
(1991). Specifically, these binaries have a log-normal pe-
riod distribution centered on log( P[days] ) = 4.8 with
σ= 2.3, and a Gaussian eccentricity distribution cen-
tered on e= 0.3. For binaries with periods below the
circularization period of 10.2 days (Meibom & Mathieu
2005), we set the eccentricity to zero. We use only solar-
massprimary stars, and a distribution in secondarymass
between0.08-1M ⊙describedby aGaussiancenteredon
M2= 0.23 M⊙withσ= 0.42 M⊙(Kroupa et al. 1990).
Duquennoy & Mayor (1991) found this Gaussian to be
the best fit to their solar-type field binaries, and this dis-
tribution is also consistent with that of Goldberg et al.
(2003) for their field binaries with primary masses >0.67
M⊙. The orbital inclinations and phases of the binaries
are chosen randomly. We then generate three RVs for
these simulated binaries distributed in time according to
the actual distribution of our first three observations for
starsin M35. The majorityofthe SM starsin oursample
haveonlythreeobservations. TotheseRVs, wealsoadda
randomerrorgeneratedfromaGaussiancenteredonzero
and with σ= 0.5 km s−1, the RV precision for narrow-
lined stars in M35. We also add a random velocity offset
generated from a Gaussian centered on zero with a stan-
dard deviation equal to an adopted one-dimensional RV
dispersion.
To this sample, we add a number of simulated single
stars to produce a desired binary frequency. We generate
three RVs for each single star from a Gaussian described
byourprecision. To themean RVforeverysinglestarwe
also add a random offset described by the assumed RV
dispersion in the same manner as for the simulated bi-
naries. We then keep only those simulated binaries (and
single stars) whose first three RVs result in an e/i <4,
and whose mean RVs are within three standard devia-
tions of the mean RV from a Gaussian fit to the simu-
lated RV distribution. This cutoff in standard deviation
reflects our membership criterion of P RV≥50% for the
M35 observations. These binaries would be undetected
within the SM sample.
We then follow the equations given above to derive β
fora rangeofbinaryfrequenciesand velocitydispersions,
σc. In Figure 10, we plot the true cluster RV dispersion
(σc) as a function of the combined RV dispersion ( σcb)
for a range of total binary frequencies, where each line
corresponds to a different binary frequency between 0%
(far left) to 100% (far right) in steps of 10%. We can
then use the results shown in Figure 10 to derive the
true RV dispersion for M35. Furthermore, the results
shown in this figure are also applicable to RV dispersionFig. 10.— The true cluster RV dispersion ( σc) plotted
against the combined RV dispersion ( σcb) for a range of total
binaryfrequencies. Eachlinecorrespondstoadifferentbin ary
frequency in steps of 10%, with 0% at the far left and 100%
at the far right. With the vertical gray rectangle, we plot th e
region included in the combined RV dispersion for M35 of
0.81±0.08 km s−1. The diagonal gray region covers the pos-
sible lines within our extrapolated true binary frequency i n
M35 of 66% ±8% (derived assuming the M35 binaries follow
a Duquennoy & Mayor (1991) period distribution). Finally,
we plot the resulting true RV dispersion in M35 of 0.65 ±
0.10 km s−1with the black point at the intersection of these
two shaded regions.
analyses for other star clusters, provided that the binary
population is consistent with the Duquennoy & Mayor
(1991) field binaries.
5.3.2.True Radial-Velocity Dispersion
To date, we have detected 55 binaries in M35 out
of 360 cluster members. If we assume a similar com-
pleteness as in Geller & Mathieu (in preparation), for
NGC 188, then we can assume that we have detected
63% of the binaries with periods less than 104days
(and a negligible fraction of binaries with longer peri-
ods). This correction results in a binary frequency of
24%±3% forP <104days. This binary frequency
is consistent with that of solar-type stars in the Galac-
tic field Duquennoy & Mayor (1991) out to the same
period limit. If we assume the M35 binaries follow
a Duquennoy & Mayor (1991) period distribution, then
our binary frequency for P <104days implies a total bi-
nary frequency of 66% ±8%, with the inclusion of wider
binaries currently beyond our detection limits. We then
take this value for the total binary frequency and correct
our combined RV dispersion for undetected binaries.
In the filled gray areas in Figure 10 we show the re-
gions defined by our M35 combined RV dispersion and
the total binary frequency. At the intersection, we plot
the derivedtrue RV dispersionin M35 of σc= 0.65±0.10
km s−1. Using a flat distribution in secondary mass (and
mass ratio), as has been suggested by some studies (e.g.,
Mazeh et al. 1992, 2003), has a negligible effect on the
derived true RV dispersion. This true RV dispersion is
consistent with the projected velocity dispersion of 1.0
±0.15 km s−1, derived by Leonard & Merritt (1989) us-
ingtheproper-motiondatafromMcNamara & Sekiguchi
(1986a).
6.SUMMARY
This is the first paper in a series studying the dynam-
ical state of the young ( ∼150 Myr) open cluster M35WOCS. RV Measurements in M35 11
(NGC 2168). In this first paper, we present our RV ob-
servations and provide initial results from this survey.
Our stellar sample extends to 30 arcminutes in radius
from the cluster center (7 pc in projection at a distance
of 805 pc or ∼4 core radii), and we have selected a region
from aV, (B−V) CMD (Figure 1) which covers a mass
range of 1.6 - 0.8 M ⊙. We have used the WIYN 3.5m
telescope with the Hydra MOS to obtain 5201 spectra of
1144 stars within this stellar sample. From these spec-
tra, we derive RV measurements with a precision of 0.5
km s−1for narrow-lined stars. The vast majority of the
observed stars have multiple measurements, allowing de-
termination of cluster membership and identification of
spectroscopic binary stars. We detect 360 cluster mem-
bers, 55 of which show significant variability in their RV
measurements. Binary orbital solutions have been ob-
tained for 39 of these RV variables, which we will present
in detail in the next paper in this series. Observations
of the rest of the RV variables and the remainder of our
stellar sample are ongoing. Table 3 provides the first RV
membership database for M35 and extends ∼1.5 magni-
tudes deeper than any previous membership catalogue.
Using the RV cluster members, we study the spa-
tial distribution and velocity dispersion of the single
and binary stars. We find their spatial distributions
to be indistinguishable. This lack of central concentra-
tion for the binaries is consistent with earlier observa-
tional studies of stars in M35 as well as with a fully re-
laxed dynamical model for the cluster (Mathieu 1983;
McNamara & Sekiguchi 1986b). In these studies, mass
segregationisseeninhigher-massstars,butdiminishesto
being undetectable for stars in our observed mass range.After correcting for measurement precision, but not for
binaries, we place an upper limit on the RV dispersion of
the cluster of 0 .81±0.08 km s−1. When we also correct
for undetected binaries, we derive a true RV dispersion
of 0.65±0.10 km s−1.
The WOCS group will continue our survey of M35 in
ordertoderiveRVmembershipsforallstarsin ourstellar
sample and obtain orbital solutions for all binaries with
periods less than a few thousand days, as well as some
with longer periods. In future papers, we will study the
binary population of M35 in detail, providing all orbital
solutions and analyzing the binary frequency and dis-
tributions of orbital parameters. These data will form
essential constraints on the hitherto poorly known initial
binary populations used in sophisticated N-body models
of open clusters.
The authors would like to express their gratitude to
the staff of the WIYN Observatory for their skillful and
dedicated work that have allowed us to obtain these ex-
cellent spectra. We thank Ata Sarajedini and Ted von
Hippel for the acquisition of the Schmidt images, Vera
Platais for work on the astrometry and photometry as
well as John Bjorkman for early photometry work. We
also thank the many undergraduate and graduate stu-
dents who have contributed late nights to obtain the
spectra for this project. This work was supported by
NSF grant AST 0406615and the Wisconsin Space Grant
Consortium.
Facilities: WIYN 3.5m
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Radial-Velocity Data Table
IDWIDMIDMcIDCRA DEC V (B−V)S N RV RV eσivsini(vsini)ePRVPPM1PPM2e/i Class Comment
96041 410 ··· ··· 6:10:28.65 24:11:52.0 16.416 0.960 1 4 51.89 1.55 0.52 11.8 1 .1 ··· ·· · · ·· 5.93 BLN ···
36042 209 ··· ··· 6:10:34.30 24:14:07.8 14.835 0.859 1 3 -8.74 0.55 0.64 21.6 0 .8 96 ·· · · ·· 1.49 SM ···
36045 209 ··· ··· 6:10:43.69 24:16:08.9 14.497 0.824 1 17 -9.58 0.19 0.50 10.3 0.2 91 ·· · · ·· 77.46 BM SB1
138057 366 ··· ··· 6:10:50.20 24:04:50.7 16.368 1.165 1 1 -25.13 0.50 0.50 ··· ··· ··· ·· · · ·· · ·· U ···
64052 312 ··· ··· 6:10:43.70 24:07:00.8 15.884 1.023 1 4 -8.85 0.64 0.55 14.2 4 .2 96 ·· · · ·· 2.34 SM ···
15036 180 ··· 731 6:10:15.70 24:11:31.7 13.450 0.690 2 1 57.98 0.50 0.50 ··· ··· ··· ·· · 0 · ·· U ···
49051 227 ··· ··· 6:10:51.32 24:11:10.6 15.086 0.890 1 4 88.83 0.34 0.50 10.0 ··· 0 ·· · · ·· 1.35 SN ···
29047 87 ··· ··· 6:10:44.59 24:13:44.3 14.948 0.895 1 4 56.95 0.28 0.50 10.0 ··· 0 ·· · · ·· 1.10 SN ···
40032 ··· ··· ··· 6:10:11.15 24:14:01.5 15.280 0.820 2 3 -7.72 0.32 0.55 14.3 0 .8 96 ·· · · ·· 1.02 SM ···
20037 193 ··· 758 6:10:22.30 24:14:39.3 14.270 0.650 2 1 3.88 0.50 0.50 ··· ··· ··· ·· · 7 · ·· U ···
The contents of each column are defined in Section 4.