A proper motions study of the globular cluster NGC 3201

5.4 MB·

by  Devesh P. Sariya

A proper motions study of the globular cluster NGC 3201.1
Devesh P. Sariya1, Ing-Guey Jiang1, R. K. S. Yadav2
7 1Department of Physics and Institute of Astronomy,
1 National Tsing-Hua University, Hsin-Chu, Taiwan
0
email: [email protected]
2
2Aryabhatta Research Institute of Observational Sciences,

n Manora Peak, Nainital 263 002, India
a
J

7
1

ABSTRACT
]
R
With a high value of heliocentric radial velocity, a retrograde orbit, and being suspected to
S
haveanextragalacticorigin,NGC 3201is an interesting globularcluster for kinematicalstudies.
.
h Our purpose is to calculate the relative proper motions (PMs) and membership probability for
p the stars in the wide region of globular cluster NGC 3201. Proper motion based membership
-
probabilitiesareusedtoisolatetheclustersamplefromthefieldstars. Themembershipcatalogue
o
r willhelpaddressthequestionofchemicalinhomogeneityinthecluster. ArchiveCCDdatataken
t
s withawide-fieldimager(WFI) mountedonthe ESO2.2mtelescopearereducedusing the high-
a precision astrometric software developed by Anderson et al. for the WFI images. The epoch
[
gap between the two observational runs is 14.3 years. To standardize the BVI photometry,
∼
1 Stetson’s secondary standard stars are used. The CCD data with an epoch gap of 14.3 years
v enables us to decontaminate the cluster stars from field stars efficiently. The media∼n precision
9 of PMs is better than 0.8 mas yr−1 for stars having V <18 mag that increases up to 1.5
5 mas yr−1 for stars with∼18 < V < 20 mag. Kinematic membership probabilities are calcul∼ated
8
4 using proper motions for stars brighter than V 20 mag. An electronic catalogue of positions,
∼
0 relative PMs, BVI magnitudes and membership probabilities in 19.7 17 arcmin2 region of
1. NGC 3201is presented. We use our membership catalogueto identi∼fy pro×bable cluster members
0 among the known variables and X-ray sources in the direction of NGC 3201.
7
1 Subject headings: Galaxy: Globular cluster: individual: NGC 3201 - astrometry - catalogs
:
v
1. Introduction tographic plates. Proper motions are the root to
i
X learn about the kinematics and orbit of the clus-
Galactic globular clusters are very important
r ters as well as providing kinematical membership
a for the study of the halo and bulge regions of our probabilities of the stars. Membership status is
Galaxy. In particular, they are the best tools to
oftenpivotaltospectroscopicstudies,toavoidob-
understand the kinematics and dynamics of the
servingfieldstarslying inthe cluster’sfield(Cud-
halo region of the Milky Way by the virtue of be-
worth1986). Atfaintermagnitudes,inparticular,
ing easily distinguishable at large distances (Cud-
field stars dominate, and proper motions become
worth1997,Dambis2006). Sincetheemergenceof
veryimportantinremovingthemfromthesample
CCDs,propermotion(PM)studiescanbecarried
(Piotto et al. 2004).
outwithunprecedentedprecisionusingCCDdata
NGC3201isasparse,metal-poor,intermediate-
withsmallerepochdifferencesthandatafrompho-
mass halo globular cluster. The basic cluster pa-
rameters of NGC 3201 taken from Harris (1996,
1Based on observations with the MPG/ESO 2.2m and
2010edition) are listedin Table 1. Since the clus-
ESO/VLT telescopes, located at La Silla and Paranal
Observatory, Chile, under DDT programs 164.O-0561(F), ter is less centrally concentrated than most other
093.A-9028(A)andthearchivematerial.
1
globular clusters, even ground based telescopes 5.28 0.32 mas yr−1, µ = 0.98 0.33 mas
δ
can probe its central region. Due to this advan- yr−1)±using a combination of p−hotogr±aphic plate
tageanditsproximity,NGC3201hasbeenstudied datawithCCD.Recently,Zloczewskietal. (2012)
extensivelyforphotometricstudies(Menzies1967, (hereafter, Zl12) have determined proper motions
Alcaino 1976, Lee 1977, Alcaino et al. 1981,1989, for the stars in the region of NGC 3201 and pro-
Cacciari 1984a, 1984b, Penny 1984, Brewer et al. vided membership probabilities in the central re-
1993, Covino & Ortolani 1997, Kravtsov et al. gion of the cluster.
2009 etc.). von Braun & Mateo (2001) presented Fromthe abovediscussion,it isnoticeable that
an extinction map for NGC 3201 and explained this kinematically interesting globular cluster is
that due to its low Galactic latitude, the effect of not well studied for proper motions over a wider
differential reddening across this globular cluster region. As reported by Brewer et al. (1993) and
is very significant. NGC 3201 has been studied Kravtsov et al. (2009), the studies of NGC 3201
for the question of chemical abundances and pos- are obstructed by significant field star contami-
sibility of inhomogeneity in its stellar population nation. Wide Field Imagers (WFIs) enable us to
by several authors (e.g., Chun 1988, Gonzalez & coverthebroadregionsofstarclusters,sometimes
Wallerstein 1998, Covey et al. 2003, Kravtsov et up to their tidal trails. The archivedata observed
al. 2010,Simmereretal. 2013,Mun˜ozetal. 2013, with [email protected] at La Silla, Chile has been used
Mucciarelli et al. 2015 and references therein). previouslyto providepropermotionsusing atime
NGC3201isknowntoharbormanyvariablestars gap of a few years (Anderson et al. 2006; Yadav
including RR Lyrae, SX Phoenicis etc. It belongs et al. 2008, 2013; Bellini et al. 2009; Sariya et
to Oosterhoff type I according to Oosterhoff di- al. 2012,2015). NGC 3201,being a sparsecluster
chotomy ofRR Lyrae Stars. The cluster has been and the available epoch gap being 14.3 years in
the subject of many investigations for searching the archivedata [email protected]∼sus to deter-
and characterizing its variable stars (e.g., Lee & mine precise proper motions over a broad region
Carney 1999, von Braun & Mateo 2002, Piersi- of the cluster.
monietal. 2002,Mazuretal. 2003,Laydenetal.
The main goal of the present article is to pro-
2003, Arellano Ferro et al. 2014, Kaluzny et al.
vide relative PMs and membership probabilities
2016 and references therein). Webb et al. (2006)
(P ) for stars having visual magnitudes up to 20
µ
studied NGC 3201using XMM Newton X-ray
− mag in the wide field of NGC 3201. We also pro-
observatory.
vide an electronic catalogue for 8322 stars which
NGC 3201is a veryinteresting globularcluster contains B,V,I magnitudes, PMs and member-
for its kinematical features. It shows a very high ship probabilities for the follow-up studies of the
valueofheliocentricradialvelocity(494.2km/sec, cluster. Our membership catalogue covers a re-
Cote et al. 1994) suggesting a retrograde orbit gionof 19.7 17arcmin2 whichiswiderthanthe
about the Galactic center (Casetti-Dinescu et al. areacov∼eredi×n the PMstudy by Zl12( 14.6 9.7
2007). It has been suspected to have an extra- arcmin2). Ourmembershipcataloguew∼illbeh×elp-
galactic originand has probably been accretedby fultoselectthe morelikelyclustermemberswhile
theMilkyWay. Dynamicsoftheclusterwasstud- addressingthequestionofchemicalinhomogeneity
ied by Da Costa et al. (1993) and Cote et al. whichhasbeenanintriguingaspectofthiscluster.
(1994, 1995). The Radial Velocity Experiment
Informationaboutthe datausedandreduction
(RAVE) catalogue was used to study this clus-
procedures are described in Section 2 where we
ter by Kunder et al. (2014) and Anguiano et al.
also discuss PMs, vector point diagrams (VPDs)
(2015, 2016). Anguiano et al. (2016) presented
withcolor-magnitudediagram(CMD)oftheclus-
the distribution of stars based on UCAC4 proper
ter. Cluster membership analysis is provided in
motions. Chen & Chen (2010) state that NGC
Section 3. We use our membership catalogue to
3201 appears to have passed through the Galac-
examinethemembershipstatusofearlierreported
tic disk a few Myr agoandthe cluster has clumps
variablesandX-raysourcesinSection4. Theelec-
along its Galactic north-south axis.
tronic catalogue being presented for the further
Casetti-Dinescu et al. (2007) provided the ab- studies of the cluster is explained in Section 5.
solute proper motion of NGC 3201 (µαcosδ = Conclusions follow in Section 6.
2
15
10
5
0
40
20
0
-20
-40
15
10
5
0
40
20
0
-20
-40
12 14 16 18
Fig. 1.— Plot of the rms of the residuals around
Fig. 2.— Proper motions of stars in the NGC
the mean B,V, and I magnitudes, for stars in
3201 field, in the globular cluster reference frame.
the NGC 3201 field imaged in this study, plotted
PropermotionsinRAandDecareplottedagainst
against V magnitude
V magnitude, along with their rms errors
.
Table1:BasicparametersofNGC3201takenfrom
Harris (1996, 2010 edition). The notations used
Table 2: Details of the [email protected] archive data.
have their usual meanings. Cluster’s heliocentric
The first epoch data were acquired on December
distance is denoted by d and the Galactocentric
05, 1999 and the second epoch data were taken
distance is denoted by R .
GC
between April 02-05, 2014.
Parameters Values
α 10h 17m 36s.82 Filters Exposure time Seeing Airmass
2000
◦ ′ ′′ (seconds) (arcsec)
δ 46 24 44.9
2000
− ◦ December 05, 1999 (First epoch)
l 277.23
◦ B 2 240 1.1 1.3
b 8.64
× ∼
V 2 240 0.9 1.3
[Fe/H] 1.59
× ∼
− I 2 240 0.8 1.2
E(B V) 0.24 mag
× ∼
− April 02-05,2014 (Second Epoch)
d 4.9 kpc
V 35 40 1.1 1.1
R 8.8 kpc
GC × ∼
3
2. Data used and reduction procedures plane, which leads the pixel scale across the field-
of-view to change effectively. The corrections to
TodeterminethePMsofthestarsinthiswork,
account for the geometric distortion were derived
we used archive images2 from observations made
using dithered observations of Baade’s window
with the 2.2m ESO/MPI telescope at La Silla,
which lies in the Galactic bulge (see, A06). The
Chile. This telescope contains a mosaic camera
corrections have been noted in a look-up table
calledthe Wide-FieldImager(WFI),consistingof
comprising 9 17 elements, for each chip. For any
4 2,i.e. 8CCDchips. SinceeachCCDhasanar- ×
particular location, a bi-linear interpolation be-
×
rayof2048 4096pixels,WFIultimatelyproduces
tween the four closest grid points from the look-
×
images with a 34 33 arcmin2 field of view.
uptabletothe targetpointdeliversthe distortion
×
Table2presentsthedetailsoftheobservational correction. Still,thedistortionmayvaryovertime
log of the archive data. The observational run of fortheWFI,andistypicallylargernearthe edges
the first epoch contain 2 images in B,V and I of the image. These factors lead to uncertainty in
bands each with 240 sec exposure time observed distortion corrections. To tackle this uncertainly,
on December 05, 1999. In the second epoch, we we followed the local transformation approach as
have 35 images with 40 sec exposure time each described in Section 7 of the article A06. Accord-
in V filter observed between April 02 05, 2014. ingtothelocaltransformationapproach,transfor-
−
Thus, the epoch gap between the data is 14.3 mations from one frame to another are obtained
∼
years. As canbe seeninthe Table2,seeinginthe locally, i.e. with respect to some stars in our
imagesusedare0.8–1.1arcsec,andairmassvalues own images. Because cluster stars exhibit lesser
lie between 1.1–1.3. amount of internal dispersion than the field stars,
∼
cluster stars based on their location in CMD and
2.1. The data reduction procedures motionarechosenasreference. Initially,wechoose
starslyingonthemainsequence,subgiantandred
To derive PMs from the [email protected] mosaic
giant branches by making blue and red envelope
CCD images, we used the astrometric procedure
for the sequences in the CMD. In subsequent at-
developed by Anderson et al. (2006, hereafter
tempts, theselectionis doneusingPMs. Thepro-
A06). The technique involves the usual initial
cess is iterated multiple times to provide the best
stepsofde-biasingandflat-fielding. Oneofthede-
possibleresults. After positionsofstarsaredeter-
cisive factors in providing precise positions of the
mined in all frames, we use six-parameter linear
starsisconstructingagoodPointSpreadFunction
transformations to transform the positions from
(PSF)forthe WFI images. Sincethe shapeofthe
one frame to another. This approach resembles
PSF changes across the mosaic CCD, we capture
the classical “plate-pair” method (e.g., Sanders
this variability by using an array of 15 PSFs per
1971a, Tian et al. 1998), but it is more gener-
CCD chip (3 across and 5 high), as explained in
alized and can be used to all possible combina-
A06. Tofurnishpositionsandfluxesoftheobjects
tions of the first and second epoch frames. The
in an image, an array of empirical PSFs are con-
relative PM of a target star will be the averageof
structed. ThesePSFsaresavedinalook-uptable
all displacements for inter epoch transformations.
on a very fine grid of a quarter pixel size. Each
Since PMs do not contribute to the intra-epoch
PSF goes out to a radius of 25 pixels and each
displacements,they areusedtocalculateerrorsin
pixel is split in 4 equal parts, thus giving (201,
PM measurements.
201)gridpoints for a PSF.The center ofthe PSF
is locatedatthe centralgridpoint(101,101). A06
2.1.1. Calibrating the photometry
presented the automated code we are now using
to iteratively determine the precise positions and Instrumental B,V and I magnitudes were
instrumentalmagnitudesforthebrightestdownto transformed into standard Johnson–Cousin sys-
faintest stars for B,V,I bands. tem using secondary standard stars provided by
As documented in A06, [email protected] is affected P. Stetson3. The standard stars used for calibra-
by significant geometric distortion in the focal
3http://www3.cadc-ccda.hia-iha.nrc-
2http://archive.eso.org/eso/eso archive main.html cnrc.gc.ca/community/STETSON/standards/
4
tion have a brightness range of 12.6 V 19.8 ing IRAF5 tasks CCMAP and CCTRAN. The
≤ ≤
and color ranges of 0.4 (B V) 1.5 and transformations have rms values of about 20
≤ − ≤ ∼
0.4 (V I) 1.9. A total of 160 stars for BV mas. The relatively high accuracy of our distor-
≤ − ≤
magnitudes and 165 stars for I magnitudes were tion corrections as well as the reasonablestability
used in the calibration process. ofthe intra-chippositionsmakesitpossibletoap-
We used the transformation equations written ply a single plate model which includes linear and
below to derive the photometric zero-points and quadratic terms and a small but significant cubic
color terms: term in each coordinate. Also, this solution re-
movesthe effects causedby differentialrefraction.
2.2. Proper motion determinations
B =B +C (B V )+Z
std ins b ins ins b
× −
Vstd =Vins+Cv (Bins Vins)+Zv We used 6 images from the first epoch and 35
× −
I =I +C (V I )+Z , images from the second epoch to determine PMs
std ins i ins ins i
× −
for NGC 3201 stars. Having a large number of
where instrumental magnitudes and secondary images minimizes the value of the standard error
standard magnitudes have been denoted by sub- in the PMs.
scripts “ins” and “std” respectively. Cb,Cv and Westartedwithaselectionofphotometricclus-
Ci denotethecolorterms,whileZb,Zv andZi are ters members, i.e. members selected on the basis
the global zero-points. As a result of the calibra- oftheirpositioninV vs(B V)CMD.Weselected
−
tion, the values of the color-terms are 0.39, 0.07 starslyingneartheclustersequencesintheCMD,
−
and0.12,whereasthezero-pointsare24.79,24.18, withbrightnessintherangeof14 V 19. These
≤ ≤
23.27 for B, V and I filters respectively. These areusedasalocalreferencetotransformthecoor-
values of color terms and zero-point agree with dinatesofthestarsbetweentheepochs. Adopting
the values posted on the [email protected] webpage4. only those stars lying on the cluster sequences in
The photometric standard deviations for indi- theCMDandhavingPMerrors<1.0masyr−1en-
vidual photometric bands were calculated by re- sure that the PMs are determined with respect to
ducing multiple observations to a common refer- the systematicmotionofthecluster. Tominimize
ence frame. Figure 1 presents the rms error in the influence of uncorrected geometric distortion
the magnitudes for B,V and I magnitudes as a residuals,alocaltransformationbasedontheclos-
function of visual magnitude. The values of aver- est 25 reference stars on the same CCD chip was
agermsarelessthan 0.01magforstarsbrighter used. We didnotfind anysystematicslargerthan
∼
than 19 mag for B and I filters and better than random errors close to the corners or edges of the
0.01 mag for V <20 mag. CCD chips.
∼
The routine described in A06 has an iterative
2.1.2. Calibrating the positions nature and we iterated it to remove some stars
from the initial photometric member list. Stars
As a part of the astrometric studies of NGC
wereeliminatediftheyhadPMsinconsistentwith
3201, we present the equatorial coordinates of
clustermembership,inspiteoftheircolorsplacing
stars in International Celestial Reference System
them near the cluster sequence in the CMD. PMs
(ICRS). We used the geometric distortion correc-
and their rms errors are plotted as a function of
tion from the look-up table given in the A06 to
visualmagnitudeinFigure2. Themedianvalueof
correct the pixel coordinates X,Y of each star in
PMerroris 0.8mas yr−1 for stars brighterthan
eachframeandaveragedbymeansofasixparame- V 18 mag∼which increases up to 1.5 mas yr−1
ter lineartransformationintoa commonreference ∼ ∼
for stars in the magnitude range of 18 < V < 20
frame. The online digitized sky ESO catalogue in
mag.
the SKYCAT software is then used to transform
the averaged X,Y positions to right ascension
5IRAFisdistributedbytheNationalOpticalAstronomical
(RA)anddeclination(Dec)inJ2000.0equinoxus-
Observatory which is operated by the Association of Uni-
versitiesforResearchinAstronomy,undercontactwiththe
4http://www.ls.eso.org/lasilla/sciops/2p2/E2p2M/WFI/zeropoints/ NationalScienceFoundation
5
Fig. 3.— (Top panels) Proper motion vector-point diagrams (VPDs). Zero point in VPD is the average
motion of the assumed cluster stars. (Bottom panels) V vs. (B V) CMDs. (Left) The whole sample;
(center) stars in VPD within 5 mas yr−1 around the cluster me−an motion. (Right) Probable field stars
in the region of NGC 3201. F∼or all the plots only stars having PM error better than 2 mas yr−1 in each
coordinate have been considered.
6
Fig. 4.— (Left:) Magnitude-binned CMD of the stars while PM errors increase from 1.2 mas yr−1 for
the brightest bin to 2.5 mas yr−1 for the faintest bin. (Middle:) VPDs for the same stars lying in the
corresponding magnitude bins. A circle in each VPD shows the adopted membership criterion. The radii of
the circles increase from 2.5 mas yr−1 to 6.0 mas yr−1 from bright to fainter bins. (Right:) CMD for stars
expected to be cluster members.
7
2.2.1. Cluster CMD decontamination is to determine membership probabilities of stars
which will yield a quantitative significant num-
One of the main reasonsto carryout PManal-
ber for a particular star belonging to the cluster.
ysisforstarclustersistoisolatetheclustersample
The credit to set up a mathematical model to use
from the field stars and to produce a CMD with
PMs to determine membership probabilities goes
onlythemostprobableclustermembers. Figure3
to Vasilevskis et al. (1958). The maximum likeli-
clearly demonstrates the strength of PM analysis
hood principle to compute membership probabili-
in separating the field stars using vector-point di-
ties was introduced by Sanders (1971b). Over the
agrams (VPDs) in the top panels, in combination
years,methods to calculatemembershipprobabil-
withV versus(B V)CMDsinthebottompanels.
− ities have been refined (e.g., Stetson 1980; Zhao
Intheleftpanelsofthefigure,theentiresampleof
& He 1990;Zhao & Shao 1994). In this study, we
stars is shown, while the middle panels and right
use the method given by Balaguer-Nu´n˜ez et al.
panels represent likely cluster members and field
(1998). This method has been previouslyused for
stars respectively. In the top middle panel, VPD
both globular clusters (Bellini et al. 2009, Sariya
hasacircleofradius 5masyr−1aroundtheclus-
∼ et al. 2012, 2015) and open clusters (Yadav et al.
ter centroid. This motion circle is our provisional
2013). According to this method, two frequency
criterion for assigning membership to the stars,
distribution functions are constructed for a par-
before membership probabilities are determined.
ticular ith star. Frequency distributions of cluster
The radius of the circle is chosen as a compro-
stars (φν) and field stars (φν) are presented by
mise between losing cluster members with poorly c f
the equations given below:
measuredPMsandincludingsomefieldstarsthat
havetheir PMsconsistentwith the cluster’smean
PM.Theshapeoftheclustermembers’PMdistri-
φν = 1
bution in the VPD is round, which suggests that c 2π√(σ2+ǫ2 )(σ2+ǫ2 )
c xi c yi
ourPMmeasurementsarenotaffectedbyanysys- exp 1[(µxi−µxc)2 + (µyi−µyc)2]
tematics. It is pretty obvious from the figure that × {−2 σc2+ǫ2xi σc2+ǫ2yi }
having a large epoch gap for CCD data has pro-
and
duced a CMD almost free from field stars.
Figure 4 shows the (B V),V CMD which is
− φν = 1
binnedalongthe magnitudeaxis. Toidentify pro- f 2π√(1−γ2)√(σ2 +ǫ2 )(σ2 +ǫ2 )
xf xi yf yi
visional cluster members, different selection crite- exp 1 [(µxi−µxf)2
ria were used in different magnitude bins. The × {−2(1−γ2) σx2f+ǫ2xi −
criterion was tighter for bright stars as they have 2γ(µxi−µxf)(µyi−µyf) + (µyi−µyf)2]
more reliable measurements, but is less stringent √(σx2f+ǫ2xi)(σy2f+ǫ2yi) σy2f+ǫ2yi }
forfainterstars. AscanbeseeninFigure4,fainter
where (µ , µ ) are the PMs of ith star, while
starshavepoorerPMdeterminationscomparedto xi yi
(ǫ , ǫ ) are the proper motion errors. (µ , µ )
brighter stars: PM uncertainty increases from 1.2 xi yi xc yc
mas yr−1 to 2.5 mas yr−1 from the brightest bin represent the cluster’s PM center and (µxf, µyf)
are the field PM center. For the cluster members,
to the faintest one. We therefore adopt a PM se-
lection radius that increases from 2.5 mas yr−1 in the intrinsic proper motion dispersion is denoted
thebrightestmagnitudebinto6.0masyr−1inthe by σc, whereas σxf and σyf exhibit the field in-
trinsicpropermotiondispersions. Thecorrelation
faintestone. However,westillhaveagoodenough
coefficient γ is calculated as:
decontamination of field stars even in the fainter
magnitudes.
γ = (µxi−µxf)(µyi−µyf).
3. Membership probabilities σxfσyf
In Figure 3, two different groups of stars are The spatial distribution of the stars was not
distinguishable based on their motion, although considered in calculating membership. In com-
a larger fraction of the stars are inside the circle puting φν and φν, we used those stars which
c f
forprovisionalclustermembership. Thenextstep have PM errors better than 2 mas yr−1. In
∼
8
4000
Fig. 5.— Membership probability P (%) of the
µ
stars in the direction of NGC 3201 plotted as a
function of the V magnitude. For stars having
magnitudes V 18 mag and fainter, the average 3000
∼
P aredecreasingfor cluster members,while they
µ
are increasing for field stars.
2000
1000
2000 3000 4000 5000
X (WFI Pixels)
Fig. 7.— Spatial distribution of stars presented
in this study. Red filled circles are the stars with
P > 80%, blue triangles show the stars having
µ
10%<P 80%,andblackopencirclesshowthe
µ
≤
starswith P 10%. Stars havingpropermotion
µ
errorbetterth≤an2masyr−1areplottedhere. The
gaps which form a “cross” like pattern are due to
the gaps in the mosaic CCD system.
Fig. 6.— Histogram of the membership probabil-
ities derived in this study.
9
VPD, the center of the cluster stars is found to Also, this CMD shows stars of various evolution-
be (µ , µ )=(0, 0) mas yr−1. The intrinsic PM ary stages like sub-giants, red giants, horizontal
xc yc
dispersion for the cluster stars (σ ) could not be branch stars and blue stragglers. All the cluster
c
ascertained reliably using our PM data. Pryor sequences in this CMD look cleaner with minimal
& Meylan (1993) list the value of radial velocity field contamination. As mentioned earlier, NGC
dispersion for NGC 3201 as 5.2 km sec−1. Con- 3201 shows differential reddening, due to which
sidering the value of the distance of NGC 3201 as the cluster sequences are broadened in CMD. As
4.9 kpc (Harris 1996, 2010 edition), the internal discussed by Kravtsov et al. (2009), the red giant
PM dispersion becomes 0.22 mas yr−1. Hence, branch of the cluster, in particular, shows signifi-
we used σ = 0.22 mas y∼r−1. For field stars, we cant broadening. In addition to this, we find gaps
c
have (µ , µ ) = (13.8, 4.8) mas yr−1 and (σ , in the red giant branch at V 13 and V 15,
xf yf xf
σ ) = (2.5, 2.1) mas yr−1. the formeronebeingmoresignifi∼cant. These∼gaps
yf
havebeenreportedbyLee(1977)inhisphotomet-
Ifn andn arethenormalizednumberofclus- ric study of NGC 3201. The horizontal branch of
c f
ter and field stars respectively (i.e., n +n =1), NGC 3201is well developedand extended, with a
c f
the total distribution function can be calculated relatively unclear instability strip.
as:
3.1. Comparison with Zl12
The PMs presented in this study were com-
φ=(n φν)+(n φν),
c × c f × f pared with the catalogue given by Zl12. For com-
parison,weplottedthespatialdistributionsofour
Asaresult,themembershipprobabilityforthe
cataloguewithZl12inFigure9. Inthisfigure,our
ith star is given by:
catalogue stars are shown with red filled circles,
while Zl12 stars are shown with blue triangles. It
P (i)= φc(i). is clearlyseenin the figure that the presentinves-
µ φ(i) tigation extends the PM studies of NGC 3201 to
In Figure 5, membership probabilities are a wider region. In the additional observed area
shown as a function of visual magnitude. The in our catalogue, we have PM information from
figure shows clear separation of cluster and field about 2000 stars. For the common stars, the dif-
stars as sharp distributions of stars around mem- ferences in both PMcomponents betweenthe two
bership values P 100% and P 0%. However, cataloguesisshowninFigure10. Valuesofthe3σ-
µ µ
∼ ∼
due to increasing errorsat fainter regime,one can clipped median of the proper motion differences
notice a number of stars with intermediate values are 0.04(σ=0.54) mas yr−1 and 0.05(σ=0.62)
of P , for magnitudes fainter than V=18 mag. mas yr−1. Our PMs exhibit consi−stency with the
µ
The histogram of membership probabilities for Zl12 data for V <20 mag.
8322 stars is shown in Figure 6. The presence of
higher peaks for the leftmost and rightmost bins 4. Membership of variables and X-ray
suggest that the method used for the member- sources
ship determination is effective for NGC 3201. We
We used the membership catalogue to ascer-
find 5981 stars that have membership probabili-
tain the membership status of the reported vari-
ties larger than 80%. The spatial distribution of
ablestarsandX-raysourcesintheregionofNGC
the stars is shown in Figure 7. To distinguish be-
3201. The details of the comparison are listed in
tweentheclustermembersandfieldstars,wehave
Table3. ThevariablestarsofNGC3201havebeen
useddifferentsymbols forstarshavingP >80%,
µ
compiled on Clement’s webpage of the catalogue
10% < P 80% and P 10%. The cut off
µ ≤ µ ≤ of variable stars in globular clusters6. Recently,
values of P are based on the histogramshown in
µ
some new variable were detected by Kaluzny et
Figure 6.
al. (2016). We found four variable stars in com-
Figure 8 presents the CMD of stars having
P > 80%. In this CMD, cluster sequences for
µ 6http://www.astro.utoronto.ca/∼cclement/cat/C1015m461
stars brighter than V 20 mag can be seen.
∼
10