The Tale of the Milky Way Globular Cluster NGC 6362 - as ... · Milky Way galaxy (Carretta et...

MNRAS 000 1ndash (0000) Preprint 6 September 2019 Compiled using MNRAS LATEX style file v30

The Tale of the Milky Way Globular Cluster NGC 6362 -I The Orbit and its possible extended star debris featuresas revealed by Gaia DR2

Richa Kundu1 Jose G Fernandez-Trincado23dagger Dante Minniti456

Harinder P Singh1 Edmundo Moreno7 Celine Reyle3 Annie C Robin3and Mario Soto21Department of Physics and Astrophysics University of Delhi Delhi-110007 India2Instituto de Astronomıa y Ciencias Planetarias Universidad de Atacama Copayapu 485 Copiapo Chile3Institut Utinam CNRS UMR 6213 Universite Bourgogne-Franche-Comte OSU THETA Franche-Comte Observatoire de Besancon

BP 1615 25010 Besancon Cedex France4Instituto Milenio de Astrofisica Santiago Chile5Departamento de Ciencias Fisicas Facultad de Ciencias Exactas Universidad Andres Bello Av Fernandez Concha 700 Las Condes

Santiago Chile6Vatican Observatory V00120 Vatican City State Italy7Instituto de Astronomıa Universidad Nacional Autonoma de Mexico Apdo Postal 70264 Mexico DF 04510 Mexico

6 September 2019

ABSTRACTWe report the identification of possible extended star debris candidates beyond thecluster tidal radius of NGC 6362 based on the second Gaia data release (Gaia DR2)We found 259 objects possibly associated with the cluster lying in the vicinity of thegiant branch and 1ndash2 magnitudes fainterbrighter than the main-sequence turn-off inthe cluster color-magnitude diagram and which cover an area on the sky of sim41 deg2

centered on the cluster We traced back the orbit of NGC 6362 in a realistic Milky-Waypotential using the GravPot16 package for 3 Gyrs The orbit shows that the clustershares similar orbital properties as the inner disk having peri-apo-galactic distancesand maximum vertical excursion from the Galactic plane inside the corotation radius(CR) moving inwards from CR radius to visit the inner regions of the Milky Way Thedynamical history of the cluster reveals that it has crossed the Galactic disk severaltimes in its lifetime and has recently undergone a gravitational shock sim 159 Myrago suggesting that less than 01 of its mass has been lost during the current disk-shocking event Based on the clusterrsquos orbit and position in the Galaxy we concludethat the possible extended star debris candidates are a combined effect of the shocksfrom the Galactic disk and evaporation from the cluster Lastly the evolution ofthe vertical component of the angular momentum shows that the cluster is stronglyaffected dynamically by the Galactic bar potential

Key words Galaxy kinematics and dynamics (Galaxy) globular clusters individ-ual NGC 6362

1 INTRODUCTION

Extra-tidal stellar material associated with globular clus-ters is spectacular evidence for satellite disruption at thepresent day which provides significant clues about the dy-

E-mail richakundu92gmailcomdagger E-mail jfernandezt87gmailcom or jfernandezobs-

besanconfr

namical history of the clusters and their host galaxies Glob-ular clusters evolve dynamically under the influence of thegravitational potential well of their host galaxy (Gnedin ampOstriker 1997 Murali amp Weinberg 1997 Leon Meylan ampCombes 2000 Kunder et al 2018 Minniti et al 2018) re-sulting in the escape of the stars close to the tidal boundaryof the cluster consequently forcing the cluster cores to con-tract and envelopes to expand (eg Leon Meylan amp Combes2000 Kunder et al 2014) Therefore globular clusters are

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2 Kundu et al

important stellar systems to study the evolution structureand dynamics of their host galaxy

Globular clusters lose stars mainly due to dynamicalprocesses like dynamical friction tidal disruption bulge anddisk shocking and evaporation (Fall amp Rees 1977 1985)Dynamical friction is due to the gravitational pull of thefield stars that are accumulated behind the cluster mo-tion These stars slow down the cluster and pull some ofthe loosely bound stars away from it This effect is morepronounced in the bulge of the Galaxy where the densityof field stars is higher Dynamical friction has been pro-posed in many studies (Chandrasekhar 1943 Mulder 1983White 1983 Tremaine amp Weinberg 1984 Capuzzo-Dolcettaamp Vicari 2005 Moreno Pichardo amp Velazquez 2014 Arca-Sedda amp Capuzzo-Dolcetta 2014) but the observational ev-idence has been more elusive while tidal disruption havebeen observed (Leon Meylan amp Combes 2000 Odenkirchenet al 2001 Belokurov et al 2006 Grillmair amp Johnson 2006Grillmair amp Mattingly 2010 Niederste-Ostholt et al 2010Jordi amp Grebel 2010 Sollima et al 2011 Balbinot et al2011 Kuzma et al 2015 Myeong et al 2017 Navarrete Be-lokurov amp Koposov 2017) and studied by many (King 1962Tremaine Ostriker amp Spitzer 1975 Chernoff Kochanek ampShapiro 1986 Capuzzo-Dolcetta 1993 Weinberg 1994 Mey-lan amp Heggie 1997 Gnedin amp Ostriker 1997 Vesperini ampHeggie 1997 Combes Leon amp Meylan 1999 Lotz et al 2001Capuzzo Dolcetta Di Matteo amp Miocchi 2005 Majewskiet al 2012a Kupper Lane amp Heggie 2012 Majewski et al2012b Torres-Flores et al 2012 Knierman et al 2013 Mu-lia amp Chandar 2014 Hozumi amp Burkert 2015 Rodruck et al2016 Fernandez-Trincado et al 2017ab Bal-binot amp Gieles 2018 Myeong et al 2018 Kundu Minniti ampSingh 2019 )

NGC 6362 is a nearby low mass globular cluster withintermediate metallicity located in the bulgedisk of theMilky Way galaxy (Carretta et al 2010) It has an age ofsim125plusmn05 Gyr which is enough to evolve under the grav-itational potential of the Milky Way Therefore identifyingpossible tidal tails around NGC 6362 is especially intrigu-ing to study the cluster dynamics in the bulgedisk regionwhich is poorly understood Recently Baumgardt amp Hilker(2018) presented a catalog of masses structural profiles andvelocity dispersion values for many Galactic globular clus-ters including NGC 6362 They found that this cluster fitsa King profile with a constant velocity dispersion as a func-tion of radius hence there was no evidence of a tidal tailHowever their measurements were concentrated to the in-ner regions extending only out to 400 arc-sec away from thecenter

In the present work we report the detection of poten-tial extended star debris associated with NGC 6362 Wehave taken advantage of the exquisite data from Gaia DataRelease 2 (Gaia DR2 Gaia Collaboration et al 2018a) tosearch for such extended star debris features around NGC6362 To give a proper explanation for the presence of theobserved possible star debris we time-integrated backwardthe orbit of NGC 6362 to 3 Gyrs under variations of theinitial conditions (proper motions radial velocity heliocen-tric distance Solar position Solar motion and the velocityof the local standard of rest) according to their estimatederrors Our analysis indicates that the cluster is dynamicallyaffected by the Galactic bar potential presently experienc-

Table 1 NGC 6362 ndashSun parameters

Parameter Value Reference

NGC 6362

α () δ () 262979 minus67048 (a)Distance (kpc) 76 (a)

Rgal (kpc) 471

microα (masyr) -5507plusmn0052 (a)microδ (masyr) -4747plusmn0052 (a)

Vlos minus1458plusmn018 (a)

Tidal Radius (pc) 3073 (b)Mass (M) sim 105 (b)

Metallicity minus107 (d)

Age (Gyr) 125plusmn05 (e)

Sun

R (kpc) 83 (f)

U VW (km sminus1) 1110 1224 725 (f)

VLSR (km sminus1) 239 (f)

(a) Vasiliev (2019) (b) Moreno Pichardo amp Velazquez (2014)

(c) Dalessandro et al (2014) (d) Massari et al (2017) (e)Dotter et al (2010) (f) Brunthaler et al (2011)

ing a bulgebar shocking with considerable amount of massloss which can be observed as stars present in the imme-diate neighborhood of the cluster A similar analysis wasrecently carried out by Minniti et al (2018) for NGC 6266(also known as M62) using extra-tidal RR Lyrae stars

This paper is organized as follows In Section 2 we se-lect the possible star debris candidates beyond the clustertidal radius of NGC 6362 In Section 3 we discussed thesignificance of the observed star debris In Section 4 we de-termine its most likely orbit using novel galaxy modelingsoftware called GravPot16 In Section 5 we discussed themass lost by the cluster due to various processes The con-cluding remarks are summarised in Section 6

2 IDENTIFICATION OF EXTENDED STARDEBRIS CANDIDATES AROUND NGC 6362

To search for the extended star debris features around thecluster NGC 6362 we have made use of the second Gaiadata release (Gaia DR2 Gaia Collaboration et al 2018a)We first download Gaia DR2 in a cone around the clusterwith radius around five tidal radii where we tried to identifythe star debris which contains 276391 objects

Since NGC 6362 is relatively far we decided to payparticular attention to avoid contamination by data pro-cessing artifacts andor spurious measurements Thereforewe adopted the following conservative cuts on the columnsof the Gaia DR2 GAIA SOURCE catalogue

(i) ASTROMETRIC GOF AL lt 3 This cut ensures that thestatistics astrometric model resulted in a good fit to thedata(ii) ASTROMETRIC EXCESS NOISE SIG le 2 This criterionensured that the selected stars were astrometrically well-behaved sources(iii) minus023 le MEAN VARPI FACTOR AL le 032 AND

MNRAS 000 1ndash (0000)

3

Figure 1 The Gaia DR2 positions for the highest likelihood star debris candidates in the region of NGC 6362 shown with unfilledwhite circles The inner and outer black dashed circles are the tidal radius (rt) and 5timesrt respectively (see text) The arrows indicate the

directions of the cluster proper motion (red arrow) with a preferential direction toward SndashW the Galactic center (GCndashgreen arrow)

and the direction perpendicular to the galactic plane (blue arrow) The computed orbit (black lines) of the cluster is displayed assumingfour different values of the bar patterns speed (35 40 45 and 50 km sminus1 kpc) in the GravPot16 package (see text) Five adjacent

regions containing field stars (foreground and background) whose proper motions and distribution in the CDM are overlapped with

cluster members and in which the contamination was evaluated The expected surface density of potential members and each adjacentfield is internally indicated which overlap all the criteria adopted in this work

VISIBILITY PERIODS USED gt 8 These cuts were usedto exclude stars with parallaxes more vulnerable to errors

(iv) G lt 19 mag This criterion minimized the chance offoreground contamination

Here we only give a rough overview and refer the readerto Marchetti Rossi amp Brown (2018) for a detailed descrip-tion of these high-quality cuts

The final sample so selected amounts to a total of 83406stars From this sample we further retain as candidate mem-


4 Kundu et al

bers of the cluster those objects which lie in an annular re-gion around the cluster with its inner radius as the tidalradius (rt =13907 arcmin Moreno Pichardo amp Velazquez2014) of NGC 6362 and an outer radius equal to 5 timesits tidal radius as displayed in Figure 1 This reduces oursample to 77549 objects

As a consistency check to verify the validity of high-est likelihood star debris candidates based on their posi-tion on the sky only the sample was restricted to the starswhose proper motions match with the proper motion of thecluster within 3σmicro where σmicro is the total uncertainty inquadrature obtained from a 2-dimensional Gaussian fit Forthis purpose a 2-dimensional Gaussian smoothing routinewas applied in proper motion space for stars with G lt 19mag within 2timesrhalfminusmass from the centre of the clusterA 2D Gaussian was fitted to this sample and membershipprobabilities are assigned With this procedure we foundmicro2Dα plusmn σα = minus5511 plusmn 0237 mas yrminus1 and micro2D

δ plusmn σδ =minus4742 plusmn 0302 mas yrminus1 and σmicro = 038 mas yrminus1 ourresults also agree remarkably well with the more recent mea-surements of PMs for NGC 6362 eg microα = minus5507plusmn 0052mas yrminus1 and microδ = minus4747plusmn 0052 from Vasiliev (2019) Astar was considered to be a GC member if its proper mo-tion differs from that of NGC 6362 by not more than 3σmicroleaving us with a grand total of 1503 stars The content ofnearby stars in our initial sample is reduced by excludingthose objects with estimated distances from confined to asphere of radius 3 kpc around the Sun This cut is motivatedby the fact that at large latitudes away from the disk thepriors would be expecting distant stars to be much closerto us than they truly are and force the stars towards thesecloser unrealistic distances Therefore the distances fromthe Bailer-Jonesrsquos catalog should just be following the pri-ors and would not account for distant over-densities Thisreduces our sample to 826 objects

Thus we found a total of 826 possible star debris candi-dates of NGC 6362 which share an apparent proper motionclose to the nominal value of the cluster suggesting thatthese stars could possibly be evaporated material from NGC6362 Therefore to be sure that our candidate members areactually part of the cluster system we selected those starswhose locations on the Colour-magnitude diagram (CMD)clearly lie on or near the prominent main branches of NGC6362 as illustrated by the red symbols in figure 2 A to-tal of 259 possible extended star debris candidates passedthese quality cuts as illustrated in Figure 1 and Figure 2(highlighted by red symbols)

To summarize the possible star debris members of thecluster in Figure 2 show the following proper motions thatare very concentrated as expected in the vector point di-agram (hereafter VPD) of a globular cluster and a CMDwith the characteristic features of a globular cluster egthe main sequence the turn-off the red giant branch andsome stars in the horizontal branch It is important to notethat the determination of the possible extended star debrisof NGC 6362 could include some field stars as members orvice versa in sect3 we perform an estimation of the degree ofcontamination of the extracted members ie the possiblenumber of field stars that could have been labelled as pos-sible extended star debris members of the cluster

This finding gives possible clues about the recent dy-namical history of NGC 6362 which suggests that this clus-

ter could eventually form tidal tails or could also be associ-ated with the recent encounter of the cluster with the disk

Table 3 lists the main parameters of the 259 possibleextended star debris Figure 2 shows consistently the validityof our probable extended star debris members which sharean apparent proper motion close to the value for NGC 6362suggesting these stars are probable members of the cluster

It is important to note that most of the stars inside2times rhalfminusmass of the cluster are spread in spread in propermotions as illustrated by black dots in Figure 2 conse-quently one may be lead to conclude that it is related tocontamination by foregroundbackground stars which wouldseem to be the most likely explanation for the significantlyhigher proper motion values Thus we also expect that oursample may be significantly contaminated from other Galac-tic stellar populations (see sect3) To alleviate this situationa detailed chemical abundance analysis will be necessary tounderstand their relation if any with the cluster

3 SIGNIFICANCE OF THE DETECTION OFPOSSIBLE EXTENDED STAR DEBRISAROUND NGC 6362

It is important to note that the main tracers of the pos-sible extended star debris of NGC 6362 identified in thiswork are main-sequence (MS) stars and subgiant stars 1ndash2magnitudes fainter and brighter than the MS turn-off (TO)respectively However the cluster stars beyond cluster tidalradius are hidden in the CMD due to the combination ofthe contributions of a minor fraction of cluster membersand fore-back-ground stellar populations from the differentMilky Way components (mainly the thin-thick disk andhalo)

In this sense we attempt to estimate the significanceof the detection in our photometry and PMs space For thispurpose we have compared the observed stellar counts withthose computed from the synthetic CMDs generated withthe updated version of the Besancon Galaxy model for thesame line-of-sight and solid angle after correcting for com-pletness For a more detailed description of the BesanconGalaxy model we refer the readers to Robin et al (2003the full basic description) Robin et al (2014 update onthe thick disc) update on kinematics and update onthe stellar evolutionary models The observed stars consid-ered to derive the significance of a subjacent population arethose contained in the CMD and PM space as illustrated inFigure 2

We calculated the expected number of Milky Way starsover the survey area and in distance range D gt3 kpc fromthe Besancon Galaxy model We found Nmodel sim 167 plusmn 13stars in the area of the Gaia footprint around NGC 6362The cited error is Poisson statistics We can then esti-mate the significance of the detection with respect to thesynthetic model in the following manner δ asymp (Nmodel minusNextraminustidal)(Nmodel +Nextraminustidal)

12 where Nextraminustidal isthe number of observed stars following the criteria describedabove We obtain a δ sim 45 detection above the foregroundand background population

Another way to perform an estimation of the degree ofcontamination of the extracted members relies in upon applyour method in adjacent regions (defined with the same area


5

Figure 2 Kernel Density Estimate (KDE) smoothed distribution of the Colour-magnitude diagram of stars within 5 times rt from the

photometric centre of NGC 6362 (top rows) and proper motions in the region of the cluster (bottom rows) Left panels illustrates thestars which pass the astrometric excess noise cutoffs for stars in the field and stars within 2times rhalfminusmass sim 41 arcmin from the centre

of the cluster (black dots) Right panels illustrates the position in the CMD and VPD for the highest likelihood of possible extended star

debris candidates (red dots) The black dashed lines show the nominal proper motion values for NGC 6362 at microα = minus5507 mas yrminus1microδ = minus4747 mas yrminus1 (Vasiliev 2019) while the white contour line encloses the density of forebackground stars and cluster itself

than our explored region) around the cluster as illustratedin Figure 1 Performing an analysis like that mentioned inthe beginning of sect2 but counting all the stars in the fieldinstead of only those potential members around the clusterwe obtain rough estimates of the expected contamination inour sample We note that the incompleteness of the GaiaDR2 catalogue itself has not been taken into account in ourcomputations therefore our estimates are upper limits tothe actual completeness for the most favorable cases (low-density fields) Figure 1 the expected surface density (Σ1

starΣ2star Σ3

star Σ4star and Σ5

star) of foregroundbackgroundstars (black dots) in five adjacent regions around NGC 6362Those densities remain low as compared to our potentialsample with the exception of Σ5

star = 00291 which ishigher due to that this region lies in the direction of the sky

containing the highest densities of field stars for this rea-son we have also avoid additional adjacent regions towardthe direction North-West of the cluster Finally based onΣ1star Σ2


star we estimate the degree of con-tamination ie the fraction of field stars that could havebeen erroneously labelled as possible extended star debrismembers which is expected that sim40 (sim 103plusmn10 stars)to 80 (sim207plusmn14 stars) of the field stars could have beenerroneously extracted as members in our sample (which wecall contamination of the members) This rough estimationpoint-out a good agreement between the Besancon Galaxymodel and the data in the degree of contamination of theextracted members by other Galactic stellar populations Inboth cases a future inventory of the chemistry of these starsin particular the elements involved in the proton-capture re-


6 Kundu et al

actions (ie C N O Mg Al among other) will be crucial toconfirm or refute the cluster nature of these star debris can-didates in a similar fashion as These stars will belater analyzed using high-resolution (R sim 22 000) spectrafrom the APOGEE-2S survey () in order to investigateits chemical composition

4 THE ORBIT OF NGC 6362

We estimated the probable Galactic orbit for NGC 6362in order to provide a possible explanation to the possibleextended star debris identified in this work For this weused a state-of-the art orbital integration model in an (asfar as possible) realistic gravitational potential that fits thestructural and dynamical parameters of the galaxy to thebest we know of the recent knowledge of the Milky Way Forthe computations in this work we have employed the rotat-ing rdquoboxypeanutrdquo bar model of the novel galactic potentialmodel called GravPot161 along with other composite stellarcomponents The considered structural parameters of ourbar model eg mass present-day orientation and patternspeeds are within observational estimations 11times1010 M20 and 35 to 50 km sminus1 kpc respectively The density-profile of the adopted rdquoboxypeanutrdquo bar is exactly theModel-S as in Robin et al (2012) while the mathematicalformalism to derive a correct global gravitational potentialof this component will be explained in a forthcoming paper(Fernandez-Trincado et al 2019 in preparation)

GravPot16 considers on a global scale a 3D steady-stategravitational potential for the Galaxy modelled as the su-perposition of axisymmetric and non-axysimmetric compo-nents The axisymmetric potential is made-up of the su-perposition of many composite stellar populations belong-ing to seven thin disks following the Einasto density-profilelaw (Einasto 1979) superposed along with two thick diskcomponents each one following a simple hyperbolic secantsquared decreasing vertically from the Galactic plane plusan exponential profile decreasing with Galactocentric radiusas described in Robin et al (2014) We also implementedthe density-profile of the interstellar matter (ISM) compo-nent with a density mass as presented in Robin et al (2003)The model also correctly accounts for the underlying stellarhalo modelled by a Hernquist profile as already describedin Robin et al (2014) and surrounded by a single sphericalDark Matter halo component Robin et al (2003) Our dy-namical model has been adopted in a score of papers (egFernandez-Trincado et al 2017ab ) Fora more detailed discussion we refer the readers to a forth-coming paper (Fernandez-Trincado et al in preparation)

For reference the Galactic convention adopted by thiswork is Xminusaxis is oriented toward l = 0 and b = 0 andthe Yminusaxis is oriented toward l = 90 and b = 0 and thedisk rotates toward l = 90 the velocity components arealso oriented along these directions In this convention theSunrsquos orbital velocity vector is [UVW] = [111 1224725] km sminus1 (Brunthaler et al 2011) The model has beenrescaled to the Sunrsquos galactocentric distance 83 kpc andthe local rotation velocity of 239 km sminus1

1 httpsgravpotutinamcnrsfr

For the computation of the Galactic orbits for NGC6362 we have employed a simple Monte Carlo scheme forthe input data listed in Table 1 and the Runge-Kutta algo-rithm of seventh-eight order elaborated by Fehlberg (1968)The uncertainties in the input data (eg distance propermotions and line-of-sight velocity errors) were propagatedas 1σ variations in a Gaussian Monte Carlo re-sampling inorder to estimate the more probable regions of the spacewhich are crossed more frequently by the simulated orbitsas illustrated in Figure 2 The error bar for the heliocentricdistance is assumed to be 1 kpc We have sampled half mil-lion orbits computed backward in time during 3 Gyr Errorsin the calculated orbital elements were estimated by takinghalf million samples of the error distributions and findingthe 16th and 84th percentiles as listed in Table 2 The aver-age value of the orbital elements was found for half millionrealizations with uncertainty ranges given by the 16th and84th percentile values as listed in Table 2 where rperi is theaverage perigalactic distance rapo is the average apogalac-tic distance and Zmax is the average maximum distance fromthe Galactic plane

Figure 3 shows the probability densities of the resultingorbits projected on the equatorial (left column) and merid-ional (right column) Galactic planes in the non-inertial refer-ence frame where the bar is at rest The orbital path (adopt-ing central values) is shown by the black line in the samefigure The green and yellow colors correspond to more prob-able regions of the space which are crossed more frequentlyby the simulated orbits We found that most of the simulatedorbits are situated in the inner bulge region which meansthat NGC 6362 is on high eccentric orbit (with eccentrici-ties greater than 045) reaching out to a maximum distancefrom the Galactic plane larger than 2 kpc with a perigalac-ticon of sim 2 kpc and an apogalactic distance of sim 6 kpcOn the other hand NGC 6362 orbits have energies allowingthe cluster to move inwards from the barrsquos corotation radius(lt 65 kpc) In this region a class of orbits appears aroundthe Lagrange points on the minor axis of the bar that canbe stable and have a banana-like shape parallel to the bar(see lower panel with Ωbar = 50 km sminus1 kpc in Figure 3)while the Lagrange orbits libating around Lagrange pointsaligned with the bar are unstable and are probably chaoticorbits Our model naturally predicts trajectories indicatingthat NGC 6362 is confined to the inner-disk

Additionally in figure 4 we show the variation of the z-component of the angular momentum in the inertial frameLz as a function of time and Ωbar Since this quantityis not conserved in a model like GravPot16 (with non-axisymmetric structures) we follow the change -Lz+Lzwhere negative Lz in our reference system means that thecluster orbit is prograde (in the same sense as the disk ro-tation) Both prograde and prograde-retrograde orbits withrespect to the direction of the Galactic rotation are clearlyrevealed for NGC 6362 This effect is strongly produced bythe presence of the galactic bar further indicating a chaoticbehavior

It is important to mention that one major limitationof our model is that it ignores secular changes in the MilkyWay potential over time and dynamical friction which mightbe important in understanding the evolution of NGC 6362crossing the inner Galaxy An in-depth analysis of such dy-namical behaviour is beyond the scope of this paper


7

Table 2 Orbital parameters of NGC 6362 with uncertainty

ranges given by the 16th (subscript) and 84th (superscript) per-

centile values

Ωbar rperi rapo Zmax eccentricity

km sminus1 kpcminus1 kpc kpc kpc

35 202218181 529568503 341383330 045049042

40 198217187 538603516 345384319 047049044

45 204222197 594689572 355414314 049053047

50 199211192 565615536 351381329 049052043

5 MASS LOSS RATE IN NGC 6362

The detailed computations of destruction rates of globu-lar clusters in our Galaxy due to the effects of bulge anddisk shocking and dynamical friction employing the Galac-tic model GravPot16 will be presented in a future studyHowever for the present work we have used destruction ratesof the galactic cluster due to dynamical friction and bulgeand disk shockings from the literature and added the cor-responding destruction rate due to evaporation to get anestimated value for its total mass loss rate

Moreno Pichardo amp Velazquez (2014) (M+14 here-after) have computed destruction rates of globular clustersdue to bulge and disk shocking using a Galactic modelwhich employs a bar component alike the GravPot16 modelbut with a greater mass the bar mass ratio being around 15For the orbit of NGC 6362 the kinematic parameters usedin the present analysis differ from those used by M+14 how-ever both models give similar orbits differing only in themaximum distance zmax reached from the Galactic planewhich in our case is around 15 times that obtained byM+14 With tb the characteristic life time due to bulgeshocking M+14 obtain the corresponding present destruc-tion rate 1tb = 135 times 10minus11 yrminus1 using a cluster massMc sim 105 M With the GravPot16 model and the de-creased value of Mc in Table 1 1tb would be more thanthe reported value of M+14 but the lower mass of the barin GravPot16 would decrease this value Thus we considerthe cited value of 1tb as representative for bulge shockingin our present analysis

With respect to disk shocking M+14 obtain the presentdestruction rate 1td = 212 times 10minus11 yrminus1 td being thecorresponding characteristic life time With the GravPot16

model this value would decrease due to the greater velocityof the cluster when it crosses the Galactic plane as it comesfrom a greater zmax () but with the lower cluster massgiven in Table 1 1td would increase

The effect of dynamical friction on globular clustershas been estimated by taking isotropic velocity disper-sion fields in the components of their axisymmetric Galacticmodels For NGC 6362 they give 1tdf = 14times 10minus12 yrminus1which is an order of magnitude shorter than 1tb and 1td

To estimate the destruction rate 1tev due to evapo-ration the corresponding life time tev is computed withtev = ftrh taking trh and f given by the equation (7108)and approximation (7142) of Taking m in that equationas 1 M Mc = 53 times 104 M (Table 1) and the half-massradius rh = 453 pc (eg M+14) the resulting present valuefor tev using f = 40 is tev = 24times1010 yr or an evaporationrate 1tev = 42times 10minus11 yrminus1

The sum of 1tb 1td 1tdf and 1tev gives the to-tal destruction rate 1ttot = 78 times 10minus11 yrminus1 or a presentmass loss rate Mc = Mc(1ttot) = 41 times 10minus6 Myr Toimprove this estimate of the mass loss rate the computa-tion of 1tdf needs to be done with a bar component in theGalactic model as GravPot16 employed here and takingnon-isotropic dispersion fields

We hypothesise that the mean absolute difference ofproper motions in right ascension and declination betweenthe cluster and the 259 possible extended star debris can-didates is around 05 mas yrminus1 This gives an approximatemean relative velocity in the plane of the sky of 25 km secminus1With this velocity the stars will move out the vicinity shownin Figure 1 in a time of about 107 yr We assume that thestar surface density in Figure 1 is maintained and with theestimated mass loss rate in this interval of time the clusterloses about 40 M Thus the majority of the star debriscandidates should be low mass stars (sim 015 M)

6 CONCLUDING REMARKS

We have used the Gaia DR2 information along with thefundamental parameters of the cluster NGC 6362 to searchfor possible extended star debris candidates We report theidentification of 259 potential stellar members of NGC 6362extending few arc minutes from the edge of the clusterrsquosradius Both astrometric information and location of thesepossible extended star debris candidates on the CMD areconsistent with the cluster membership Unfortunately thepresently available astrometric information from Gaia is notsufficient to determine with certainty how many of the starsmay be truly extended star debris members Neverthelessthis initial Gaia DR2 sample significantly contributes to thetask of compiling a more thorough census of possible ex-tended star debris in the area of the sky around NGC 6362and portends the promising results to be expected from fu-ture spectroscopic follow-up observations

If the newly discovered objects are part of the maincluster these results would suggest the presence of anasymmetrically extended stellar material in the outer partsof the cluster whose surface density profile is mainly shapedby evaporation andor tidal stripping at its current locationin the Galaxy tracing their dynamical evolution in theMilky Way (evaporation and tidal shocking) Also thereis no apparent correlation between the distribution of thenewly identified extended star debris candidates and theorbit of the cluster ruling out any evidence of elongationalong the tidal field gradient

The possible extended star debris candidates observedin the cluster can be either due to tidal disruption or dynam-ical friction or a combined effect of both Therefore to findan explanation for these extended star debris candidateswe computed the orbits for the cluster using four differentvalues of Ωbar = 35 40 45 50 kmskpc Half million or-bits were computed for different initial conditions consider-ing boxy bar potential perturbations in an inertial referenceframe where the bar is considered at an angle of 20 with theline joining Sun and the Galactic center Earlier DinescuGirard amp van Altena (1999) also determined the orbital pa-rameters for the cluster but without the contribution of the


8 Kundu et al

bar to the potential However the Lz evolution modeled hereindicates that the cluster is affected by the bar potential ofthe Galaxy Figure 1 shows the asymmetric distribution ofthe possible extended star debris candidates along with theorbit of the cluster traced back for 3 Gyr with three differentbar speeds

Figure 3 shows the orbit of the cluster in the meridionalGalactic plane and equatorial Galactic plane simulated inthe inertial reference frame It is clear from the figure thatthe cluster is circulating the inner-disk within a distanceof 3 Kpc above and below the disk As the cluster neverenters the bulge of the Galaxy the dynamical friction ex-perienced by the cluster is negligible but this cluster haspassed through the Galactic disk many times experiencinga shock every time it crosses the disk Due to these shocksmany stars must have been stripped away from the clusterHence the observed extended star debris candidates canbe a result of tidal disruption and shocks from the Galacticdisk which happened more than 159 Myr Thanks to therelatively short distance of NGC 6362 and its high release ofunbound material during its current disk shocking we esti-mate the mass variation to be in the order of sim 41times 10minus6

M yrminus1All the raw data used in this work are available through

the VizieR Database (I345gaia2) Furthermore in orderto facilitate the reproducibility and reuse of our results wehave made available all the data and the source codes avail-able in a public repository2

ACKNOWLEDGEMENTS

The authors would like to thank the anonymous refereefor herhis constructive comments and improvements mak-ing this a better paper RK is thankful to the Coun-cil of Scientific and Industrial Research New Delhi fora Senior Research Fellowship (SRF) (File number 09045(1414)2016-EMR-I) JGF-T is supported by FONDE-CYT No 3180210 DM gratefully acknowledges sup-port provided by the BASAL Center for Astrophysicsand Associated Technologies (CATA) through grant AFB170002 and the Ministry for the Economy Developmentand Tourism Programa Iniciativa Cientıfica Milenio grantIC120009 awarded to the Millennium Institute of Astro-physics (MAS) and from project Fondecyt No 1170121HPS and RK are thankful to the Council of Scientificand Industrial Research New Delhi for the grants-in-aid(Ref No 03(1428)18EMR-II) RK and DM are alsovery grateful for the hospitality of the Vatican Observatorywhere this work was started EM acknowledge support fromUNAMPAPIIT grant IN105916

Funding for the GravPot16 software has been providedby the Centre national drsquoetudes spatiales (CNES) throughgrant 0101973 and UTINAM Institute of the Universitede Franche-Comte supported by the Region de Franche-Comte and Institut des Sciences de lrsquoUnivers (INSU) Sim-ulations have been executed on computers from the UtinamInstitute of the Universite de Franche-Comte supported

2 httpsgithubcomFernandez-TrincadoTidal-debris-GaiatreemasterKundu2B2019

by the Region de Franche-Comte and Institut des Sciencesde lrsquoUnivers (INSU) and on the supercomputer facilitiesof the Mesocentre de calcul de Franche-Comte This workhas made use of results from the European Space Agency(ESA) space mission Gaia the data from which were pro-cessed by the Gaia Data Processing and Analysis Consor-tium (DPAC) Funding for the DPAC has been providedby national institutions in particular the institutions par-ticipating in the Gaia Multilateral Agreement The Gaiamission website is httpwwwcosmosesaintgaia

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Albareti F D et al 2017 ApJs 233 25

Arca-Sedda M Capuzzo-Dolcetta R 2014 ApJ 785 51

Balbinot E Gieles M 2018 MNRAS 474 2479

Balbinot E Santiago B X da Costa L N Makler M Maia

M A G 2011 MNRAS 416 393

Baumgardt H Hilker M 2018 MNRAS 478 1520

Belokurov V Evans N W Irwin M J Hewett P C Wilkinson

M I 2006 ApJl 637 L29

Brunthaler A et al 2011 Astronomische Nachrichten 332 461

Capuzzo-Dolcetta R 1993 ApJ 415 616

Capuzzo Dolcetta R Di Matteo P Miocchi P 2005 AJ 1291906

Capuzzo-Dolcetta R Vicari A 2005 MNRAS 356 899

Carretta E Bragaglia A Gratton R G Recio-Blanco A Lu-

catello S DrsquoOrazi V Cassisi S 2010 AAP 516 A55

Chandrasekhar S 1943 ApJ 97 255

Chernoff D F Kochanek C S Shapiro S L 1986 ApJ 309

183

Combes F Leon S Meylan G 1999 AAP 352 149

Contreras Ramos R et al 2018 ApJ 863 78

Dalessandro E et al 2014 ApJl 791 L4

Dinescu D I Girard T M van Altena W F 1999 AJ 117

1792

Dotter A et al 2010 ApJ 708 698

Einasto J 1979 in IAU Symposium Vol 84 The Large-Scale

Characteristics of the Galaxy Burton W B ed pp 451ndash

458

Fall S M Rees M J 1977 MNRAS 181 37P

Fall S M Rees M J 1985 ApJ 298 18

Fehlberg E 1968 NASA Technical Report 315

Fernandez-Alvar E et al 2018 ArXiv e-prints

Fernandez-Trincado J G Geisler D Moreno E Zamora O

Robin A C Villanova S 2017a in SF2A-2017 Proceedingsof the Annual meeting of the French Society of Astronomy and

Astrophysics Reyle C Di Matteo P Herpin F Lagadec E

Lancon A Meliani Z Royer F eds pp 199ndash202

Fernandez-Trincado J G Robin A C Moreno E Perez-Villegas

A Pichardo B 2017b in SF2A-2017 Proceedings of the An-nual meeting of the French Society of Astronomy and As-

trophysics Reyle C Di Matteo P Herpin F Lagadec ELancon A Meliani Z Royer F eds pp 193ndash198

Fernandez-Trincado J G et al 2016a ApJ 833 132

Fernandez-Trincado J G Robin A C Reyle C Vieira K

Palmer M Moreno E Valenzuela O Pichardo B 2016b

MNRAS 461 1404

Fernandez-Trincado J G et al 2015a AAP 583 A76

Fernandez Trincado J G Vivas A K Mateu C E Zinn R

2013 MEMSAI 84 265

Fernandez-Trincado J G Vivas A K Mateu C E Zinn R

Robin A C Valenzuela O Moreno E Pichardo B 2015bAAP 574 A15

Fernandez-Trincado J G et al 2017c ApJl 846 L2

Gaia Collaboration et al 2018a AAP 616 A1


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Gaia Collaboration et al 2018b AAP 616 A12

Gnedin O Y Ostriker J P 1997 ApJ 474 223

Grillmair C J Johnson R 2006 ApJl 639 L17

Grillmair C J Mattingly S 2010 in Bulletin of the American

Astronomical Society Vol 41 American Astronomical Soci-ety Meeting Abstracts 216 p 833

Harris W E 1996 AJ 112 1487

Hozumi S Burkert A 2015 MNRAS 446 3100

Jordi K Grebel E K 2010 AAP 522 A71

King I 1962 AJ 67 471

Knierman K A Scowen P Veach T Groppi C Mullan B

Konstantopoulos I Knezek P M Charlton J 2013 ApJ774 125

Kunder A et al 2014 AAP 572 A30

Kunder A et al 2018 AJ 155 171

Kundu R Minniti D Singh H P 2019 MNRAS 483 1737

Kupper A H W Lane R R Heggie D C 2012 MNRAS 4202700

Kuzma P B Da Costa G S Keller S C Maunder E 2015

MNRAS 446 3297

Leon S Meylan G Combes F 2000 AAP 359 907

Libralato M et al 2018 ApJ 854 45

Lotz J M Telford R Ferguson H C Miller B W Stiavelli M

Mack J 2001 ApJ 552 572

Majewski S R et al 2012a in American Astronomical Society

Meeting Abstracts Vol 219 American Astronomical Society

Meeting Abstracts 219 p 41005

Majewski S R Nidever D L Smith V V Damke G J Kunkel

W E Patterson R J Bizyaev D Garcıa Perez A E 2012b

ApJl 747 L37

Marchetti T Rossi E M Brown A G A 2018 MNRAS

Massari D et al 2017 MNRAS 468 1249

Meylan G Heggie D C 1997 AAPr 8 1

Minniti D Fernandez-Trincado J G Ripepi V Alonso-Garcıa

J Contreras Ramos R Marconi M 2018 ApJ 869 L10

Moreno E Pichardo B Velazquez H 2014 ApJ 793 110

Mulder W A 1983 AAP 117 9

Mulia A Chandar R 2014 in American Astronomical Society

Meeting Abstracts Vol 223 American Astronomical SocietyMeeting Abstracts 223 p 44234

Murali C Weinberg M D 1997 MNRAS 291 717

Myeong G C Evans N W Belokurov V Sanders J L Ko-posov S E 2018 MNRAS 478 5449

Myeong G C Jerjen H Mackey D Da Costa G S 2017 ApJl840 L25

Navarrete C Belokurov V Koposov S E 2017 ApJl 841 L23

Niederste-Ostholt M Belokurov V Evans N W Koposov SGieles M Irwin M J 2010 MNRAS 408 L66

Odenkirchen M et al 2001 ApJl 548 L165

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Robin A C Marshall D J Schultheis M Reyle C 2012 AAP

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Robin A C Reyle C Fliri J Czekaj M Robert C P Martins

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Schiappacasse-Ulloa J et al 2018 AJ 156 94

Sollima A Martınez-Delgado D Valls-Gabaud D PenarrubiaJ 2011 ApJ 726 47

Torres-Flores S de Oliveira C M de Mello D F Scarano S

Urrutia-Viscarra F 2012 MNRAS 421 3612

Tremaine S Weinberg M D 1984 MNRAS 209 729

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Vasiliev E 2019 MNRAS 484 2832

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Weinberg M D 1994 AJ 108 1414

White S D M 1983 ApJ 274 53


10 Kundu et al

Table 3 Possible extended star debris candidates of NGC 6362 from Gaia DR2

ID α δ microα microδ G GBP GRP() () (masyr) (masyr) (mag) (mag) (mag)

5810760588765404672 263950 -68123 -4546 plusmn 0150 -4631 plusmn 0202 17932 18331 173625810766331142949376 264066 -68122 -4999 plusmn 0129 -5362 plusmn 0166 17641 18063 17058

5810767636813138304 264222 -68057 -5224 plusmn 0028 -4442 plusmn 0037 14585 15153 13881


5811500457010583552 263041 -68198 -5140 plusmn 0218 -5427 plusmn 0318 18662 18993 18140


Note Table 3 is published in its entirety in a public repository athttpsgithubcomFernandez-TrincadoTidal-debris-GaiatreemasterKundu2B2019 A portion is shown here for guidance

regarding its form and content


11

Figure 3 Kernel Density Estimate (KDE) smoothed distributionof simulated orbits employing a Monte Carlo approach show-

ing the probability densities of the resulting orbits projected onthe equatorial (left) and meridional (right) Galactic planes inthe non-inertial reference frame where the bar is at rest The

green and yellow colors correspond to more probable regions of

the space which are crossed more frequently by the simulatedorbits The black line is the orbit of NGC 6362 adopting the cen-

tral inputs The small white star marks the present position ofthe cluster whereas the white square marks its initial position

In all orbit panels the white dotted circle show the location of

the co-rotation radius (CR) the horizontal white solid line showsthe extension of the bar

Figure 4 Kernel Density Estimate (KDE) smoothed distribution

of the variation of the z-component of the angular momentum(Lz) in the inertial frame vs time for four assumed bar pattern

speeds 35 40 45 and 50 km sminus1 kpc


1 Introduction

2 Identification of extended star debris candidates around NGC 6362

3 Significance of the detection of possible extended star debris around NGC 6362

4 The Orbit of NGC 6362

5 Mass loss rate in NGC 6362

6 Concluding remarks

2 Kundu et al

important stellar systems to study the evolution structureand dynamics of their host galaxy

Globular clusters lose stars mainly due to dynamicalprocesses like dynamical friction tidal disruption bulge anddisk shocking and evaporation (Fall amp Rees 1977 1985)Dynamical friction is due to the gravitational pull of thefield stars that are accumulated behind the cluster mo-tion These stars slow down the cluster and pull some ofthe loosely bound stars away from it This effect is morepronounced in the bulge of the Galaxy where the densityof field stars is higher Dynamical friction has been pro-posed in many studies (Chandrasekhar 1943 Mulder 1983White 1983 Tremaine amp Weinberg 1984 Capuzzo-Dolcettaamp Vicari 2005 Moreno Pichardo amp Velazquez 2014 Arca-Sedda amp Capuzzo-Dolcetta 2014) but the observational ev-idence has been more elusive while tidal disruption havebeen observed (Leon Meylan amp Combes 2000 Odenkirchenet al 2001 Belokurov et al 2006 Grillmair amp Johnson 2006Grillmair amp Mattingly 2010 Niederste-Ostholt et al 2010Jordi amp Grebel 2010 Sollima et al 2011 Balbinot et al2011 Kuzma et al 2015 Myeong et al 2017 Navarrete Be-lokurov amp Koposov 2017) and studied by many (King 1962Tremaine Ostriker amp Spitzer 1975 Chernoff Kochanek ampShapiro 1986 Capuzzo-Dolcetta 1993 Weinberg 1994 Mey-lan amp Heggie 1997 Gnedin amp Ostriker 1997 Vesperini ampHeggie 1997 Combes Leon amp Meylan 1999 Lotz et al 2001Capuzzo Dolcetta Di Matteo amp Miocchi 2005 Majewskiet al 2012a Kupper Lane amp Heggie 2012 Majewski et al2012b Torres-Flores et al 2012 Knierman et al 2013 Mu-lia amp Chandar 2014 Hozumi amp Burkert 2015 Rodruck et al2016 Fernandez-Trincado et al 2017ab Bal-binot amp Gieles 2018 Myeong et al 2018 Kundu Minniti ampSingh 2019 )

NGC 6362 is a nearby low mass globular cluster withintermediate metallicity located in the bulgedisk of theMilky Way galaxy (Carretta et al 2010) It has an age ofsim125plusmn05 Gyr which is enough to evolve under the grav-itational potential of the Milky Way Therefore identifyingpossible tidal tails around NGC 6362 is especially intrigu-ing to study the cluster dynamics in the bulgedisk regionwhich is poorly understood Recently Baumgardt amp Hilker(2018) presented a catalog of masses structural profiles andvelocity dispersion values for many Galactic globular clus-ters including NGC 6362 They found that this cluster fitsa King profile with a constant velocity dispersion as a func-tion of radius hence there was no evidence of a tidal tailHowever their measurements were concentrated to the in-ner regions extending only out to 400 arc-sec away from thecenter

In the present work we report the detection of poten-tial extended star debris associated with NGC 6362 Wehave taken advantage of the exquisite data from Gaia DataRelease 2 (Gaia DR2 Gaia Collaboration et al 2018a) tosearch for such extended star debris features around NGC6362 To give a proper explanation for the presence of theobserved possible star debris we time-integrated backwardthe orbit of NGC 6362 to 3 Gyrs under variations of theinitial conditions (proper motions radial velocity heliocen-tric distance Solar position Solar motion and the velocityof the local standard of rest) according to their estimatederrors Our analysis indicates that the cluster is dynamicallyaffected by the Galactic bar potential presently experienc-

Table 1 NGC 6362 ndashSun parameters

Parameter Value Reference

NGC 6362

α () δ () 262979 minus67048 (a)Distance (kpc) 76 (a)

Rgal (kpc) 471

microα (masyr) -5507plusmn0052 (a)microδ (masyr) -4747plusmn0052 (a)

Vlos minus1458plusmn018 (a)

Tidal Radius (pc) 3073 (b)Mass (M) sim 105 (b)

Metallicity minus107 (d)

Age (Gyr) 125plusmn05 (e)

Sun

R (kpc) 83 (f)

U VW (km sminus1) 1110 1224 725 (f)

VLSR (km sminus1) 239 (f)

(a) Vasiliev (2019) (b) Moreno Pichardo amp Velazquez (2014)

(c) Dalessandro et al (2014) (d) Massari et al (2017) (e)Dotter et al (2010) (f) Brunthaler et al (2011)

ing a bulgebar shocking with considerable amount of massloss which can be observed as stars present in the imme-diate neighborhood of the cluster A similar analysis wasrecently carried out by Minniti et al (2018) for NGC 6266(also known as M62) using extra-tidal RR Lyrae stars

This paper is organized as follows In Section 2 we se-lect the possible star debris candidates beyond the clustertidal radius of NGC 6362 In Section 3 we discussed thesignificance of the observed star debris In Section 4 we de-termine its most likely orbit using novel galaxy modelingsoftware called GravPot16 In Section 5 we discussed themass lost by the cluster due to various processes The con-cluding remarks are summarised in Section 6

2 IDENTIFICATION OF EXTENDED STARDEBRIS CANDIDATES AROUND NGC 6362

To search for the extended star debris features around thecluster NGC 6362 we have made use of the second Gaiadata release (Gaia DR2 Gaia Collaboration et al 2018a)We first download Gaia DR2 in a cone around the clusterwith radius around five tidal radii where we tried to identifythe star debris which contains 276391 objects

Since NGC 6362 is relatively far we decided to payparticular attention to avoid contamination by data pro-cessing artifacts andor spurious measurements Thereforewe adopted the following conservative cuts on the columnsof the Gaia DR2 GAIA SOURCE catalogue

(i) ASTROMETRIC GOF AL lt 3 This cut ensures that thestatistics astrometric model resulted in a good fit to thedata(ii) ASTROMETRIC EXCESS NOISE SIG le 2 This criterionensured that the selected stars were astrometrically well-behaved sources(iii) minus023 le MEAN VARPI FACTOR AL le 032 AND


3











4 Kundu et al

















5






starΣ2star Σ3








6 Kundu et al












7



centile values



35 202218181 529568503 341383330 045049042

40 198217187 538603516 345384319 047049044

45 204222197 594689572 355414314 049053047

50 199211192 565615536 351381329 049052043















8 Kundu et al





ACKNOWLEDGEMENTS





REFERENCES





M A G 2011 MNRAS 416 393



M I 2006 ApJl 637 L29









183





1792




458















MNRAS 461 1404



2013 MEMSAI 84 265






9






Harris W E 1996 AJ 112 1487



King I 1962 AJ 67 471








MNRAS 446 3297




Mack J 2001 ApJ 552 572






ApJl 747 L37


















538 A106


523


A M M 2014 AAP 569 A13













10 Kundu et al




5810767636813138304 264222 -68057 -5224 plusmn 0028 -4442 plusmn 0037 14585 15153 13881


5811500457010583552 263041 -68198 -5140 plusmn 0218 -5427 plusmn 0318 18662 18993 18140





11












1 Introduction






3











4 Kundu et al

















5






starΣ2star Σ3








6 Kundu et al












7



centile values



35 202218181 529568503 341383330 045049042

40 198217187 538603516 345384319 047049044

45 204222197 594689572 355414314 049053047

50 199211192 565615536 351381329 049052043















8 Kundu et al





ACKNOWLEDGEMENTS





REFERENCES





M A G 2011 MNRAS 416 393



M I 2006 ApJl 637 L29









183





1792




458















MNRAS 461 1404



2013 MEMSAI 84 265






9






Harris W E 1996 AJ 112 1487



King I 1962 AJ 67 471








MNRAS 446 3297




Mack J 2001 ApJ 552 572






ApJl 747 L37


















538 A106


523


A M M 2014 AAP 569 A13













10 Kundu et al




5810767636813138304 264222 -68057 -5224 plusmn 0028 -4442 plusmn 0037 14585 15153 13881


5811500457010583552 263041 -68198 -5140 plusmn 0218 -5427 plusmn 0318 18662 18993 18140





11












1 Introduction






4 Kundu et al

















5






starΣ2star Σ3








6 Kundu et al












7



centile values



35 202218181 529568503 341383330 045049042

40 198217187 538603516 345384319 047049044

45 204222197 594689572 355414314 049053047

50 199211192 565615536 351381329 049052043















8 Kundu et al





ACKNOWLEDGEMENTS





REFERENCES





M A G 2011 MNRAS 416 393



M I 2006 ApJl 637 L29









183





1792




458















MNRAS 461 1404



2013 MEMSAI 84 265






9






Harris W E 1996 AJ 112 1487



King I 1962 AJ 67 471








MNRAS 446 3297




Mack J 2001 ApJ 552 572






ApJl 747 L37


















538 A106


523


A M M 2014 AAP 569 A13













10 Kundu et al




5810767636813138304 264222 -68057 -5224 plusmn 0028 -4442 plusmn 0037 14585 15153 13881


5811500457010583552 263041 -68198 -5140 plusmn 0218 -5427 plusmn 0318 18662 18993 18140





11












1 Introduction






5






starΣ2star Σ3








6 Kundu et al












7



centile values



35 202218181 529568503 341383330 045049042

40 198217187 538603516 345384319 047049044

45 204222197 594689572 355414314 049053047

50 199211192 565615536 351381329 049052043















8 Kundu et al





ACKNOWLEDGEMENTS





REFERENCES





M A G 2011 MNRAS 416 393



M I 2006 ApJl 637 L29









183





1792




458















MNRAS 461 1404



2013 MEMSAI 84 265






9






Harris W E 1996 AJ 112 1487



King I 1962 AJ 67 471








MNRAS 446 3297




Mack J 2001 ApJ 552 572






ApJl 747 L37


















538 A106


523


A M M 2014 AAP 569 A13













10 Kundu et al




5810767636813138304 264222 -68057 -5224 plusmn 0028 -4442 plusmn 0037 14585 15153 13881


5811500457010583552 263041 -68198 -5140 plusmn 0218 -5427 plusmn 0318 18662 18993 18140





11












1 Introduction






6 Kundu et al












7



centile values



35 202218181 529568503 341383330 045049042

40 198217187 538603516 345384319 047049044

45 204222197 594689572 355414314 049053047

50 199211192 565615536 351381329 049052043















8 Kundu et al





ACKNOWLEDGEMENTS





REFERENCES





M A G 2011 MNRAS 416 393



M I 2006 ApJl 637 L29









183





1792




458















MNRAS 461 1404



2013 MEMSAI 84 265






9






Harris W E 1996 AJ 112 1487



King I 1962 AJ 67 471








MNRAS 446 3297




Mack J 2001 ApJ 552 572






ApJl 747 L37


















538 A106


523


A M M 2014 AAP 569 A13













10 Kundu et al




5810767636813138304 264222 -68057 -5224 plusmn 0028 -4442 plusmn 0037 14585 15153 13881


5811500457010583552 263041 -68198 -5140 plusmn 0218 -5427 plusmn 0318 18662 18993 18140





11












1 Introduction






7



centile values



35 202218181 529568503 341383330 045049042

40 198217187 538603516 345384319 047049044

45 204222197 594689572 355414314 049053047

50 199211192 565615536 351381329 049052043















8 Kundu et al





ACKNOWLEDGEMENTS





REFERENCES





M A G 2011 MNRAS 416 393



M I 2006 ApJl 637 L29









183





1792




458















MNRAS 461 1404



2013 MEMSAI 84 265






9






Harris W E 1996 AJ 112 1487



King I 1962 AJ 67 471








MNRAS 446 3297




Mack J 2001 ApJ 552 572






ApJl 747 L37


















538 A106


523


A M M 2014 AAP 569 A13













10 Kundu et al




5810767636813138304 264222 -68057 -5224 plusmn 0028 -4442 plusmn 0037 14585 15153 13881


5811500457010583552 263041 -68198 -5140 plusmn 0218 -5427 plusmn 0318 18662 18993 18140





11












1 Introduction






8 Kundu et al





ACKNOWLEDGEMENTS





REFERENCES





M A G 2011 MNRAS 416 393



M I 2006 ApJl 637 L29









183





1792




458















MNRAS 461 1404



2013 MEMSAI 84 265






9






Harris W E 1996 AJ 112 1487



King I 1962 AJ 67 471








MNRAS 446 3297




Mack J 2001 ApJ 552 572






ApJl 747 L37


















538 A106


523


A M M 2014 AAP 569 A13













10 Kundu et al




5810767636813138304 264222 -68057 -5224 plusmn 0028 -4442 plusmn 0037 14585 15153 13881


5811500457010583552 263041 -68198 -5140 plusmn 0218 -5427 plusmn 0318 18662 18993 18140





11












1 Introduction






9






Harris W E 1996 AJ 112 1487



King I 1962 AJ 67 471








MNRAS 446 3297




Mack J 2001 ApJ 552 572






ApJl 747 L37


















538 A106


523


A M M 2014 AAP 569 A13













10 Kundu et al




5810767636813138304 264222 -68057 -5224 plusmn 0028 -4442 plusmn 0037 14585 15153 13881


5811500457010583552 263041 -68198 -5140 plusmn 0218 -5427 plusmn 0318 18662 18993 18140





11












1 Introduction






10 Kundu et al




5810767636813138304 264222 -68057 -5224 plusmn 0028 -4442 plusmn 0037 14585 15153 13881


5811500457010583552 263041 -68198 -5140 plusmn 0218 -5427 plusmn 0318 18662 18993 18140





11












1 Introduction






11












1 Introduction






The Tale of the Milky Way Globular Cluster NGC 6362 - as ... · Milky Way galaxy (Carretta et...

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Transcript of The Tale of the Milky Way Globular Cluster NGC 6362 - as ... · Milky Way galaxy (Carretta et...