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The tale of the Milky Way globular cluster NGC 6362 ndashI The orbit and its possible extended star debris

features as revealed by Gaia DR2Richa Kundu Joseacute Fernaacutendez-Trincado Dante Minniti Harinder Singh

Edmundo Moreno Ceacuteline Reyleacute Annie Robin Mario Soto

To cite this versionRicha Kundu Joseacute Fernaacutendez-Trincado Dante Minniti Harinder Singh Edmundo Moreno et alThe tale of the Milky Way globular cluster NGC 6362 ndash I The orbit and its possible extendedstar debris features as revealed by Gaia DR2 Monthly Notices of the Royal Astronomical SocietyOxford University Press (OUP) Policy P - Oxford Open Option A 2019 489 (4) pp4565-4573101093mnrasstz2500 hal-02393987

MNRAS 489 4565ndash4573 (2019) doi101093mnrasstz2500Advance Access publication 2019 September 7

The tale of the Milky Way globular cluster NGC 6362 ndash I The orbit andits possible extended star debris features as revealed by Gaia DR2

Richa Kundu1lsaquo Jose G Fernandez-Trincado23lsaquo Dante Minniti456 HarinderP Singh1 Edmundo Moreno7 Celine Reyle3 Annie C Robin3 and Mario Soto2

1Department of Physics and Astrophysics University of Delhi Delhi-110007 India2Instituto de Astronomıa y Ciencias Planetarias Universidad de Atacama Copayapu 485 Copiapo Chile-15300003Institut Utinam CNRS UMR 6213 Universite Bourgogne-Franche-Comte OSU THETA Franche-Comte Observatoire de Besancon BP 1615 F-25010Besancon Cedex France4Instituto Milenio de Astrofisica Santiago-8970117 Chile5Departamento de Ciencias Fisicas Facultad de Ciencias Exactas Universidad Andres Bello Av Fernandez Concha 700 Las Condes Santiago-7550196Chile6Vatican Observatory I-V00120 Vatican City State Italy7Instituto de Astronomıa Universidad Nacional Autonoma de Mexico Apdo Postal 70264 Mexico DF 04510 Mexico

Accepted 2019 September 2 Received 2019 August 15 in original form 2019 February 28

ABSTRACTWe report the identification of possible extended star debris candidates beyond the clustertidal radius of NGC 6362 based on the second Gaia data release (Gaia DR2) We found 259objects possibly associated with the cluster lying in the vicinity of the giant branch and 1ndash2magnitudes fainterbrighter than the main-sequence turn-off in the cluster colourndashmagnitudediagram and which cover an area on the sky of sim41 deg2 centred on the cluster We tracedback the orbit of NGC 6362 in a realistic Milky Way potential using the GRAVPOT16 packagefor 3 Gyr The orbit shows that the cluster shares similar orbital properties as the inner dischaving peri-apogalactic distances and maximum vertical excursion from the Galactic planeinside the corotation radius (CR) moving inwards from CR radius to visit the inner regionsof the Milky Way The dynamical history of the cluster reveals that it has crossed the Galacticdisc several times in its lifetime and has recently undergone a gravitational shock sim159 Myrago suggesting that less than 01 per cent of its mass has been lost during the current disc-shocking event Based on the clusterrsquos orbit and position in the Galaxy we conclude that thepossible extended star debris candidates are a combined effect of the shocks from the Galacticdisc and evaporation from the cluster Lastly the evolution of the vertical component of theangular momentum shows that the cluster is strongly affected dynamically by the Galactic barpotential

Key words globular clusters individual NGC 6362 ndash Galaxy kinematics and dynamics

1 IN T RO D U C T I O N

Extra-tidal stellar material associated with globular clusters isspectacular evidence for satellite disruption at the present daywhich provides significant clues about the dynamical history ofthe clusters and their host galaxies Globular clusters evolve dy-namically under the influence of the gravitational potential well oftheir host galaxy (Gnedin amp Ostriker 1997 Murali amp Weinberg

E-mail richakundu92gmailcom (RK) jfernandezt87gmailcom(JGFT)

1997 Leon Meylan amp Combes 2000 Kunder et al 2018 Minnitiet al 2018) resulting in the escape of the stars close to the tidalboundary of the cluster consequently forcing the cluster cores tocontract and envelopes to expand (eg Leon et al 2000 Kunderet al 2014) Therefore globular clusters are important stellarsystems to study the evolution structure and dynamics of their hostgalaxy

Globular clusters lose stars mainly due to dynamical processeslike dynamical friction tidal disruption bulge and disc shockingand evaporation (Fall amp Rees 1977 1985) Dynamical friction isdue to the gravitational pull of the field stars that are accumulatedbehind the cluster motion These stars slow down the cluster and pull

Ccopy Crown copyright 2019This article contains public sector information licensed under the Open Government Licence v30(httpwwwnationalarchivesgovukdocopen-government-licenceversion3)

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4566 R Kundu et al

some of the loosely bound stars away from it This effect is morepronounced in the bulge of the Galaxy where the density of field starsis higher Dynamical friction has been proposed in many studies(Chandrasekhar 1943 Mulder 1983 White 1983 Tremaine ampWeinberg 1984 Capuzzo-Dolcetta amp Vicari 2005 Arca-Sedda ampCapuzzo-Dolcetta 2014 Moreno Pichardo amp Velazquez 2014)but the observational evidence has been more elusive while tidaldisruption have been observed (Leon et al 2000 Odenkirchen et al2001 Belokurov et al 2006 Grillmair amp Johnson 2006 Grillmair ampMattingly 2010 Jordi amp Grebel 2010 Niederste-Ostholt et al2010 Balbinot et al 2011 Sollima et al 2011 Kuzma et al2015 Myeong et al 2017 Navarrete Belokurov amp Koposov 2017)and studied by many (King 1962 Tremaine Ostriker amp Spitzer1975 Chernoff Kochanek amp Shapiro 1986 Capuzzo-Dolcetta1993 Weinberg 1994 Gnedin amp Ostriker 1997 Meylan amp Heggie1997 Vesperini amp Heggie 1997 Combes Leon amp Meylan 1999Lotz et al 2001 Capuzzo Dolcetta Di Matteo amp Miocchi 2005Kupper Lane amp Heggie 2012 Majewski et al 2012a b Torres-Flores et al 2012 Fernandez Trincado et al 2013 Knierman et al2013 Mulia amp Chandar 2014 Fernandez-Trincado et al 2015ab2016ab 2017abc Rodruck et al 2016 Hozumi amp Burkert 2015Balbinot amp Gieles 2018 Myeong et al 2018 Kundu Minniti ampSingh 2019 Mackereth et al 2019)

NGC 6362 is a nearby low-mass globular cluster with interme-diate metallicity located in the bulgedisc of the Milky Way galaxy(Carretta et al 2010) It has an age of sim125 plusmn 05 Gyr whichis enough to evolve under the gravitational potential of the MilkyWay Therefore identifying possible tidal tails around NGC 6362 isespecially intriguing to study the cluster dynamics in the bulgediscregion which is poorly understood Recently Baumgardt amp Hilker(2018) presented a catalogue of masses structural profiles andvelocity dispersion values for many Galactic globular clustersincluding NGC 6362 They found that this cluster fits a King profilewith a constant velocity dispersion as a function of radius hencethere was no evidence of a tidal tail However their measurementswere concentrated to the inner regions extending only out to 400arcsec away from the centre

In this work we report the detection of potential extendedstar debris associated with NGC 6362 We have taken advantageof the exquisite data from Gaia Data Release 2 (Gaia DR2Gaia Collaboration 2018) to search for such extended star debrisfeatures around NGC 6362 To give a proper explanation for thepresence of the observed possible star debris we time-integratedbackward the orbit of NGC 6362 to 3 Gyr under variations ofthe initial conditions (proper motions radial velocity heliocentricdistance Solar position Solar motion and the velocity of thelocal standard of rest) according to their estimated errors Ouranalysis indicates that the cluster is dynamically affected by theGalactic bar potential presently experiencing a bulgebar shockingwith considerable amount of mass-loss which can be observedas stars present in the immediate neighbourhood of the cluster Asimilar analysis was recently carried out by Minniti et al (2018)for NGC 6266 (also known as M62) using extra-tidal RR Lyraestars

This paper is organized as follows In Section 2 we select thepossible star debris candidates beyond the cluster tidal radius ofNGC 6362 In Section 3 we discussed the significance of theobserved star debris In Section 4 we determine its most likelyorbit using novel galaxy modelling software called GRAVPOT16In Section 5 we discussed the mass lost by the cluster due tovarious processes The concluding remarks are summarized inSection 6

2 IDENTI FI CATI ON O F EXTENDED STA RD E B R I S C A N D I DAT E S A RO U N D N G C 6 3 6 2

To search for the extended star debris features around the clusterNGC 6362 we have made use of the second Gaia DR2 (GaiaCollaboration 2018) We first download Gaia DR2 in a cone aroundthe cluster with radius around five tidal radii where we tried toidentify the star debris which contains 276 391 objects

Since NGC 6362 is relatively far we decided to pay particularattention to avoid contamination by data processing artefacts andorspurious measurements Therefore we adopted the following con-servative cuts on the columns of the Gaia DR2 GAIA SOURCEcatalogue

(i) ASTROMETRIC GOF AL lt 3 This cut ensures that thestatistics astrometric model resulted in a good fit to the data

(ii) ASTROMETRIC EXCESS NOISE SIG le 2 This crite-rion ensured that the selected stars were astrometrically well-behaved sources

(iii) minus023 le MEAN VARPI FACTOR AL le 032 ANDVISIBILITY PERIODS USED gt 8 These cuts were used toexclude 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 reader toMarchetti Rossi amp Brown (2018) for a detailed description of thesehigh-quality cuts

The final sample so selected amounts to a total of 83 406 starsFrom this sample we further retain as candidate members of thecluster those objects that lie in an annular region around the clusterwith its inner radius as the tidal radius (rt =13907 arcmin Morenoet al 2014) of NGC 6362 and an outer radius equal to five timesits tidal radius as displayed in Fig 1 This reduces our sample to77 549 objects

As a consistency check to verify the validity of highest likelihoodstar debris candidates based on their position on the sky only thesample was restricted to the stars whose proper motions match withthe proper motion of the cluster within 3σμ where σμ is the total un-certainty in quadrature obtained from a two-dimensional Gaussianfit For this purpose a two-dimensional Gaussian smoothing routinewas applied in proper motion space for stars with G lt 19 mag within2 times rhalf-mass from the centre of the cluster A 2D Gaussian wasfitted to this sample and membership probabilities are assignedWith this procedure we found μ2D

α plusmn σα = minus5511 plusmn 0237 masyrminus1 μ2D

δ plusmn σδ = minus4742 plusmn 0302 mas yrminus1 and σμ = 038 masyrminus1 our results also agree remarkably well with the more recentmeasurements of PMs for NGC 6362 eg μα = minus5507 plusmn 0052mas yrminus1 and μδ = minus4747 plusmn 0052 from Vasiliev (2019) A starwas considered to be a Galactic Centre (GC) member if its propermotion differs from that of NGC 6362 by not more than 3σμ leavingus with a grand total of 1503 stars The content of nearby stars in ourinitial sample is reduced by excluding those objects with estimateddistances from Bailer-Jones et al (2018) confined to a sphere ofradius 3 kpc around the Sun This cut is motivated by the fact thatat large latitudes away from the disc the priors would be expectingdistant stars to be much closer to us than they truly are and forcethe stars towards these closer unrealistic distances Therefore thedistances from the Bailer-Jonesrsquos catalogue should just be followingthe priors and would not account for distant overdensities Thisreduces our sample to 826 objects

Thus we found a total of 826 possible star debris candidatesof NGC 6362 which share an apparent proper motion close to

MNRAS 489 4565ndash4573 (2019)

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The tale of the Milky Way globular cluster NGC 6362 4567

Figure 1 The Gaia DR2 positions for the highest likelihood star debris candidates in the region of NGC 6362 shown with unfilled white circles The innerand outer black dashed circles are the tidal radius (rt) and 5times rt respectively (see the text) The arrows indicate the directions of the cluster proper motion(red arrow) with a preferential direction towards S-W the Galactic Centre (GC ndash green arrow) and the direction perpendicular to the galactic plane (bluearrow) The computed orbit (black lines) of the cluster is displayed assuming four different values of the bar patterns speed (35 40 45 and 50 km sminus1 kpc)in the GRAVPOT16 package (see the text) Five adjacent regions containing field stars (foreground and background) whose proper motions and distribution inthe CDM are overlapped with cluster members and in which the contamination was evaluated The expected surface density of potential members and eachadjacent field is internally indicated which overlap all the criteria adopted in this work

the nominal value of the cluster suggesting that these stars couldpossibly be evaporated material from NGC 6362 Therefore to besure that our candidate members are actually part of the clustersystem we selected those stars whose locations on the colourndashmagnitude diagram (CMD) clearly lie on or near the prominentmain branches of NGC 6362 as illustrated by the red symbols inFig 2 A total of 259 possible extended star debris candidates passedthese quality cuts as illustrated in Figs 1 and 2 (highlighted by redsymbols)

To summarize the possible star debris members of the cluster inFig 2 show the following proper motions that are very concentratedas expected in the vector point diagram (hereafter VPD) of a globularcluster and a CMD with the characteristic features of a globularcluster eg the main sequence the turn-off the red giant branchand some stars in the horizontal branch It is important to notethat the determination of the possible extended star debris of NGC6362 could include some field stars as members or vice versa inSection 3 we perform an estimation of the degree of contaminationof the extracted members ie the possible number of field stars thatcould have been labelled as possible extended star debris membersof the cluster

This finding gives possible clues about the recent dynamicalhistory of NGC 6362 which suggests that this cluster couldeventually form tidal tails or could also be associated with therecent encounter of the cluster with the disc

Table 1 lists the main parameters of the 259 possible extendedstar debris Fig 2 shows consistently the validity of our probable

extended star debris members that share an apparent proper motionclose to the value for NGC 6362 suggesting these stars are probablemembers of the cluster

It is important to note that most of the stars inside 2 times rhalf-mass

of the cluster are spread in proper motions as illustrated by blackdots in Fig 2 consequently one may be lead to conclude that it isrelated to contamination by foregroundbackground stars that wouldseem to be the most likely explanation for the significantly higherproper motion values Thus we also expect that our sample may besignificantly contaminated from other Galactic stellar populations(see Section 3) To alleviate this situation a detailed chemicalabundance analysis will be necessary to understand their relationif any with the cluster

3 SI G N I F I C A N C E O F T H E D E T E C T I O N O FPOSSI BLE EXTENDED STA R D EBRI S ARO UNDN G C 6 3 6 2

It is important to note that the main tracers of the possible extendedstar debris of NGC 6362 identified in this work are main-sequence(MS) stars and subgiant stars 1ndash2 mag fainter and brighter than theMS turn-off (TO) respectively However the cluster stars beyondcluster tidal radius are hidden in the CMD due to the combinationof the contributions of a minor fraction of cluster members andfore-background stellar populations from the different Milky Waycomponents (mainly the thin-thick disc and halo)

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Figure 2 Kernel density estimate (KDE) smoothed distribution of the CMD of stars within 5 times rt from the photometric centre of NGC 6362 (top rows) andproper motions in the region of the cluster (bottom rows) Left-hand panels illustrates the stars that pass the astrometric excess noise cut-offs for stars in thefield and stars within 2 times rhalf-mass sim 41 arcmin from the centre of the cluster (black dots) Right-hand panels illustrates the position in the CMD and VPD forthe highest likelihood of possible extended star debris candidates (red dots) The black dashed lines show the nominal proper motion values for NGC 6362 atμα = minus5507 mas yrminus1 μδ = minus4747 mas yrminus1 (Vasiliev 2019) while the white contour line encloses the density of forebackground stars and cluster itself

Table 1 Possible extended star debris candidates of NGC 6362 from Gaia DR2

ID α δ μα μδ G GBP GRP

() () (mas yrminus1) (mas yrminus1) (mag) (mag) (mag)

5810760588765404672 263950 minus 68123 minus 4546 plusmn 0150 minus 4631 plusmn 0202 17932 18331 173625810766331142949376 264066 minus 68122 minus 4999 plusmn 0129 minus 5362 plusmn 0166 17641 18063 170585810767636813138304 264222 minus 68057 minus 5224 plusmn 0028 minus 4442 plusmn 0037 14585 15153 138815811490290829953280 263323 minus 68172 minus 6203 plusmn 0163 minus 4243 plusmn 0230 18149 18547 176235811498086186458752 262698 minus 68193 minus 4615 plusmn 0167 minus 4520 plusmn 0222 18143 18515 175985811500457010583552 263041 minus 68198 minus 5140 plusmn 0218 minus 5427 plusmn 0318 18662 18993 181405811501212924838144 262897 minus 68194 minus 5095 plusmn 0158 minus 5473 plusmn 0233 18115 18477 175895811501973141042304 263066 minus 68188 minus 4907 plusmn 0087 minus 5626 plusmn 0136 17035 17492 16410

Note This table is published in its entirety in a public repository at httpsgithubcomFernandez-TrincadoTidal-debris-GaiatreemasterKundu2B2019 A portion is shown here for guidance regarding its form and content

In this sense we attempt to estimate the significance of thedetection in our photometry and PMs space For this purpose wehave compared the observed stellar counts with those computedfrom the synthetic CMDs generated with the updated version of theBesancon Galaxy model for the same line of sight and solid angleafter correcting for completeness For a more detailed descriptionof the Besancon Galaxy model we refer the readers to Robin et al(2003 the full basic description) Robin et al (2014 update onthe thick disc) Robin et al (2017 update on kinematics) andLagarde et al (2017 update on the stellar evolutionary models) Theobserved stars considered to derive the significance of a subjacentpopulation are those contained in the CMD and PM space asillustrated in Fig 2

We calculated the expected number of Milky Way stars over thesurvey area and in distance range D gt 3 kpc from the BesanconGalaxy model We found Nmodel sim 167 plusmn 13 stars in the area ofthe Gaia footprint around NGC 6362 The cited error is Poisson

statistics We can then estimate the significance of the detectionwith respect to the synthetic model in the following manner δ asymp(Nmodel minus Nextra-tidal)(Nmodel + Nextra-tidal)12 where Nextra-tidal is thenumber of observed stars following the criteria described above Weobtain a δ sim 45 detection above the foreground and backgroundpopulation

Another way to perform an estimation of the degree of con-tamination of the extracted members relies in upon apply ourmethod in adjacent regions (defined with the same area thanour explored region) around the cluster as illustrated in Fig 1Performing an analysis like that mentioned in the beginning ofSection 2 but counting all the stars in the field instead of only thosepotential members around the cluster we obtain rough estimatesof the expected contamination in our sample We note that theincompleteness of the Gaia DR2 catalogue itself has not been takeninto account in our computations therefore our estimates are upperlimits to the actual completeness for the most favourable cases

MNRAS 489 4565ndash4573 (2019)

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nloaded from httpsacadem

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nrasarticle489445655565065 by guest on 07 Decem

ber 2020

The tale of the Milky Way globular cluster NGC 6362 4567

Figure 1 The Gaia DR2 positions for the highest likelihood star debris candidates in the region of NGC 6362 shown with unfilled white circles The innerand outer black dashed circles are the tidal radius (rt) and 5times rt respectively (see the text) The arrows indicate the directions of the cluster proper motion(red arrow) with a preferential direction towards S-W the Galactic Centre (GC ndash green arrow) and the direction perpendicular to the galactic plane (bluearrow) The computed orbit (black lines) of the cluster is displayed assuming four different values of the bar patterns speed (35 40 45 and 50 km sminus1 kpc)in the GRAVPOT16 package (see the text) Five adjacent regions containing field stars (foreground and background) whose proper motions and distribution inthe CDM are overlapped with cluster members and in which the contamination was evaluated The expected surface density of potential members and eachadjacent field is internally indicated which overlap all the criteria adopted in this work

the nominal value of the cluster suggesting that these stars couldpossibly be evaporated material from NGC 6362 Therefore to besure that our candidate members are actually part of the clustersystem we selected those stars whose locations on the colourndashmagnitude diagram (CMD) clearly lie on or near the prominentmain branches of NGC 6362 as illustrated by the red symbols inFig 2 A total of 259 possible extended star debris candidates passedthese quality cuts as illustrated in Figs 1 and 2 (highlighted by redsymbols)

To summarize the possible star debris members of the cluster inFig 2 show the following proper motions that are very concentratedas expected in the vector point diagram (hereafter VPD) of a globularcluster and a CMD with the characteristic features of a globularcluster eg the main sequence the turn-off the red giant branchand some stars in the horizontal branch It is important to notethat the determination of the possible extended star debris of NGC6362 could include some field stars as members or vice versa inSection 3 we perform an estimation of the degree of contaminationof the extracted members ie the possible number of field stars thatcould have been labelled as possible extended star debris membersof the cluster

This finding gives possible clues about the recent dynamicalhistory of NGC 6362 which suggests that this cluster couldeventually form tidal tails or could also be associated with therecent encounter of the cluster with the disc

Table 1 lists the main parameters of the 259 possible extendedstar debris Fig 2 shows consistently the validity of our probable

extended star debris members that share an apparent proper motionclose to the value for NGC 6362 suggesting these stars are probablemembers of the cluster

It is important to note that most of the stars inside 2 times rhalf-mass

of the cluster are spread in proper motions as illustrated by blackdots in Fig 2 consequently one may be lead to conclude that it isrelated to contamination by foregroundbackground stars that wouldseem to be the most likely explanation for the significantly higherproper motion values Thus we also expect that our sample may besignificantly contaminated from other Galactic stellar populations(see Section 3) To alleviate this situation a detailed chemicalabundance analysis will be necessary to understand their relationif any with the cluster

3 SI G N I F I C A N C E O F T H E D E T E C T I O N O FPOSSI BLE EXTENDED STA R D EBRI S ARO UNDN G C 6 3 6 2

It is important to note that the main tracers of the possible extendedstar debris of NGC 6362 identified in this work are main-sequence(MS) stars and subgiant stars 1ndash2 mag fainter and brighter than theMS turn-off (TO) respectively However the cluster stars beyondcluster tidal radius are hidden in the CMD due to the combinationof the contributions of a minor fraction of cluster members andfore-background stellar populations from the different Milky Waycomponents (mainly the thin-thick disc and halo)

MNRAS 489 4565ndash4573 (2019)

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4568 R Kundu et al

Figure 2 Kernel density estimate (KDE) smoothed distribution of the CMD of stars within 5 times rt from the photometric centre of NGC 6362 (top rows) andproper motions in the region of the cluster (bottom rows) Left-hand panels illustrates the stars that pass the astrometric excess noise cut-offs for stars in thefield and stars within 2 times rhalf-mass sim 41 arcmin from the centre of the cluster (black dots) Right-hand panels illustrates the position in the CMD and VPD forthe highest likelihood of possible extended star debris candidates (red dots) The black dashed lines show the nominal proper motion values for NGC 6362 atμα = minus5507 mas yrminus1 μδ = minus4747 mas yrminus1 (Vasiliev 2019) while the white contour line encloses the density of forebackground stars and cluster itself

Table 1 Possible extended star debris candidates of NGC 6362 from Gaia DR2

ID α δ μα μδ G GBP GRP

() () (mas yrminus1) (mas yrminus1) (mag) (mag) (mag)

5810760588765404672 263950 minus 68123 minus 4546 plusmn 0150 minus 4631 plusmn 0202 17932 18331 173625810766331142949376 264066 minus 68122 minus 4999 plusmn 0129 minus 5362 plusmn 0166 17641 18063 170585810767636813138304 264222 minus 68057 minus 5224 plusmn 0028 minus 4442 plusmn 0037 14585 15153 138815811490290829953280 263323 minus 68172 minus 6203 plusmn 0163 minus 4243 plusmn 0230 18149 18547 176235811498086186458752 262698 minus 68193 minus 4615 plusmn 0167 minus 4520 plusmn 0222 18143 18515 175985811500457010583552 263041 minus 68198 minus 5140 plusmn 0218 minus 5427 plusmn 0318 18662 18993 181405811501212924838144 262897 minus 68194 minus 5095 plusmn 0158 minus 5473 plusmn 0233 18115 18477 175895811501973141042304 263066 minus 68188 minus 4907 plusmn 0087 minus 5626 plusmn 0136 17035 17492 16410

Note This table is published in its entirety in a public repository at httpsgithubcomFernandez-TrincadoTidal-debris-GaiatreemasterKundu2B2019 A portion is shown here for guidance regarding its form and content

In this sense we attempt to estimate the significance of thedetection in our photometry and PMs space For this purpose wehave compared the observed stellar counts with those computedfrom the synthetic CMDs generated with the updated version of theBesancon Galaxy model for the same line of sight and solid angleafter correcting for completeness For a more detailed descriptionof the Besancon Galaxy model we refer the readers to Robin et al(2003 the full basic description) Robin et al (2014 update onthe thick disc) Robin et al (2017 update on kinematics) andLagarde et al (2017 update on the stellar evolutionary models) Theobserved stars considered to derive the significance of a subjacentpopulation are those contained in the CMD and PM space asillustrated in Fig 2

We calculated the expected number of Milky Way stars over thesurvey area and in distance range D gt 3 kpc from the BesanconGalaxy model We found Nmodel sim 167 plusmn 13 stars in the area ofthe Gaia footprint around NGC 6362 The cited error is Poisson

statistics We can then estimate the significance of the detectionwith respect to the synthetic model in the following manner δ asymp(Nmodel minus Nextra-tidal)(Nmodel + Nextra-tidal)12 where Nextra-tidal is thenumber of observed stars following the criteria described above Weobtain a δ sim 45 detection above the foreground and backgroundpopulation

Another way to perform an estimation of the degree of con-tamination of the extracted members relies in upon apply ourmethod in adjacent regions (defined with the same area thanour explored region) around the cluster as illustrated in Fig 1Performing an analysis like that mentioned in the beginning ofSection 2 but counting all the stars in the field instead of only thosepotential members around the cluster we obtain rough estimatesof the expected contamination in our sample We note that theincompleteness of the Gaia DR2 catalogue itself has not been takeninto account in our computations therefore our estimates are upperlimits to the actual completeness for the most favourable cases

MNRAS 489 4565ndash4573 (2019)

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nloaded from httpsacadem

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4568 R Kundu et al

Figure 2 Kernel density estimate (KDE) smoothed distribution of the CMD of stars within 5 times rt from the photometric centre of NGC 6362 (top rows) andproper motions in the region of the cluster (bottom rows) Left-hand panels illustrates the stars that pass the astrometric excess noise cut-offs for stars in thefield and stars within 2 times rhalf-mass sim 41 arcmin from the centre of the cluster (black dots) Right-hand panels illustrates the position in the CMD and VPD forthe highest likelihood of possible extended star debris candidates (red dots) The black dashed lines show the nominal proper motion values for NGC 6362 atμα = minus5507 mas yrminus1 μδ = minus4747 mas yrminus1 (Vasiliev 2019) while the white contour line encloses the density of forebackground stars and cluster itself

Table 1 Possible extended star debris candidates of NGC 6362 from Gaia DR2

ID α δ μα μδ G GBP GRP

() () (mas yrminus1) (mas yrminus1) (mag) (mag) (mag)

5810760588765404672 263950 minus 68123 minus 4546 plusmn 0150 minus 4631 plusmn 0202 17932 18331 173625810766331142949376 264066 minus 68122 minus 4999 plusmn 0129 minus 5362 plusmn 0166 17641 18063 170585810767636813138304 264222 minus 68057 minus 5224 plusmn 0028 minus 4442 plusmn 0037 14585 15153 138815811490290829953280 263323 minus 68172 minus 6203 plusmn 0163 minus 4243 plusmn 0230 18149 18547 176235811498086186458752 262698 minus 68193 minus 4615 plusmn 0167 minus 4520 plusmn 0222 18143 18515 175985811500457010583552 263041 minus 68198 minus 5140 plusmn 0218 minus 5427 plusmn 0318 18662 18993 181405811501212924838144 262897 minus 68194 minus 5095 plusmn 0158 minus 5473 plusmn 0233 18115 18477 175895811501973141042304 263066 minus 68188 minus 4907 plusmn 0087 minus 5626 plusmn 0136 17035 17492 16410

Note This table is published in its entirety in a public repository at httpsgithubcomFernandez-TrincadoTidal-debris-GaiatreemasterKundu2B2019 A portion is shown here for guidance regarding its form and content

In this sense we attempt to estimate the significance of thedetection in our photometry and PMs space For this purpose wehave compared the observed stellar counts with those computedfrom the synthetic CMDs generated with the updated version of theBesancon Galaxy model for the same line of sight and solid angleafter correcting for completeness For a more detailed descriptionof the Besancon Galaxy model we refer the readers to Robin et al(2003 the full basic description) Robin et al (2014 update onthe thick disc) Robin et al (2017 update on kinematics) andLagarde et al (2017 update on the stellar evolutionary models) Theobserved stars considered to derive the significance of a subjacentpopulation are those contained in the CMD and PM space asillustrated in Fig 2

We calculated the expected number of Milky Way stars over thesurvey area and in distance range D gt 3 kpc from the BesanconGalaxy model We found Nmodel sim 167 plusmn 13 stars in the area ofthe Gaia footprint around NGC 6362 The cited error is Poisson

statistics We can then estimate the significance of the detectionwith respect to the synthetic model in the following manner δ asymp(Nmodel minus Nextra-tidal)(Nmodel + Nextra-tidal)12 where Nextra-tidal is thenumber of observed stars following the criteria described above Weobtain a δ sim 45 detection above the foreground and backgroundpopulation

Another way to perform an estimation of the degree of con-tamination of the extracted members relies in upon apply ourmethod in adjacent regions (defined with the same area thanour explored region) around the cluster as illustrated in Fig 1Performing an analysis like that mentioned in the beginning ofSection 2 but counting all the stars in the field instead of only thosepotential members around the cluster we obtain rough estimatesof the expected contamination in our sample We note that theincompleteness of the Gaia DR2 catalogue itself has not been takeninto account in our computations therefore our estimates are upperlimits to the actual completeness for the most favourable cases

MNRAS 489 4565ndash4573 (2019)

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nrasarticle489445655565065 by guest on 07 Decem

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The tale of the Milky Way globular cluster NGC 6362 4569

(low-density fields) Fig 1 shows the expected surface density (1star

2star 3

star 4star and 5

star) of foregroundbackground stars (blackdots) in five adjacent regions around NGC 6362 Those densitiesremain low as compared to our potential sample with the exceptionof 5

star = 00291 which is higher due to that this region lies in thedirection of the sky containing the highest densities of field stars forthis reason we have also avoid additional adjacent regions towardsthe direction north-west of the cluster Finally based on 1

star 2star

3star and 4

star we estimate the degree of contamination ie thefraction of field stars that could have been erroneously labelledas possible extended star debris members which is expected thatsim40 per cent (sim103 plusmn 10 stars) to 80 per cent (sim207 plusmn 14 stars)of the field stars could have been erroneously extracted as membersin our sample (which we call contamination of the members)This rough estimation point-out a good agreement between theBesancon Galaxy model and the data in the degree of contaminationof the extracted members by other Galactic stellar populations Inboth cases a future inventory of the chemistry of these stars inparticular the elements involved in the proton-capture reactions(ie C N O Mg Al among other) will be crucial to confirm orrefute the cluster nature of these star debris candidates in a similarfashion as Fernandez-Trincado et al (2016a 2017b 2019abde)These stars will be later analysed using high-resolution (R sim 22 000)spectra from the APOGEE-2S survey (Majewski APOGEE Team ampAPOGEE-2 Team 2016 Zasowski et al 2017) in order to investigateits chemical composition

4 TH E O R B I T O F N G C 6 3 6 2

We estimated the probable Galactic orbit for NGC 6362 in order toprovide a possible explanation to the possible extended star debrisidentified in this work For this we used a state-of-the art orbitalintegration model in an (as far as possible) realistic gravitationalpotential that fits the structural and dynamical parameters of thegalaxy to the best we know of the recent knowledge of the MilkyWay For the computations in this work we have employed the ro-tating lsquoboxypeanutrsquo bar model of the novel galactic potential modelcalled GRAVPOT161 along with other composite stellar componentsThe considered structural parameters of our bar model eg masspresent-day orientation and pattern speeds are within observationalestimations 11 times 1010 M 20 and 35ndash50 km sminus1 kpc respectivelyThe density profile of the adopted lsquoboxypeanutrsquo bar is exactly theModel-S as in Robin et al (2012) while the mathematical formalismto derive a correct global gravitational potential of this componentwill be explained in a forthcoming paper (Fernandez-Trincado et alin preparation)

GRAVPOT16 considers on a global scale a 3D steady-state gravi-tational potential for the Galaxy modelled as the superposition ofaxisymmetric and non-axisymmetric components The axisymmet-ric potential is made-up of the superposition of many compositestellar populations belonging to seven thin discs following theEinasto density-profile law (Einasto 1979) superposed along withtwo thick disc components each one following a simple hyperbolicsecant squared decreasing vertically from the Galactic plane plusan exponential profile decreasing with Galactocentric radius asdescribed in Robin et al (2014) We also implemented the densityprofile of the interstellar matter component with a density mass aspresented in Robin et al (2003) The model also correctly accountsfor the underlying stellar halo modelled by a Hernquist profile

1httpsgravpotutinamcnrsfr

Table 2 NGC 6362 ndash Sun parameters

Parameter Value Reference

NGC 6362α () δ () 262979 minus67048 (a)Distance (kpc) 76 (a)Rgal (kpc) 471μα (mas yrminus1) minus5507 plusmn 0052 (a)μδ (mas yrminus1) minus4747 plusmn 0052 (a)Vlos minus1458 plusmn 018 (a)Tidal radius (pc) 3073 (b)Mass (M) sim 105 (b)Metallicity minus107 (d)Age (Gyr) 125 plusmn 05 (e)

SunR (kpc) 83 (f)U V W (km sminus1) 1110 1224 725 (f)VLSR (km sminus1) 239 (f)

Note (a) Vasiliev (2019) (b) Moreno et al (2014) (c) Dalessandro et al(2014) (d) Massari et al (2017) (e) Dotter et al (2010) (f) Brunthaleret al (2011)

as already described in Robin et al (2014) and surrounded by asingle spherical dark matter halo component Robin et al (2003)Our dynamical model has been adopted in a score of papers (egFernandez-Trincado et al 2016ab 2017abc 2019abcde Robinet al 2017) For a more detailed discussion we refer the readers toa forthcoming paper (Fernandez-Trincado et al in preparation)

For reference the Galactic convention adopted by this work is X-axis is oriented towards l = 0 and b = 0 and the Y-axis is orientedtowards l = 90 and b = 0 and the disc rotates towards l = 90the velocity components are also oriented along these directionsIn this convention the Sunrsquos orbital velocity vector is [UVW]= [111 1224 725] km sminus1 (Brunthaler et al 2011) The modelhas been rescaled to the Sunrsquos galactocentric distance 83 kpc andthe local rotation velocity of 239 km sminus1

For the computation of the Galactic orbits for NGC 6362 we haveemployed a simple Monte Carlo scheme for the input data listed inTable 2 and the RungendashKutta algorithm of seventhndasheighth orderelaborated by Fehlberg (1968) The uncertainties in the input data(eg distance proper motions and line-of-sight velocity errors)were propagated as 1σ variations in a Gaussian Monte Carlo re-sampling in order to estimate the more probable regions of thespace which are crossed more frequently by the simulated orbitsas illustrated in Fig 2 The error bar for the heliocentric distance isassumed to be 1 kpc We have sampled half million orbits computedbackward in time during 3 Gyr Errors in the calculated orbitalelements were estimated by taking half million samples of the errordistributions and finding the 16th and 84th percentiles as listed inTable 3 The average value of the orbital elements was found for halfmillion realizations with uncertainty ranges given by the 16th and84th percentile values as listed in Table 3 where rperi is the averageperigalactic distance rapo is the average apogalactic distance andZmax is the average maximum distance from the Galactic plane

Fig 3 shows the probability densities of the resulting orbitsprojected on the equatorial (left-hand column) and meridional(right-hand column) Galactic planes in the non-inertial referenceframe where the bar is at rest The orbital path (adopting centralvalues) is shown by the black line in the same figure The green andyellow colours correspond to more probable regions of the spacewhich are crossed more frequently by the simulated orbits Wefound that most of the simulated orbits are situated in the inner bulge

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Table 3 Orbital parameters of NGC 6362 with uncertainty ranges givenby the 16th (subscript) and 84th (superscript) percentile values

bar rperi rapo Zmax Eccentricity(km sminus1 kpcminus1) (kpc) (kpc) (kpc)

35 202218181 529568

503 341383330 045049

042

40 198217187 538603

516 345384319 047049

044

45 204222197 594689

572 355414314 049053

047

50 199211192 565615

536 351381329 049052

043

region which means that NGC 6362 is on high eccentric orbit (witheccentricities greater than 045) reaching out to a maximum distancefrom the Galactic plane larger than 2 kpc with a perigalacticon ofsim2 kpc and an apogalactic distance of sim6 kpc On the other handNGC 6362 orbits have energies allowing the cluster to move inwardsfrom the barrsquos corotation radius (CR lt65 kpc) In this region aclass of orbits appears around the Lagrange points on the minor axisof the bar that can be stable and have a banana-like shape parallelto the bar (see lower panel with bar = 50 km sminus1 kpc in Fig 3)while the Lagrange orbits libating around Lagrange points alignedwith the bar are unstable and are probably chaotic orbits Our modelnaturally predicts trajectories indicating that NGC 6362 is confinedto the inner disc

Additionally in Fig 4 we show the variation of the z-componentof the angular momentum in the inertial frame Lz as a functionof time and bar Since this quantity is not conserved in a modellike GRAVPOT16 (with non-axisymmetric structures) we follow thechange -Lz + Lz where negative Lz in our reference systemmeans that the cluster orbit is prograde (in the same sense as thedisc rotation) Both prograde and progradendashretrograde orbits withrespect to the direction of the Galactic rotation are clearly revealedfor NGC 6362 This effect is strongly produced by the presence ofthe galactic bar further indicating a chaotic behaviour

It is important to mention that one major limitation of our model isthat it ignores secular changes in the Milky Way potential over timeand dynamical friction which might be important in understandingthe evolution of NGC 6362 crossing the inner Galaxy An in-depthanalysis of such dynamical behaviour is beyond the scope of thispaper

5 MASS-LOSS RATE IN NGC 6362

The detailed computations of destruction rates of globular clustersin our Galaxy due to the effects of bulge and disc shocking anddynamical friction employing the Galactic model GRAVPOT16 willbe presented in a future study However for this work we haveused destruction rates of the galactic cluster due to dynamicalfriction and bulge and disc shockings from the literature and addedthe corresponding destruction rate due to evaporation to get anestimated value for its total mass-loss rate

Moreno et al (2014) (M + 14 hereafter) have computed destruc-tion rates of globular clusters due to bulge and disc shocking using aGalactic model that employs a bar component alike the GRAVPOT16model but with a greater mass the bar mass ratio being around15 For the orbit of NGC 6362 the kinematic parameters used inthe present analysis differ from those used by M + 14 howeverboth models give similar orbits differing only in the maximumdistance zmax reached from the Galactic plane which in our case isaround 15 times that obtained by M + 14 With tb the characteristiclifetime due to bulge shocking M + 14 obtain the correspondingpresent destruction rate 1tb = 135 times 10minus11 yrminus1 using a cluster

Figure 3 Kernel density estimate (KDE) smoothed distribution of simu-lated orbits employing a Monte Carlo approach showing the probabilitydensities of the resulting orbits projected on the equatorial (left) andmeridional (right) Galactic planes in the non-inertial reference frame wherethe bar is at rest The green and yellow colours correspond to more probableregions of the space which are crossed more frequently by the simulatedorbits The black line is the orbit of NGC 6362 adopting the central inputsThe small white star marks the present position of the cluster whereas thewhite square marks its initial position In all orbit panels the white dottedcircle show the location of the corotation radius (CR) the horizontal whitesolid line shows the extension of the bar

mass Mc sim 105 M With the GRAVPOT16 model and the decreasedvalue of Mc in Table 2 1tb would be more than the reported valueof M + 14 but the lower mass of the bar in GRAVPOT16 woulddecrease this value Thus we consider the cited value of 1tb asrepresentative for bulge shocking in our present analysis

With respect to disc shocking M + 14 obtain the presentdestruction rate 1td = 212 times 10minus11 yrminus1 td being the correspondingcharacteristic lifetime With the GRAVPOT16 model this value woulddecrease due to the greater velocity of the cluster when it crosses theGalactic plane as it comes from a greater zmax (Spitzer 1987) butwith the lower cluster mass given in Table 2 1td would increase

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The tale of the Milky Way globular cluster NGC 6362 4571

Figure 4 Kernel density estimate (KDE) smoothed distribution of thevariation of the z-component of the angular momentum (Lz) in the inertialframe versus time for four assumed bar pattern speeds 35 40 45 and 50 kmsminus1 kpc

The effect of dynamical friction on globular clusters has beenestimated by Aguilar Hut amp Ostriker (1988) taking isotropicvelocity dispersion fields in the components of their axisymmetricGalactic models For NGC 6362 they give 1tdf = 14 times 10minus12 yrminus1which is an order of magnitude shorter than 1tb and 1td

To estimate the destruction rate 1tev due to evaporation thecorresponding lifetime tev is computed with tev = ftrh taking trh andf given by the equation 7108 and approximation 7142 of Binney ampTremaine (2008) Taking m in that equation as 1 M Mc = 53 times 104

M (Table 2) and the half-mass radius rh = 453 pc (eg M + 14)the resulting present value for tev using f = 40 is tev = 24 times 1010

yr or an evaporation rate 1tev = 42 times 10minus11 yrminus1The sum of 1tb 1td 1tdf and 1tev gives the total destruction

rate 1ttot = 78 times 10minus11 yrminus1 or a present mass-loss rate Mc =Mc(1ttot) = 41 times 10minus6 M yrminus1 To improve this estimate of themass-loss rate the computation of 1tdf needs to be done with a barcomponent in the Galactic model as GRAVPOT16 employed hereand taking non-isotropic dispersion fields

We hypothesize that the mean absolute difference of propermotions in right ascension and declination between the cluster andthe 259 possible extended star debris candidates is around 05 masyrminus1 This gives an approximate mean relative velocity in the planeof the sky of 25 km sminus1 With this velocity the stars will move outthe vicinity shown in Fig 1 in a time of about 107 yr We assumethat the star surface density in Fig 1 is maintained and with theestimated mass-loss rate in this interval of time the cluster losesabout 40 M Thus the majority of the star debris candidates shouldbe low-mass stars (sim015 M)

6 C O N C L U D I N G R E M A R K S

We have used the Gaia DR2 information along with the fundamentalparameters of the cluster NGC 6362 to search for possible extendedstar debris candidates We report the identification of 259 potentialstellar members of NGC 6362 extending few arcminutes fromthe edge of the clusterrsquos radius Both astrometric information andlocation of these possible extended star debris candidates on theCMD are consistent with the cluster membership Unfortunately

the presently available astrometric information from Gaia is notsufficient to determine with certainty how many of the stars may betruly extended star debris members Nevertheless this initial GaiaDR2 sample significantly contributes to the task of compiling amore thorough census of possible extended star debris in the areaof the sky around NGC 6362 and portends the promising results tobe expected from future spectroscopic follow-up observations

If the newly discovered objects are part of the main cluster theseresults would suggest the presence of an asymmetrically extendedstellar material in the outer parts of the cluster whose surface densityprofile is mainly shaped by evaporation andor tidal stripping at itscurrent location in the Galaxy tracing their dynamical evolution inthe Milky Way (evaporation and tidal shocking) Also there is noapparent correlation between the distribution of the newly identifiedextended star debris candidates and the orbit of the cluster rulingout any evidence of elongation along the tidal field gradient

The possible extended star debris candidates observed in thecluster can be either due to tidal disruption or dynamical frictionor a combined effect of both Therefore to find an explanationfor these extended star debris candidates we computed the orbitsfor the cluster using four different values of bar = 35 40 4550 km sminus1 kpcminus1 Half million orbits were computed for differentinitial conditions considering boxy bar potential perturbations in aninertial reference frame where the bar is considered at an angleof 20 with the line joining Sun and the Galactic centre EarlierDinescu Girard amp van Altena (1999) also determined the orbitalparameters for the cluster but without the contribution of the barto the potential However the Lz evolution modelled here indicatesthat the cluster is affected by the bar potential of the Galaxy Fig 1shows the asymmetric distribution of the possible extended stardebris candidates along with the orbit of the cluster traced back for3 Gyr with three different bar speeds

Fig 3 shows the orbit of the cluster in the meridional Galacticplane and equatorial Galactic plane simulated in the inertial refer-ence frame It is clear from the figure that the cluster is circulatingthe inner disc within a distance of 3 kpc above and below the discAs the cluster never enters the bulge of the Galaxy the dynamicalfriction experienced by the cluster is negligible but this cluster haspassed through the Galactic disc many times experiencing a shockevery time it crosses the disc Due to these shocks many starsmust have been stripped away from the cluster Hence the observedextended star debris candidates can be a result of tidal disruption andshocks from the Galactic disc that happened more than 159 MyrThanks to the relatively short distance of NGC 6362 and its highrelease of unbound material during its current disc shocking weestimate the mass variation to be of the order of sim41 times 10minus6 Myrminus1

All the raw data used in this work are available through theVizieR Database (I345gaia2) Furthermore in order to facilitatethe reproducibility and reuse of our results we have made availableall the data and the source codes available in a public repository2

AC K N OW L E D G E M E N T S

The authors would like to thank the anonymous referee for herhisconstructive comments and improvements making this a betterpaper RK is thankful to the Council of Scientific and IndustrialResearch New Delhi for a Senior Research Fellowship (SRF)

2httpsgithubcomFernandez-TrincadoTidal-debris-GaiatreemasterKundu2B2019

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The tale of the Milky Way globular cluster NGC 6362 4571

Figure 4 Kernel density estimate (KDE) smoothed distribution of thevariation of the z-component of the angular momentum (Lz) in the inertialframe versus time for four assumed bar pattern speeds 35 40 45 and 50 kmsminus1 kpc

The effect of dynamical friction on globular clusters has beenestimated by Aguilar Hut amp Ostriker (1988) taking isotropicvelocity dispersion fields in the components of their axisymmetricGalactic models For NGC 6362 they give 1tdf = 14 times 10minus12 yrminus1which is an order of magnitude shorter than 1tb and 1td

To estimate the destruction rate 1tev due to evaporation thecorresponding lifetime tev is computed with tev = ftrh taking trh andf given by the equation 7108 and approximation 7142 of Binney ampTremaine (2008) Taking m in that equation as 1 M Mc = 53 times 104

M (Table 2) and the half-mass radius rh = 453 pc (eg M + 14)the resulting present value for tev using f = 40 is tev = 24 times 1010

yr or an evaporation rate 1tev = 42 times 10minus11 yrminus1The sum of 1tb 1td 1tdf and 1tev gives the total destruction

rate 1ttot = 78 times 10minus11 yrminus1 or a present mass-loss rate Mc =Mc(1ttot) = 41 times 10minus6 M yrminus1 To improve this estimate of themass-loss rate the computation of 1tdf needs to be done with a barcomponent in the Galactic model as GRAVPOT16 employed hereand taking non-isotropic dispersion fields

We hypothesize that the mean absolute difference of propermotions in right ascension and declination between the cluster andthe 259 possible extended star debris candidates is around 05 masyrminus1 This gives an approximate mean relative velocity in the planeof the sky of 25 km sminus1 With this velocity the stars will move outthe vicinity shown in Fig 1 in a time of about 107 yr We assumethat the star surface density in Fig 1 is maintained and with theestimated mass-loss rate in this interval of time the cluster losesabout 40 M Thus the majority of the star debris candidates shouldbe low-mass stars (sim015 M)

6 C O N C L U D I N G R E M A R K S

We have used the Gaia DR2 information along with the fundamentalparameters of the cluster NGC 6362 to search for possible extendedstar debris candidates We report the identification of 259 potentialstellar members of NGC 6362 extending few arcminutes fromthe edge of the clusterrsquos radius Both astrometric information andlocation of these possible extended star debris candidates on theCMD are consistent with the cluster membership Unfortunately

the presently available astrometric information from Gaia is notsufficient to determine with certainty how many of the stars may betruly extended star debris members Nevertheless this initial GaiaDR2 sample significantly contributes to the task of compiling amore thorough census of possible extended star debris in the areaof the sky around NGC 6362 and portends the promising results tobe expected from future spectroscopic follow-up observations

If the newly discovered objects are part of the main cluster theseresults would suggest the presence of an asymmetrically extendedstellar material in the outer parts of the cluster whose surface densityprofile is mainly shaped by evaporation andor tidal stripping at itscurrent location in the Galaxy tracing their dynamical evolution inthe Milky Way (evaporation and tidal shocking) Also there is noapparent correlation between the distribution of the newly identifiedextended star debris candidates and the orbit of the cluster rulingout any evidence of elongation along the tidal field gradient

The possible extended star debris candidates observed in thecluster can be either due to tidal disruption or dynamical frictionor a combined effect of both Therefore to find an explanationfor these extended star debris candidates we computed the orbitsfor the cluster using four different values of bar = 35 40 4550 km sminus1 kpcminus1 Half million orbits were computed for differentinitial conditions considering boxy bar potential perturbations in aninertial reference frame where the bar is considered at an angleof 20 with the line joining Sun and the Galactic centre EarlierDinescu Girard amp van Altena (1999) also determined the orbitalparameters for the cluster but without the contribution of the barto the potential However the Lz evolution modelled here indicatesthat the cluster is affected by the bar potential of the Galaxy Fig 1shows the asymmetric distribution of the possible extended stardebris candidates along with the orbit of the cluster traced back for3 Gyr with three different bar speeds

Fig 3 shows the orbit of the cluster in the meridional Galacticplane and equatorial Galactic plane simulated in the inertial refer-ence frame It is clear from the figure that the cluster is circulatingthe inner disc within a distance of 3 kpc above and below the discAs the cluster never enters the bulge of the Galaxy the dynamicalfriction experienced by the cluster is negligible but this cluster haspassed through the Galactic disc many times experiencing a shockevery time it crosses the disc Due to these shocks many starsmust have been stripped away from the cluster Hence the observedextended star debris candidates can be a result of tidal disruption andshocks from the Galactic disc that happened more than 159 MyrThanks to the relatively short distance of NGC 6362 and its highrelease of unbound material during its current disc shocking weestimate the mass variation to be of the order of sim41 times 10minus6 Myrminus1

All the raw data used in this work are available through theVizieR Database (I345gaia2) Furthermore in order to facilitatethe reproducibility and reuse of our results we have made availableall the data and the source codes available in a public repository2

AC K N OW L E D G E M E N T S

The authors would like to thank the anonymous referee for herhisconstructive comments and improvements making this a betterpaper RK is thankful to the Council of Scientific and IndustrialResearch New Delhi for a Senior Research Fellowship (SRF)

2httpsgithubcomFernandez-TrincadoTidal-debris-GaiatreemasterKundu2B2019

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(File number 09045 (1414)2016-EMR-I) JGF-T is supported byFONDECYT No 3180210 DM gratefully acknowledges supportprovided by the BASAL Center for Astrophysics and AssociatedTechnologies (CATA) through grant AFB 170002 and the Ministryfor the Economy Development and Tourism Programa IniciativaCientıfica Milenio grant IC120009 awarded to the MillenniumInstitute of Astrophysics (MAS) and from project Fondecyt No1170121 HPS and RK are thankful to the Council of Scientificand Industrial Research New Delhi for the grants-in-aid (Ref No03(1428)18EMR-II) RK and DM are also very grateful for thehospitality of the Vatican Observatory where this work was startedEM acknowledges support from 〈0funding-source 〉UNAMPAPIIT〈0funding-source〉 grant IN105916

Funding for the GRAVPOT16 software has been provided bythe Centre national drsquoetudes spatiales (CNES) through grant0101973 and UTINAM Institute of the Universite de Franche-Comte supported by the Region de Franche-Comte and Institut desSciences de lrsquoUnivers (INSU) Simulations have been executed oncomputers from the Utinam Institute of the Universite de Franche-Comte supported by the Region de Franche-Comte and Institut desSciences de lrsquoUnivers (INSU) and on the supercomputer facilitiesof the Mesocentre de calcul de Franche-Comte This work hasmade use of results from the European Space Agency (ESA) spacemission Gaia the data from which were processed by the GaiaData Processing and Analysis Consortium (DPAC) Funding forthe DPAC has been provided by national institutions in particularthe institutions participating in the Gaia Multilateral AgreementThe Gaia mission website is http wwwcosmosesaintgaia

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2001 ApJ 552 572Mackereth J T et al 2019 MNRAS 482 3426Majewski S R et al 2012a American Astronomical Society Meeting

Abstracts 219 p 41005Majewski S R Nidever D L Smith V V Damke G J Kunkel W

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Majewski S R APOGEE Team APOGEE-2 Team 2016 Astron Nachr337 863

Marchetti T Rossi E M Brown A G A 2018 MNRAS preprint (arXiv180410607)

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Irwin M J 2010 MNRAS 408 L66Odenkirchen M et al 2001 ApJ 548 L165

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The tale of the Milky Way globular cluster NGC 6362 4573

Robin A C Reyle C Derriere S Picaud S 2003 AampA 409 523Robin A C Marshall D J Schultheis M Reyle C 2012 AampA 538

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2014 AampA 569 A13Robin A C Bienayme O Fernandez-Trincado J G Reyle C 2017 AampA

605 A1Rodruck M et al 2016 MNRAS 461 36Sollima A Martınez-Delgado D Valls-Gabaud D Penarrubia J 2011

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Torres-Flores S de Oliveira C M de Mello D F Scarano S Urrutia-Viscarra F 2012 MNRAS 421 3612

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407Vasiliev E 2019 MNRAS 484 2832Vesperini E Heggie D C 1997 MNRAS 289 898Weinberg M D 1994 AJ 108 1414White S D M 1983 ApJ 274 53Zasowski G et al 2017 AJ 154 198

This paper has been typeset from a TEXLATEX file prepared by the author

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