The orbital motion of the Quintuplet cluster - a common

origin for the Arches and Quintuplet clusters?∗

A. Stolte1, B. Hußmann1, M. R. Morris2, A. M. Ghez2, W. Brandner3, J. R. Lu4,W. I. Clarkson5, M. Habibi1, K. Matthews6

ABSTRACT

We investigate the orbital motion of the Quintuplet cluster near the Galactic centerwith the aim of constraining formation scenarios of young, massive star clusters in nuclearenvironments. Three epochs of adaptive optics high-angular resolution imaging with theKeck/NIRC2 and VLT/NAOS-CONICA systems were obtained over a time baseline of 5.8years, delivering an astrometric accuracy of 0.5-1 mas/yr. Proper motions were derivedin the cluster reference frame and were used to distinguish cluster members from themajority of the dense field star population toward the inner bulge. Fitting the clusterand field proper motion distributions with 2D gaussian models, we derive the orbitalmotion of the cluster for the first time. The Quintuplet is moving with a 2D velocity of132±15 km/s with respect to the field along the Galactic plane, which yields a 3D orbitalvelocity of 167±15 km/s when combined with the previously known radial velocity. Froma sample of 119 stars measured in three epochs, we derive an upper limit to the velocitydispersion in the core of the Quintuplet cluster of σ1D < 10 km/s. Knowledge of thethree velocity components of the Quintuplet allows us to model the cluster orbit in thepotential of the inner Galaxy. Under the assumption that the Quintuplet is located inthe central 200 pc at the present time, these simulations exclude the possibility that thecluster is moving on a circular orbit. Comparing the Quintuplet’s orbit with our earliermeasurements of the Arches orbit, we discuss the possibility that both clusters originatedin the same area of the central molecular zone. According to the model of Binney etal. (1991), two families of stable cloud orbits are located along the major and minor axesof the Galactic bar, named x1 and x2 orbits, respectively. The formation locus of theseclusters is consistent with the outermost x2 orbit and might hint at cloud collisions at thetransition region between the x1 and x2 orbital families located at the tip of the minoraxis of the Galactic bar. The formation of young, massive star clusters in circumnuclearrings is discussed in the framework of the channeling in of dense gas by the bar potential.We conclude that the existence of a large-scale bar plays a major role in supportingongoing star and cluster formation, not only in nearby spiral galaxies with circumnuclearrings, but also in the Milky Way’s central molecular zone.

Subject headings: Open clusters and associations: individual (Quintuplet)–Galaxy: center–Galaxy: kinematics and dynamics–techniques: high angular resolution–astrometry1

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1. Introduction

The Galactic center is host to 3 young, mas-sive star clusters, the Arches and Quintupletclusters at projected distances of 26 to 32 pcfrom the supermassive black hole (Nagata etal. 1990, 1995, Okuda et al. 1990, Cotera etal. 1996, Figer et al. 1999ab, Stolte et al. 2008),and the young nuclear cluster inside the cen-tral few parsecs (e.g., Genzel et al. 2003, Ghezet al. 2005, Paumard et al. 2006, Schödelet al. 2007, Do et al. 2009, 2013, Bartko etal. 2010, Lu et al. 2013). Each of these clustersis known to host at least 104M� in stars, withthe Arches and Quintuplet likely containingstellar masses in excess of 2 × 104M� (Figeret al. 1999a, Espinoza et al. 2009, Clarksonet al. 2012, Habibi et al. 2013), similar to thestellar content in the Young Nuclear Cluster(Bartko et al. 2010, Lu et al. 2013). At agesof only a few Myr, these clusters harbour arich population of Wolf-Rayet stars and super-

1Argelander Institut für Astronomie, Auf demHügel 71, 53121 Bonn, Germany, astolte@astro.uni-bonn.de

2Division of Astronomy and Astrophysics, UCLA,Los Angeles, CA 90095-1547, ghez@astro.ucla.edu,morris@astro.ucla.edu

3Max-Planck-Institut für Astronomie, Königstuhl17, 69117 Heidelberg, Germany, brandner@mpia.de

4Institute for Astronomy, University of Hawai’i,2680 Woodlawn Drive, Honolulu, HI 96822,jlu@ifa.hawaii.edu

5Department of Natural Sciences, University ofMichigan-Dearborn, 125 Science Building, 4901 Ever-green Road, Dearborn, MI 48128, wiclarks@umich.edu

6Caltech Optical Observatories, California Insti-tute of Technology, MS 320-47, Pasadena, CA 91225,kym@caltech.edu

*This paper is based on observations obtainedwith the VLT at Paranal Observatory, Chile, underprogramme 71.C-0344 (PI: Eisenhauer) and 081.D-0572(B) (PI: Brandner), and obtained with the Kecktelescopes at Mauna Kea, Hawai’i (PI: Morris).

giants, which are the youngest and most ex-treme post-main sequence evolutionary phasesof O-type stars (Crowther 2007, Martins etal. 2008). The Quintuplet cluster in particu-lar is associated with at least two sources inthe short-lived Luminous Blue Variable (LBV)phase and contains several carbon-enrichedWolf-Rayet (WC) stars (Figer et al. 1999b,Liermann et al. 2009, 2010, Mauerhan etal. 2010a). The short dynamical lifetime ofyoung clusters in the GC of only a few 10 Myr(Kim et al. 2000, Portegies Zwart et al. 2002)suggests that the Arches and Quintuplet clus-ters contribute to the apparently isolated fieldpopulation of evolved, high-mass stars (Mauer-han et al. 2010b).

At the same time, the origin of these mas-sive clusters is unknown. The dynamical prop-erties of a young star cluster are indicators ofthe cluster’s origin and stability during its evo-lutionary timescale. In contrast to spiral armclusters, clusters emerging near the center ofthe Galaxy are moving rapidly from their birthsites and do not appear affiliated with theirnatal clouds. The orbital motion of these clus-ters, combined with the cluster age, providesthe only clue to their birth sites by tracing thecluster orbit backwards in time. In addition,the orbital velocity is an important determi-nant for the chances of cluster survival. Clus-ters on orbits very close to the Galactic centerexperience stronger tidal losses, but a larger or-bital velocity decreases the effect of dynamicalfriction in the central potential.

With the goal of tracing back the dynamicalevolution of the Arches and Quintuplet clustersto their potential formation locus, we have setout to measure the orbital motion and the in-ternal velocity dispersion of both clusters fromproper motions, covering a time baseline of sixyears. With the first derivation of the 3D or-

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bital velocity of the Arches cluster and its or-bital path for a family of nested orbits at var-ious line-of-sight distances (Stolte et al. 2008),we constrained the most likely formation locusof this cluster to the inner 200 pc and henceshowed for the first time that these massiveclusters might form within the boundaries ofthe central molecular zone (CMZ). One pre-destined location where cloud collisions mighttrigger cluster formation are the regions whereinstreaming clouds on x1 orbits from the outerGalactic bar collide with CMZ clouds on orbitsaround the bar’s minor axis (x2 orbits, Binneyet al. 1991). In our previous paper, we sug-gested a formation locus for the Arches clus-ter near the transition region of the x1 andx2 orbital families (Binney et al. 1991). Re-cent results by the Herschel satellite have fos-tered the notion of a star-forming ring in theinner 240 pc (diameter) of the CMZ (Molinariet al. 2011). Additional support to cluster for-mation in the Galactic center stems from thediscovery of dense, compact clouds with suf-ficient masses to form 104M� clusters (Long-more et al. 2012, 2013). The clouds are lo-cated in projection along the star-forming ringproposed by Molinari et al. (2011). Althoughboth the Arches and Quintuplet clusters werealso suggested to be located on this structure(Longmore et al. 2013), their orbital velocitiesare higher by about a factor of two as comparedto the terminal cloud velocities of ∼ 100 km/s(Molinari et al. 2011).

In this contribution, we present the orbitalvelocity and obtain an upper limit to the in-ternal velocity dispersion of the Quintupletcluster. Combining the proper motion of theQuintuplet with its radial velocity, we modelthe cluster’s orbital motion as a function ofthe line-of-sight distance, which provides clueson the formation locus of the cluster. Ul-

timately, the comparison with N-body sim-ulations will yield the expected tidal lossesthat have occured during the cluster’s life-time. Comparable results for the - presumablyyounger - Arches cluster are presented in Stolteet al. (2008) and Clarkson et al. (2012).

The paper is organized as follows: The ob-servations are described in Sec. 2, followed bythe data reduction, astrometry and photome-try procedures. The orbital motion and veloc-ity dispersion are fitted using the proper mo-tion plane in Sec. 3, while simulations of thefamily of cluster orbits are shown in Sec. 3.3.We also present an updated version of theArches cluster orbit for comparison, adjustedfor the slightly lower orbital velocity found inour new multi-epoch investigation (Clarkson etal. 2012). In Sec. 4, we discuss the implica-tions for cluster formation in the nucleus of theMilky Way and other galaxies. Sec. 5 summa-rizes the main findings of the proper motionanalysis.

2. Observations

For the proper motion analysis of the centralregion of the Quintuplet, data from the ESOVery Large Telescope (VLT) taken in 2003 werecombined with Keck observations obtained in2008 and 2009. A second epoch of NACO ob-servations obtained in July 2008 was used toconstrain the 2D cluster motion from a sampleof stars at larger radii from the cluster center.All positions are approximately centered on thecentral Quintuplet star Q12 (Glass et al. 1990)at RA 17:46:15.12, DEC -28:49:35.06. A tech-nical summary of the observations is providedin Table 1.

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2.1. Keck/NIRC2

Keck observations were carried out us-ing the NIRC2 near-infrared camera (PI:K. Matthews) behind laser guide star adaptiveoptics on 2008 May 14 and 2009 May 4. Thenarrow camera was used with a field of view of10′′, delivering a pixel scale of 9.942 milliarc-seconds (mas) per pixel. A detector integrationtime of 1s with 30 co-added frames led to a to-tal integration time of 30s per image using theK ′ filter (λc = 2.124µm, ∆λ = 0.351µm), sim-ilar to the specifications of the NACO Ks filter(Sec. 2.2). A small dither pattern of ±0.35′′in 2008 and of ±0.60′′ in 2009 was used to fa-cilitate bad-pixel removal. The small dithermovements minimize optical distortion effects,which enhances the astrometric accuracy ofthe NIRC2 data set. In the 2008 campaign, 58images were obtained with Strehl ratios rang-ing from 8% to 34%, with a spatial resolutionbetween 57 and 108 mas (Full Width at HalfMaximum, FWHM). As spatial resolution isthe limiting factor for the astrometric accu-racy, only the 33 frames with FWHM < 70mas and Strehl ratios SR > 20% were selectedfor the astrometric analysis. In the 2009 cam-paign, the same exposure time setup was usedto obtain 117 images with Strehl ratios be-tween 12 and 47% and spatial resolutions of50 < FWHM < 116 mas. In total 60 frameswith SR > 28% and FWHM < 62 mas wereselected for image combination.

The data reduction was carried out with ourcustom-made NIRC2 data pipeline (see Lu etal. 2009 for a detailed description). The rawdata were reduced using dark images with thesame exposure time, readout mode, and num-ber of co-adds, and were then divided by themaster flat-field created from on-off lamp flatstaken during the same night. During the com-bination of the master dark and flat-field im-

ages, a 3 sigma clipping routine was applied todetect hot and dark pixels and create a fixedNIRC2 bad pixel mask. In addition to the fixedNIRC2 bad pixel mask, individual mask imageswere extracted for each image using a standardcosmic ray detection routine (crrej in IRAF).At the end of the cluster observing sequence,9 sky images were obtained with the same ob-servational setup and at an airmass compara-ble to that of the science observations. Thesky images were scaled to a common mean skylevel prior to image combination, and the re-sulting master sky was scaled with scaling fac-tors of 0.99-1.03 to the background flux of eachscience frame before sky subtraction. The re-duced images were combined using the driz-zle task (Fruchter & Hook 2002) in IRAF1. Inaddition to a deep image encompassing all 33(60) selected frames in 2008 (2009) shown inFig. 1, 3 auxiliary images were drizzled fromthree subsets of 11 (20) frames each, where thefull range of spatial resolutions is included ineach stack to achieve a comparable data qualityamong all three subsets. Photometry is derivedon these auxiliary images in the same way as onthe deep combined image to obtain photomet-ric and astrometric uncertainties from repeatedmeasurements.

2.2. VLT/NAOS-CONICA

The Quintuplet cluster was observed in 2003with the Very Large Telescope (VLT) NasmythAdaptive Optics System NAOS (Rousset etal. 2003) attached to the infrared camera CON-ICA (Lenzen et al. 2003, hereafter NACO) aspart of the guaranteed time observations of the

1IRAF is distributed by the National Optical Astron-omy Observatory, which is operated by the Associationof Universities for Research in Astronomy (AURA) un-der cooperative agreement with the National ScienceFoundation.

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NACO instrument consortium. Observationswere carried out on 2003 July 22 and 23, usingthe infrared wavefront sensor with the N20C80dichroic splitting the beam such that 20% ofthe light serves the adaptive optics control loopand 80% is diverted to the science detector.The infrared-bright star Q2 (Glass et al. 1990)with K = 7.3 mag at a distance of 8′′ from thecluster center (Q12) served as the natural guidestar for the infrared wavefront sensor. Imageswere observed with the S27 camera covering a27′′ × 27′′ field of view with a pixel scale 27.1milliarcseconds (mas) per pixel and the Ks fil-ter with λc = 2.18µm, ∆λ = 0.35µm, similarto the NIRC2 K ′ filter (Sec. 2.1). Two sets ofexposures with different integration times wereobtained to minimize saturation effects whileensuring astrometric and photometric perfor-mance at the faint end. Short exposures withdetector integration times of 2.0s with 15 co-added frames aided avoiding saturation of thebrighter cluster members, and 20.0s exposureswith two co-added frames enhanced the sensi-tivity towards the faintest stars. The telescopewas moved in a wide dither pattern with max-imum offsets of ±10′′ to avoid artefacts due toghost images of the very bright central clus-ter stars (Ks ∼ 6 mag) and to facilitate badpixel correction. Dithering increased the ob-served field of view to 40′′×40′′, and the central15′′×15′′ of this field were extracted for match-ing with the narrow field NIRC2 data sets. Asecond, shallower epoch of NACO Ks imageswith 2.0s individual exposure times and ±7′′maximum dithers was obtained in July 2008with the same instrumental setup under worseatmospheric conditions. For all NACO datasets, the FWHM ranged from 71 to 83 maswith Strehl ratios of 3-12% (see Table 1).

The raw data were extracted from theESO archive facility, including flat-field and

dark calibration frames taken during adjacentnights. A custom-made pipeline which catersto the special needs of the NACO S27 perfor-mance was used to reduce the data. The majorreduction steps are briefly summarized here,while a detailed overview of the reduction pro-cedures is presented in Hußmann et al. (2012).As 50Hz noise is sometimes prevalent in theNACO images2, manifesting itself in a densepattern of horizontal stripes moving across theimages during consecutive exposures, both sci-ence and sky frames were dark-subtracted andflat-fielded to allow for 50Hz correction priorto sky subtraction. A master dark was gen-erated from 3 individual dark exposures withthe same exposure time and readout mode asthe science images. The master flat-field wasderived from sensitivity measurements in eachpixel obtained at varying twilight flux levels.The master sky was created from sky exposuresof semi-empty fields observed without AO cor-rection. Residual star flux was removed fromthe master sky image by rejecting bright pixelsduring the combination of the individual skyframes. As in the case of the NIRC2 data, abad pixel mask was created during the com-bination of the darks and flat-fields, to whichindividual bad pixel masks are added for eachimage marking cosmic ray events detected withthe IRAF crrej routine. The reduced imagesare combined using the IRAF/PYRAF taskdrizzle, with the individual bad pixel maskapplied to each frame during image combina-tion. From the 2.0s and 20.0s 2003 and 2.0s2008 data sets, one deep image was generatedfor each by selecting 16, 16, and 33 individ-ual frames, respectively. The deep images ofthe 2003 and 2008 2s exposures are displayedin Fig. 1. The combined sets are termed 2s

2http://www.eso.org/observing/dfo/quality/NACO/ServiceMode/naco noise.html

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http://www.eso.org/observing/dfo/quality/NACO/

and 20s (combined) images for simplicity inthe remainder of the paper. Auxiliary imageswere generated from one third of the individualscience exposures in each of these sets to per-form repeated flux measurements for a realisticjudgement of the astrometric und photometricuncertainties.

2.3. Astrometry and Photometry

2.3.1. Keck/NIRC2

Positions and fluxes were extracted usingthe Starfinder crowded field point spread func-tion (PSF) fitting tool (Diolaiti et al. 2000).In the 10′′ NIRC2 field of view, ten isolatedsources were selected as PSF reference stars.Photometry of all sources in the field was ex-tracted with a flux threshold of three sigmaabove the background, and three source extrac-tion iterations were performed. In addition tothe deep images, Starfinder was run on eachof the three auxiliary images in each epoch.As these three images are independent, a re-peated flux and position measurement is ob-tained for each star, albeit at the cost of pho-tometric sensitivity and astrometric precisiondue to the fact that each subset contains onlyone-third of the images combined in each deepimage. Stars are required to be detected in atleast two auxiliary images in addition to thedeep science image. For stars detected in allthree auxiliary images, the uncertainty in theposition and magnitude of each star is derivedas the root-mean-square (rms) deviation fromthe mean of the three subsets divided by thesquare root of the number of independent mea-surements, here

√(3), which compensates for

the lack of photometric depth in the auxiliaryimages as compared to the deep science image.In the case that a star is only detected in twoauxiliary images, the uncertainty is derived asthe deviation from the mean of the two mea-

surements, divided by√

(2). The positionaluncertainties for all data sets are displayed inFig. 2.

2.3.2. VLT/NACO

Ks 2003 central field

The larger field of view of 27′′×27′′ provided bythe NACO camera shows severe anisoplanaticeffects across the field. These effects were es-pecially pronounced in the 20s images due tothe long integration time. For the central areaoverlapping the NIRC2 data, it proved suffi-cient to perform PSF fitting photometry withStarfinder in the same manner as describedabove. The extracted field of view covered15′′ × 15′′, which allowed for a constant PSFconstruction with 30 to 40 stars in the 2s and20s exposures. The use of the same Starfinderalgorithms ensured that the relative astromet-ric uncertainty between NACO and NIRC2 wasminimized. Matching the NACO 2003 sourcelist with the NIRC2 2008 and 2009 photom-etry provided a catalogue of 226 sources ofwhich 119 had 3-epoch measurements suitablefor linear-motion fitting (see Sec. 2.4). Thiscatalogue provides the highest astrometric ac-curacy available in the Quintuplet cluster cen-ter.

Ks 2003 & 2008 full field

For the extraction of the wider field of viewwith substanially increased source counts, theanisoplanatic effects in both the NACO 2003and 2008 data sets could not be ignored. Thedaophot PSF package with a spatially varyingPSF was therefore used to perform the photom-etry on these data sets. While the 2s combinedimages in 2003 and 2008 could be well modelledwith a quadratically varying PSF, the anisopla-natic effects across the 20s exposures proved

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neither linear nor quadratic. To minimize theresidual positional errors from anisoplanatism,the 2003 20s combined image was split into fourquadrants and the PSF fitting was performedon each quadrant separately. A linearly vary-ing PSF across each quadrant image providedthe lowest flux residuals after PSF subtraction.The astrometric and photometric source listsof all quadrant images were re-combined andmatched with the 2s 2003 photometry to re-place saturated stars with Ks < 14 mag inthe deep observations. The combined 2003 Kssource list was then matched with the NACO2008 daophot photometry to yield 2134 sourceswith proper motion uncertainties of less than3 mas/yr and Ks < 18 mag suitable for fittingthe cluster motion.

The three auxiliary images providing thephotometric and astrometric uncertaintieswere treated in the same way as the deep im-age, and uncertainties were derived as in thecase of the NIRC2 data discussed above.

2.3.3. Photometric calibration

Absolute photometric calibration was ob-tained by referencing bright stars against theUKIDSS source catalogue. The UKIDSS sur-vey is a near-infrared JHKs survey conductedwith the UKIRT telescope on Mauna Kea,Hawai’i (Lawrence et al. 2007). The Galacticcenter region is covered as part of the Galac-tic plane survey (GPS) described in detail inLucas et al. (2008). The survey provides a uni-form spatial resolution of better than 1 arc-second defined by the median seeing condi-tions at UKIRT (Warren et al. 2007). Thelarger NACO field of view is used to identifysemi-isolated stars with reliable fluxes in theUKIDSS GPS survey. The zeropoint was de-rived for the combined NACO image with theshort 2.0s individual exposure time to avoid

saturation effects. Magnitudes reported in theGPS are derived from aperture fluxes withinthe FWHM resolution of 1′′. In order to mit-igate a systematic error in the zeropoint dueto the difference in spatial resolution, the fluxof stars detected in the NACO frame withinthe 1′′ radius from each calibration source wasadded prior to the zeropoint derivation. This isparticularly crucial as the flux is systematicallybrighter for UKIDSS stars where the aperturecontains several fainter sources next to the cal-ibration star. As a consequence, the uncor-rected flux zeropoint is 0.2 mag larger thanthe zeropoint after correcting for the sum ofresolved stars in each aperture. To avoid starspartially contributing to each 1′′ circular aper-ture, stars located closer than one FWHM (3.2pixel or 0.083′′) from the aperture edge were ex-cluded, such that only stars within raper,PSF =0.917′′ contribute to the total flux of PSF-fitted stars in each aperture. For most cali-bration sources, corrections due to flux addingare below 0.1 mag, yet the maximum correc-tion reaches 0.3 mag in two cases. This con-structed aperture flux on the NACO 2.0s imageis then compared to the UKIDSS photometriccatalogue for zeropoint calibration. The sam-ple of local, reddened stars used as calibratorsensures that color effects are minimized, andno color terms were found between the MaunaKea K ′ and VLT Ks filters. A total of 15 non-saturated stars with 10.5 < Ks < 12.5 magprovided a zeropoint of 23.26 ± 0.10 mag.

After calibrating the Ks 2.0s source list toUKIDSS, the 20.0s NACO catalogue was refer-enced to the 2.0s calibrated catalogue using atotal of 860 stars in the common linear regime,15 < Ks < 17 mag. The deeper NIRC2 2009observations were calibrated with respect tothe NACO 2.0s 2003 observations using ∼ 80stars in the range 11 < Ks < 17 mag, and

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the shallower NIRC2 2008 observations werethen calibrated against the NIRC2 2009 obser-vations with ∼ 130 stars with 9 < K ′ < 18mag. The three auxiliary frames of each dataset were calibrated with respect to their respec-tive deep image in all cases. The high numberof available calibration sources between eachhigh-resolution 2003/2008/2009 data set led toa zeropoint error of less than δKZPT,rms < 0.01mag for each calibration, which is consistentwith the deviation between all cross-matcheddata sets after zeropointing. The absoluteaccuracy of the final photometry is thereforelimited by the calibration with respect to theUKIDSS sample with a zeropoint uncertaintyof ±0.10 mag.

2.4. Geometric transformation & propermotions

2.4.1. NACO 2003 & NIRC2 2008 & 2009

Proper motions are derived in the clusterreference frame, adopting our earlier approachas laid out in Stolte et al. (2008) and Clark-son et al. (2012). As there are no known high-resolution radio sources in the cluster field, wecannot derive the cluster motion in the abso-lute reference frame. Systematic effects causedby the necessary choice of the cluster refer-ence frame, such as the higher number of de-tected foreground stars as compared to red-dened background sources, are discussed in de-tail in Sec. 3.2 of Stolte et al. (2008).

All epochs were transformed to the NIRC22009 image, which served as the referenceepoch. The NIRC2 2009 observations werechosen as astrometric reference because i) theoptical distortion solution is extremely wellknown for NIRC2 (Yelda et al. 2010), whileit is not sufficiently known for the NACO S27camera, and ii) the 2009 observations are pho-

tometrically the most sensitive data set, suchthat positions have the highest astrometric pre-cision (see Fig. 2). Geometric transformationswere calculated individually and iteratively us-ing the IRAF task geomap for the NACO 2.0sshort exposure combined image, the NACO20.0s deep combined image, and the NIRC22008 image. An initial estimate of the transfor-mation was obtained from bright stars, whichare dominated by cluster members. The propermotion diagram created from this initial guess,where cluster stars are concentrated around theorigin in the cluster reference frame, was thenused to iteratively improve the transformation.In the second step, the transformations were re-fined using all stars with proper motions withina 2-sigma selection circle around the origin ascluster member candidates. This selection en-sured that only stars not moving significantlywith respect to the cluster are used to derivethe final geometric solution. Stars with signifi-cant motions between the considered epochsare excluded from the fit. A second-orderpolynomial including first-order cross termsprovided the most accurate geometric trans-formation solution in all cases. The residualrms in the proper motion of cluster membersafter the transformation was applied served asa probe for the accuracy of the transformationmatrix. In the case of the NIRC2 2008 trans-formation, 38 stars with 11 < K < 16 magprovided a residual rms of 0.032 (0.022) pixelsor 0.32 (0.22) mas in the x and y directions, re-spectively, in the final geometric solution. Forthe NACO 2003 2.0s observations, a final se-lection of 41 cluster member candidates withK < 17 mag yielded a residual rms of 0.63 and0.70 mas in the x and y coordinates, respec-tively. For the NACO 20.0s deep combinedimage, 32 stars with 14 < Ks < 17 mag ledto residual rms values of 0.85 and 0.76 mas inx and y, respectively. As expected, the posi-

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tional uncertainty is larger for the lower resolu-tion NACO observations due to the larger pixelsize and the unknown instrumental optical dis-tortions, but is mitigated by the longer timebaseline. As there is no significant differencebetween the x and y directions, the mean ofthe x and y rms residuals divided by the timebaseline provide an indication of the propermotion uncertainty from each transformation.The contribution of the geometric transforma-tion to the proper motion uncertainty is 0.27mas/yr when referencing the NIRC2 2008 tothe NIRC2 2009 positions, and 0.80 mas/5.78yrs = 0.14 mas/yr when referencing the NACO2003 epoch to NIRC2 2009. The x and y rmsuncertainties of the transformation are addedin quadrature to the individual x and y posi-tional uncertainties to derive the proper motionuncertainty of each star measured in only twoepochs.

For the final proper motion source list, starlists from all epochs were matched with theNIRC2 2009 reference list. For the 5.8 yearbaseline between NACO and NIRC2, a match-ing radius of 5 pixels (50 mas) was used toallow for all field stars to be included in theproper motion sample. The NIRC2 2008 posi-tions were matched to the 2009 catalogue witha matching radius of 2.0 pixels (20 mas), whichaccounts for the smaller time baseline of only1 year. The final proper motion catalogue con-tains 119 sources detected in all three epochs,and an additional 107 sources only detected in2003 and 2009.

For the 119 sources detected in all threeepochs, proper motions were obtained from lin-ear fits to the x and y coordinate with re-spect to the time baseline. The linear fitwas performed with respect to the uncertainty-weighted mean epoch,

tmean =∑

(epoch(i)/σ2x/y

(i))∑(1/σ2

x/y(i))

,

where epoch(i) is the time, in fractional years,of each measurement at each epoch i, andσx/y(i) denotes the astrometric uncertainty inx or y at the same epoch, respectively.

Note that the dependency of the weightedmean epoch on the x and y positional uncer-tainties implies that it is different for each star.The linear fit of the change in x or y posi-tion over time is performed with respect to thedifference between each epoch and the meanepoch, which minimizes the uncertainty fromthe intercept and facilitates the derivation ofrealistic fitting uncertainties in the proper mo-tion plane. Otherwise, the extrapolation backto zero from an epoch of 2003.56 causes unre-alistically large uncertainties in the intercept.

The combined proper motion uncertaintiesfor all data sets are shown in Fig. 3. For starsbrighter than Ks = 16 mag, the uncertainty isdominated by the lower resolution NACO 2003data set, while between 16 < Ks < 17 mag,the shallower NIRC2 2008 data determine theproper motion uncertainty. Because of the sig-nificant difference in detection sensitivity, starswithKs > 17 mag are only detected in the 2003and 2009 epochs. The combined proper motionuncertainty of these sources is shown as opendiamonds in Fig. 3 (left panel).

As the fainter field stars were predominantlylost in the 2008 observations, the 3-epoch sam-ple is heavily biased towards cluster stars. Inorder to measure the relative motion betweenthe cluster and the field, we therefore had to in-clude the faint field stars detected in the 2003and 2009 epochs alone. For the 107 sourcesnot detected in 2008, the proper motion hadto be estimated from the positional differencebetween 2009 and 2003, and no goodness-of-fit evaluation was possible. As most of these

9

stars are fainter than Ks = 17.5 mag, the largerpositional uncertainties are reflected in largerproper motion uncertainties than in the case ofthe 3-epoch linear-fitting proper motions.

The proper motion uncertainty for starsmeasured in all three epochs is determinedfrom the linear fitting error of the slope of thethree measurements, leading to a median un-certainty of 0.34 mas/yr for stars with Ks < 17mag for the 3-epoch sample (Fig. 3, left panel,asterisks). The median proper motion uncer-tainty for stars detected in 2003 and 2009, butnot in 2008, was 0.66 mas/yr (Fig. 3, left panel,open symbols).

2.4.2. NACO 2003 & 2008 full field

The same iterative procedure is employedwhen matching the NACO 2003 and 2008epochs covering the full 40′′ field of view. Forthese two data sets, obtained with the sameCONICA S27 camera and hence similar op-tical properties, the geometric transformationresulted in a residual x and y rms of 1.1 and1.3 mas. These transformation uncertaintiescontribute 0.24 mas/yr to the final astrometricuncertainty, which is dominated by the posi-tional uncertainties of the PSF fitting proce-dure in both NACO epochs (see Fig. 2, bottomtwo panels). After matching the NACO 2003& 2008 source catalogues, the median propermotion uncertainty of stars with Ks < 18 magin both x and y results in 0.5 mas/yr for thetime baseline of 5.0 years (Fig. 3, right panel).The final proper motion catalogue contains2137 sources across a combined field of viewof 41′′ × 41′′.

2.5. Combined proper motion cata-logues

The source counts of all proper motion cat-alogues are summarised in Table 2. In the final

proper motion source list as published in Table3, the central cluster area is covered with theNACO-NIRC2 astrometry and photometry of226 sources covered in 2003, (2008), and 2009,providing the highest astometric performance.All sources in this catalogue have proper mo-tion uncertainties of less than 1.5 mas/yr. Inaddition, a more complete coverage of the clus-ter center is provided due to the sensitivity ofthe NACO-NACO sample in Table 4, albeit atthe cost of astrometric accuracy. The outercluster areas contain NACO-NACO astrome-try exclusively, and the full NACO-NACO cat-alogue contains 2137 stars with proper mo-tion uncertainties of less than 3 mas/yr andKs < 18 mag. Sources with larger uncertain-ties are not included in the final NACO-NACOcatalogue. The full version of both tables isavailable electronically from the cds database3.

3. Proper motion analysis

In this section we derive the orbital motionof the Quintuplet cluster. We will then use theknowledge of the 3D velocity of the cluster toconstrain the cluster orbit in the central Galac-tic potential. An upper limit to the internalvelocity dispersion is also provided.

3.1. Quintuplet’s orbital motion

The proper motion diagram with all 226 cen-tral sources is shown in Fig. 4 (left panel), andthe proper motion distribution of all stars inthe extended NACO field is shown in Fig. 4(right panel). As cluster members are on aver-age brighter, they dominate the dense clump ofstars around the origin, which implies zero mo-tion with respect to the cluster reference frameas defined above. Hence, these stars are clustermember candidates, denoted cluster members

3Full data tables are available from the journal webpage.

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for simplicity in the following. The absolutemotion of the cluster with respect to the fieldis obtained for the two proper motion samplesindividually. The NIRC2-NACO sample pro-vides the more accurate astrometric measure-ments while being limited to a small number offield reference stars. The NACO-NACO sam-ple, on the other hand, contains a ten timeslarger number of stars while being limited bythe larger proper motion uncertainties. In thecase of the field stars used to derive the rela-tive motion between the cluster and the fieldpopulation in the inner bulge, the uncertaintyin each individual measurement does not influ-ence the fit to the ensemble substantially. Thevelocity dispersion, however, is derived fromthe standard deviation of cluster members, andis therefore strongly influenced by the individ-ual motion uncertainties. It is crucial for thederivation of an upper limit to the velocitydispersion that the sample with the smallestproper motion uncertainties be used, such thatthe motions are reliably determined. We there-fore employ the NACO-NIRC2 sample of thecentral cluster to derive both the absolute mo-tion of the Quintuplet with respect to the fieldand to constrain the velocity dispersion. Fromthe NACO-NACO sample of the extended field,an independent estimate of the absolute clus-ter motion is obtained using a large sample offield reference stars.

3.1.1. Fitting the cluster proper motion

Following the procedures developed in ourprevious investigation of the Arches cluster(Clarkson et al. 2012), we have employeda binning-independent fitting method to theproper motion distribution using ExpectationMaximization (EM). As a statistical method,EM is particularly useful for sparse or incom-plete datasets. This is particularly the case

for the low number of field stars as comparedto cluster stars in the NIRC2-NACO sample.This method allows us to derive the proba-bility of a star occupying a given location inproper motion space to belong either to thecluster or to the field distribution (see Clark-son et al. 2012, equ. 1). Taking into accountthe proper motion uncertainty of each star,individual membership likelihoods are also de-rived. The distribution of sources in the propermotion diagram is modelled by two bivariategaussian functions, and the best-fit model is de-rived from EM fitting following Bishop (2006,Chapter 9, see also Press et al. 2007, Chapter16, pp. 842).

Two elliptical gaussian functions are fittedto the ensemble of field and cluster stars in theproper motion plane, with one gaussian repre-senting the cluster and one the field. Clusterand field distributions are allowed to overlap.No further constraints need be assumed a pri-ori for the fit. Even with relatively large devia-tions of the initial guess from the final solution,the two gaussians converge towards the samecluster and field solution. The peak distancebetween the two elliptical gaussians yields theabsolute motion between the cluster and thefield sample, while the semi-major axis of thecluster ellipse provides an estimate of, or an up-per limit on, the internal velocity dispersion.The fitting method is described in numericaldetail in Clarkson et al. (2012) and follows theprocedures established for the Quintuplet clus-ter in Hußmann (2014), and only the majorfeatures are recaptured here.

In addition, the membership probabilityof each star is derived taking into accountthe individual uncertainties in the proper mo-tion of each star following the procedures inKozhurina-Platais et al. (1995). In the mini-

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mization procedure to fit the relative motionof the Quintuplet with respect to the field, allstars are included in the fit of the cluster andfield motion ellipses, and no distinction is madebetween cluster and field stars. Hence, for thederivation of the motion the membership prob-abilities are not relevant. Nevertheless, thesemembership indicators are included in Tables3 and 4 for future reference.

As outliers tend to skew the elliptical fit,especially to the field distribution, stars signif-icantly distant from the Galactic plane wereremoved from the fit. Stars were rejectedif their proper motion vertical to the Galac-tic Plane was larger than ±3.5 mas/yr, or iftheir motion parallel to the plane was largerthan +3.5 mas/yr or more negative than −10mas/yr to remove outliers from the field sample(Fig. 5, see also Hußmann 2014 for a detailedexplanation). Only stars with proper motionuncertainties of less than 1.5 mas/yr are in-cluded in the NIRC2-NACO source list (seeSec. 2.4), such that the scattered distributionof stars beyond the selection limits does notoriginate from particularly large proper motionuncertainties in these objects. Therefore, thesestars are likely rapidly moving foreground in-terlopers. All remaining stars were then fittedwith a field and cluster ellipsoid in the shapeof two bivariate gaussian functions simultane-ously, where both minor and major axes pa-rameters and centroids as well as position an-gles are unconstrained. In Fig. 6, we show thetwo bivariate gaussian fits to the proper mo-tion diagram, and fitting parameters are givenin Table 5. Likely cluster members are shownin red. The Quintuplet’s proper motion is mea-sured as the distance between the centroids ofthe field and the cluster ellipsoids. Fitting allremaining 215 stars in the NIRC2-NACO sam-

ple yields a bulk motion of µ = 3.16 mas/yrfor the Quintuplet cluster with respect to thefield, which corresponds to 120 km/s at theGC distance of 8.0 kpc. Including only the119 stars measured in 3 epochs, and hence themost accurate proper motion ensemble fromlinear motion fitting, results in a bulk motionof µ = 3.87 mas/yr or 147 km/s. The largedifference between the two values reflects thesensitivity of the bulk motion to the centroid ofthe extended field ellipse, which is particularlysensitive to changes in the distribution of fieldstars in the proper motion plane and hence thesample selection. The left panel of Fig. 6 illus-trates the sparse field population contributingto the centroiding distance between the clus-ter and the field ellipse. The 3-epoch sampleyields the maximum proper motion of the clus-ter along the Galactic plane, and hence sug-gests this value is an upper limit to the true1D motion of the Quintuplet. The positionangle of the field ellipse is fitted to be 32 to33 degrees in all samples, which is in excellentagreement with the position angle of 34.8 de-grees of the Galactic plane. The proper motionof the Quintuplet is therefore consistent with acluster orbit oriented along the Galactic plane,with no evidence for a significant motion com-ponent out of the Galactic plane.

Given the sensitivity of the fit to the sampleselection, we have used the wider, albeit lesswell resolved, NACO field coverage to verifythe derived velocity of the cluster with respectto the field. The same proper motion selectionwas applied as above (Fig. 5, right panel), asless restrictive selection criteria did not influ-ence the fit. Only stars with proper motionuncertainties of σµ < 3 mas/yr were includedin the fit. From the 1968 stars with Ks < 18.0mag selected in the central 1 pc square Quintu-plet field, a bulk motion of 3.08 mas/yr or 117

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km/s is found, and the motion is again witha position angle of 33 degrees aligned alongthe Galactic plane. The larger proper mo-tion uncertainties intrinsic to the NACO ob-servations are reflected in the more extendedcluster member distribution around the originas compared to the member candidates in theNIRC2-NACO sample (upper vs. lower panelin Fig. 6). Correspondingly, a larger numberof cluster stars scatter into the field popula-tion. The centroid of the field ellipse is there-fore pulled towards the center of the cluster el-lipse (i.e. the origin of the proper motion plane,Fig. 6), such that the absolute motion of thecluster with respect to the field is estimated tobe smaller than in the case of the Keck data.This value can hence be considered a lowerlimit to the cluster motion along the Galacticplane.

Combining all three fitted values provides anabsolute uncertainty to the orbital motion ofthe Quintuplet cluster. We therefore concludethat the 2D motion of the Quintuplet cluster,i.e. the relative motion of stars in the clusterreference frame with respect to the surround-ing field population, is found to be 132 ± 15km/s along the Galactic plane. This 3D ve-locity is similar to the orbital velocity of theArches cluster and is oriented along the Galac-tic plane, as illustrated in Figure 7.

3.1.2. Quintuplet’s 3D orbital motion

In order to derive the 3D orbital motion ofthe Quintuplet cluster with respect to the field,we assume that the field is on average at rest.As we discussed in Stolte et al. (2008), the rel-ative motion between blue and red fore- andbackground stars in the Arches field samplewas found to be in excellent agreement withthe velocity deviation observed in bulge giants(Sumi et al. 2003, see especially the red clump

sample in their Fig. 8). This consistency im-plies that the field population consists of a rep-resentative sample of bulge motions along theline of sight, which are on average at zero veloc-ity with respect to the Sun. We therefore con-cluded that the mean motion of the detectedfield stars is consistent with the field being atrest. As the Quintuplet field sample is verysimilar in velocity space and in number to theArches field sample, as expected from the iden-tical observational setup, the field sample isalso considered to be at rest, with the clustermoving with respect to this field. A detaileddiscussion of the field contribution in the centerof the Quintuplet cluster is provided in Huß-mann et al. (2012). The CMD of field stars isentirely dominated by red bulge giants at thefaint end, H > 19 mag, and red clump starsat intermediate magnitudes, 16 < H < 18 mag(see their Fig. 8, left panel). Only very fewGalactic disk sources, clearly discerned due totheir blue colors at H − Ks < 1.3 mag, con-taminate the field sample. These Galactic disksources are expected to be on the flat part ofthe Galactic rotation curve and tend to havecomoving orbital velocities of v3D,circ ∼ 230km/s, on the same order as the clusters withrespect to the bulge population. We thereforeassume that the centroid of the reference ve-locity ellipsoid is not biased by disk stars. Asthey comprise a minor fraction of field stars ofat most a few percent, they do not influencethe derivation of the relative motion betweenthe cluster and the field. With the assumptionthat the field reference sample is on average atrest, the mean apparent proper motion of thefield in the proper motion plane represents theabsolute 2D motion of the cluster through thebulge.

The radial velocities of stars in a widerQuintuplet field were reported by Liermann et

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al. (2009). In order to deduce the mean ra-dial velocity of the young cluster population,we include only the early-type cluster membersfrom their sample and we exclude the Wolf-Rayet stars and other stars with uncertain ra-dial velocity measurements. From this sam-ple with reliable velocity measurements, themean radial velocity of the 52 early-type clus-ter members is found to be 102 ± 2 km/s (thestandard deviation of 13 km/s is divided bysqrt(52) to obtain the standard error of themean, whic hwe use as the radial velocity un-certainty). Note that the standard deviation ofthe radial velocity measurements is dominatedby the fitting accuracy to the line centroids inthe spectral fits (see Liermann et al. 2009 fordetails), and does not provide an independentestimate of the (radial) velocity dispersion ofthe cluster. Combining the proper motion of132± 15 km/s with this radial velocity, we de-rive the present-day 3D orbital velocity of theQuintuplet cluster to be 167 ± 15 km/s. This3D velocity is similar to the orbital velocityof the Arches cluster and is oriented along theGalactic plane, as illustrated in Figure 7.

3.2. Quintuplet’s velocity dispersion

As discussed above, the most accurateproper motions least affected by residual as-trometric uncertainties are given by the 3-epoch sample. Of the 119 stars in this sample,55%, or 65 stars, are found to be likely propermotion members (red points in Fig. 6). Forthese cluster candidates, the velocity disper-sions in the x- and y-direction are measuredto be σx = 0.271 mas/yr and σy = 0.246mas/yr, corresponding to 10.3 km/s and 9.3km/s, respectively. The mean proper motionuncertainties for this sample of cluster mem-bers are with xpmerr,mean = 0.259 mas/yr andypmerr,mean = 0.253 mas/yr, about the same

as the fitted dispersions, suggesting that thedispersion measurement is dominated by theindividual motion uncertainties. The valuestherefore comprise an upper limit to the in-trinsic velocity dispersion of the Quintupletcluster.

The fact that the mean uncertainty of 0.253mas/yr in the y-direction is larger than the ap-parent velocity dispersion measured in clustermembers suggests that the individual uncer-tainties are slightly overestimated. The un-certainties used to weight each motion mea-surement in the 3-epoch fit contain both theindividual positional uncertainties as well asthe rms residuals of the transformation. How-ever, the transformation rms is comprised ofthe derivation of the mapping solution at eachpoint, and therefore includes a contributionfrom the individual astrometric uncertainties.Because the astrometric uncertainties and thetransformation residuals are a function of x,yposition on the images, the two componentscannot be separated. The overestimated un-certainties in each motion fit is likely causedby this combination of transformation resid-ual error with the individual astrometric un-certainties in the transformed epochs. In thestandard procedure when deriving the velocitydispersion from proper motions, the mean as-trometric uncertainty would be subtracted inquadrature. As this mean is larger especiallyin the y-direction than the dispersion value,the velocity dispersion cannot be reduced fromthe astrometric uncertainties in this way. Theslightly lower median errors of xpmerr,median =0.243 mas/yr and ypmerr,median = 0.229 mas/yrwould lead to a reduced velocity dispersion ofsqrt(σ2x − xpm2err,median) = 0.119 mas/yr (4.53km/s) and sqrt(σ2y − ypm2err,median) = 0.089mas/yr (3.39 km/s), and hence a mean 1D ve-locity dispersion of 4.0 ± 0.6 km/s. Neverthe-

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less, the fact that the mean astrometric uncer-tainties are larger than the measured disper-sion values suggests that the 3-epoch sample isjust not accurate enough to provide a realisticdispersion measurement.

In summary, an upper limit of the velocitydispersion of ∼10 km/s is obtained for the coreof the Quintuplet cluster. The photometricmass in the cluster center was recently mea-sured by Hußmann et al. (2012) to be M ∼6000M� for 0.5 < M/M� < 60 within a ra-dius of 0.5 pc. Inverting the equation for thevirial mass within radius r, Mvir = 2 ·r ·σ23D/Gwithin 0.5 pc of the cluster center (where Gis the gravitational constant), the expected 3Dvelocity dispersion would be on the order ofσ3D ∼5 km/s, and σ1D could be as small as∼ 3 km/s. Such a low central velocity dis-persion would be consistent with the measure-ments in other young, massive clusters suchas the Arches (σ1D = 5.7 km/s

4, Clarksonet al. 2012) and NGC 3603 (σ1D = 4.5 km/s,Rochau et al. 2010). Further proper motionepochs are therefore required to alleviate theconstraints on the derived upper limit.

3.3. Orbit simulations

Orbital simulations were carried out follow-ing the prescription in Stolte et al. (2008).With the measurement of the 3D orbital ve-locity and the two spatial coordinates on theplane of the sky, the only unknown is the line-of-sight distance to the cluster (from the Sun),which is represented in the following as theline-of-sight distance between the cluster andthe Galaxy’s center of mass (henceforth called“line-of-sight distance” for simplicity). As thecluster is evolved in the gravitational potential

4This value is deduced from the dispersion measurementof 0.15 mas/yr for a GC distance of 8.0 kpc.

of the inner Galaxy, no assumption needs tobe made about the absolute distance betweenthe GC and the Sun. As shown in the caseof the Arches cluster, orbits at large radii be-come increasingly self-similar, as expected atlarger distances within the tidal field of the in-ner Galaxy. Dramatic changes do occur in theorbital characteristics, and in particular in theclosest approach of the cluster to the supermas-sive black hole (Sgr A∗), if the cluster is locatedat small seperations from the center of the po-tential, which implies that its present-day pro-jected distance is close to its true distance fromthe Galaxy’s center of mass. We evolved a setof orbits with line-of-sight distances between -200 pc and +200 pc from the Galactic center.As in the case of the Arches cluster, the Quin-tuplet was assumed to be a point mass orbitingin the gravitational potential of the inner cen-tral molecular zone. The potential consists ofthe central black hole, the nuclear stellar clus-ter (r < 10pc), the nuclear stellar disk (r < 200pc), beyond which the flattened potential issmoothly transitioned into the potential of theGalactic bar.5 For a detailed set of parametersand the fit to the enclosed mass, see Stolte etal. (2008).

The Quintuplet orbital family is calculatedusing the 3D velocity derived in the previoussection as the boundary condition for the clus-ter’s present-day motion (Fig. 8). For clarity,the left panel shows the orbits in the case that

5The Galactic bar is mesaured to have a pattern speedof 1.9×Ωcirc, where Ωcirc is the local angular rotationvelocity of the Milky Way (Gardner & Flynn 2010).For an observer at the solar circle, this pattern speedimplies a rotation period of 124 Myr for the bar, whichmight influence the orbital motion for cluster distancesbeyond 200 pc from the GC. This period is long com-pared to the lifetime and the orbital timescale of eachcluster (< 5 Myr), such that we have not incorporatedbar rotation in our orbital simulation.

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the cluster is located in front of the Galacticcenter today, while orbits for a present-day lo-cation behind the GC are shown in the rightpanel. Note that there is weak evidence fromthe extinction towards the Quintuplet (AKs =2.35 mag, Hußmann et al. 2012), which is lowerthan the extinction of sources in the vicinity ofSgr A∗ (AKs = 2.54 mag, Schödel et al. 2010)and in the Arches cluster (AKs = 2.5 − 2.6mag, Habibi et al. 2013), that the cluster issituated in front of the GC today. A locationin front of the GC implies that the Quintupletis on a prograde orbit, which is also consistentwith the gas velocities in the central molecu-lar zone (e.g., Dame et al. 2001, see especiallytheir Fig. 3) and with the angular precession ofthe Galactic bar (Binney et al. 1991).

Assuming an age of 4.0 Myr (Figer etal. 1999b, but see also Liermann et al. 2010),the orbital motion was integrated backwards intime to the point of the Quintuplet’s expectedorigin. Within this time, the cluster concludedapproximately one orbital revolution for mostpresent-day line-of-sight distances. Only onthe two innermost orbits would the Quintuplethave completed several revolutions within itspresent lifetime. The past and future orbitsand the cluster’s approach to the center of thegravitational potential are analysed in Fig. 9.

If the cluster is located within the centralmolecular zone, RGC < 200 pc, its initial dis-tance from the supermassive black hole rangedfrom 20 to 230 pc (Fig. 9, top panel). Onlyin a narrow range of orbital solutions was thecluster located close to the supermassive blackhole during its first circumnuclear passage (seedashed line in Fig. 9, top panel). Especiallyon the innermost orbits, the natal cloud of theQuintuplet had to approach the GC to withinless than 100 pc, well inside the central molec-ular ring. Even if the progenitor cloud was a

member of the central molecular zone, it didnot follow the Keplerian orbits with moderatevelocities as found in the central star-formingring (Molinari et al. 2011). Instead, the in-nermost orbits require that the Quintuplet’sparental cloud had an improbable inward ve-locity that let to a strong deviation from a cir-cular orbit (see Fig. 8).

The uncertainty in the proper motion ofthe cluster, ±15 km/s, is used to model theuncertainty in the orbital parameters. Mini-mum velocity orbits were calculated assuminga present-day proper motion of 117 km/s, andmaximum velocity orbits were derived from apresent-day proper motion of 147 km/s. Thepresent-day 3D minimum and maximum or-bital velocities then correspond to 155 and 180km/s when combined with the radial velocityof 102 km/s. The uncertainty in the closestand furthest approach to Sgr A∗ and the initialcluster velocity at its presumed birth time aredisplayed as grey areas around the lines, whichrepresent the orbital parameters for the mea-sured proper motion of µ = 132 km/s. It is par-ticularly striking that the closest and furthestapproach from Sgr A∗ do not change substan-tially given the uncertainty in the velocity mea-surement. This is true for both the initial or-bit (integrated backwards to the cluster’s pre-sumed origin) and the next revolution aroundthe GC (see Fig. 9). The maximum velocity inthe next (future) orbit is most sensitive to thevelocity uncertainty on the few innermost or-bits where the cluster is proceeding very closeto Sgr A∗, as expected. The largest uncertaintyis observed in the initial velocity. The initialvelocity depends severely on the exact point ofthe cluster’s origin. If the velocity is read offslightly earlier along the orbit (for a faster orbitor a slightly older cluster age, see also Fig. 8),the cluster will have moved to a different lo-

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cation in the gravitational potential. Likewise,if the initial velocity is read off closer to itspresent position (for a slower orbital motion ora slightly younger cluster age), the velocity canhave changed substantially. As a consequence,the grey areas in the second panel of Fig. 9 par-tially represent a phase shift. For the minimumvelocity orbit with µ = 117 km/s the slow clus-ter motion implies a stronger influence from thegravitational potential, and hence more varia-tion in the velocity at each position. In sum-mary, while the exact value of the initial veloc-ity of the Quintuplet is sensitive to the uncer-tainty in the present-day proper motion, boththe minimum and maximum velocities as wellas the closest and furthest approach from thecenter of the Galaxy are robust against themeasured proper motion uncertainty.

3.4. The Quintuplet’s approach to SgrA∗

Early after the discovery of the central clus-ters, Gerhard (2001) suggested that inspiralingclusters might fuel the young stellar popula-tion surrounding the supermassive black hole.Follow-up simulations by Kim & Morris (2003)and Portegies Zwart et al. (2002) suggestedthat clusters need be on eccentric orbits or needextreme properties in terms of cluster densityand mass in order to deposit stars near SgrA∗. The eccentric orbits suggested by our sim-ulations for the Quintuplet might provide thenecessary setup for the cluster to closely ap-proach the nucleus. In order to evaluate howclose the Quintuplet could possibly have cometo the central parsec, the properties of the nextfull orbit after the present-day location are alsoshown in Fig. 9. There is only one extreme casewhere the cluster would migrate into the innerfew parsecs. For a line-of-sight distance of 20pc behind the GC today, the cluster could havecome as close as 2 pc to Sgr A∗ during its 4 Myr

lifetime (at an age of 1.1 Myr), and it wouldagain pass Sgr A∗ with a minimum distance of∼ 2 pc with a 3D orbital velocity of 380 km/sat an age of 7.2 Myr on this orbit. Accord-ing to these simplistic simulations, the clusterwould need to be at a line-of-sight distance be-tween 10 and 40 pc behind the GC today inorder to reach the central 10 pc around Sgr A∗.The high velocity of 300-400 km/s of the clus-ter during the passage through the inner fewparsecs limits the number of stars that couldhave been tidally stripped. Even in the caseof the most eccentric orbit, the nuclear popu-lation of more than 80 young, early-type starsresiding in the central parsec today (Bartko etal. 2010, Do et al. 2013) could not easily be ex-plained by tidal stripping from the Quintupletcluster. Given its likely location in front of theGC today, an interaction between the clusterand the nuclear population or the supermassiveblack hole seems quite unlikely.

3.5. Orbital inclination

In Fig. 10, the minimum and maximum ele-vations above the Galactic plane are comparedfor both the Arches and the Quintuplet clus-ters. These extrema are derived for the entireduration of each cluster’s orbit from its ori-gin (2.5 and 4.0 Myr ago, respectively) until 8Myr into the future from their present-day lo-cation. For most orbits, the Quintuplet clusterremains closer to the Galactic plane than theArches. This results directly from the currentlocation of the Quintuplet very close to the diskplane, and the negligible out-of-the-plane mo-tion component. The typical out-of-the-plane(z) motion is similar for all orbits where theQuintuplet remains far from the nucleus. Here,the cluster stays within ±5 pc of the Galac-tic plane for most orbits, and in some cases atline-of-sight distances of 100-200 pc behind the

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GC today reaches a maximum z-elevation of12 pc. Only for orbits where the cluster entersthe zone of influence of the nuclear cluster andblack hole, migrating to distances of a few par-secs from the gravitational center, is the orbitheavily perturbed. In these cases, the orbitalmotion can reach altitudes of as much as 60pc below and 40 pc above the Galactic plane(Fig. 10). Exclusively at present-day line-of-sight distances of 20 to 30 pc behind the GC,does the Quintuplet penetrate as close as 2 to4 pc into the gravitational center. The highvelocities cause the cluster to experience sling-shot perturbations out of the Galactic plane.

This general pattern is similar for the Archesorbit (Fig. 10). Yet, the Arches’s current posi-tion 10 pc above the plane causes the maximumelevation to remain at 10 to 20 pc for most or-bits, such that the cluster crosses the Galacticplane multiple times during one orbit. Evenwith the revised, and slightly lower, 3D orbitalvelocity of 172 km/s, which facilitates the in-ward motion of the cluster, the Arches neverpenetrates the inner 5 pc of the nucleus. TheArches therefore does not experience equallydramatic sling-shot perturbations, and stayswithin distances of ±40 pc above and belowthe Galactic plane during all orbits up to theconsidered timescale of 8 Myr.

4. Discussion

4.1. Deviation from a circular orbit

The 3D orbital velocity of the Quintupletcluster appears high in comparison to the cir-cular velocity at its projected distance of 31 pcfrom the GC. Assuming the enclosed mass esti-mates from Launhardt et al. (2002), the circu-lar velocity at RGC = 31 pc is only 90 km/s foran enclosed mass of Menc = 6 × 107M�, andstays below 150 km/s out to a galactocentric

radius of 100 pc (Menc < 7×108M�). Between100 and 200 pc distance from the GC, the Ke-plerian velocity vcirc theoretically increases to190 km/s according to an increase in the en-closed mass from Menc = 6× 108M� at 100 pcto Menc = 2×109M� at 200 pc. Note, however,that such velocity values are not measured inobjects located in the central molecular zone.The study of OH/IR stars by Lindqvist etal. (1992) constrained terminal radial veloci-ties to less than 120 km/s at all radii (see alsothe detailed discussion in Stolte et al. 2008).Likewise, radio surveys of dense clouds in theinner central molecular zone indicate velocitiesbelow 120 km/s for the x2 orbital family (Dameet al. 2001, their Fig. 3, see also Binney etal. 1991). From this observational evidence,a 3D orbital velocity of 167 km/s is substan-tially higher than maximum radial velocitiesobserved in both clouds and stars in the centralmolecular zone. The simulations of the clusterorbit support the expectation that the motionof the cluster is not consistent with a circularorbit. One could argue that the cluster mightbe located several hundred parsecs in front ofthe Galactic center. However, the recently ob-tained HST/NICMOS Paschen alpha survey ofthe Galactic center (Wang et al. 2010, Dong etal. 2011) clearly shows strong interaction be-tween the massive cluster stars and the nearestcloud (Fig. 11). The pillars and fringes at thecloud edge in front of the cluster’s motion indi-cate that the ionising radiation and wind pres-sure from the Wolf-Rayet cluster members iseating into the cloud towards which the clusteris presently moving.

Three-dimensional hydrodynamic simula-tions of clumpy cloud surfaces exposed to ion-ising radiation from a single nearby O-typestar result in pillared structures on timescalesof 2 to 4 × 105 yrs (Mackey & Lim 2010).

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Comparing the radial velocity of the Quintu-plet, vrad = 102 km/s, with the cloud velocityof 20 − 40 km/s at the location of the Sickle(Molinari et al. 2011, see their Fig. 4), thecluster would move 15 pc for a relative veloc-ity of ∆vrad ∼ 80 km/s within 2 × 105 yrs.However, the Quintuplet is located only 2-3 pcfrom the illuminated cloud rim in projectionat the present epoch. The higher radiationand wind pressure of ∼ 100 O-type and Wolf-Rayet stars (Liermann et al. 2009, Hußmannet al. 2012) might accelerate the carving ofthe pillars, and the fact that no ionised rimsare observed behind the direction of motion ofthe Quintuplet, where the cluster might havecleared its path, corroborates the suggestionthat the cluster is moving towards the ionisa-tion rim. The increasing flux incident on thecloud rim during the cluster’s approach mightcause additional instabilities aiding in the for-mation of the pillars. Such a scenario was sug-gested for the individual, rapidly moving starξ Per (Elmegreen & Elmegreen 1978), and willbe enhanced for the large number of high-massstars in the Quintuplet. These authors alreadysuggested a shortened formation timescale forpillared structures in the case of relative mo-tion between the ionising star and the cloud,accelerated further by instabilities forming atthe cloud rim. It would be interesting to probewhether the cluster-cloud interaction is capa-ble of triggering the next generation of starformation. Right now, however, there is nodirect evidence for young stellar objects in thecompressed cloud. The interaction providesstringent evidence that the Quintuplet clusteris indeed moving through the CMZ, implyinga location at a radial distance of less than 200pc from the GC at the present time and a non-circular motion of the Quintuplet with signifi-cant differences between the cluster’s apocenterand pericenter passages.

4.2. Comparison with the Arches clus-ter

A revised version of the Arches orbits fora proper motion of 172 km/s for the clusterwith respect to the field (Clarkson et al. 2012)is shown in Fig. 12. Only orbits where theArches is located in front of the GC today aredirectly compared with the respective orbits ofthe Quintuplet cluster. The orbits where theArches cluster is behind the GC today are verysimilar albeit less chaotic and even more regu-larly nested than the orbits of the Quintupletcluster shown for a location behind the GC to-day in Fig. 8. For a location behind the GCtoday, both clusters would have to be on ret-rograde orbits, and orbiting against the rota-tion direction of the Galactic bar. However,the ionisation rim near the Quintuplet alongthe Galactic plane in the direction of motion aswell as the apparent interaction of the Archesmoving into a nearby cloud observed in the ra-dio regime (Lang et al. 2003) suggest that bothclusters are comoving. A formation scenariofor massive clusters on retrograde orbits wouldbe even harder to find. While the Arches ve-locities suggest a family of self-similar, nestedorbits, the Quintuplet orbital family displaysmore intersection points. It is striking that es-pecially the approach of the Arches and Quin-tuplet clusters to the supermassive black holeis very sensitive to the differences in their 3Dorbital velocities. In the case of the Arches, thesimulations forced us to conclude that the clus-ter is not able to reach the central parsec beforeit disperses into the GC field (rGC > 5 pc atall times and for all line-of-sight distances, seealso the discussion in Stolte et al. 2008). Theparticular motion vectors of the Quintuplet, onthe other hand, and its location on the Galac-tic plane, promote extreme orbits for line-of-sight distances of 20-30 pc behind the GC to-

19

day, where the cluster approaches the center ofgravity to within 2-4 pc at closest approach.Yet, as discussed above, this would require theQuintuplet to be on a retrograde orbit.

The fact that both the Quintuplet and theArches cluster appear far from a circular orbitsolution has severe implications for their dy-namical evolution. N-body simulations treat-ing self-consistently the stellar component ofthe inner Galaxy and the internal dynamicsof a dense star cluster have recently shownthat clusters on eccentric orbits develop chaotictidal tails (Fujii et al. 2008, see especially theirFig. 2). According to Kim & Morris (2003) andFujii et al. (2008), clusters on eccentric orbitsmigrate faster towards the center than the clus-ters in earlier circular orbit models (e.g., Kimet al. 2000, Portegies Zwart et al. 2002). Thedevelopment of chaotic tidal tails additionallyimplies that tidally stripped stars can end upin positions far away from the position of thecluster orbit, as might be evidenced in the pop-ulation of dispersed Wolf-Rayet stars in the GC(Mauerhan et al. 2010b, M. Habibi et al. 2014).

Because of the more chaotic behaviour of theQuintuplet orbital family as compared to theArches orbits and because of its older age, thelocation of the Quintuplet’s origin is less con-strained. For the Arches, the orbit simulationssuggest that the cluster likely emerged towardthe upper left quadrant of the motion planeor close to the x2 orbital family (red ellipse inFig. 12). A similar origin close to the outer-most x2 orbit is likely for the Quintuplet if itis located at a line-of-sight distance of -50 to-200 pc in front of the GC today. Especiallynear a present line-of-sight distance of -150 to-200 pc, the origin of the Quintuplet was closeto the tangent point of the x2 orbital zone in-dicated as the solid ellipse in Figs. 8 and 12.As we already noted in the discussion of the

Arches orbit (Stolte et al. 2008), a location nearthe outermost x2 orbit is consistent with a for-mation region between the x1 and x2 orbits ofthe Galactic bar. This transition region is lo-cated at the outer edge of the central molecu-lar zone, where instreaming and circumnuclearclouds are prone to collisions. This formationscenario is also consistent with both clustersbeing on prograde orbits, which implies a loca-tion of both clusters in front of the GC today.

Both on orbits located further inward and onorbits where the Quintuplet is located behindthe GC today, the cluster would have emergedfrom its natal cloud at vastly different loca-tions from the most likely place of birth of theArches. One should keep in mind, however,that these conclusions are sensitive to the as-sumed Quintuplet cluster age of 4.0 Myr (oneto a few orbital periods for outer and innerorbits, respectively), and that the embeddedphase during which the cloud fragmented andthe cluster contracted into its current dynami-cal state are not accounted for. Most of the or-bits where the cluster is located in front of theGC today, with the exception of the innermostcases, would be consistent with a formation lo-cus near one of the x1/x2 transition points ifthe cluster were slightly older (∼ 0.5 Myr). Forthe case that both clusters have emerged atone of the end-points of the x2 orbital family(see Fig. 12), a consistent formation scenario ofthese two massive clusters is presented in thenext section.

4.3. The origin of the GC clusters

The close proximity of the Arches and Quin-tuplet clusters in the central molecular zone,at a projected spatial separation of only 12pc from each other, and their similar motionparallel to the Galactic plane, raise the ques-tion of whether these two clusters have a com-

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mon origin, or, at least, have originated in asimilar fashion. It is striking that the Archesand the Quintuplet are the only compact, mas-sive young clusters in the central region out-side the nucleus. Previously, with cluster agesof 2.5 ± 0.5 Myr for the Arches and 4 ± 1Myr for Quintuplet, the age discrepancy wasconsidered too large for both clusters to orig-inate from the same molecular cloud. At thetime when the Arches must have formed, theQuintuplet’s most massive stars would alreadyhave excavated the native cloud substantially,such that the formation of a second, equallymassive twin would seem unlikely. This argu-ment is somewhat diminished by the recent agedating of five hydrogen-rich Quintuplet WNstars by Liermann et al. (2010), suggesting thatthese stars have ages between 2.4 and 3.6 Myr,and that the main sequence OB population isin the age range of 3.3-3.6 Myr (Liermann etal. 2012). Such ages would bring both clustersmuch closer in their evolution, and hence wouldrender a common origin more likely. Never-theless, one has to bear in mind that Wolf-Rayet evolutionary models still harbour signifi-cant uncertainties. In addition, the luminosityof these objects might be biased if the WNsare located in binary systems (Liermann etal. 2010), as is the case for the Quintuplet WCmembers (Tuthill et al. 2006). In this case, theWNs would be affected by binary mass transferand hence appear rejuvenated as compared tothe main sequence population (see Liermann etal. 2012 for a discussion). Despite the knownuncertainties in the age determination of Wolf-Rayet stars, the fact that the carbon-rich vari-ety of WC stars is already heavily present in theQuintuplet cluster, and in fact led to its earlydiscovery by Okuda et al. (1990) and Nagataet al. (1990), suggests a more evolved evolu-tionary stage than the Arches population. TheWC evolutionary stage is expected to follow

the WN phase after a brief hydrogen-free WNperiod (Crowther 2007, Martins et al. 2008).Especially the dust-rich interacting-wind bina-ries resolved into spectacular spiral patterns byTuthill et al. (2006) are entirely absent in theArches cluster. Indeed, spectral analysis sug-gests that all of the Arches WN population areof types WNh6-7 close to or on the high-massmain sequence, with strong hydrogen emissionline spectra (Martins et al. 2008). Hence, whilethe exact age difference between the Archesand Quintuplet clusters is still not well estab-lished, there is strong evidence that both clus-ters did not form at the same time, but at least0.5 to 1 Myr apart.

Even if the Arches and Quintuplet did notemerge from the same cloud, we may be ableto identify a consistent formation scenario forboth clusters that might explain their similarorbits and their present-day proximity. In ex-tragalactic circumnuclear rings, the endpointsof the inner bar were shown recently to bringforth star clusters at regular intervals. Espe-cially striking is the case of the spiral galaxyNGC 613, where a string of circumnuclearclusters with ages between 2-10 Myr is foundemerging from both fueling points of the in-ner ring of circumnuclear clouds (Böker etal. 2008). This ring of young star clusters dis-plays a continuous age sequence of clusters be-ing formed every 2-3 Myr on each side of theinner bar. At these points, N-body simulationsshow strong cloud-cloud collisions after gas hasefficiently streamed in through the outer barpotential (Regan & Teuben 2003, Rodriguez-Fernandez & Combes 2008, Kim et al. 2011, seealso the early gas flow models by Athanassoula1992). In these simulations, dust lanes formalong the inner x1 orbit, and meet infallingclouds in the circumnuclear ring at the con-tact points between the x1 and x2 orbital fam-

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ilies. The efficiency of this mechanism suggeststhat this scenario should be present in most, ifnot all, gas-rich barred spirals, at least in thecase that an inner bar, or circumnuclear ring, isformed from the in-streaming material. In fact,numerous galaxies are found to have circumnu-clear rings lined with young star clusters (Maz-zuca et al. 2008, and references therein), with50% of their sample displaying a systematic agesequence. As pointed out in the detailed dis-cussion of Mazzuca et al. (2008), the youngestHii regions frequently emerge near the contactpoints between the observed dust lanes and thecircumnuclear rings, as expected from the sim-ulations.

In the Milky Way, the existence of an innerbar is still disputed, as such characteristics aremuch more difficult to corroborate by observa-tions through the dense Galactic plane (see thediscussion in Rodriguez-Fernandez & Combes2008). Nevertheless, the circumnuclear ring ofmolecular clouds observed in extragalactic sys-tems can be identified with the central molec-ular zone, which is comparable in its spatialdimensions (r ∼ 200 pc) to the circumnuclearrings in other spiral galaxies (see Table 1 inMazzuca et al. 2008). In addition, the presenceof a star-forming ring was recently postulatedby Molinari et al. (2011), and several of thedense, compact clouds along this ring are ex-pected to form massive clusters comparable tothe Arches and Quintuplet systems (Longmoreet al. 2012, 2013). If the large outer bar is re-sponsible for fueling the central molecular zone,the points where infalling clouds are collidingwith the existing circumnuclear ring at a radiusof about 200 pc would be a pre-destined placefor cluster formation. In this scenario, the mostmassive clusters would form in pseudo-regularintervals, whenever a cloud having a sufficientmass reservoir collides with material in the cen-

tral molecular zone. This would naturally ex-plain how both clusters could have inheritedsimilar velocities and orbital motions. In ad-dition, if an inner bar exists, the endpointsof this bar would be the places where gas ischanneled in. As seen in extragalactic systems,in-streaming clouds collide with the circumnu-clear ring of molecular clouds at these contactpoints (Mazzuca et al. 2008), rendering thempreferred cluster-formation loci. Following thediscussion in Molinari et al. (2011) and Long-more et al. (2013), Sgr B2 and Sgr C repre-sent the overdensities at the endpoints of thestar-forming ring, which would then trace thecluster formation loci in the Milky Way’s CMZ.The approximate starting points of the orbits(thick triangles in Fig. 8 and Fig. 12) suggestthat both clusters formed at different loci nearthe outer boundary of the CMZ. In this case,the spatial proximity of the clusters would bea coincidence, but would be reconciled by thefact that they formed at similar Galactocen-tric radii, and hence again are found on similarorbits.

While the recent observations support clus-ter formation from dense CMZ clouds, it re-mains an open question how these clouds mi-grate into the central region. One possibil-ity to channel gas into the CMZ, and pos-sibly to smaller radii, is provided by modelsof nested bars. A nested bar model with a3.5 kpc outer bar and a nested 150 pc innerbar can explain several of the kinematic fea-tures in the longitude-velocity diagram towardsthe inner Galaxy in a self-consistent gas flowmodel (Rodriguez-Fernandez & Combes 2008,see also Namekata et al. 2009). In particular,the l = 1.3◦ molecular cloud complex corre-sponds in this model to the far branch of aninner two-arm spiral pattern that channels gasfrom the 300-800 pc HI ring into the central

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molecular zone. The lack of a counterpart ofthe l = 1.3◦ complex is interpreted as only oneof the two theoretically predicted spiral armsbeing active at the present time. Intriguingly,this complex is located in the same quadrantwhere the Quintuplet and Arches orbit simu-lations suggest a possible formation locus ofthese star clusters. The projected distance ofthe complex from the Galactic center is 180 pc,consistent with the formation of the star clus-ters at the edge of the x2 orbital zone.

The present set of large-scale simulations ofthe fueling of the central molecular zone in theframework of barred potentials cannot traceparticles down to the spatial scales required toprobe star formation. Due to efficiency andthe large spatial scales involved, self-gravityand feedback effects have so far been ignored.Recent high-resolution simulations of the in-ner few hundred parsecs conducted by Kimet al. (2011) include self-gravity and feedbackfor the first time. It will be intriguing to seewhether these N-body simulations of infallingcloud particles can account for the formationof massive clusters on non-circular orbits, suchas suggested from the Arches and Quintupletorbital solutions.

5. Summary and Conclusions

We obtained the proper motion of stars inthe Quintuplet cluster and the field populationalong the line of sight towards the Galactic cen-ter from three epochs of high-spatial resolutionnear-infrared imaging with Keck and VLT. Therelative proper motion of the cluster with re-spect to the field is derived to be 132±15 km/sfrom two-dimensional fits to the proper motiondensity distribution. The motion axis is consis-tent with the Quintuplet cluster moving alongthe Galactic plane, while the motion perpen-dicular to the plane is negligible. Combining

the proper motion with the known radial ve-locity leads to a 3D orbital motion of 167 ± 15km/s, with the cluster moving outwards fromthe Galactic center and receding from the Sun.This orbital motion is surprisingly similar tothe orbital motion of the Arches cluster (Stolteet al. 2008, Clarkson et al. 2012).

Simulations of the cluster orbit in a multi-component potential of the inner Galaxy sug-gest that the orbit of the cluster is non-circularif the cluster is located in the central molecularzone (RGC < 200 pc). A revised orbit solutionfor the Arches cluster is also presented. Trac-ing the orbital motion of both clusters back for2.5 and 4.0 Myr to the possible points of ori-gin, a common cluster formation scenario forthe Arches and Quintuplet clusters is identifiedif the Quintuplet is at a line-of-sight positionin front of the GC today. In this scenario, thecluster-forming clouds are located inside the in-ner 200 pc of the CMZ and at the far side ofthe Galactic center, towards increasing Galac-tic longitudes. When compared to simulationsfueling the central molecular zone with nestedbar potentials, this location is intriguingly sim-ilar to the tentative collision point of the rear-ward spiral arm of the inner bar. Today, thel = 1.3◦ molecular complex has accumulateda total mass of ≥ 2 × 105M� at this position(Oka et al. 1998). Although there are presentlyno signposts of star formation in the form ofHII regions in this complex, it is conceivablethat the next compact, massive cluster will beforged in the near future at this exceptional lo-cus. Further simulations might provide insightas to whether the collisional properties of theinfalling gas into the central molecular zone aresufficient to explain the high velocities of theArches and Quintuplet clusters, and their non-circular orbits.

The current velocity measurement provides

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the basis for a new set of simulations to re-construct the tidal losses over each cluster’slifetime. Especially the diffusion of high-massstars from the young population might havegiven rise to the population of apparently iso-lated young, high-mass stars in the GC. Thesesimulations would solve the mystery of appar-ently isolated high-mass star formation in theGC environment. Observationally, increasingthe proper motion accuracy with more epochsover a longer time baseline will lead to the mea-surement of the internal velocity dispersion ofthe Quintuplet cluster, for which we obtain anupper limit of ∼ 10 km/s. An accurate mea-surement of the internal velocity dispersion willadditionally constrain the virial state and thelong-term dynamical stability of the young starcluster in the Galactic center tidal field.

The authors sincerely thank the referee forthe careful reading of the manuscript, and forthe very positive and helpful referee’s report.AS, BH and MH acknowledge support by theDFG Emmy Noether programme under grantSTO 496/3-1, and generous travel support byUCLA under NSF grant AST-0909218. AMGand MRM and the work carried out at UCLAwas supported by the NSF under grant AST-0909218 as well. We are grateful for numer-ous discussions with colleagues at both UCLAand the Argelander Institute, and for the lifelyatmosphere at both places and their ongoingscientific support.

This work is based on observations obtainedat the VLT Paranal and Keck, Mauna Kea ob-servatories, and the authors are most gratefulto the support teams of both facilities. Thiswork would not have been possible without theintense effort and dedication of the Keck LGS-AO staff. We are deeply greatful for their sup-

port enabling these observations. The W. M.Keck Observatory is operated as a scientificpartnership among the California Institute ofTechnology, the University of California, andthe National Aeronautics and Space Admin-istraction. The Observatory was made possi-ble by the generous financial support of theW. M. Keck Foundation. The authors wish torecognize and acknowledge the very significantcultural role and reverence that the summit ofMauna Kea has always had within the indige-nous Hawaiian community. We are most fortu-nate to have the opportunity to conduct obser-vations from this mountain. We also sincerelythank the VLT/NACO staff for their substan-tial efforts to provide high-quality observationsacross our multi-epoch campaigns.

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Table 1: Log of Keck/NIRC2 and VLT/NAOS-CONICA Quintuplet imaging observationsUT Date Instrument pixscale FOV Filter texp [s] coadds Nobs Nused tint [s] FWHM [mas] Strehl

2003 July 23 VLT/NACO 27.1 27′′ Ks 2.0 30 16 16 960 75-83 7-10%2003 July 22 VLT/NACO 27.1 27′′ Ks 20.0 2 16 16 640 71-82 3-5%2008 July 24 VLT/NACO 27.1 27′′ Ks 2.0 15 44 33 990 73-81 4-12%2008 May 14 Keck/NIRC2 9.942 10′′ K′ 1.0 30 58 33 990 57-70 20-34%2009 May 3-4 Keck/NIRC2 9.942 10′′ K′ 1.0 30 117 60 1800. 50-62 28-47%

The pixel scale is given in milliarcseconds/pixel, FOV is the field of view, texp is the exposure timeof the individual integration, coadds the number of co-added individual exposures in each frame, Nobs thetotal number of frames observed, Nused the total number of high-quality frames entering the deep drizzledimage, and tint is the total integration time in seconds of this deep image. FWHM provides the resolutionof the deep image after drizzling in milliarcseconds, and Strehl an estimate of the Strehl ratio.

Table 2: Proper motion source counts in NACO and NIRC2 data setsPM data set Number of sources notationNACO 2003 & NIRC2 2008 & NIRC2 2009 119 3-epoch sampleNACO 2003 & NIRC2 2009 107 2-epoch sampleNACO 2003 & NIRC2 2008 & 2009 all 226 cluster center sampleNACO 2003 & NACO 2008 2137 extended field sample

Table 3: Astrometry & photometry of NACO 2003 & NIRC2 2008 & 2009 sourcesSeq δRA δDEC µα cos δ eµα cos δ µδ eµδ Kp2009 eK2009 Kp2008 eK2008 Ks2003 eK2003 pclus

[”] [”] [mas/yr] [mas/yr] [mas/yr] [mas/yr] [mag] [mag] [mag] [mag] [mag] [mag]1 -0.000 0.000 -0.1561 0.1853 -0.4454 0.1522 9.404 0.144 9.302 0.154 9.858 0.157 0.8452 -0.092 -2.244 0.0557 0.3342 0.4961 0.2287 8.412 0.143 8.252 0.154 8.914 0.163 0.8403 -4.317 0.541 -1.0946 0.2427 0.0388 0.2179 7.606 0.164 7.738 0.154 7.930 0.159 0.1424 0.697 3.326 0.1949 0.1281 0.4563 0.2261 9.256 0.140 9.295 0.154 9.591 0.133 0.908

Positions are given as offsets relative to the Quintuplet proper member Q12 (RA 17:46:15.13, DEC-28:49:35.07). The proper motion µα cos δ corresponds to the motion in the East-West direction (µα cosδ,with α Right Ascension and δ Declination), µδ corresponds to the North-South motion of each star.Photometry of all three epochs is also provided, with photometry of stars with Ks < 14 mag taken fromthe NACO 2003 2s exposures, while fainter photometry is supplemented from the deep 20s integrations.Columns 5 and 7 contain the proper motion uncertainties in each direction, and columns 9, 11, and13 contain the photometric uncertainties in each epoch. Column 14 provides a membership probabilityindicator. Monte Carlo simulations of the proper motion plane for one of the outer cluster fields (thePistol field, Field 2 in Hußmann 2014) suggest that cluster and field stars are most efficiently separatedwith a formal probability threshold of pcluster > 0.4 (see Sections 4.2.2.1 to 4.2.2.3 in Hußmann (2014) fordetails). Table 3 is published in its entirety in the electronic edition of ApJ, with the first rows shown hereas guidance regarding its form and content.

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Table 4: Astrometry & photometry of NACO 2003 & NACO 2008 sourcesSeq δRA δDEC µα cos δ eµα cos δ µδ eµδ Ks2003 eK2003 Ks2008 eK2008 pclus

[”] [”] [mas/yr] [mas/yr] [mas/yr] [mas/yr] [mag] [mag] [mag] [mag]1 10.754 -3.031 -0.1680 1.0420 0.1060 0.9900 9.359 0.139 9.040 0.015 0.3032 3.622 0.268 -0.2560 0.4310 -0.3700 0.5930 9.379 0.051 8.970 0.007 0.5793 -0.300 5.447 -3.0900 0.2830 -0.6450 0.7540 9.385 0.064 9.511 0.007 0.0004 0.695 3.338 -0.3330 0.2210 0.1230 0.3020 9.41