Online material

Appendix A: Proper motion diagrams of the outer cluster fields

As a consequence of the variation in stellar density across the wide-field coverage of the cluster images, the proper motion

diagrams are populated with varying levels of source density. In order to avoid confusion, especially given the dense environment in the cluster centres, the proper motion diagrams of the individual data sets are shown here.

Fig. A.1 Proper motion diagrams of the Quintuplet fields beyond the cluster centre. L-band excess sources are marked as red diamonds, while Wolf-Rayet candidates are shown in blue. The criterion for cluster member selection (circle) depends on the astrometric quality of each data set and on the corresponding dispersion in the cluster population around the origin. For the outer Quintuplet fields exclusively, membership probabilities were used to distinguish cluster members from field stars. The indicated membership criterion is therefore approximate, as the probabilities account for individual astrometric uncertainties and the location of each star with respect to the cluster centre. See Fig. 7 for further details.

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Fig. A.2 Proper motion diagrams of the outer Arches fields. Labels are described in Fig. A.1, and for further details see Fig. 8. The larger scatter observed in the Arches proper motion diagrams compared to the Quintuplet proper motions is a consequence of the shallower Arches NACO photometry and mitigated adaptive optics performance. The circles indicate the membership selection criterion as derived from the central field in Fig. 9.

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Appendix B: Colour–magnitude and colour–colour diagrams of the outer cluster fields

The foreground extinction towards the Galactic centre is patchy and varies widely with position. Each of the Arches and Quintuplet fields feature varying levels of foreground extinction,

such that a single extinction value could not be used for the selection of the main-sequence reference samples. The colour selection was adapted visually in each field to include the proper motion members along the observed cluster main sequence and exclude the red clump population starting at J ~ 20 mag.

Fig. B.1 J − H,Ks − L′ colour–colour diagrams of the Quintuplet outer fields. Proper motion members are shown in green, while non-members are shown in red. The black line denotes the extinction vector (Nishiyama et al. 2009). The red solid line shifted parallel to the reddening vector marks the 3σ selection criterion for L-band excess sources (red diamonds). Wolf-Rayet candidates (Ks< 12 mag) are marked in blue, while fainter excess sources marked as red diamonds are candidates for circumstellar disc emission. The J − H,Ks − L′ diagram of the Quintuplet central field can be found in Fig. 15.

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	Fig. B.2 J − H,Ks − L′ colour–colour diagrams of the Arches outer fields. Labels are as described in Fig. B.1, and the J − H,Ks − L′ diagram of the Arches central field is shown in Fig. 18.
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Fig. B.3 J, J − Ks colour–magnitude diagrams of the Quintuplet outer fields. Proper motion members are shown in green, while non-members are shown in red. Disc and Wolf-Rayet candidates are also marked. The diagonal overdensity at J ~ 20 mag marks the onset of the red clump. The dotted lines mark the Ks = 17.5 mag boundary for proper motion member selection. The horizontal dashed line indicates the J = 22 mag limit, above which the combined cluster disc fractions are derived. The main-sequence selection is indicated by vertical dashed lines. The variation in main-sequence colour between fields is caused by the locally varying extinction across the cluster area. The J, J − Ks diagram of the central Quintuplet field is shown in Fig. 16.

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	Fig. B.4 J, J − Ks colour–magnitude diagrams of the Arches outer fields. Labels are as described in Fig. B.3, and the J, J − Ks diagram of the Arches central field is shown in Fig. 19. The variation in main-sequence colour between fields caused by the locally varying extinction is more pronounced than in the Quintuplet fields. Notably, several L′-excess sources do not show excess emission at Ks.
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Fig. B.5 Ks, Ks − L′ colour–magnitude diagrams of the Quintuplet outer fields. Labels are as in the previous figures, and the Ks, Ks − L′ diagram of the central Quintuplet field can be found in Fig. 17. A distinct main sequence of cluster members can be seen in Field 2 (top left panel), while in all other fields the proper motion information is required to exhibit the rare cluster stars at these increasing radii.

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	Fig. B.6 Ks, Ks − L′ colour–magnitude diagrams of the Arches outer fields. Labels are as in the previous figures, and the Ks, Ks − L′ diagram of the central Arches field can be found in Fig. 20. While a pronounced main sequence is observed in the central field, in all outer fields the proper motion membership provides the best evidence for the distinction between cluster and field samples.
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Appendix C: Variable stars

From our multi-epoch K_s proper motion campaign, we obtain a list of candidates for variable sources. Stars are defined as variable if the standard deviation of their magnitudes across three epochs deviates by more than 3σ from the median of the standard deviations of all stars in their respective magnitude bin. The expected (median) standard deviation is calculated in bins of ΔK_s = 1 mag to account for the increase in photometric error towards fainter stars. In the case that only two epochs are available, the magnitude difference between epoch 1 and epoch 2 has to exceed 3 times the standard deviation of the magnitude differences of all stars in the respective magnitude bin of a variable candidate. With the exception of one prominent source in Arches Field 5, only stars brighter than K_s< 16 mag are searched for variability, as photometric uncertainties in the crowded cluster fields trigger many false detections beyond this limit. Two additional constraints are imposed to ensure that variable candidates are not affected by positional and/or PSF fitting uncertainties. The absolute magnitude difference or standard deviation for a star to be a variable candidate has to exceed ΔK_s> 0.1 mag, and the difference in the source position in both the x and y coordinates has to be less than 0.5 pixel after the geometric transformation to the reference epoch. By imposing this astrometric consistency, incorrect matches with very close neighbouring stars are avoided. Finally, all variable candidates were inspected visually in all K_s epoch images to ensure that sources are not affected by background noise fluctuations, corrupt PSF cores, edge effects, and especially that their photometry is not compromised by the haloes of bright neighbours. As only two epochs were available in all Quintuplet fields except Field 2, no variable candidates could be identified unambiguously in the Quintuplet cluster fields. The photometry of all variable stars identified in the Arches cluster is summarised in Table C.1.

Appendix D: L-band luminosity of the discs

The L-band luminosity of the excess sources can be estimated for a central B2V star from the difference between the stellar brightness and the excess emission.

The 2.5 Myr Geneva isochrone yields an L-band brightness of L(B2V) = − 1.35 mag for a 10 M_⊙ star. For our approximation here, we assume this L-band brightness to be close to the Vega system, such that L_Vega = 0 mag, and Inserting the Vega flux of Tokunaga & Vacca (2005) leads to The absolute flux within the passband is given by the filter width Δλ_L′ = 0.62 μm times the expected flux at the central wavelength:

If the disc is about 1 mag brighter in L′ than the star, then ΔL = 1 mag implies a factor of 2.5 higher flux, which is already the flux we expect to measure within the passband of L′ with filter width 0.62 μm. In this estimate, no assumptions about the distance have been made, as all fluxes are derived for absolute magnitudes only, hence at a standard distance of 10 pc. This flux is used to derive an order of magnitude limit of the disc masses in Sect. 5.2.2.

Appendix E: Complete source lists

The JHK_s combined source lists for the Arches and Quintuplet clusters are made available at the CDS. Proper motion memberships are meant as indicator values for candidacy, and might change as further proper motion epochs become available.

© ESO, 2015