Astronomy & Astrophysics manuscript no. main ©ESO 2021 August 2, 2021

Radio observations of massive stars in the Galactic centre: The Gallego-Calvente1,?, A. T., Schödel1, R., Alberdi1, A., Najarro2, F., Yusef-Zadeh3, F., Shahzamanian1, B., and Nogueras-Lara4, F.

1 Instituto de Astrofísica de Andalucía (IAA-CSIC), Glorieta de la Astronomía s/n, 18008 Granada, Spain e-mail: [email protected] 2 Centro de Astrobiología (CSIC/INTA), Ctra. de Ajalvir Km. 4, 28850 Torrejón de Ardoz, Madrid, Spain 3 CIERA, Department of Physics and Astronomy Northwestern University, Evanston, IL 60208, USA 4 Max-Planck-Institut für Astronomie, Königstuhl 17, Heidelberg, D-69 117, Germany

ABSTRACT

We present high-angular-resolution radio continuum observations of the Quintuplet cluster, one of the most emblematic massive clusters in the Galactic centre. Data were acquired in two epochs and at 6 and 10 GHz with the Karl J. Jansky Very Large Array. With this work, we have quadrupled the number of known radio stars in the cluster. Nineteen of them have spectral indices consistent with thermal emission from ionised stellar winds, five are consistent with colliding wind binaries, two are ambiguous cases, and one was only detected in a single band. Regarding variability, remarkably we find a significantly higher fraction of variable stars in the Quintuplet cluster (∼ 30%) than in the (< 15%), probably due to the older age of the Quintuplet cluster. Our determined mass-loss rates are in good agreement with theoretical models. Finally, we show that the radio luminosity function can be used as a tool to constrain the age and the mass function of a cluster. 1. Introduction the stellar initial mass function that is a steep power-law of mass (Hosek et al. 2019) and due to the very short lifetimes (at most The Quintuplet cluster, along with the Arches and the Central a few Myr) of these stars. The latter fact means that massive clusters, is a young, massive stellar cluster in the Galac- stars are typically not only located at distances of many kilo- tic centre (GC). Separated just a few arcminutes from the Arches from Earth, but also frequently still enshrouded in dusty cluster, the Quintuplet cluster is located at a projected distance of 0 molecular clouds and therefore highly extinguished. As two of approximately 30 pc (or 12.5 in angular distance) to the north- the most massive young clusters in the , the Arches east of Sagittarius A* (Sgr A*), the at the centre of our and the Quintuplet have been the object of intense study over the Galaxy. Given its position at the GC, Quintuplet can only be ob- past three decades (Figer et al. 1999; Najarro et al. 2009, 2017; served (along with at radio frequencies) at wavelengths, Clark et al. 2018b; Liermann et al. 2009, 2010, 2012; Hosek which poses a difficulty in identifying its stellar content, because et al. 2019, among others), driven by ever improving infrared intrinsic stellar colours are small in the infrared and reddening imaging and spectroscopy instruments. Imaging, spectroscopic and the related uncertainty will dominate the observed colours and proper motion measurements in the infrared have provided (Nogueras-Lara et al. 2018, 2021). us with our current ideas of mass, age, and metallicity of these The Quintuplet cluster owes its name to five prominent clusters as the spectral types and mass of their ∼100 most mas- infrared-bright sources, later named Q1, Q2, Q3, Q4 and Q9 sive stars, as described in the references cited above. by Figer et al. (1999) (see Fig. 1). It has a similar mass as the 4 Arches cluster, about 1 − 2 × 10 M (Figer et al. 1999; Rui et al. Highly complementary information on the properties of mas- 2019), but is considered to be roughly 1 Myr older than the for- sive young stars can be obtained from radio observations. Radio mer (Arches: 2.5−4 Myr, Quintuplet: 3−5 Myr; Figer et al. 1999; continuum emission arises in the ionised winds of massive stars Clark et al. 2018a,b; Schneider et al. 2014), which is reflected in (see, e.g., Leitherer et al. 1997; Güdel 2002; Umana et al. 2015) its larger core radius – probably a sign of its ongoing dissolution and can provide essential information on mass-loss rates through in the GC tidal field (Rui et al. 2019) – and its content of more stellar winds. Lang et al. (2005) carried out a multi-frequency, evolved stars than the Arches cluster (Clark et al. 2018b). The multi-configuration, and multi-epoch study of the Arches and extended nature of the Quintuplet not only poses a problem with arXiv:2107.14481v1 [astro-ph.GA] 30 Jul 2021 Quintuplet clusters with the Very Large Array (VLA). They de- respect to confusion with the (mostly old) stars of the nuclear tected ten more or less compact radio sources. The majority of stellar disk (Nogueras-Lara et al. 2019b; Launhardt et al. 2002), them had rising spectral indices as expected for young massive in which it is embedded, but there may also be problems to in- stars with powerful stellar winds and a few of them had clear terlopers of young stars that have formed in the vicinity of the near-infrared counterparts. Quintuplet, but at a somewhat different time (Clark et al. 2018b). Massive young stellar clusters are of great interest to study In this work, we study the Quintuplet with the Karl G. Janksy the evolution of the most massive stars, with masses in excess Very Large Array (JVLA) taking advantage of its significantly of a few tens of solar masses. The observable number of such increased sensitivity in comparison with the old VLA, as we did stars in the Milky Way is small because they are very rare due to for the Arches cluster aiming to pick up the thermal and non- thermal emission from the ionised gas in the outer wind regions ? e-mail: [email protected] of young, massive stars (see Gallego-Calvente et al. 2021).

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Fig. 1: JHKs false colour image of the Quintuplet cluster from the GALACTICNUCLEUS survey. Credits: Nogueras-Lara et al. (2018, 2019a).

2. Observations and imaging Table 1: Summary of observations

We observed the radio continuum emission from the Quintu- Observation Band a JVLA On source time plet cluster using the National Observatory date configuration (minutes) (NRAO)1 JVLA in 2016 and 2018. We acquired data in two bands (C and X), with X-band observations in three epochs, as Oct 04, 2016 X A 55 detailed in Table 1. The phase centre was taken at the position Oct 27, 2016 X A 55 h m s − ◦ 0 00 Mar 24, 2018 X A 55 α, δ(J2000) = 17 46 15.26 , 28 49 33.0 . All observations Jun 10, 2018 C A 74 were carried out in the A configuration to achieve the highest angular resolution. This configuration also helped us to filter a Frequency range of 8 − 12 GHz for X-band and 4 − 8 GHz for C- out part of the extended emission that surrounds the Quintuplet band. Therefore, the total bandwidth was 4 GHz on each band. The cluster whose center is located at a few arcminutes to the south- number of spectral windows was 32 and the number of channels 64 east of the Sickle H II region (G0.18−0.04) and at approximately in both cases. 1000due north of the Pistol (G0.15−0.05) H II region. J1744−3116 was used as phase calibrator and J1331+305 (3C286) as band-pass and flux density calibrator at all frequen- −28◦ 500 03.1100. We identified it as SgrA-N3 using the VizieR cies. The raw data were processed automatically performing an Catalogue Service2. We carried out data reduction with the Com- initial flagging and calibration through the JVLA calibration mon Astronomy Software Applications package (CASA) devel- pipeline. Extra flagging was necessary to remove lost or cor- oped by an international consortium of scientists3 as follows. rupted data. The entire cluster was visible within the Field of View (FoV) of the observations. A very bright source was present in the FoV in both 2 http://vizier.u-strasbg.fr/ h m s 3 bands. This source is located at α, δ(J2000) = 17 46 21.04 , Scientists based at the National Radio Astronomical Observatory (NRAO), the European Southern Observatory (ESO), the National As- 1 The NRAO is a facility of the National Science Foundation (NSF) tronomical Observatory of Japan (NAOJ), the Academia Sinica Institute operated under cooperative agreement by Associated Universities, Inc. of Astronomy and Astrophysics (ASIAA), the CSIRO division for As-

Article number, page 2 of 14 Gallego-Calvente, A. T. et al.: Radio observations of massive stars in the Galactic centre: The Quintuplet cluster

We used the task tclean to create a model for the intense onto the 2016 X-band image and a closeup onto the 2018 C-band source in order to, later on, self-calibrate on this source. The image of the cluster, both images corrected for primary beam u − v range was constrained to frequencies > 200 kλ to filter attenuation, with radio stars labelled. We note that some of the out some of the extended emission near and around the tar- detected point sources lie outside of the FoV shown in the figure. get field while detecting the compact sources. These two steps, that is model generation and calibration of the time-dependent antenna-based gains on the bright source, were repeated several times, thereby iteratively changing the parameter that controls the solution interval, solint, in the gaincal task. An improve- ment of 15% in the dynamic range was achieved through this iterative approach. We inserted the final model by means of the task ft from CASA. Since the diffraction pattern residuals of the bright (∼40 mJy) SgrA-N3 source interfered with our aim to detect faint sources, we subtracted it in the Fourier plane. Sub- sequently, we cleaned our new visibility data set, stored in a new table as a Measurement Set (MS), using tclean in interactive mode. We chose the interactive mode because the subtraction of SgrA-N3 was not completely perfect and the restriction of the u − v range did not entirely remove the extended emission. We atempted to improve the images in all epochs through testing the more advanced form of imaging multi-scale clean, that distinguishes emitting features with angular scales between point sources and extended emis- sion. Its use did not improve the quality of the final images. Additionally, we probed different weighting schemes to correct for visibility sampling effects. The natural weighting scheme resulted in the images with the highest signal-to-noise (S/N). The gain parameter in the clean algorithm was set to 0.05. With this procedure we reached an off-source rms noise level of 4.3 µJy beam−1 in the 2016 X-band image in the central regions of the FoV. The off-source thermal noise in the 2018 epochs was 5.7 and 6.6 µJy beam−1 for X- and C-bands, respectively. All the images were primary beam corrected to account for the change in sensitivity across the primary beam. Table 2 sum- marises the properties of the final images.

3. Results 3.1. Point source detection and flux density Point sources were selected interactively in the cleaning proce- dure, as we specified in section 2, restricting ourselves to those at above five times the off-source rms noise level. We used the image-plane component fitting (imfit) task from CASA that takes into account the quality of the fit and each im- age rms, to estimate the positions of the maxima, the total flux densities, and the errors of these values over the final primary- beam-corrected images for all bands in all epochs. We have de- termined the uncertainties in the positions of the detected sources by adding in quadrature to the formal error of the fit, 0.5 θ/SNR (Reid et al. 1988) a systematic error of 0.0500(Dzib et al. 2017). Fig. 2: Top: Closeup onto the Quintuplet cluster from the 2016 In the formal error, θ is the source size convolved with the beam X-band image corrected for primary beam attenuation. The clean beam is 0.4700× 0.1500, P.A. = 25.29◦. The off-source rms noise and SNR the S/N. The systematic error addresses the thermal −1 noise and uncertainties introduced by the phase calibration pro- level is 4.3 µJy beam . The contour levels represent -1, 1, 2, 3, cess. 4, 5, and 6 times 5 σ. Bottom: Closeup onto the Quintuplet clus- Likewise, we considered the percentage in the calibration error ter showing most of the detected sources from the 2018 C-band of the peak flux densities at the observed frequencies (Perley & image corrected for primary beam attenuation. The resolution is 0.4100× 0.1600, P.A. = −6.84◦. The off-source rms noise level is Butler 2013) and the factor that considers whether a source is −1 resolved or unresolved to evaluate the flux-density uncertainties. 5.7 µJy beam . The contour levels represent -1, 1, 2, 3, 4, 5, and This process led us to detect 29 and 28 point sources above 6 times 5 σ. 5 σ at 10 GHz and 6 GHz, respectively. Figure 2 shows a closeup The 2016 X-band image turned out to be the image with tronomy and Space Science (CASS), and the Netherlands Institute for the highest S/N, so it provides the most complete list of point Radio Astronomy (ASTRON) under the guidance of NRAO. sources. Besides the rms noise, there is systematic noise present

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Table 2: Properties of the images

Epoch Band Frequency a Synthesised beam P. A. b rms noise c (u, v) cut-off (GHz) (arcsec × arcsec) (degrees) (µJy beam−1) (kλ) 2016 X 10.0 0.47 × 0.15 25.29 4.3 200 2018 X 10.0 0.41 × 0.16 −6.84 5.7 200 2018 C 6.0 0.62 × 0.21 19.97 6.6 200

a Representative frequency, in Gigahertz. b The position angle (P. A.) of the fitted major axis for the synthesised beam, in degrees. c Off-source root mean square noise level reached.

Fig. 3: HST/WFC3 F153M image of the Quintuplet cluster with identified radio stars labelled. in the radio image, caused by remnant side lobes of SgrA-N3 archive4. All radio stars must necessarily be very bright infrared that could not be fully removed from the image and some dif- sources (massive, young stars) that are detected at S/N ratios ex- fuse flux still present in the u − v range considered for the image ceeding a few times 100. Only sources coincident within 0.0500 reconstruction. Also, the Quintuplet region is full of ionised gas with the position of stars detected in the NIR were accepted as in clouds of variable compactness. The systematic noise and the real. The tagged HST/WFC3 F153M image is shown in Fig. 3. ionised gas can give rise to numerous spurious detections, even Finally, we matched our sources with the ones pro- at 5 σ above the rms noise. Therefore, we compared the posi- vided by (Clark et al. 2018b, Tables A.1 and A.2), based tions of detected radio point sources in our 2016 X-band image on HST/NICMOS+WFC3 photometry and VLT/SINFONI+ with the positions of stars on an HST/WFC3 F153M image of the 4 Quintuplet cluster (Rui et al. 2019), downloaded from the HST Based on observations made with the NASA/ESA , obtained from the data archive at the Space Telescope Sci- ence Institute. STScI is operated by the Association of Universities for Research in Astronomy, Inc. under NASA contract NAS 5-26555.

Article number, page 4 of 14 Gallego-Calvente, A. T. et al.: Radio observations of massive stars in the Galactic centre: The Quintuplet cluster

KMOS spectroscopy for ∼ 100 and 71 cluster members, respec- quency observations as better tracer of the thermal component tively. In this way we could obtain the spectral type of the radio and so give more reliable mass-loss rates because contamination stars. of the flux density by the non-thermal component can occur at Lang et al. 2005 reported nine compact radio sources and the the lower frequencies (according to Contreras et al. 1996). Lang . They referred to the former as QR1−QR9. QR1−3 et al. (2005) assumed a terminal wind velocity of 1000 Km s−1 were interpreted as the first detections of embedded massive and a mean molecular weight equal to 2 for all sources. Thus, stars in the Quintuplet cluster. As we can observe in Fig. 3, in order to compare our data with their data, we have re-scaled those sources have no bright, stellar NIR counterparts, as was Lang’s values multiplying them by v∞/1000 and µ/2, where v∞ clearly indicated by Lang et al. (2005) as well. To further in- and µ are the values adopted in this work. We derived a sig- vestigate these sources, we superposed the HST/WFC3 F153M nificantly lower mass-loss rate for the Pistol star than Lang et al. image from HST archive with a Paschen α image by Dong et al. (2005) because the latter work reports a roughly ten times higher (2011), see Figure 4. From this figure we can see that QR1−3 flux density for this source. This may be explained through vari- are not stellar sources but related to ionised gas clouds that have ability of the source (see below) or, possibly also, the lower an- similar appearance as many other such objects in this region. gular resolution of the observations of Lang et al. (2005) which Considering this finding, we have renamed the Quintuplet may have resulted in the flux of the Pistol star being contam- cluster members to reassign a number to the detected radio inated by flux coming from the , where it is em- sources from #1 to #29. We do not use the prefix QR used by bedded. Similar factor ∼ 10 discrepancies exist for the sources Lang et al. (2005) to avoid confusion between the old QR1−3 qG13/QR4 and qG11/QR7. and the new 1−3 numbered members. We confirm seven sources reported by Lang et al. (2005) as radio stars (QR4, QR5, QR6, 4. Properties of the sources QR7, QR8, QR9, Pistol Star). With a total of 29 sources reported here, this work quadruples the number of known radio stars asso- According to the spectral classification, most of detected sources ciated with the Quintuplet cluster, with the faintest radio source in the Quintuplet cluster are young, massive, post-main sequence having a flux density of 30 ± 7 µJy at X-Band. stars, being the majority of the Wolf-Rayet spectral type (see Table 3 shows the new and the old nomenclature, the iden- Table 3). In particular, two , eight WC, tified NIR counterparts as listed in Clark et al. (2018b), deter- six WN, seven B supergiants and three sources of type O Ia have mined positions, the X- and C-band flux densities for all radio been found. sources measured in our 2016 and 2018 data sets or the upper After considering the inferred spectral indices, even though limits of the undetected sources, and the spectral classification the corresponding uncertainties are relatively high, we show that according to Clark et al. (2018b). qG1, qG2, qG4, qG6, qG9, qG10, qG12−15, qG17, qG18, and qG21−27 have spectral indices consistent with thermal emission from ionised stellar winds. The divergence of α from the canon- 3.2. Spectral indices ical value of 0.6 can occur for a number of reasons, such as deviations in the wind conditions possibly due to the presence We calculated the spectral indices (or their limits) of the ra- of condensations (clumps) that produce a non-standard electron dio stars, as well as the corresponding uncertainties using their density profile (n ∝ r−s, with s 2) and/or changes in the measured X- and C-band fluxes. We proceeded as described in e , run of ionisation or wind geometry with radius due to internal Gallego-Calvente et al. (2021). The spectral indices are listed in shocks. Leitherer et al. (1997) suggested that there is little varia- column 8 of Table 3. tion in the mass-loss rates for Wolf-Rayet stars, with an averaged −5 −1 value of ∼ 4 × 10 M yr . The WR stars from our data set have −5 −5 −1 3.3. Mass-loss rates M˙ values ranging from 1.3 × 10 to 7.9 × 10 M yr , which agrees well with the results of Leitherer et al. (1997), as well as We determined the mass-loss rates for the detected radio stars for other young, massive stellar types. This conclusion lead us following the recipe described in Gallego-Calvente et al. (2021). to choose B1−2 Ia+ and B0−1 Ia+ as the most probable spectral We derived mass-loss rates corresponding to the observed flux types for qG13 and qG17, respectively, as their mass-loss rates densities at 6 (C-Band) and 10 GHz (X-Band) assuming that are not in that range. the observed radio emission is due to free-free emission from On the other hand, qG5, qG7, qG11, qG19, and qG20 have ionised extended envelopes with a steady and completely ionised flat or inverted spectral indices, which indicates the presence of wind, with a volume filling factor f = 1, and an electron den- non-thermal emission that may be attributed to colliding winds −2 sity profile ne ∝ r . In the case of non-thermal contributions in binaries. our values, showed in Table 4, represent upper limits to the true qG8, and qG16 are ambiguous cases. No measurement of α mass-loss rates. is available for the star qG28 because it is only detected in a For most Quintuplet cluster members, we can assume that single band. helium stays singly ionised in the radio emitting region of the We can probe the existence of long-term variability since we stellar wind, so the number of free electrons per ion and the mean have two epochs with X-band measurements. We contemplate ionic charge can be set γ = 1 = Z (Leitherer et al. 1997). How- the existence of flux density variability when the differences in ever, in the case of Pistol Star and qG3 (the two luminous blue the flux densities between the two epochs are higher than 5 σ. variables (LBVs)) accounting for the fact that helium is predom- With this criterion we consider the two LBVs, qG3 and the Pis- inantly neutral in the winds of these cool stars, we take γ = 0.8, tol star as variable sources, as well as the sources qG1, qG8, and Z = 0.9 similarly to other LBVs studies (e.g. Leitherer et al. qG12, qG20, and qG29. For qG10, and qG11, the variability is 1995; Agliozzo 2019). rather small, but taking into account the possible binary nature Table 4 also shows the estimations done by Lang et al. (2005) of qG11, we speculate that the contribution from non-thermal from their 22.5 GHz flux densities when possible, and otherwise emission may be modulated by the orbital motion of the system. from their 8.5 GHz flux densities. They used their higher fre- Further investigation would be necessary to find a correlation

Article number, page 5 of 14 A&A proofs: manuscript no. main Continued on next page... OB?) f + OB?) OB?) WNLh OB) WNLh WNLh + + OB) / / / + + + + + + + Spectral B0 I < 3 WN11h 3 LBV 3 LBV 3 WN10h 3 3 WN9h 3 O7-8 Ia 3 WC8-9(d? 3 WC9d ( 4 WN8-9ha 3 WC9d( 4 O7-8 Ia 4 B1-2 Ia 4 B1-2 Ia 4 WC8(d? 3 WC8(d? 9 B0-1 Ia 1 WN6 4 3 B1-2 Ia ...... 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± α 8 1 4 8 2 9 6 2 3 2 8 5 7 6 5 9 2 1 6 ...... 0 0 0 0 − − − − 0302 0 01 2 02 2 03 0 05 0 0202 0 0201 0 009 0 0 01 01009 1 0 01009 0 0 01 0 008 1 00801 2 ...... 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 34 17 10 14 30 45 16 20 20 09 09 07 07 09 08 ...... 060 060 050 040 030 . . . . . d 0505 0 03 0 02 0 02 0 0 05 0 0202 0 0 0201 0 0 01 0 009 0 02 0 0101 0 0 01 0 01 0 03 0 009 0 03 0 ...... 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 52 50 34 21 19 49 22 18 23 10 09 17 08 09 08 10 07 07 ...... 070 060 . . Flux density (mJy) 0201 0 0 01 0 01 0 0101 0 009 0 0 009 0 008 0 008007 0 0 05 0 0403 0 02 0 02 0 0 1 0 0202 0 0 01 0 ...... 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 1 . 50 40 26 23 23 22 17 15 12 12 10 10 09 09 ...... 080 080 074 072 060 . . . . . 0.010.01 0 0.01 0 0.01 0 0 0.010.01 1 0 0.01 0 0.01 0 0.010.01 0 0 0.010.01 0 0 0.01 0 0.010.01 0 0.02 0 0 0.01 0 0.01 0 0.01 0 0.01 0 c ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± -source rms noise level. ff 28 49 03.20 28 50 03.37 28 49 37.73 28 50 04.20 28 49 32.46 28 49 37.00 28 50 07.16 28 49 16.47 28 50 03.47 28 49 45.46 28 49 31.73 28 49 40.65 28 50 18.05 28 49 29.31 28 49 20.17 28 49 39.47 28 49 41.61 28 48 59.12 28 49 05.85 28 48 44.08 − − − − − − − − − − − − − − − − − − − − 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.02 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± R.A. Dec. X-Band (2016) X-Band (2018) C-band (2018) type Table 3: JVLA flux densities of the compact sources of the Quintuplet cluster from these observations. b qF134 17 46 15.24 ) qF231, LHO042 17 46 14.71 ) qF270S, LHO110 17 46 15.10 a a ) qF362 17 46 17.98 )) qF257, LHO096 qF241, LHO071 17 46 15.14 17 46 15.12 ) qF320, LHO158 17 46 14.05 a a a a a name counterpart Source Near-IR Positions in X band (J2000.0) Nomenclature for cluster members adoptedStellar by identification Lang as et listed al. in (2005). Units Clark of et right al. ascension (2018b) are accordingFlux hours, to densities minutes, Figer measured and et from seconds, al. images and (1999)Upper corrected units and limit for of Liermann of primary declination et the beam are al. undetected attenuation. degrees, (2009). source arcminutes, was and fixed arcseconds. as Errors 2 are times in the seconds o and in arcseconds, respectively. Spectral classification by Clark et al. (2018b). f a c e b d qG14qG15 qF307A, LHO146 17 qF235N, 46 LHO047 15.48 17 46 15.15 qG16 qF235S, LHO034 17 46 15.17 qG17 qF381 17 46 13.45 qG19 17 46 16.50 qG18 qF353E 17 46 11.13 qG3 (QR9 Pistol Star qG4qG5 qF240, LHO067 17 46 15.94 17 46 14.77 qG1 (QR6 qG2 (QR5 qG7 17 46 17.83 qG6 (QR8 qG8qG9 qF211, LHO019 17 46 15.87 17 46 15.05 qG11 (QR7 qG10 qF256, LHO099 17 46 16.55 qG12 17 46 15.56 qG13 (QR4

Article number, page 6 of 14 Gallego-Calvente, A. T. et al.: Radio observations of massive stars in the Galactic centre: The Quintuplet cluster OB?) + f OB) OB) + + + + Spectral 3 9 WC9d( 6 6 WC9d( 6 7 B2-3Ia 6 WC8-9(d? 6 WN8-9ha 6 O7-8 Ia 7 B0-1 Ia ...... 0 0 1 0 0 0 0 0 0 0 ± ± ± ± ± ± ± ± ± > α 2 8 4 6 1 4 4 8 4 ...... 1 − e 02 0 008 0 008 0 01 008 0 0101 0 01 0 01 0 1 ...... 0 0 0 0 0 0 0 0 0 ± ± ± ± ± ± ± ± ± 0132 . 0 15 04 04 04 04 03 ...... < 020 030 030 . . . d 007 02 0 007 0 007 0 006 0 007 0 009 0 008008 0 008 0 0 ...... 0 0 0 0 0 0 0 0 0 0 ± ± ± ± ± ± ± ± ± ± 17 . 030 030 040 023 037 060 050 050 060 ...... Flux density (mJy) 005009 0 0 005 0 006 0 006 0 006 0 007007 0 0 007 0 007 0 ...... 0 0 0 0 0 0 0 0 0 0 ± ± ± ± ± ± ± ± ± ± Table 3: – continued from previous page 031 080 032 044 050 050 060 050 050 050 ...... -source rms noise level. ff 0.03 0 0.02 0 0.03 0 0.02 0 0.02 0 0.02 0 0.02 0 0.02 0 0.02 0 0.02 0 c ± ± ± ± ± ± ± ± ± ± 28 49 29.42 28 49 39.36 28 49 36.60 28 49 31.39 28 49 25.10 28 49 35.26 28 49 18.61 28 49 28.87 28 49 09.24 28 49 34.75 − − − − − − − − − − 0.03 0.02 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02 ± ± ± ± ± ± ± ± ± ± R.A. Dec. X-Band (2016) X-Band (2018) C-band (2018) type b Nomenclature for cluster members adoptedStellar by identification Lang as et listed al. in (2005). Units Clark of et right al. ascension (2018b) are accordingFlux hours, to densities minutes, Figer measured and et from seconds, al. images and (1999)Upper corrected units and limit for of Liermann of primary declination et the beam are al. undetected attenuation. degrees, (2009). source arcminutes, was and fixed arcseconds. as Errors 2 are times in the seconds o and in arcseconds, respectively. Spectral classification by Clark et al. (2018b). f a c e b d name counterpart qG28qG29 17 46 13.09 17 46 09.69 Source Near-IRqG20 LHO100 Positions in X band (J2000.0) 17 46 15.18 qG26qG27 WR 102ca qF243, LHO075 17 46 14.13 17 46 13.05 qG25 LHO076 17 46 14.14 qG21qG22 qF309qG23 qF274qG24 qF344 qF278, LHO077 17 46 17 15.12 46 17.50 17 46 17.53 17 46 16.67

Article number, page 7 of 14 A&A proofs: manuscript no. main 1 − 1000 Km s = ∞ v Continued on next page... 2018). / d 5 4 5 5 5 6 5 − − − − − − − 10 10 10 10 10 10 10 × × × × × × × Lang 2005 9 8 2 2 0 2 1 ˙ ...... M 2 2 4 1 3 5 3 5 6 6 5 5 5 5 4 5 5 5 5 6 5 5 5 − − − − − − − − − − − − − − − − 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 × × × × × × × × × × × × × × × × 0) 0) 7) 5) 0) 4) 0) 2) 7) 7) 2) 3) 0) 3) 5) 4) 2018 ...... for qG2 and qG4 estimated by Najarro (private communication); for sources of spectral ˙ 1 1 0 0 1 0 1 0 0 0 0 0 1 0 0 0 M µ ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 9 0 3 3 5 7 8 1 0 5 0 1 3 1 2 8 ...... (4 (6 (3 (2 (4 (1 (5 (1 (3 (3 (1 (2 (1 (7 (1 (1 5 6 6 5 5 5 5 5 5 5 5 5 5 6 5 5 − − − − − − − − − − − − − − − − 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 × × × × × × × × × × × × × × × × 0) 0) 8) 4) 0) 4) 0) 0) 6) 7) 3) 8) 2) 0) 3) 4) 2016 ...... ˙ 1 1 0 0 1 0 1 2 0 0 0 0 0 1 0 0 M ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 9 0 6 9 8 0 7 9 9 5 2 8 1 8 3 8 ...... (4 (6 (3 (1 (5 (2 (6 (7 (2 (3 (1 (3 (1 (5 (1 (1 5 6 6 5 5 5 5 5 5 5 5 5 6 6 6 5 − − − − − − − − − − − − − − − − 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 × × × × × × × × × × × × × × × × 7) 0) 6) 3) 0) 3) 0) 0) 7) 6) 3) 4) 3) 6) 0) 3) 2018 ...... ˙ 0 1 0 0 1 0 1 2 0 0 0 1 0 2 0 0 M ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 5 9 6 5 4 2 4 8 3 7 5 9 8 2 0 3 ...... 1 − yr

c µ s) (#) 6.0 GHz 10.0 GHz 10.0 GHz 22.5 GHz c / Table 4: Radio mass-loss rates in the C-band (2018) and in the two X-band epochs (2016 ∞ 500 1.3 (4 500 1.3 (2 v (Km , are in units of M ˙ M OB?) 1250 4.7 (9 + OB?) 1250 4.7 (3 WNLh 1500 1.3 (3 OB) 1250 4.7 (5 WNLh 300 1.3 (2 + OB) 1250 4.7 (5 / / + + + + + + b B0 I 500 1.3 (1 < type ) B1-2 Ia ) WC9d( a a ) WN9h 700 2.78 (2 )) B1-2 Ia ) WN11h LBV 300 1.8 170 (1 1.9 (5 a a a a 2. All mass-loss rates, = µ It is shown a comparison to estimations done by (Lang et al. 2005) from their 22.5 GHz and their 8.5 GHz observations, re-scaled for taking into account their assumed and Nomenclature for cluster members adoptedSpectral by classification Lang by et Clark al. et (2005). Wind al. parameters (2018b). for qG3Najarro and et Pistol al. (2017); stars parameters from for Table qG2, 1 qG4, by qG6, qG10, Najarro and et qG22 al. by Liermann (2009); et values al. for (2010), except qG8, qG9, qG11, qG15, qG16, qG21, qG25, and qG27 based on measurements for GSC4 star by types WN6, B supergiants andDerived OIa from we adopted the values 22.5 of GHzdescribed stars flux in of density Table 4 similar for by type. qG1 Lang (QR6), et al. qG2 (2005). (QR5), Values qG6 have been (QR8) re-scaled sources (see and above). Pistol Star, and from the 8.5 GHz flux density for qG13 (QR4), qG11 (QR7) and qG3 (QR9), as a c b d qG15 WC8(d? qG14 B1-2 Ia qG13 (QR4 qG12 O7-8 Ia 1500 1.3 (1 qG11 (QR7 qG10 WN8-9ha 900 2.0 (1 qG9 WC9d ( qG8 WC8-9(d? qG7 O7-8 Ia qG6 (QR8 qG5 SourceqG1 (QR6 Spectral qG2 (QR5 qG3 (QR9 Pistol StarqG4 LBV WN10h 105 400 2.2 (2 1.8 (9 Notes.

Article number, page 8 of 14 Gallego-Calvente, A. T. et al.: Radio observations of massive stars in the Galactic centre: The Quintuplet cluster d Lang 2005 ˙ M 5 5 6 5 5 5 6 5 6 5 for qG2 and qG4 estimated by Najarro (private communication); for sources of spectral − − − − − − − − − − µ 10 10 10 10 10 10 10 10 10 10 × × × × × × × × × × 6) 7) 0) 3) 3) 8) 6) 0) 0) 0) 2018 ...... ˙ 0 0 1 0 0 0 0 2 2 1 M ± ± ± ± ± ± ± ± ± ± 4 8 4 3 1 5 1 8 8 8 ...... (2 (2 (4 (1 (1 (3 (2 (4 (4 (5 . 5 5 6 5 5 5 6 5 6 5 1 − − − − − − − − − − − yr 10 10 10 10 10 10 10 10 10 10

× × × × × × × × × × 6) 7) 9) 3) 2) 8) 0) 0) 0) 0) 2016 ...... ˙ 0 0 0 0 0 0 1 1 1 1 M ± ± ± ± ± ± ± ± ± ± 5 2 8 2 1 5 4 1 1 9 Table 4.4: – continued from previous page ...... (2 (3 (3 (1 (1 (3 (4 (5 (5 (4 5 5 6 6 6 5 6 5 6 5 − − − − − − − − − − , are in units of M ˙ 10 10 10 10 10 10 10 10 10 10 M × × × × × × × × × × 6) 7) 8) 0) 0) 8) 9) 7) 8) 0) 2018 ...... ˙ 0 0 0 3 2 0 0 0 0 1 M ± ± ± ± ± ± ± ± ± ± 7 4 6 7 0 9 2 6 2 4 ...... c µ 2. All mass-loss rates, s) (#) 6.0 GHz 10.0 GHz 10.0 GHz 22.5 GHz = c / µ ∞ 500 1.3 (2 500 1.3 (3 v (Km and 1 − OB?) 1250 4.7 (2 + OB?) 1250 4.7 (5 WNLh 500 1.3 (3 + OB) 1250 4.7 (1 OB) 1250 4.7 (2 / + + + + + 1000 Km s b = ∞ v type It is shown a comparison to estimations done by (Lang et al. 2005) from their 22.5 GHz when possible, and otherwise from their 8.5 GHz observations, re-scaled for taking into account their assumed Nomenclature for cluster members adoptedSpectral by classification Lang by et Clark al. et (2005). Wind al. parameters (2018b). for qG3Najarro and et Pistol al. (2017); stars parameters from for Table qG2, 1 qG4, by qG6, qG10, Najarro and et qG22 al. by Liermann (2009); et values al. for (2010), except qG8, qG9, qG11, qG15, qG16, qG21, qG25, and qG27 based on measurements for GSC4 star by types WN6, B supergiants andDerived OIa from we adopted the values 22.5 of GHzdescribed stars flux in of density Table 4 similar for by type. qG1 Lang (QR6), et al. qG2 (2005). (QR5), Values qG6 have been (QR8) re-scaled sources (see and above). Pistol Star, and from the 8.5 GHz flux density for qG13 (QR4), qG11 (QR7) and qG3 (QR9), as a c b d qG28 qG29 qG26 qG27 WC9d( qG25 WC9d( qG24 B0-1 Ia qG23 O7-8 Ia 1500 1.3 (9 qG22 WN8-9ha 900 2.0 (9 qG21 WC8-9(d? qG19 qG20 B2-3Ia qG18 WN6 1600 4.1 (2 qG17 B0-1 Ia Source Spectral qG16 WC8(d? Notes.

Article number, page 9 of 14 A&A proofs: manuscript no. main

Fig. 4: Composition of the HST/WFC3 F153M image from HST archive with a Paschen α image by Dong et al. (2011). BLue: HST WFC3 F153M; Red: HST NIC3 Paschen α. QR1−3 sources by Lang et al. (2005) are encircled. between the periodicity and the orbital period. In conclusion, we number of sources as well as their flux density for comparison find that 9 out of the 29 radio sources, approximately 30%, dis- with the models. We have done this first for the Arches cluster play significant variability. This is a remarkably higher fraction and then for the Quintuplet cluster. We emphasise that we cannot than in the Arches cluster, where we find that . 15% of the radio undertake an exhaustive study here, which would require taking stars display variability (see Gallego-Calvente et al. 2021). We into account a large number of potentially important parameters, speculate that this may be related to the advanced evolutionary such as, for example, the role of metallicity or the wind volume state of the older Quintuplet stars. filling factor, which we neglect here. Nevertheless, we show that our simple toy modelling, with these basic assumptions, indi- cates that current theoretical models of the evolution of massive 5. Analysis of the radio luminosity function stars appear to be fairly realistic, and that we can infer constraints on the properties of the clusters by comparing radio observations 5.1. Basic assumptions with predictions from isochrones.

With assumptions about the age and mass of a young cluster, We use PARSEC5 (release v1.2S + COLIBRI S_37, Bres- a comparison between the number and the observed flux of de- san et al. 2012; Chen et al. 2014, 2015; Tang et al. 2014; Marigo tected radio stars with predictions from theoretical stellar evo- et al. 2017; Pastorelli et al. 2019, 2020) and MIST6 (Dotter 2016; lutionary models (isochrones) can help to assess the quality of Choi et al. 2016; Paxton et al. 2011, 2013, 2015) theoretical those models, and also, if the theoretical isochrones are consid- isochrones for solar metallicity. To convert the mass-loss rates ered sufficiently reliable, to infer basic properties of the clus- from the theoretical isochrones to observable radio flux, we use ter. In Gallego-Calvente et al. (2021) we have shown that the the relation observed number of radio stars in the Arches cluster appears to require a top-heavy initial mass function with a power-law exponent αIMF = −1.8 (at odds with the Solar environment “Salpeter” exponent αIMF = −2.35). In this work, we tentatively take a step further and use the 5 http://stev.oapd.inaf.it/cmd radio luminosity function (RLF) of the stars, i.e. we use both the 6 https://waps.cfa.harvard.edu/MIST/

Article number, page 10 of 14 Gallego-Calvente, A. T. et al.: Radio observations of massive stars in the Galactic centre: The Quintuplet cluster

and a lower mass of 0.8 M . Our results are not sensitive to rea- sonable changes of these parameters. Also, since our sources of     −4/3 S ν M˙ v∞ interest represent only the very tip of the mass distribution, as- . × −4 −4/3 f 1/2 = (5 34 10 ) clump −1 −1 mJy M yr km s suming a two-segment IMF does not introduce any significant  d −2  ν 2/3  µ2 −2/3 changes. , We tested whether the random sampling of the high mass 2 (1) kpc Hz Z γgν end of the IMF is biasing our results by random realisations of clusters of given age, mass, and IMF. We only used MIST mod- els for this test and assumed that we could only detect stars with which has been reported before in similar versions (e.g. Gallego- a radio flux density & 0.04 mJy, the approximate detection limit Calvente et al. 2021; Montes et al. 2009; Leitherer et al. 1997). here and in Gallego-Calvente et al. (2021). We found that the The observing frequency is ν = 10 GHz. We assume typical val- age of the clusters can typically be recovered well (± 1 Myr) and ues, with a mean molecular weight µ = 1.3, a mean ion charge that the cluster parameters could best be recovered for an age of Z = 1, and a mean number of electrons per ion γ = 1. As con- ∼ 3 Myr, where the number of bright radio stars peaks. Whether cerns the Gaunt factor the IMF was top-heavy or not could also be recovered with great  3/2  reliability. However, we found a degeneracy between the RLFs Te gν = 9.77 · 1 + 0.13 · log , (2) for the ages of 2 and 6 Myrs. Since these values lie safely out- Zν side (or at the very extreme) of the ages reported for the Arches and Quintuplet clusters, we do not use them in our subsequent T 4 we use e = 10 K. Any changes to these assumed values of analyses. the parameters by factors of two to a few do not significantly change the resulting radio flux. A potentially important factor, that we have not yet mentioned, is wind clumping. The volume 5.2. Models filling factor, f , is one for a homogeneous stellar wind and clump Figure 6 shows predictions at two different ages for a model clus- smaller than one for a clumpy wind. For simplicity, we here as- 4 ter with a total initial of 10 M and a power-law sume fclump = 1. IMF with an exponent αIMF = −1.8 (Hosek et al. 2019), us- ing MIST isochrones. We averaged and used the 1 σ confidence intervals of the result of 10 simulations of the cluster. The up- per panel shows the present-day mass function, the middle one histograms of the predicted radio flux density, and the lower one cumulative histograms of the predicted radio flux density. Observed values in Arches and Quintuplet are overplotted in black. Finally, we show the same models, created with PARSEC isochrones, in Figure 7. We can see differences due to the use of different theoretical isochrones, but we can also see the overall similarity of the predictions. Given the low flux density of radio stars and the sensitivity of our observations we can only observe the bright tail of the distribution. We show that the RLF can change drastically as a function of age. This is due to the rapid development of the ex- tremely massive stars at such young ages. The latter also means that single models are expected to work well because we do not expect any significant effects such as mass- transfer to occur in binaries at these time scales. Also, stellar evolution happens so fast at these young ages that the radio flux Fig. 5: Blue, solid: Histogram of observed flux densities of radio of a binary will typically be dominated by one of the two sources, stars in the Arches cluster (Gallego-Calvente et al. 2021). Or- except in the unlikely case that the two stellar masses are exactly ange, outline: Histogram of radio fluxes of the same stars, using equal. Of course, colliding wind binaries will be a source of un- the mass-loss rates reported by Gallego-Calvente et al. (2021) certainty, but their numbers in our sample are small according to and converting to radio flux density with Equation 1 assuming the reported spectral indices and we do not think that they will the same parameters for all stars. affect the observed population statistics significantly. We do not test this assumption here, however, given that this would go be- The validity of such a rule-of-thumb approach is demon- yond the simple model presented here. To avoid having to deal strated in Fig. 5, where we compare the observed flux densities with complex binning issues we will use cumulative luminosity of radio stars in the Arches cluster with the ones computed from functions from this point on. their individually determined mass-loss rates (Gallego-Calvente A parameter of significant interest is the exponent of the et al. 2021) and using the simplified assumptions. The differ- power-law of the IMF, αIMF , because it has a strong influence ences appear to be small enough to justify an efficient, simplified on the number of massive stars that initially form the cluster. computation of the radio flux densities. From here on we will use In Gallego-Calvente et al. (2021) we showed that the observed these simplified assumptions on the parameters that enter Equa- number of radio stars in the Arches cluster favoured a top-heavy tion 1 and only consider the observed radio flux densities, not the IMF. In Fig. 8 we illustrate how the bright end of the RLF mass-loss rates. changes as a function of αIMF . The RLF of the model cluster For our cluster models we always use a one-segment power- with a Salpeter IMF will only be similar to the one of a cluster law initial mass function (IMF) with an upper mass of 150 M with a top-heavy IMF (αIMF = −1.8) for an initial mass that is

Article number, page 11 of 14 A&A proofs: manuscript no. main

Fig. 6: Radio flux densities of massive stars in a model cluster, Fig. 7: Radio flux densities of massive stars in a model cluster, using MIST isochrones. Top: Present-day mas function. Mid- using PARSEC isochrones. Top: Present-day mas function. Mid- dle: Histograms of predicted radio flux densities. Bottom: Cu- dle: Histograms of predicted radio flux densities. Bottom: Cu- mulative histograms of predicted radio flux densities. The black mulative histograms of predicted radio flux densities. The black histogram are observed values for the Arches cluster (Gallego- histogram are observed values for the Arches cluster (Gallego- Calvente et al. 2021, dotted) and for the Quintuplet cluster (this Calvente et al. 2021, dotted) and for the Quintuplet cluster (this work, solid). work, solid). four to five times higher. While uncertainties up to a factor two varied randomly assuming for each source a Gaussian normal are possible in the observational determination of a young, mas- distribution centred on the observed radio flux density and a sive cluster’s mass (for example from optical or infrared obser- conservative standard deviation of 30% from the mean value vations), higher factors can generally be ruled out safely. There- (assuming the same uncertainty for all sources). The parame- fore, the observed RLF can help to constrain the exponent of the ter space was spanned by two values of αIMF = −1.8, −2.35, power-law IMF of a young massive cluster. The most important ages of 2.5, 3, 3.5, 4, 4.5, 5 Myr and cluster masses of 1.0 and 4 degeneracy to keep in mind is the one between cluster mass and 1.5 × 10 M . IMF exponent. There is also some degeneracy with age, but less relevant, because the shape of the bright end of the RLF changes 5.3. Arches cluster sensitively as a function of age. With reasonable constraints on the age and mass of a cluster, one may therefore constrain its We determined the best fit parameters for each of the 100 MC re- properties via the RLF. alisations of the RLF observed by Gallego-Calvente et al. (2021). Following the previous considerations, we proceed to fit Figure 9 shows the resulting distribution of the parameters of cluster models to the observed radio luminosity functions of the the best fit models with MIST isochrones and Fig. 10 for Par- Arches and Quintuplet clusters. This is a demonstration of the sec isochrones. There is no clear preference for the total cluster principle, so we limit ourselves to a crude exploration of param- mass, but the top-heavy IMF provides the best solution in the eter space with simple, brute-force Monte Carlo simulations. To vast majority of cases. The cluster age is broadly distributed, but create the MC samples, the observed radio flux densities were peaks at 3 to 3.5 Myr, in agreement with literature.

Article number, page 12 of 14 Gallego-Calvente, A. T. et al.: Radio observations of massive stars in the Galactic centre: The Quintuplet cluster

Fig. 8: Simulated radio luminosity functions for a 3 Myr old clus- 4 ter with an initial stellar mass of 10 M , using αIMF = −1.8 and the standard Salpeter value of αIMF = −2.35.

Fig. 10: Results of MC simulations of the Arches RLF, using PARSEC isochrones.

Fig. 9: Results of MC simulations of the Arches RLF, using MIST isochrones.

5.4. Quintuplet cluster We determined the best fit parameters for each of the 100 MC realisations of the RLF observed by here. Figure 11 shows the resulting distribution of the parameters of the best fit models with MIST isochrones and Fig. 12 for Parsec isochrones. As in the Fig. 11: Results of MC simulations of the Quintuplet RLF, using case of the Arches cluster, the cluster mass does not appear to be MIST isochrones. well constrained, but again the top-heavy IMF provides the best solution in the vast majority of cases. The cluster age is broadly distributed and peaks at 3.5 to 4 Myr, in agreement with literature that assigns an older age to the Quintuplet than to the Arches. – show that theoretical isochrones appear to provide reason- able matches to the observed RLFs of the two clusters;

6. Discussion – confirm a top-heavy IMF for the two clusters. This agrees with the conclusions of observational studies of the present- We have fitted very basic models to MC simulations of the Quin- day mass functions of these clusters (Hußmann et al. 2012; tuplet and Arches RLFs. These models: Hosek et al. 2019);

Article number, page 13 of 14 A&A proofs: manuscript no. main

A. T. G.-C., R. S., and B. S. acknowledge financial support from national project PGC2018-095049-B-C21 (MCIU/AEI/FEDER, UE). A. A. acknowledges support from national project PGC2018-098915-B-C21 (MCIU/AEI/FEDER, UE). F. N. acknowledges financial support through Spanish grants ESP2017-86582- C4-1-R and PID2019-105552RB-C41 (MINECO/MCIU/AEI/FEDER) and from the Spanish State Research Agency (AEI) through the Unidad de Excelencia “María de Maeztu”-Centro de Astrobiología (CSIC-INTA) project No. MDM- 2017-0737. F. N.-L. gratefully acknowledges funding by the Deutsche Forschungsgemein- schaft (DFG, German Research Foundation) – Project-ID 138713538 – SFB 881 (“The Milky Way System”, subproject B8). F.N.-L. acknowledges the sponsorship provided by the Federal Ministry for Ed- ucation and Research of Germany through the Alexander von Humboldt Foun- dation. The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement n◦ [614922].

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