Photometric classification of stars around the Milky Way’s central black hole I. Central parsec

A&A, 689, A190 (2024) h ps://doi.o g/10.1051/0004-6361/202449881 c The Au ho s 2024 As onomy & As ophysics Pho ome ic classi ica ion o s a s a ound he Milky Way’s cen al black hole I. Cen al pa sec E. Gallego-Cano1,?, T. F i z2, R. Schödel1, A. Feldmeie -K ause3, T. Do4, and S. Nishiyama5 1Ins i u o de As o ísica de Andalucía (CSIC), Glo ie a de la As onomía s/n, 18008 G anada, Spain 2Depa men o As onomy, Uni e si y o Vi ginia, 530 McCo mick Road, Cha lo es ille, VA 22904, USA 3Depa men o As ophysics, Uni e si y o Vienna, Tü kenschanzs aße 17, Wien 1180, Aus ia 4Physics and As onomy Depa men , Uni e si y o Cali o nia, Los Angeles, CA 90095-1547, USA 5Miyagi Uni e si y o Educa ion, Sendai, Miyagi, Japan Recei ed 6 Ma ch 2024 /Accep ed 6 June 2024 ABSTRACT Con ex . The p esence o young massi e s a s in he Galac ic Cen e (GC) aises ques ions abou how such s a s could o m nea he massi e black hole Sagi a ius A* (Sg A*). Fu he mo e, he shape o he ini ial mass unc ion (IMF) in his egion seems o di e om i s s anda d Salpe e /K oupa law. Due o obse a ional challenges such as ex eme ex inc ion and c owding, ou unde s anding o he s ella popula ion in his egion emains limi ed, wi h spec oscopic da a a ailable only o selec ed small and compa ably b igh sou ces. Aims. We aim o imp o e ou knowledge abou he dis ibu ion and he IMF o young, massi e, s a s in he icini y o Sg A*. Me hods. We used in e media e band (IB) pho ome y o iden i y candida es o massi e young s a s. To ensu e obus classi ica ion, we applied h ee di e en , bu complemen a y me hods: Bayesian in e ence, a basic neu al ne wo k, and a as g adien -boos ed ees algo i hm. Resul s. We ob ain spec al ene gy dis ibu ions o 6590 s a s, 1181 o which ha e been p e iously classi ied spec oscopically. We iden i y 351 s a s ha a e classi ied as ea ly ypes by all h ee classi ica ion me hods, wi h 155 o hem being newly iden i ied candida es. The adial densi y p o iles o la e and ea ly- ype s a s i well wi h b oken powe laws, e ealing a b eak adius o 9.2±0.600 o ea ly- ype s a s. The la e- ype s a s show a co e-like dis ibu ion a ound Sg A* while he densi y o he ea ly- ype s a s inc eases s eeply owa ds he black hole, consis en wi h p e ious wo k. We in e a op-hea y IMF o he young s a s nea Sg A* (R<900), wi h a powe -law o 1.6±0.1. A g ea e dis ances om Sg A* a s anda d Salpe e /K oupa IMF can explain he da a. Addi ionally, we demons a e ha IB pho ome y can also cons ain he me allici ies o la e- ype s a s, es ima ing me allici ies o o e 600 la e- ype s a s. Conclusions. The a ia ion o he IMF wi h adial dis ance om Sg A* sugges s ha di e en mechanisms o s a o ma ion may ha e been a wo k in his egion. The op-hea y IMF in he inne mos egion is consis en wi h s a o ma ion in a disc a ound Sg A*. Key wo ds. Galaxy: cen e – Galaxy: kinema ics and dynamics – Galaxy: s ella con en 1. In oduc ion As he nea es galaxy nucleus, si ua ed a only ∼8 kpc om Ea h (Do e al. 2019;Abu e e al. 2019,2021), he Galac ic Cen e (GC) ha bou s in i s cen e a supe massi e black hole Sagi a ius A* (Sg A*) wi h 4.04 ±0.06 ×106M(Abu e e al. 2018;Do e al. 2019) su ounded by a nuclea s a clus e (NSC) o 2.5×107M(Abu e e al. 2018;Do e al. 2019; F i z e al. 2016;Feldmeie -K ause e al. 2017a;Schödel e al. 2014;Launha d e al. 2002) and a hal -ligh adius o e ec- i e adius o ∼4.2−7 pc (Schödel e al. 2014;F i z e al. 2016; Alexande 2017;Gallego-Cano e al. 2020). Thanks o hei nea ness, he s a s can be esol ed obse a ionally on scales o millipa sec inside he adius o in luence o he black hole (Alexande 2005;Gallego-Cano e al. 2018;Schödel e al. 2018). The Cen e o he Milky Way he e o e p o ides a unique possibili y o s udy he s ella popula ion in he mos ex eme as ophysical en i onmen o ou Galaxy and o s udy he in e - ac ion o s a s wi h a massi e black hole. ?Co esponding au ho ; [email p o ec ed] O e he las ew decades, nume ous s udies ha e un eiled he p esence o young (∼2−8 My old), massi e s a s wi hin ∼0.5 pc o he black hole (e.g. Ghez e al. 2003;Pauma d e al. 2006;Lu e al. 2008;Ba ko e al. 2009;Genzel e al. 2010; Do e al. 2013;Yelda e al. 2014). This disco e y is unexpec ed, as s a o ma ion is ypically hough o be supp essed in he icini y o a massi e black hole due o i s s ong idal ield. The e is a peculia popula ion o appa en ly main-sequence B s a s wi hin 0.0800 o he black hole, called ‘S-clus e ’. A a la ge adius, he young s a s a e dis ibu ed in wo main ea u es: he clockwise (CW) o a ing disk in he egion ∼100 (∼0.04 pc) o ∼800 (∼0.32) om he black hole, and he coun e clockwise (CCW) disk a dis ances la ge han 800 (∼0.32 pc) om Sg A*. Howe e , he la e ea u e is con o e sial, wi h some s ud- ies suppo ing i s exis ence (Genzel e al. 2003;Pauma d e al. 2006;Ba ko e al. 2009) while o he s e u e i (Lu e al. 2008; Yelda e al. 2014). While all s udies ind a op-hea y mass unc- ion o he young s a s nea Sg A*, he e a e signi ican dis- c epancies as o i s exac powe -law slope, om a alue o −0.45 epo ed by Ba ko e al. (2010) o −1.7 epo ed by Open Access a icle, published by EDP Sciences, unde he e ms o he C ea i e Commons A ibu ion License (h ps://c ea i ecommons.o g/licenses/by/4.0), which pe mi s un es ic ed use, dis ibu ion, and ep oduc ion in any medium, p o ided he o iginal wo k is p ope ly ci ed. This a icle is published in open access unde he Subsc ibe o Open model.Subsc ibe o A&A o suppo open access publica ion. A190, page 1 o 34 Gallego-Cano, E., e al.: A&A, 689, A190 (2024) Lu e al. (2013). This inconsis ency may a ise om he lim- i ed and di e en comple eness o he da a in hese s udies. Recen ly, on Fellenbe g e al. (2022) examined an ex ensi e a ea (∼3000 ×3000), he mos ex ensi e s udy o young s a s in he GC o his da e. They con i m he p esence o he wa ped CW disk, an ou e kinema ic ea u e (F2), and he CCW ea u e a la ge dis ances. Addi ionally, a p e iously un epo ed ea u e (F3) was iden i ied beyond a p ojec ed adius o R=800 om Sg A*. The s a s om he wa ped CW disk exhibi a op-hea y mass unc ion, in con as o he s a s a la ge dis ances. An impo an ques ion ega ds he o ma ion mechanism o he young s a s. While mos s udies suppo in si u s a o ma- ion om a massi e gaseous disk, none can p o ide a comple e explana ion. Iden i ying mo e ea ly- ype s a s will enhance ou comp ehension o hei dis ibu ion and, consequen ly, shed ligh on hei ini ial mass unc ion (IMF), po en ially p o iding u he insigh s. Gi en he ex eme in e s ella ex inc ion and he ex eme sou ce c owding owa ds he GC (e.g. Nishiyama e al. 2009; Schödel e al. 2010;F i z e al. 2011;Nogue as-La a e al. 2018) i is ex emely challenging o s udy he s ella popula ion nea Sg A*. The classi ica ion o s a s is p ima ily ca ied ou using spec oscopy wi h Adap i e Op ics (AO)-assis ed high-angula esolu ion In eg al Field Uni s, such as SINFONI/ERIS a he ESO-VLT o he OSIRIS spec og aph a he W. M. Keck obse a- o y. In he mos ecen s udy by on Fellenbe g e al. (2022), he analysis is limi ed o s a s b igh e han 15 mag in he KS-band. Se e al s udies sugges ha conduc ing imaging obse - a ions using in e media e-band (IB) pho ome y in he KS- band (e.g. Nishiyama & Schödel 2013;Nishiyama e al. 2023; Buchholz e al. 2009;Plewa 2018) can be a powe ul app oach o iden i ying young and in e media e-age s a s in he GC. These s udies o e a signi ican ad an age in de ec ing ain e s a s wi hin la ge ields compa ed o spec oscopic s udies. None heless, i is c ucial o emphasize ha subsequen in- dep h spec oscopic ollow-up obse a ions a e essen ial o con i ma ion. In his wo k, we use se en in e media e bands co e ing he nea in a ed (NIR) ob ained by he AO-assis ed NIR came a NACO ins alled a he ESO-VLT. We use he same da a as Buchholz e al. (2009) bu apply an imp o ed me hodology and analysis. In ecen yea s, he da a has also been eanalyzed by Plewa (2018), who used a machine- ained classi ie . Ou wo k aims o imp o e on and go beyond he p e ious wo k in se e al aspec s: 1. We s udy a somewha la ge egion, co e ing an a ea o e 12% la ge han ha examined in p e ious s udies, due o he exclusion o he H-band om ou analysis, which has a smalle ield o iew (FoV). 2. We enhance he image educ ion p ocess. The inco po a ion o noise maps and he u iliza ion o a spa ially a iable PSF, no only esul s in deepe da a bu also imp o es he quali y o he pho ome y. 3. We de e mine obus pho ome ic unce ain ies by applying a boo s apping p ocedu e and including PSF unce ain ies. 4. We explo e he e ec o di e en models o i he measu ed spec al ene gy dis ibu ions (SEDs). 5. We employ h ee dis inc ye complemen a y classi ica ion me hods, encompassing Bayesian in e ence, a basic neu al ne wo k, and a as g adien -boos ed ees algo i hm. 6. Thanks o nume ous spec oscopic s udies pe o med in he pas decade, we can use hund eds o classi ied s a s o e a la ge ield, which leads o inc eased p ecision and accu acy o ou classi ica ion. Ou app oach allows us o iden i y new candida es o ea ly s a s nea Sg A*. Wi h hese new da a, we s udy he su ace-densi y p o ile, o e ing a glimpse in o he dynamical s a e o he clus e , and he luminosi y unc ion, a undamen al pa ame e ha can be employed o de e mine p ope ies such as age, s a o ma- ion his o y, and he IMF o he clus e . In Sec ion 2, we ou line he da a educ ion p ocess and highligh he no el imp o emen s made. Ou pho ome ic analysis, along wi h as ome ic and pho- ome ic calib a ion, is de ailed in Sec ion 3. Sec ion 4p esen s ou applica ion o Bayesian in e ence o s ella classi ica ion. Addi ionally, wo machine-lea ning me hods–Mul i-Laye Pe - cep on and XGBoos –a e discussed in Sec ion 5. We summa ize he esul s in Sec ion 6and delibe a e hem u he in Sec ion 7. We p esen ou conclusions in Sec ion 8. In his pape , we adop a dis ance o Sg A* o 8.28 kpc (Abu e e al. 2021), wi h 100 co esponding o app oxima ely 0.04 pc. 2. Da a educ ion 2.1. Basic educ ion The da a we e ob ained by using se en IB il e s in KS-band ob ained wi h he S27 came a o NACO/VLT, wi h a pixel scale o 0.02700. The AO was locked on he NIR b igh supe gian GCIRS 7 ha is loca ed abou 5.500 no h o Sg A*. The da a used a e summa ised in Table 1. Mos o he da a we e acqui ed wi h a simila ec angula di he pa e n, oughly cen ed on Sg A*, bu some o hem we e subjec ed o andom di he ing. The obse a ions a e desc ibed in de ail in Buchholz e al. (2009). In con as o Buchholz e al. (2009), we chose no o include H-band da a in ou analysis because he a ea obse ed by he H-band da a has a mo e limi ed FoV in compa ison o he IB da a. Fu he mo e, as discussed in Sec ion 7, his da a is no essen ial o ou analysis. We applied s anda d da a educ ion, wi h sky sub ac ion, bad pixel emo al, and la ielding. A e wa ds, we aligned he indi idual images wi h he KS-band wide- ield mosaic om 11 h May 2011 ob ained wi h he S27 came a o NACO and desc ibed in Gallego-Cano e al. (2018). The inal mosaics o each epoch we e c ea ed by mean-combining he indi idual exposu es. The co esponding noise maps we e compu ed using he e o o he mean. Be o e mosaicing, we had ebinned he da a wi h a ac o o wo and quad a ic in e pola ion, which can imp o e he as ome y and pho ome y o he inal p oduc (see Gallego-Cano e al. 2018;Schödel e al. 2018). We p esen he KLF o he inal mosaic images and he pho ome ic unce - ain ies in Appendix A. The quali y o he di e en IB da a a ies: IB224, IB233, IB227, and IB230 ha e a c owding limi o a ound 19 mag, IB200 and IB236 a ound 17.8 mag, and IB206 a ound 19.5 mag. 2.2. Repai ing sa u a ed s a s Repai ing sa u a ed s a s is essen ial o ob aining accu a e pho- ome ic measu emen s because he b igh es s a s will p o ide he mos accu a e es ima es o he poin sp ead unc ion (PSF) wings. We epai ed he sa u a ed co es o b igh s a s wi h he PSF o nea by unsa u a ed s a s, a me hodology based on he S a Finde IDL ou ine REPAIR_SATURATED (Diolai i e al. 2000). The main di e ence o he la e is ha we also applied an addi i e o se when ma ching he PSF om unsa u a ed s a s o one o he sa u a ed s a s, which is necessa y because o he di e en no maliza ion ac o s o he PSFs. The selec ion o he PSF e e ence s a s is desc ibed in Sec ion 3.1. A190, page 2 o 34 Gallego-Cano, E., e al.: A&A, 689, A190 (2024) Table 1. De ails o he imaging obse a ions used in his wo k. Da e (a)λcen al ∆λN(b)NDIT (c)DIT (d) [µm] [µm] [s] 09 July 2004 2.00 0.06 8 4 36 12 June 2004 2.06 0.06 96 1 30 12 June 2004 2.24 0.06 99 1 30 09 July 2004 2.27 0.06 8 4 36 09 July 2004 2.30 0.06 8 4 36 12 June 2004 2.33 0.06 119 1 30 09 July 2004 2.36 0.06 8 4 36 No es. (a)UTC da e o beginning o nigh . (b)Numbe o (di he ed) expo- su es. (c)Numbe o in eg a ions ha we e a e aged on-line by he ead- ou elec onics. (d)De ec o in eg a ion ime. The o al in eg a ion ime o each obse a ion amoun s o N×NDIT ×DIT. The app oxima e spa- ial esolu ion o he images is 0.0700–0.1000/pixel. We e e o he di e - en IB bands by adding he numbe o hei cen al wa eleng h: IB200, IB206, IB224, IB230, IB233, and IB236. 3. Da a analysis 3.1. PSF i ing S ella pho ome y and as ome y we e acqui ed wi h he PSF i ing p og am S a Finde (Diolai i e al. 2000). The FoV o all images is 2800 ×2800, la ge han he isoplana ic angle in he KS- band, he e o e special a en ion was gi en o add essing he spa- ial a iabili y o he PSF by using local PSFs. We di ided he images in o sub- ields o app oxima ely 10.800 ×10.800 size ol- lowing he p ocedu e desc ibed in Gallego-Cano e al. (2018). Since anisoplana ic e ec s ha e a ela i ely limi ed impac on he seeing halo, as no ed Schödel (2010), we employed he b igh es s a , GCIRS7, o es ima e he seeing halo o he PSF o all sub- ields (see Gallego-Cano e al. 2018). We i s emo ed any ex ended sou ces om he lis o de ec ed s a s and hen selec ed he en b igh es and mos iso- la ed s a s o pe o m an i e a i e ex ac ion o he local PSF wi hin each sub- ield. Di e ences in mean ex inc ion and sou ce densi y be ween he sub- ields imply ha no all o hem con ain e e ence s a s wi h uni o m b igh ness, leading o small sys- ema ic o se s in he ze o-poin s. We add ess his p oblem in Sec ion 3.3.2. The posi ions and luxes o each s a we e de e - mined by a e aging mul iple measu emen s om o e lapping ames. Finally, we applied he boo s apping esampling me hod o compu e he pho ome ic unce ain ies. This me hod allowed us o ob ain obus and eliable unce ain ies in a c owded ield wi hou loss o sensi i i y, as desc ibed by Gallego-Cano e al. (2022). The de ails o he p ocess a e included in Appendix A. To ob ain he inal lis o s a s, we combined he inal lis s o he se en IB-band da a se s in o a single lis con aining s a s ha we e de ec ed in e e y il e . The quali y o he da a is e y di e en o he di e en bands, as we see in Figs. A.1 and A.3. The numbe o s a s ha we e ound in all il e s is limi ed o 6590 because in e s ella ex inc ion ises s eeply owa ds sho e wa eleng hs. 3.2. As ome ic calib a ion In o de o ob ain he as ome ic solu ions, we used he adio posi ions om eigh mase s a s (IRS9, IRS12N, IRS28, SiO−15, IRS10EE, IRS15NE, IRS17, IRS19NW) in he FoV (Reid e al. 2007). We applied a linea solu ion o ob ain he Fig. 1. Calib a ion s a s used o he basic calib a ion. The labels indica e he iden i ica ion numbe s co esponding o he lis o Feldmeie -K ause e al. (2015). The axes show he o se dis ances om Sg A* (yellow s a ) in a csecond. The backg ound image is om he 2004 June 12 obse a ion co esponding o he IB224 il e . The FoV o he image is ∼4200 ×4200 (∼1.7 pc ×1.7 pc). Wo ld Coo dina e Sys ems (WCSs) and o con e he pixel posi ion o celes ial coo dina es, igh ascension, and declina ion (IDL As olib ou ine SOLVE_ASTRO). 3.3. Pho ome ic calib a ion In his sec ion, we desc ibe he wo s eps in ol ed in ou pho o- me ic calib a ion. Fi s , we applied a basic calib a ion o con e s a luxes in o magni udes. Second, we applied a local calib a- ion o ake in o accoun ze o-poin a ia ions ac oss he ield. While ou app oach is simila o ha ollowed in Buchholz e al. (2009), we ha e included some essen ial di e ences o imp o e he p ocedu e. 3.3.1. Basic calib a ion We chose OB s a s as pho ome ic calib a o s because hey can be closely app oxima ed as blackbodies and lack dis inc i e ea- u es in hei SED a he wa eleng hs o ou da a (see Fig. 4 in Feldmeie -K ause e al. 2015). We selec ed OB s a s om Feldmeie -K ause e al. (2015), and emo ed he a iable s a s iden i ied by Gau am e al. (2019). Subsequen ly, we selec ed isola ed and b igh s a s, esul ing in 28 OB calib a o s, shown in Fig. 1and lis ed in Table B.1. We compu ed an ex inguished blackbody SED wi h an e ec- i e empe a u e Te o ∼30 000 K o each OB s a , aking i s AKex inc ion alue om Schödel e al. (2010). The absolu e mean ex inc ion alue in KSis a ound 2.54. We assumed ha he ex inc ion cu e in he NIR can be app oxima ed by a powe law, as sugges ed by p e ious s udies (Nishiyama e al. 2009; F i z e al. 2011). Speci ically, we chose α=2.21 (Schödel e al. 2010;Nogue as-La a e al. 2019). Subsequen ly, we mul iplied he blackbody SEDs wi h he ansmission cu es o he IB il e s A190, page 3 o 34 Gallego-Cano, E., e al.: A&A, 689, A190 (2024) Fig. 2. Compa ison be ween eal spec a in K-band and he low- esolu ion SEDs compu ed wi h IB pho ome y ( ed poin s, op imally shi ed o ma ch he spec a). The iden i ica ion numbe s a e indica ed in he panels. The spec a displayed in he le and middle panels co espond o an OB, and a Wol -Raye s a , espec i ely, om Feldmeie -K ause e al. (2015). The igh panel shows a spec um o a la e- ype s a om Feldmeie -K ause e al. (2017b). and in eg a ed hem in each band. These heo e ical luxes we e hen u ilized o he compa ison wi h he obse ed luxes, om which we de i ed se en IB ze o poin s o each OB s a . The 28 ze o poin s o each IB band we e median combined o ob ain he bes ze o poin es ima es. In o de o ix he absolu e magni udes, we assigned he KS-band magni udes om Schödel e al. (2010) o he IB224 magni ude because i is he mos cen al magni ude among all IB il e s and emains una ec ed by emission o abso p ion ea- u es. The selec ion o he same Te o all e e ence s a s does no a ec he inal calib a ion due o he excellen app oxima- ion p o ided by he Rayleigh-Jeans law o he SED o ho s a s in he nea -in a ed egion. We es ed di e en alues o Te =15 000, 35 000 K, and he a ia ion in calib a ed magni- udes was ≤0.01, 0.002, espec i ely. To assess he quali y o he calib a ion, we compa ed he low- esolu ion SEDs compu ed wi h IB pho ome y wi h eal spec a in he K-band o known s a s. Figu e 2shows he spec a o eal s a s si ua ed in he inne mos egion, and hei co esponding IB magni udes ( ed poin s). The le and middle panels co espond o spec a om indi idual s a s om Feldmeie -K ause e al. (2015) ha a e iden i ied as ea ly- ype OB, and Wol -Raye s a s, espec i ely. The igh panel co esponds o a spec um o a la e- ype s a om Feldmeie -K ause e al. (2017b). The iden- i ica ion numbe s a e indica ed in he panels. The SEDs ollow e y well he main ea u es o he spec a. We can see ha he main cha ac e is ic o dis inguishing be ween ea ly- ype and la e- ype s a s wi h ou low esolu ion in hese wa eleng hs is he CO bandhead ea u e om KS≥2.3µm. In Sec ion 3.4, we explo e a ious app oaches o measu e he dep h o he ea u e o use in ou analysis when classi ying he s a s. 3.3.2. Local calib a ion We analysed he pho ome ic calib a ion quali y ac oss he FoV because ac o s such as he dis ance o he AO guide s a , AO pe o mance, and he numbe o exposu es pe pixel a e unc- ions o he posi ion in he ield. In pa icula , he inne egions a e deepe han he ou e egions in he inal mosaics because o a la ge numbe o obse ed ames. We di ided he FoV in o 25 squa es o a ound 8.600 ×8.600 size (see Fig. C.1). We selec ed s a s wi h magni udes be ween he KSluminosi y unc ion (KLF) peak and ±0.5 mag o each squa e, which, in mos cases, a e Red Clump (RC) s a s. We in es iga ed he mean SED o he RC s a s wi hin he sub- ields in Appendix C, and disco e ed a ia ions in he expec ed Fig. 3. Mean SED o 29 RC s a s selec ed in he inne egion used as he empla e o local calib a ion. The conside ed s a s a e classi ied la e- ype by Gau am e al. (2019). E o ba s indica ing he s anda d e o s a e also depic ed. SEDs o hese ypes o s a s, especially in he ou e egions, as depic ed in Fig. C.1 (blue poin s). The e o e, we applied a local calib a ion wi h dual pu poses: i s ly, o add ess sys em- a ic e o s associa ed wi h he dis ance o he calib a o s a s and image quali y, as p e iously no ed, and secondly, o co ec o di e en ial ex inc ion. This seconda y calib a ion is di e en om he app oach o Buchholz e al. (2009), bu simila o he me hod used by Plewa (2018). The calib a ion wi hin he cen al egion (i2, j2 in Fig. C.1) exhibi s minimal sensi i i y o sys ema ic e o s and s a is ical unce ain ies because o he la ge numbe o exposu es, close- ness o he AO guide s a and high densi y o calib a ion s a s. We selec ed 29 RC s a s classi ied by Gau am e al. (2019) in his egion and de i ed hei mean SED, which was subsequen ly employed as ou SED empla e o he nex s ep (see Fig. 3). Fo he local calib a ion, we selec ed RC s a s ac oss he FoV by conside ing he s a s wi h magni udes in he IB224 band be ween he peak o he KLF (a ound 15.6 mag) and ±0.5 mag. We excluded s a s wi h signi ican pho ome ic e o s exceeding 0.5 magni udes. The o al numbe o selec ed RC s a s is 2742. Fo each s a in ou lis , we hen c ea ed a mean SED om he 20 closes RC s a s and de e mined he co ec ion o each il e om he di e ences be ween he local RC SED and he em- pla e c ea ed om he RC s a s in he cen al egion. Finally, he A190, page 4 o 34 Gallego-Cano, E., e al.: A&A, 689, A190 (2024) Fig. 4. SEDs o ou spec oscopically classi ied s a s. The op panel displays b igh s a s, and he bo om panel shows ain s a s, wi h ea ly- ype s a s on he le and la e- ype s a s on he igh . The blue lines deno e he linea i o he i s ou da a poin s, while he o ange lines ep esen he exponen ial i o all se en da a poin s. The g ey shadows indica e he unce ain ies o he exponen ial i s, as ob ained om Mon e Ca lo simula ions. The panels include no a ions o he CBDs o he s a s. magni ude co ec ions we e applied o each o he co esponding IB magni udes o he s a . This local calib a ion p ocedu e also co ec s o di e en ial ex inc ion. In Fig. C.1, we compa e he mean SED o RC s a s in he sub- ields along he FoV. The blue poin s ep esen he SED a e he basic calib a ion, while he ed poin s depic he SED a e applying he local calib a ion. The o me is shi ed o achie e o e lap. The local calib a ion p ocess enables us o ob ain he inal lis o s a s co ec ed o di e en ial ex inc ion while homogenizing he calib a ion qual- i y ac oss he en i e FoV o di e en bands. 3.4. CO band La e- ype s a s display a cha ac e is ic CO band head abso p- ion a wa eleng hs λ > 2.27 µm (see he igh panel in Fig. 2). By examining he obse ed and calib a ed SEDs o his ea- u e, we can ca ego ize s a s as la e- ype candida es (spec al ypes ∼GKM) when i is obse ed, o as ea ly- ype candida es (spec al ypes ∼OB) when i is absen . The i s ou IB il e s (λ=2.00−2.27 µm) a e used o es ima e he con inuum. To measu e he CO band dep h (CBD), we employed wo di e en SED i ing me hods. The i s me hod was simila o Buchholz e al. (2009), bu we i ed a s aigh line o he i s ou da a poin s (λ=2.00−2.27 µm) ins ead o an ex inguished black body, as hey did. We also es ed he la e me hod bu ound a s aigh -line i o be mo e obus and o esul in mo e eli- able unce ain ies, in pa icula o ain s a s. Subsequen ly, we applied a hi d-o de polynomial o he en i e SED, eplacing he i s ou da a poin s wi h he i ed s aigh line o ensu e a con- sis en i . In he second me hod, we simila ly i ed a s aigh line o he i s ou da a poin s, ollowed by an exponen ial unc ion ep esen ed by he equa ion: (x)=a+b·x+10−0.4·c·ex·d,(1) whe e a,b,c, and da e he model pa ame e s. We used he expo- nen ial unc ion in wo s eps. Fi s , we applied an exponen ial i o he s a s. Then, in he second s ep, we pe o med ano he i , se ing he dpa ame e o he median alue o 10.33 ob ained in he i s s ep o classi ied la e- ype s a s. This was done o p e en con e gence issues, especially o s a s wi h signi ican unce ain ies. Finally, we compu ed he CBD alues o bo h me hods by sub ac ing he ex apola ed alues o he linea i a λ= 2.36 µm om he ex apola ed alues o he exponen ial i , and he polynomial i , espec i ely, a he same wa eleng h. Figu e 4 A190, page 5 o 34 Gallego-Cano, E., e al.: A&A, 689, A190 (2024) Fig. 5. CBD diag am o he en i e sample. The median e o s o he CBD o bins o 0.5 mag a e ep esen ed by g ey ba s on he le side o he panel. The spec oscopically classi ied s a s a e ma ked by blue (ea ly- ype) and ed (la e- ype) poin s. shows he SEDs and hei co esponding i s by using he expo- nen ial i o ou s a s classi ied spec oscopically as ea ly (le panel) and la e ( igh panel), espec i ely. The igu e includes he i s o b igh s a s ( op panel), and o ain s a s (bo om panel). The CBD alues a e indica ed in he panels. We employed a Py hon-based1p ocedu e using he cu e_ i ool p o ided by he SciPy2package, u ilizing non- linea leas squa es o ob ain op imal pa ame e alues in bo h cases and including he pho ome ic unce ain ies in he i . In Appendix D, we compa e bo h me hods, demons a ing ha while he i s a e e y simila o mos s a s, signi ican di e - ences eme ge in cases whe e he SED exhibi s no able i egula - i ies (see Appendix D o de ailed insigh s). The esul s ob ained using exponen ial i s a e mo e consis en , leading us o conside he CBD alues de i ed om his me hod. Figu e 5illus a es he compu ed CBD alues o he en i e sample. On he y-axis, we depic he IB224 magni ude. We selec ed his speci ic band o cons uc he diag am due o i s cen al posi ion wi hin he SED and i s independence om he in luence o CO band dep h. Fu he mo e, he da a in his band exhibi high quali y, wi h ewe emission lines compa ed o he IB206-band, which co esponds o he da a wi h he highes quali y. In he le panel, ypical e o s o CBD alues in bins o 0.5 magni udes a e displayed. The e o s a e adjus ed as we explain in de ail in Appendix A.3. We s udied he a ia ion o he CBD diag ams ac oss he FoV. Figu e 6displays he CBD alues wi hin he di e en sub- cubes in o which we p e iously di ided he FoV, as desc ibed in Sec ion 3.3.2. We can obse e ha in he egions close o he cen e, a b anch o b igh young s a s (small alue o CBD) is mo e p ominen compa ed o he ou e egions as we expec ed. 1Py hon So wa e Founda ion. Py hon Language Re e ence, e sion 3.9. A ailable a h p://www.py hon.o g 2h ps://scipy.o g/ 3.5. C oss ma ching wi h spec oscopic s udies We conduc ed a comp ehensi e compa ison wi h se e al wo ks om he li e a u e. The ollowing s udies we e included in ou analysis: Do e al. (2013,2015), Feldmeie e al. (2014), Feldmeie -K ause e al. (2015,2017b,2020), on Fellenbe g e al. (2022), F i z e al. (2016), Gillessen e al. (2009,2017), Habibi e al. (2019), S øs ad e al. (2015), Yelda e al. (2014). We excluded Feldmeie e al. (2014) om ou analysis due o i s low spa ial esolu ion, which posed challenges when a emp ing o ma ch i wi h ou high- esolu ion da a. Mo eo e , all he s a s men ioned in Feldmeie e al. (2014) we e accoun ed o ei he in Feldmeie -K ause e al. (2015,2017b). We exclusi ely conside ed s a s wi h posi ions no based on o bi al in o ma ion. Hence, ou inpu ca alogs do no include he s a s S175 (ea ly), and S145 (la e) (Gillessen e al. 2017; on Fellenbe g e al. 2022). The p ima y sou ce o posi ion da a in he cen al MPE da ase is gene ally Gillessen e al. (2009) because i p o ides mo e polynomial i s o posi ion agains ime and o e s he ad an age o an ea ly ze o poin . This is pa icu- la ly use ul since ou da a was acqui ed in 2004. We ob ained he posi ion o S2 in 2004 using Fig. 13 om Gillessen e al. (2009). Fo he emaining s a s, we employed a polynomial i o de e - mine hei posi ion in 2004.5. Howe e , we upda ed he s a ypes using he ype ables om Gillessen e al. (2017) and Habibi e al. (2019) o ensu e he mos cu en in o ma ion. All s a s om F i z e al. (2016) wi h adial eloci ies a e conside ed la e ype. We conside ed ma ches as s a s coinciding wi hin 0.100 in posi ion and 0.76 mag in b igh ness (a ac o o 2 in lux). In cases o ambigui y, we selec ed he nea es neighbou , co ec ing o any sys ema ic o se s be ween he used ca alogues and ou da a using median o se s and an i e a i e p ocedu e. We compa ed he classi ica ions ob ained using his me hod. We obse ed occasional disc epancies in classi ica ions om F i z e al. (2016), likely due o hei ully au oma ed p ocedu e. Consequen ly, we excluded s a s classi ied solely as la e- ype in F i z e al. (2016), excep hose used in P uhl e al. (2011), as he la e unde wen igo ous analysis, ensu ing hei la e- ype classi- ica ionce ain y.The esul ingma chedlis s illincludes i es a s wi h con lic ing spec al ypes om di e en sou ces. We classi- ied hese s a s using he CBD diag am, whe e hey a e clea ly dis inguishable and exhibi magni udes b igh e han 14. In all bu one con lic ing case, hey we e classi ied as ea ly- ype s a s. As a inal s ep, we compa ed he spec oscopic classi ica- ions wi h ou s used in Sec ion 3.3, which led o he inclusion o a ew mo e s a s bu also e ealed some disc epancies. We e- examined he ea ly and la e s a s om Feldmeie -K ause e al. (2017b), which ha e been assigned o di e en ca alogue s a s using di e en me hods. The co ec ma ch was always iden i- iable o ea ly- ype s a s. Howe e , o la e- ype s a s, in some cases, he Feldmeie -K ause e al. (2017b) classi ica ion likely esul ed om wo simila b igh s a s me ging in he seeing- limi ed spec um. In hese cases, nei he s a was de ini i ely assigned a ce ain ype, and hey a e excluded om bo h he ea ly and la e samples in he ollowing sec ions. Fu he de ails on in e es ing s a s can be ound in Appendix E. Figu e 5shows he CBD diag am o all spec oscopically classi ied s a s: 982 la e- ype s a s ( ed poin s) and 212 ea ly- ype s a s (blue poin s). We explo ed also some in e es ing s a s in Appendix E. 3.6. Iden i ica ion o o eg ound and backg ound s a s Be o e applying he classi ica ion me hods, we elimina ed o e- g ound and backg ound s a s om ou inal lis . Ou me hod A190, page 6 o 34 Gallego-Cano, E., e al.: A&A, 689, A190 (2024) Fig. 6. CBD diag ams along he FoV. The size o each sub- ield is a ound 8.600 ×8.600 size. The panels co esponding o he di e en sub- ields o e lay he speci ic sub- ield in he backg ound image, co esponding o he epoch on June 12, 2004. o de ec ing o eg ound and backg ound s a s is based on he me hodology ou lined by Buchholz e al. (2009), wi h se e al e inemen s. Speci ically, we employed he H-IB224 colou o ex inc ion de e mina ion. To calib a e, we adop ed he ex inc- ion alues de e mined by Buchholz e al. (2009), adjus ed o he scale o he new ex inc ion law (Schödel e al. 2010;F i z e al. 2011) using a scaling ac o o 0.84. In addi ion o he H- IB224 colou , we inco po a ed he CBD alue as he second pa ame e o accoun o he changing empe a u e in a lin- ea way, complemen ing he in o ma ion p o ided by he H- IB224 colou in ou analysis. Fo s a s lacking an H-band mea- su emen , pa icula ly p e alen a he lowe end ou side he H-band image co e age, we used he linea i slope mand ecalib a ed using he same me hodology. The lowe H-IB224 colou cu o excluding o eg ound s a s is se a 1.68, align- ing wi h he alue used by Buchholz e al. (2009) and ans- la ed in o ou ex inc ion sys em. Op ing o a mo e inclusi e cu esul s in a no iceable concen a ion o o eg ound s a s, a phe- nomenon no an icipa ed, and his adjus men does no con ibu e addi ional ea ly- ype s a s o he o eg ound classi ica ion. By analogy, we designa ed s a s wi h a colou g ea e han 4.2 as backg ound. Addi ionally, we included s a 5251 (IRS34) in he backg ound ca ego y, as i dis inc ly aligns wi h he ed popula- ion o b igh s a s. This esul s in a o al o 37 o eg ound and 22 backg ound s a s, p edominan ly excluded om subsequen analyses. A190, page 7 o 34 Gallego-Cano, E., e al.: A&A, 689, A190 (2024) Fig. 7. CBD his og ams o he excess o s a s, wi h CBD <2σ(le excess), and wi h CBD >2σ( igh excess). We excluded o eg ound and backg ound s a s p ima ily due o he magni ude-dependen na u e o he CBD alue. The a y- ing dis ances o hese s a s lead o he conclusion ha a di e en model is mo e sui able o hem han o GC s a s, which a e ou p ima y a ge s. Al hough mos o he b igh s a s (IB224 <12) wi h high ex inc ion a e likely GC membe s, we s ill excluded hem, as e y ew unknown s a s sha e he combina ion o being bo h b igh and ed. Fu he mo e, many o hese b igh and ed s a s a e o known ypes3. Consequen ly, ou inal sample com- p ises 201 ea ly and 980 la e s a s wi h spec al ypes, which a e likely o be GC s a s and exhibi minimal eddening. 3.7. P elimina y classi ica ion In his sec ion, we conduc a p elimina y classi ica ion o he s a s ollowing he me hod o Nishiyama e al. (2023). They used also na ow-band il e s o iden i y po en ial ho , massi e s a s, and in e media e-age s a s in he GC. We selec ed s a s wi h magni ude e o s in IB224 <0.1, and wi h adjus ed CBD e o <0.2. We c ea ed CBD his og ams o s a s wi hin 0.5 mag wide bins in IB224. The majo i y o s a s a all magni udes lie on he Red Gian B anch (RGB). We i - ed each his og am wi h Gaussian unc ions o ex ac he mean magni ude µand he s anda d de ia ion σo he RGB CBD al- ues in each bin. Fo IB224 <15 mag, we conside ed he s a s wi h a CBD alue o 0.15 o be cen ed on he RGB. Subse- quen ly, we compu ed he excesses o s a s wi h CBD <2σ(le excess) and wi h CBD >2σ( igh excess) in each magni ude bin. Figu e 7shows ha he e is a clea excess o s a s wi h low CBD alues o magni udes b igh e han 15. In ou inal classi ica ion, we conside ed bins whe e he le excess coun was mo e han double he igh excess coun . This ensu ed a p obabili y o o e 50% o s a s in hese bins o be classi ied as ea ly- ype. We iden- i ied 248 s a s wi h a likelihood exceeding 50% o being ea ly- ype, 93 o which a e new candida es. Addi ionally, 133 ha e been spec oscopically con i med as ea ly- ype s a s, while 22 3Excep ou Id 1573, which is iden i ied as a la e Mi a (Feldmeie -K ause e al. 2017b), and IRS2L, o which a speci ic ype could no be de e mined despi e he a ailabili y o nume ous spec a, as discussed in Feldmeie -K ause e al. (2015), he majo i y o he s a s a e ea ly ypes. Fig. 8. CBD diag am o he sample. The g een ho izon al ba s ep e- sen ±2σ, whe e σs ands o he s anda d de ia ion o CBD wi hin each magni ude bin. S a s wi h CBD alues below 2σa e ca ego ized as young candida es and deno ed by blue da a poin s in he diag am. Limi ing he sample o s a s b igh e han 15 mag, and ocusing solely on he new candida es no p e iously spec oscopically iden i ied, ea ly- ype candida es a e ep esen ed by g ey ci cles. a e misclassi ied due o hei spec oscopic iden i ica ion as la e- ype s a s. Figu e 8shows in blue poin s all s a s co esponding o he le excess wi h magni udes <15. New ea ly candida es a e ep esen ed by g ey ci cles in he diag am. When compa ing he esul o his simple classi ica ion wi h he sample o spec oscopically classi ied s a s wi h IB224 <15, we ind ha we ha e success ully iden i ied 82.1% o he known ea ly- ype s a s and 96.5% o he la e- ype s a s. Al hough his p elimina y classi ica ion is a good i s s ep, i does no p o ide he p obabili ies which a e use ul o explo a o y analysis. In he nex sec ions, we explo e h ee classi ica ion me hods o p o ide p obabili ies o being ea ly- ype o he lis o s a s. 4. Bayesian in e ence A e he ini ial app oxima e classi ica ion, we employed a mo e e ined Bayesian analysis. We i ed models o he wo b anches in he CBD diag am (CBDD) co esponding o la e and ea ly- ype s a s (see Fig. 9). Subsequen ly, we in e ed he p obabil- i ies o each s a belonging o ei he he ea ly- ype o la e- ype b anch. Th oughou he ollowing sec ions, we e e o he pa s o he CBDD ha p edominan ly con ain ea ly o la e- ype s a s as he ‘ea ly- ype b anch’ and ‘la e- ype b anch’, espec i ely. The p io is de e mined by he ini ially es ima ed densi y o spec- oscopically classi ied GC s a s in he espec i e b anches. In he ini ial s ep, we conduc ed a sepa a e analysis o he p ope ies o known la e and ea ly- ype s a s. This sepa- a ion was essen ial due o signi ican di e ences in he a ail- able li e a u e da a o ea ly and la e s a s in he GC. The da a we e acqui ed using di e se ins umen s, obse a ional me h- ods, se ups, and analysis echniques. We i ed sepa a e models o he wo b anches. The esul s ob ained om hese wo models A190, page 8 o 34 Gallego-Cano, E., e al.: A&A, 689, A190 (2024) Fig. 9. Bayesian s uden - i o ea ly- ype s a s and a wo-componen model i o la e- ype s a s. The la e includes sub-models o s a s b igh e and ain e han 14 mag, using a wo-componen no mal model wi h a quad a ic mean equa ion and a s uden - model wi h a linea mean equa ion, espec i ely. The le side o he igu e displays median e o s o all s a s in cons an bins (0.65 mag), wi h lines ep esen ing he mean and 1-σ ange o he models. enabled us o assess he p obabili y ha a s a is o he ea ly- ype ca ego y based on obse ed pa ame e s such as IB224 magni- ude, CBD and i s unce ain y. The second s ep in ou me hodology in ol ed e ining he p io p obabili y dis ibu ion. In he i s s ep, we conside ed a la o uni o m p io p obabili y dis ibu ion wi h a alue o 0.5. Howe e , ecognizing he limi a ions o a la p io , we adop ed an i e a i e app oach o enhance i s accu acy. This e inemen was achie ed h ough a unc ion ha conside ed bo h IB224 magni ude and he dis ance om Sg A*. 4.1. Likelihood i s We used he PyMC34package o i models o he ea ly and la e- ype b anches in he CBDD sepa a ely. We assumed a no mal dis ibu ion o he unce ain ies as ou baseline. We ea ed he s anda d de ia ion o he da a poin s ela i e o he model as a ee pa ame e , which was added in quad a u e o he CBD e o s. This was necessa y because he CBD unce ain ies alone we e insu icien o accoun o he sp ead obse ed in he CBD alues. We ound ha a second-o de polynomial unc ion o magni- ude led o he bes esul s o i he ea ly5and la e- ype b anches. We sub ac ed he alue o 14 om all magni udes o educe he co ela ions be ween he di e en polynomial pa ame e s. Ou base model is he no mal dis ibu ion, bu we equen ly expanded i by inco po a ing addi ional pa ame e s o accommo- da e de ia ions. We employed wo dis inc a ian s: – S uden - Dis ibu ion: This symme ic dis ibu ion has a e ails han he no mal dis ibu ion, which can be use ul when a da a se has a s onge ku osis han he la e . – An addi ional componen wi h a cons an o se . This op ion is p ima ily aluable o dis ibu ions wi h signi ican skew- ness and equi es wo addi ional pa ame e s. 4h ps://www.pymc.io/ 5Fo he ea ly- ype b anches, he signi icance o he quad a ic e m is no always subs an ial; in some cases, he bes i is close o linea . We e ained he quad a ic e m o main ain consis ency in he model s uc u e. In p ac ice, he impac o he quad a ic e m can be minimal. We employed wide p io s when i ing he model pa ame e s, ensu ing ha hei impac on he ele an esul s emained neg- ligible6. A e he ini ial i wi h he no mal model, we u ilized he bes - i pa ame e s o no malize he CBD alues. Subsequen ly, we calcula ed he ku osis and skewness o he dis ibu ion. Bo h had alues o en exceeding 2.5 and, in many cases, e en 5 o mo e, especially in he case o he ku osis o he la e b anch. In e ms o sign, he ku osis was consis en ly posi i e, as expec ed when ou lie s play a signi ican ole. The skewness ypically showed a posi i e di ec ion o ea ly- ype s a s and a nega i e one o la e- ype s a s. Subsequen ly, we p edominan ly employed a S uden - dis- ibu ion o bo h ea ly- ype and la e- ype s a s. The choice o la e- ype s a s was e iden due o he highly signi ican ku o- sis, while o ea ly- ype s a s, he signi icance o skewness was app oxima ely 1 sigma la ge . Howe e , a emp s o add ess his by using an asymme ic dis ibu ion o ea ly- ype s a s esul ed in implausible ea ly-s a candida es wi hin he CBD diag am. Consequen ly, we op ed o a S uden - dis ibu ion o ea ly- ype s a s as well. This choice is jus i ied by he absence o a clea mechanism causing asymme y in he ea ly CBD diag am, while a S uden - dis ibu ion can accoun o unde es ima ed e o s in ce ain s a s. While we explo ed al e na i e dis ibu- ions o ea ly- ype s a s, ou indings indica e ha he speci ic choice o model o ea ly- ype s a s did no signi ican ly impac he esul s. In con as , he model selec ion o la e- ype s a s is mo e c ucial, as he in luence o he la e model becomes mo e p onounced in he wings o he dis ibu ion, gi en he la ge numbe o la e- ype s a s. We u he in es iga ed he possibili y o employing wo S uden - dis ibu ions o la e- ype s a s, conside ing he impac o la e- ype s a s wi h a wa me han a e age e ec i e empe - a u e (P uhl e al. 2011;Do e al. 2015;Feldmeie -K ause e al. 2017b). We iden i ied a second componen shi ed by 0.2 mag owa ds edde CBD alues, sugges ing he p esence o low me allici y s a s (see Sec ion 7). This componen co esponds o 4.4+1.9 −1.4% o all la e- ype s a s, consis en wi h he li e a u e. P uhl e al. (2011) epo ed a ac ion o 10%, while Do e al. (2015) and Feldmeie -K ause e al. (2017b) epo ed ac ions o 6% and 5.2%, espec i ely. F om he da a, i is appa en ha we unde es ima e he second componen . This sugges s ha he sec- ond componen canno be a ibu ed o he RC due o i s dis- inc cha ac e is ics. In esponse, we explo ed models ha di ide he la e s a s by magni ude a 14, in oducing a second compo- nen only o he b igh e po ion. Consequen ly, ou p ima y model inco po a ed a wo-componen no mal dis ibu ion wi h a quad a ic mean model o s a s b igh e han 14 mag and a s uden - dis ibu ion wi h a linea mean model o ain e s a s. This esul s in a wa m s a ac ion o 8.9+5.6 −3.5% consis en wi h he li e a u e. Figu e 9show he bes i s. 4.2. I e a ion on p io s In he second s ep, we e ined he p io . Wi hou addi ional in o - ma ion, he p io would assume equal p obabili y o ea ly and la e, which leads o an o e es ima ion o ea ly- ype s a s in con as o he eal si ua ion a he GC, whe e he e a e mo e 6The excep ion is when he cu e co esponding o he model o he ea ly b anch c osses he cu e om he model co esponding o he la e b anch. In such cases, we used he CBD alue and unce ain y a he ain end o la e as a p io o he CBD alue o he la e- ype i in ha egion. A190, page 9 o 34 Gallego-Cano, E., e al.: A&A, 689, A190 (2024) Table 7. Summed ea ly p obabili ies o ma ched s a s wi h Plewa (2018). Me hod m<14.5 & R<1100 m>14.5 & R<1100 m<14.5 & R>1100 m>14.5 & R>1100 Plewa 162.1 139.1 116.3 141.9 MLP 188.2 84.3 56.9 54.2 XGBoos 175.1 75.0 43.4 35.2 Bayesian 199.6 71.7 44.0 23.1 Table 8. Summed ea ly p obabili ies o ma ched s a s wi h Buchholz e al. (2009). Me hod m<14.5 & R<1100 m>14.5 & R<1100 m<14.5 & R>1100 m>14.5 & R>1100 Buchholz 141.8 99.6 33.5 13.0 MLP 155.5 102.6 36.4 42.7 XGBoos 144.7 88.5 28.1 24.5 Bayesian 166.5 90.6 29.1 18.8 No es. We use a p obabili y o 1.0 o E1, 0.98 o E2 and 0.8 o E3 o hei classes aligning a hei σde ini ions o he classes. Since mos a e E1 he p ecise alues a e no so impo an . only he ea ly s a s om Pauma d e al. (2006), which included e y ew ain e ea ly s a s, making ex apola ion mo e impo - an in his analysis. We belie e ha he main eason o hese di e ences lies in he way he da a we e educed and analysed. We ha e se se ious emphasis on ca e ul pho ome y wi h obus unce ain y es ima ion as well as on explo ing di e en ways o analysing he da a. Buchholz e al. (2009) iden i y 312 new ea ly- ype candi- da es in addi ion o he 90 ea ly- ype s a s ha we e spec o- scopically iden i ied a he ime. We success ully ma ched 3908 o hei 5914 s a s wi h ou ca alogue, including 280 o hei ea ly- ype classi ica ions. We c oss-checked hei classi ica ions wi h ou compila ion o spec oscopic da a. 19 o hei ea ly- ype candida es a e spec oscopically classi ied as la e- ype, 139 as ea ly- ype. As o hei 124 candida es wi hou a spec oscopic ma ch, he majo i y is no ea ly acco ding o ou p obabili ies, wi h 59% in he case o ou Bayesian me hod. This indica es be e pe o mance compa ed o Plewa (2018), aligning mo e closely wi h ou indings. Tha is also con i med when compa - ing he o al numbe o ea ly s a s, as shown in Table 8. In mos bins, he Buchholz e al. (2009) sum is be ween ou 3 a ian s, excep o ain s a s u he ou – he mos challenging egion wi h he ewes s a s. I is also possible ha some o ou ea ly p obabili ies a e unclassi ied by hei wo k. Thus, his ime, he main con ibu ing ac o is andom di e ences in he CBD al- ues. Simila o he case in Plewa (2018), he ag eemen is min- imal o mos RC s a s and some b igh e s a s loca ed beyond app oxima ely 1200. The inc eased dep h also esul s in ag ee- men o some s a s ain e han he RC wi hin abou 700 7.2. K-band luminosi y unc ion We de e mine a slope pa ame e o he KLF o la e- ype s a s, ob aining a alue o 0.25. This pa ame e exhibi s only mino a ia ions ac oss di e en classi ica ion me hods and adial anges. Compa ed wi h p e ious s udies, Buchholz e al. (2009) epo ed a s eepe slope o 0.31 ±0.01 using s a s up o m= 14.5 mag, while Plewa (2018) ob ained a s eepe slope o 0.36 using s a s up o 14.5 mag. The di e ences in slopes can be a ibu ed o comple eness co ec ions o he b oade magni ude ange conside ed in he cu en s udy. No ably, in he case o Plewa (2018), hei RC is a he ain , which means ha he b igh end ail ma e s mo e o hei i , likely con ibu ing o he obse ed s eep slope. Tha obse a ion is suppo ed by he s eepe slope, anging om 0.29 o 0.32, ob ained when exclud- ing s a s wi hin he RC o hose wi h ain e magni udes. Fo ea ly- ype s a s, we obse e a shallowe slope com- pa ed o la e- ype s a s, wi h a calcula ed alue o 0.18 using he Bayesian me hod. The ob ained alues o he inne egion (R<900) and he en i e ange a e e y consis en ac oss he h ee me hods. Howe e , a ia ions become mo e appa en o la ge dis ances, whe e he MLP me hod yields a s eepe slope. The di e ence in he KLF be ween he egion o he clockwise o a - ing disc o young s a s (0.800 <R<1200) and he ou e a ea was also iden i ied by Ba ko e al. (2010), wi h a la e p o- ile in he disk egion. Buchholz e al. (2009) epo a slope o 0.13 ±0.02 o he cen al 700 and 0.14 o e all, la e han wha we ind he e. A possible explana ion o his di e ence could be he limi o m=15.5 mag used by Buchholz e al. (2009), while we i ain e s a s as we explained p e iously. Ou KLF inside o R=900 looks somewha la e o b igh s a s and s eepe o ain e s a s, which may explain some o he di e ence. In ou analysis, he KLFs o ea ly- ype s a s show a consis en inc ease wi h magni ude, lacking e idence o he maximum a mK∼13 epo ed by Ba ko e al. (2010) be ween 0.8 and 12 a csec. 7.3. Densi y p o iles o he s a s Ou esul s shown in Table 6ag ee wi h o he wo k, includ- ing Buchholz e al. (2009), Ba ko e al. (2010), Plewa (2018), and Do e al. (2009). We obse e a e y shallow, nea ly cons an inne p o ile o la e- ype s a s and a s eepe one u he ou . The ea ly ype s a s show a b oken powe law, oo, bu hei densi y inc eases s eeply owa ds Sg A* a all dis ances (see Fig. 16). Quan i a i ely, he slopes epo ed by Buchholz e al. (2009) o ea ly- ype s a s a e 1.08 ±0.12 be ween 100 and 1000, and 3.46 ±0.58 be ween 1000 and 2000. Howe e , di e ences become mo e appa en o ou e ea ly- ype s a s a la ge p ojec ed dis- ances. Ou MLP classi ica ion me hod – and o a lesse deg ee XGBoos – inds ha he numbe densi y o ea ly- ype s a s may inc ease again a R&2000. This e y in e es ing possibil- i y should be ollowed up wi h pho ome ic and spec oscopic wo k. A190, page 16 o 34 Gallego-Cano, E., e al.: A&A, 689, A190 (2024) Fig. 18. Rela ionship be ween he CBD alue and spec oscopic e ec i e empe a u e o la e s a s using da a om Do e al. (2015) and Feldmeie -K ause e al. (2017b). Linea ela ionships we e i ed wi hin magni ude bins, wi h esul s depic ed by he lines. The bins o he i s we e ca ego ized as ollows: [M/H] <−0.5 dex (blue), −0.5<[M/H] <0, 0 <[M/H] <0.25, 0.25 <[M/H] <0.5, 0.5 <[M/H] <0.75, and [M/H] >0.75 ( ed). The colou o he lines indica es he espec i e mean me allici y. 7.4. Tempe a u e and me allici y o la e- ype s a s Bo h empe a u e and me allici y will a ec he s eng h o he CO bandhead abso p ion. This aises he possibili y o applying IB pho ome y o measu e hese s ella p ope ies. We began ou analysis by examining he e ec i e empe a- u e o la e- ype s a s, which is mo e di ec ly ela ed o he CBD han me allici y. Ou analysis encompasses wo p ima y objec i es: i s ly, o explo e he isibili y and signi icance o wa me - han-a e age la e- ype s a s on he classi ica ion p obabili ies, and secondly, o explo e he use o CBD and CBDD o es ima ing empe a u es and me allici ies. We excluded s a s wi h a me allici y [M/H] <−2, which we do no conside eliable. Ou analysis o 25 s a s wi h da a om bo h wo ks e ealed no signi ican empe a u e o se be ween hem. In o al, we analyzed 394 s a s, 51 om Do e al. (2015) and he majo i y (318 s a s) om Feldmeie -K ause e al. (2017b). When plo ing he empe a u es agains CBD (Fig. 18) we ound a linea ela ionship. This allows us o connec hese wo pa ame e s ia he ollowing ela ionship: Te =(4157 ±44) +(−1109 ±101) ·CBD,(6) simila o he indings in Feldmeie -K ause e al. (2017b). Unlike P uhl e al. (2011), we ound ha highe -o de pa ame- e s a e unnecessa y. Howe e , i is impo an o no e ha ou da ase co e s a na owe empe a u e ange and uses a di e en CBD de ini ion han hei wo k. When we spli he sample by me allici y, no iceable di - e ences become isible, as depic ed in Fig. 18. Be ween [M/H] =0.75 and 0 dex, he i s exhibi a high deg ee o simi- la i y12. The CBD alues a e shi ed o lowe alues o lowe me allici ies. This is plausible, as ewe me als should esul in less p onounced spec al lines. Hence, he da a indica e ha he mean CBD dec eases as a unc ion o me allici y. 12 The disc epancy in he i o [M/H] >0.75 may be a ibu ed o he lowe eliabili y o he spec oscopic and CBD da a o hese highly me al- ich s a s, possibly due o he highe abundance o AGB s a s in ha ange. The dependency o CO dep h on me allici y is also obse ed in he mo e na owly de ined spec oscopic CO index (see F i z e al. 2021). In ou case, he dependence is mo e in lu- enced by con inuum ex apola ion because we measu e he dep h a 2.36 µm. The dependency on me allici y sugges s ha he wo-pa ame e con e sion o e ec i e empe a u e o CBD (Equa ion (6)) is o e ly simplis ic, necessi a ing addi ional pa ame e s. We used ollowing equa ion which uses also as [M/H] and [M/H] squa ed o con e Te o ou CBD: CBD =1.08167498 −0.00018242 ·Te +0.07098599 ·[M/H] −0.05281159 ·[M/H]2.(7) The inclusion o [M/H] squa ed accoun s o sa u a ion e ec s a high me allici y le els. Nex , we used he ob ained ela ionship in Equa ion (7) o look in o he me allici y. F om he same 25 s a s wi h me allici y as be o e, we ound a consis en o se o 0.34 dex be ween he me allici ies es ima ed by Do e al. (2015) and Feldmeie -K ause e al. (2017b). To align bo h da ase s on he same s a s, we adjus ed by adding o sub ac ing hal o his o - se . We p esen he spec oscopically es ima ed me allici ies in he CBDD shown in he op panel o Fig. 19 and o e plo - ed 12 Gy 13 isoch ones om B essan e al. (2012), Chen e al. (2015), Ma igo e al. (2017). We ocus only on he gian b anch, which is he leas popula ed egion o ou CBDD. The majo i y o s a s ha e a me allici y [M/H] ≈0.70 dex. We exclude s a s ain e han 14.7 mag, because hose s a s a e in hei majo i y RC s a s, which a e mo e challenging o model. We ansla e hei spec oscopically es ima ed e ec i e empe a u es (Te ) in o CBD alues using Equa ion (7). As becomes appa en om he op panel o Fig. 19 a combina ion o he CBD wi h magni udes o e s a p omising app oach o es ima ing me allici ies. We used isoch ones in s eps o 0.05 dex o es ima e me allici ies by iden i ying he clos- es neighbou on he CBDD. This esul ed in a p edic ed [M/H] ange o −1.5 o 0.7, which closely aligns wi h he lowes mea- su ed [M/H] o −1.44. Howe e , he di e ence is mo e p o- nounced on he me al- ich side. I emains unce ain whe he he e y me al- ich s a s a e genuine, as highe spec al esolu ion obse a ions (e.g. Rich e al. 2017;Do e al. 2018;Jönsson e al. 2020;Tho sb o e al. 2020) do no de ec hem. I is e iden ha he esul s a e less p ecise on he me al- ich side due o he close spacing o isoch ones. Subsequen ly, we applied his echnique o es ima e he me allici ies o s a s lacking spec oscopic da a. We omi ed s a s iden i ied spec oscopically explici ly as ea ly- ype, bu e ained all ea ly- ype candida es. Addi ionally, we excluded s a s b igh e han 0.5 mag han he op o he isoch ones because hese could be AGB s a s o may ha e un eliable pho ome y. We hus p edic he me allici ies o 700 s a s. Among hem, 120 a e classi ied as me al-poo wi h [M/H] <−0.5, wi h app ox- ima ely hal o hem iden i ied as p e e able ea ly. When exclud- ing p e e able ea ly s a s, as iden i ied h ough he Bayesian me hod, 58 me al-poo s a s emain. Fu he exclusion o p e e - ably ea ly- ype s a s iden i ied h ough any o ou classi ica ion me hods esul s in a sample o 617 s a s. In his la e case, 6.3% o he likely la e- ype s a s a e classi ied as me al-poo . The ac ion o low-me allici y s a s de e mined om ou pho ome ic da a aligns wi h spec oscopic assessmen s sug- ges ing ha wa m,low-me allici y s a s comp ise up o 10% o 13 Due o he weak dependence o he gian b anch on age, he p ecise age used in his analysis is no c ucial. A190, page 17 o 34 Gallego-Cano, E., e al.: A&A, 689, A190 (2024) Fig. 19. Me allici y es ima ion analysis. The op panel illus a es he CBDD o la e s a s wi h spec oscopic me allici y om Do e al. (2015) and Feldmeie -K ause e al. (2017b). We used 12 Gy Gian b anch isoch ones wi h di e en me allici ies om B essan e al. (2012), Chen e al. (2015), Ma igo e al. (2017) o con e Te in o CBD al- ues. The bo om panel shows he CBDD diag am o s a s lacking spec- oscopic me allici ies and no classi ied as spec oscopic ea ly. Me al- lici ies a e assigned using hese isoch ones. Bo h plo s u ilize he same colou scale and a e es ic ed o s a s b igh e han 14.7, as his is whe e he p esence o he RC, no included in ou model, becomes signi ican . S a s enci cled in g ey ep esen hose classi ied as likely ea ly by he Bayesian me hod. he o al popula ion, as epo ed in s udies such as P uhl e al. (2011), Do e al. (2015), Feldmeie -K ause e al. (2017b). While ou es ima e is in line wi h hese indings, i emains unce ain due o he po en ial inclusion o ea ly- ype s a s in ou sample, as well as he likelihood o o e looking low-me allici y la e- ype s a s, which may be misclassi ied as ea ly- ype due o weake CO band heads, see also Appendix K. Add essing bo h ac- o s comp ehensi ely would necessi a e modelling he spa ial and magni ude dis ibu ions o all h ee classes (la e me al- ich, la e me al-poo , ea ly), a ask ha alls beyond he scope o his pape . 7.5. IMF o ea ly- ype s a s To in e he IMF o he young clus e o med wi h he ea ly- ype candida es b igh e han 16 mag and loca ed wi hin a dis ance smalle han he compu ed b eak adius o 900, we employed an Fig. 20. Compa ison be ween di e en models simula ed wi h SPISEA and he obse ed KLF o he di e en me hods summing up p obabili- ies and co ec ed by comple eness (see Sec ion 6.2). The ed line ep- esen s he KLF co esponding o a simula ed clus e wi h he op imal powe -law IMF, ea u ing an IMF slope o −1.6, while he shaded egion indica es he unce ain y in he model. Addi ionally, he KLFs o clus e models compu ed wi h SPISEA using he K oupa IMF (K oupa 2001) and employing a op-hea y IMF (Ba ko e al. 2010) a e p esen ed o compa ison. op imiza ion algo i hm ha compa es obse a ional da a wi h heo e ical simula ions. U ilizing SPISEA (Hosek e al. 2020), we cons uc ed a g id o syn he ic single-age s a clus e s a y- ing in age, clus e mass, ex inc ion, and IMF slope index. To gen- e a e syn he ic pho ome y o each s a , we u ilized he NACO KS il e , assuming a dis ance o 8.25 kpc and a me allici y o [M/H] =0.15. SPISEA allows us o conside mul iplici y in he gene a ed clus e s by cons uc ing a mul iplici y objec (‘mul i- plici y.Mul iplici yUn esol ed’) based on Lu e al. (2013). This con igu a ion ea s s a sys ems as un esol ed, combining all componen s in o a single s a wi hin he clus e . Due o he absence o s a s wi h lowe masses in ou obse ed magni ude anges, he mass limi s o s a s in he simula ed clus e s we e se o 5 M–120 M. We used he MIST (MESA Isoch ones & S ella T acks; Choi e al. 2016) e olu ion model and adop ed he eddening law om Nishiyama e al. (2009). We examined isoch ones spanning a ange o clus e ages om 2 o 8 My and cons uc ed syn he ic KLFs o each combina ion o pa ame e s. Subsequen ly, we compa ed he heo e ical KLFs o he obse ed KLF by compu ing he chi-squa ed s a is ic. Finally, we iden i- ied he pa ame e se ha minimizes he chi-squa ed alue. The op imal i co esponds o a clus e age o 4 My . We u ilized a Mon e Ca lo (MC) app oach o inco po a e he unce ain y a is- ing om he sampling o he IMF in each ealiza ion o a clus e wi h SPISEA. I is impo an o no e ha he choice o he e o- lu ion model can impac he i alues, pa icula ly he in e ed age. The bes powe -law IMF index alue is 1.6±0.1, ob ained o he h ee se s o ea ly- ype candida es using di e en me h- ods. To alida e ou esul s, we also i ed he IMF by limi ing he magni ude ange up o 15. In his analysis, we de e mined ha he IMF slope is app oxima ely 1.7, alling wi hin he expec ed ange and accoun ing o unce ain ies in ou esul s. Figu e 20 illus a es he cons uc ed KLF de i ed om ou ea ly- ype candida es u ilizing di e en me hods. The ed shaded egion indica es bo h he op imal model i and i s associa ed unce ain y. Addi ionally, we p esen clus e models compu ed A190, page 18 o 34 Gallego-Cano, E., e al.: A&A, 689, A190 (2024) wi h SPISEA, employing he IMF slopes de i ed om K oupa (2001) and Ba ko e al. (2010) o compa ison. We also conduc ed an analysis o he IMF o dis ances g ea e han 900. In his scena io, no able di e ences eme ged in he bes - i models ob ained h ough he h ee di e en me h- ods, consis en wi h ou expec a ions ou lined in Sec ion 7.2. The IMF slopes o Bayesian, RF, and MLP me hods we e 1.8, 2.0, and 1.9, espec i ely, sugges ing la ge alues o egions beyond he inne egions. The op imal i co esponds o a clus e age la ge han 5.6 My o he h ee me hods. This dispa i y sugges s dis inc o igins o s a s in he inne and ou e egions, imply- ing di e se mechanisms d i ing s a o ma ion ac oss he NSC. The de ia ions om he s anda d Salpe e /K oupa IMF (slope −2.3) obse ed in he cen al egion sugges unique o ma ion p ocesses, while he po en ial p esence o a s anda d IMF u he ou indica es an e ol ing en i onmen . These indings empha- size he complexi y o s a o ma ion dynamics wi hin he clus e and highligh he in luence o local condi ions on s ella bi h. 8. Conclusions In his pape , we classi y s a s wi hin he cen al pa sec a ound Sg A*, u ilizing NIR IB images ob ained wi h NACO/VLT. While hese da a ha e been p e iously in es iga ed, we e isi hei analysis, imp o ing he educ ion and pho ome ic p o- cesses, leading o enhanced sensi i i y and mo e eliable es i- ma es o pho ome ic unce ain ies compa ed o p io e o s. Addi ionally, we employ h ee dis inc ye complemen a y clas- si ica ion me hods o dis inguishing s a s as ea ly o la e ype: Bayesian in e ence, a basic neu al ne wo k, and a as g adien - boos ed ees algo i hm. Thanks o he in o ma ion om ex en- si e spec oscopic s udies conduc ed o e he pas decade, we expand ou da abase, enhancing he aining da ase o ou mod- els and he eby ob aining mo e obus and con iden esul s. Despi e challenges associa ed wi h s udying his egion, such as ex eme in e s ella ex inc ion and c owding, we iden i y 155 new ea ly s a candida es using Bayesian and MLP me hods. The iden i ied candida es p esen p omising a ge s o upcom- ing spec oscopic obse a ions, which a e c ucial o alida - ing hei classi ica ion and p o iding addi ional suppo o ou esul s. These candida es, while in iguing as po en ial spec o- scopic a ge s, a e no he p ima y ou come o ou p obabilis ic app oaches. Consis en wi h p e ious wo k we ind ha b oken powe laws p o ide adequa e i s o he adial densi y dis ibu ion o he la e and ea ly- ype s a s. Ou in es iga ion e eals a b eak adius o 7.4±1.200 o he la e- ype dis ibu ion and 9.2±0.600 o he ea ly- ype dis ibu ion. The slopes o he la e- ype dis ibu ion a e de e mined o be β=0.46±0.07 (ou side o he b eak adius) and γ=0±0.08, while he ea ly- ype dis ibu ion exhibi s slopes o β=3.65 ±0.47 and γ=0.81 ±0.08. The compa ison wi h spec oscopic empe a u e e eals ha ou CBD p ima ily ollows a linea end wi h empe - a u e, al hough me allici y also plays a signi ican ole o [M/H] <0. When p edic ing me allici ies o o e 600 s a s, we ind ha app oxima ely 6% exhibi me al-poo cha ac e is ics ([M/H] <−0.5), a esul consis en wi h spec oscopic me allici- ies. We ind ha he mass unc ion o he ea ly ype s a s appea s o be op-hea y nea Sg A*, wi h a powe -law slope o 1.6±0.1. Con a y o Ba ko e al. (2010) we ind no peak o he luminos- i y unc ion a ound 14 mag and a signi ican ly s eepe mass unc- ion. This is p obably ela ed o he incomple eness o he ea ly spec oscopic da a a ain magni udes. A la ge p ojec ed dis ances, he bes - i models a y sig- ni ican ly among he me hods, wi h all IMF slopes exceeding 1.6 and possibly in ag eemen wi h a s anda d Salpe e /K oupa IMF. These indings sugges dis inc s a o ma ion mechanisms be ween he inne and ou e egions, wi h de ia ions om he s anda d Salpe e /K oupa IMF indica ing unique p ocesses in he cen al egion and a po en ially e ol ing en i onmen u he ou . The obse ed slope and p o ile o ea ly- ype s a s a e con- sis en wi h he o ma ion o he young s a s nea Sg A* on a gaseous disc (Bonnell & Rice 2008). A la ge dis ances, o he o ma ion mechanisms may ha e been a wo k. We demons a e he e sa ili y o IB pho ome y, which no only aids in iden i ying p omising a ge s o upcoming spec- oscopic obse a ions bu also plays a c ucial ole in alida - ing hei classi ica ion. Mo eo e , IB pho ome y enables he explo a ion o impo an s ella ea u es such as me allici y and empe a u e, p o iding aluable insigh s in o he o ma ion his- o y o he NSC. Consequen ly, he impo ance o IB pho ome y ex ends o he design o IB il e s o elescopes. Da a a ailabili y The ca alog is a ailable a he CDS ia anonymous p o cdsa c.cds.unis a. (130.79.128.5) o ia h ps:// cdsa c.cds.unis a. / iz-bin/ca /J/A+A/689/A190 Acknowledgemen s. This wo k is based on obse a ions made wi h ESO Telescopes a he Pa anal Obse a o y unde p og ams 073.B-0084(A), 073.B-0745(A), 077.B-0014(A). 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We de eloped a dedica ed p ocedu e o compu e he unce ain ies by using he boo s apping me hod (E on 1979; And ae 2010). We applied wo di e en app oaches depending on he epochs. On he one hand, o epochs wi h a la ge (N g ea e han 96 exposu es) numbe o obse ed ames (see in Table 1), we applied he no mal p ocedu e, as is desc ibed in Gallego-Cano e al. (2022). On he o he hand, we de eloped a new noise boo s apping p ocedu e o epochs whe e he numbe o exposu es is eigh . A.1. Boo s apping Fo IB206, IB224, and IB233 epochs, we c ea ed 100 mosaic images using he boo s apping wi h eplacemen me hod. The numbe o ames conside ed in each boo s ap image is equal o he o al numbe o ames obse ed o he epoch. A e - wa ds, we epai ed he sa u a ed s a s as desc ibed in Sec ion 2.2, and de ec ed and sub ac ed he poin sou ces om 100 mosaic images o each epoch ollowing he pho ome ic analysis desc ibed in Sec ion 3.1. We de ined he de ec ion equency pa ame e as he pe cen age o boo s ap deep images whe e each s a is de ec ed and we ob ained a inal lis wi h all he s a s de ec ed in all he images and hei associa ed de ec ion equency alue. We selec ed de ec ion equency=50%, which means ha we conside ed s a s de ec ed in 50% o mo e o he mosaic deep images. Finally, we compu ed unce ain ies om he s anda d de ia ion o he posi ion and lux o each s a . Figu e A.1 shows a compa ison be ween he KLFs o he h ee epochs a e he boo s apping p ocedu e. In Fig. A.2 we show a compa ison be ween he pho ome ic unce ain ies ob ained wi h his me hod and he e o om S a Finde p og am. In he igu e, we can see ha S a Finde ends o unde es ima e unce ain ies, whe eas ou app oach enables us o ob ain eliable unce ain y es ima es wi hou comp omising sensi i i y. Fig. A.1. KLFs o he inal boo s apping mosaics. The di e en colou s co espond o he di e en bands. A.2. Boo s apping wi h noise Fo IB200, IB227, IB230, and IB236 epochs, we canno apply he p e ious me hod because he numbe o ames is no la ge enough. The e o e, we c ea ed 100 mosaic images by combin- ing andom noise a ibu ed o bo h he pho on noise om he signal and he ead noise om he de ec o . In he i s place, o assess he alidi y o he app oach, we applied o IB224 whose unce ain ies we e compu ed using he no mal p ocedu e and compa ed he esul s. Figu e A.4 shows a compa ison be ween he KLFs and he pho ome ic e o s, espec i ely, ob ained wi h he wo di e en app oaches. We ob ained e y simila esul s wi h he new p ocedu e. We applied his me hod o he es o he epochs o ob ain he e o s. Figu e A.3 shows a com- pa ison be ween he KLFs o he ou epochs a e he new p ocedu e. Figu e A.5 illus a es he pho ome ic unce ain ies ob ained h ough his me hod, shown as blue poin s. While his me hod allows o he es ima ion o ealis ic pho ome ic unce - ain ies, a dis inc pa e n becomes appa en in he ou plo s. This pa e n is obse ed o s a s wi h b igh ness be ween 15 and 16 magni udes, whe e e o s exceed 0.1, and a e si ua ed a he ou co ne s o he inal mosaics, whe e he coun o obse ed ames is limi ed o 2. I is impo an o no e ha his pa e n is no a e lec ion o ealis ic condi ions; a he , i is linked o he ac ha he mosaic in hose egions con ains only wice as many ames as he indi idual images. This esul s in he gene a ed images ha - ing excessi e noise. Excessi e e o s in ce ain bands a e unde- si able because hey lead o he p ac ical e ec o p edominan ly elying on bands wi h smalle e o s, o en limi ed o only h ee bands. As a esul , he ob ained alues become mo e unce ain. To imp o e e o p edic ions, we ained a machine lea ning algo i hm, XGBoos 14 lib a y, as de ailed in Chen & Gues in (2016), u ilizing ou da ase . The a ge ea u e o p edic ion was he e o in each o he ou p oblema ic bands (IB200, IB227, IB230, IB236), and each was add essed sepa a ely. We applied a loga i hmic ans o ma ion o hese e o s because, wi hou i , he algo i hm ends o o e emphasize a ew ex eme cases, leading o poo o e all pe o mance. The ea u es u ilized o aining consis ed o he magni udes and he e o s in he h ee o he bands (IB206, IB224, IB233) wi h a la ge numbe o obse ed ames (see Table 1). Du ing he algo i hm aining, we excluded da a poin s asso- cia ed wi h bands ha ing h ee o ewe obse ed ames a ail- able. This selec ion is based on ou obse a ion ha s a s wi h exac ly h ee images ha e no ably inc eased s a is ical signi i- cance compa ed o o he s a s. Howe e , hei o e all in luence emains limi ed due o he smalle numbe o s a s wi h exac ly h ee obse ed ames. To p e en o e i ing, we employed an 80% aining se and a 20% es ing se . P ima ily, we employed a non andom es app oach by ese ing he 20% o he da a ha is a hes om he cen e in ei he he RA o Dec di ec ion. This app oach es ablishes spa ial connec i i y in he co ne egions, p e en ing he algo i hm om achie ing supe io pe o mance h ough in e pola ion ac oss he gaps c ea ed by missing s a s dis ibu ed h oughou he image. In p ac ice, we obse ed ha his did no happen, and he esul s ob ained using andom and spa ially connec ed es se s we e simila . We pe o med g id i - ing wi h a ious eg_alpha15 alues o p e en o e i ing and selec he one ha yields he smalles s anda d de ia ion in he 14 h ps://xgboos . ead hedocs.io/ 15 This pa ame e de ines he size o subse s o he da a which ha e he same cons an esul s by binning. A la ge eg_alpha implies ha mo e neighbou ing da a poin s sha e he same esul s. A190, page 21 o 34 Gallego-Cano, E., e al.: A&A, 689, A190 (2024) Fig. A.2. Compa ison be ween pho ome ic unce ain ies e sus magni ude ob ained wi h he boo s apping p ocedu e (blue poin s) and S a Finde p og am (o ange poin s) o IB206, IB224, and IB233. Fig. A.3. KLFs o he inal noise boo s apping mosaics. The di e en colou s co espond o he di e en bands. es se . I is c ucial o inco po a e bo h he magni ude in he a - ge band and an es ima ion o he e o in he good bands o accu a e esul s. The signi icance o including magni ude as a ea u e is ob ious, and he inclusion o e o s in o he bands is also no su p ising. Many cha ac e is ics a e simila o iden ical ac oss di e en bands, such as he p esence o close neighbou s, he a io o he numbe o images o he maximum possible numbe o images, and he posi ioning o AO guide s a s. We achie ed ema kably simila esul s whe he we used he mag- ni ude e o s o all h ee bands o hei mean. In he end, we conside ed he mean o he h ee because ou da ase is no ex en- si e enough o conclusi ely es ablish ha a pu ely pe o mance- based selec ion is supe io . The e o e, we p e e ed he simple and mo e in e p e able model. In addi ion o add essing s a s wi h limi ed exposu es, we also made co ec ions o s a s whose e o s exceed 0.33. Such a subs an ial e o is no easible o 3-sigma de ec ions, and all ou sou ces mee his c i e ion due o he S a Finde se ings. These signi ican e o s a e likely spu ious, as hey do no consis- en ly appea ac oss di e en bands. We ex ended his co ec ion o he h ee o he bands as well. Fo hese bands, we excluded he a ge band om he mean e o calcula ion. Only a small numbe o s a s, app oxima ely a dozen, display such subs an ial e o s in each band. While hese co ec ions may no be as obus as boo s apping e o s de i ed om high-quali y da a, we also ma k he co ec ed magni ude e o s wi h lags o u u e e e - ence. In summa y, we u ilize he unce ain ies de i ed om he XGBoos p ocedu e o s a s in egions whe e he numbe o ames in a gi en epoch is less han o equal o h ee. Fo s a s loca ed in he emaining egions, we employ he noise boo s ap- ping p ocedu e o compu e he unce ain ies. A.3. Unce ain ies o CBD Al hough we p ima ily elied on he SciPy cu e_ i unc ion o es ima e unce ain ies in he CBD alues, we also explo ed al e na i e me hods, including hose based on he χ2 o lin- ea , polynomial, and exponen ial i s, espec i ely, simila o he app oach ou lined in Gillessen e al. (2009). The educed χ2 ypically exceeds he expec ed alue o 1, and his di e ence is pa icula ly signi ican o b igh s a s, gi en hei smalle absolu e e o s. This beha iou is no unex- pec ed, and i can be a ibu ed o a ious ac o s, such as he complexi y o s a spec a compa ed o ou simpli ied models o po en ial a iabili y be ween he di e en images. No e ha he e is nea ly a mon h be ween he acquisi ion o he i s and las image, which may con ibu e o hese disc epancies. Fi s ly, we pe o med a i o he median log(χ2) as a unc ion o magni ude using a linea model. The p edic ed alue ob ained om his model se es as he de aul χ2 a. Secondly, we di ided he o iginal χ2o each s a by χ2 aand de e mined he h eshold abo e which he numbe o alues exceeded wice he expec ed om he χ2dis ibu ion o he deg ees o eedom (d.o. ) o he model i . In cases whe e his condi ion is me , he o iginal χ2 is employed in subsequen calcula ions; o he wise, χ2 ais used. Thi dly, he e o s o he linea and o he i s a e adjus ed by mul iplying hem wi h pχ2/d.o. , using he p e iously de i ed χ2 alue o each s a . Finally, we calcula ed he CBD e o by aking he squa e oo o he sum o he wo i e o s. A190, page 22 o 34 Gallego-Cano, E., e al.: A&A, 689, A190 (2024) Fig. A.4. Compa ison be ween he esul s ob ained by using he no mal boo s apping p ocedu e and he new boo s apping o IB224. Le : KLF. Righ : Pho ome ic e o s. Fig. A.5. Compa ison be ween pho ome ic unce ain ies e sus magni ude ob ained wi h he boo s apping (blue poin s) and XGBoos (o ange poin s) p ocedu es, espec i ely, o IB200, IB227, IB230, and IB236. A190, page 23 o 34 Gallego-Cano, E., e al.: A&A, 689, A190 (2024) Appendix B: Calib a o s In his sec ion, we p o ide he inal lis o 28 OB s a s (see Table B.1) used in he basic calib a ion p ocess, as discussed in Sec ion 3.3.1. Figu e 1illus a es he spa ial dis ibu ion o hese s a s ac oss he FoV. The da a in he able is sou ced om Feldmeie -K ause e al. (2015), excep he KSmagni udes, which a e ob ained om Schödel (2010). Table B.1. OB s a s used o he basic calib a ion. ID RA Dec ∆RA ∆Dec Ks Name Type [◦] [◦] [00] [00] [mag] 00109 266.41724 -29.008343 -1.060 -1.916 10.65 MPE+1.0-7.4(16S) B0.5-1 00096 266.41437 -29.007425 6.613 1.387 10.66 00166 266.41397 -29.009418 7.660 -5.788 10.96 00209 266.41571 -29.009912 3.014 -7.567 11.02 00230 266.41681 -29.005444 0.082 8.521 11.07 O9-B 00205 266.41882 -29.007736 -5.305 0.268 11.14 IRS1E B1-3 00273 266.41684 -29.004976 -0.000 10.204 11.22 O9-B 00227 266.41742 -29.009571 -1.548 -6.338 11.24 ? 00366 266.41705 -29.010412 -0.570 -9.366 11.43 00445 266.41647 -29.005707 0.981 7.574 11.58 O9-B 00372 266.41827 -29.008778 -3.832 -3.481 11.60 00483 266.42029 -29.005968 -9.237 6.633 11.70 IRS 5SE B3 00516 266.41754 -29.006582 -1.879 4.422 11.71 B0-3 00567 266.41855 -29.006989 -4.574 2.959 11.96 00507 266.41632 -29.008602 1.386 -2.850 11.98 O8.5-9.5 00610 266.41849 -29.009783 -4.399 -7.100 12.01 00722 266.41489 -29.010849 5.209 -10.938 12.10 00757 266.41400 -29.008787 7.583 -3.516 12.12 00508 266.41867 -29.007784 -4.897 0.096 12.13 O9.5-B2II 00617 266.41415 -29.009539 7.171 -6.221 12.14 00721 266.41904 -29.006376 -5.884 5.164 12.22 00725 266.41602 -29.008396 2.202 -2.108 12.31 O9-B0 00728 266.41425 -29.008633 6.932 -2.959 12.31 00785 266.41705 -29.008959 -0.571 -4.134 12.34 B0-1 00707 266.41733 -29.008621 -1.305 -2.918 12.41 B0-3 00936 266.41479 -29.009893 5.458 -7.498 12.42 00838 266.41455 -29.006830 6.126 3.529 12.43 00853 266.41730 -29.010958 -1.221 -11.330 12.45 No es. The alue o KSmagni udes a e aken om Schödel (2010), while all o he alues o igina e om Feldmeie -K ause e al. (2015). A190, page 24 o 34 Gallego-Cano, E., e al.: A&A, 689, A190 (2024) Appendix C: SEDs o RC s a s along FoV In his sec ion, we show a compa ison be ween he mean SED o RC s a s in he di e en sub- ields using he IB da a a e he basic calib a ion and a e applying he local calib a ion along he FoV. In Fig. C.1, he in luence o he local calib a ion is clea ly illus a ed, pa icula ly in he ou e egions. The blue poin s ep esen he SED a e he basic calib a ion, while he ed poin s depic he SED a e applying he local calib a ion. The o me is shi ed in magni ude o achie e o e lap. Fig. C.1. Compa ison be ween he mean SED o RC s a s in he di e en sub- ields using he IB da a a e he basic calib a ion (blue poin s) and a e applying he local calib a ion ( ed poin s). The SEDs a e shi ed in magni ude o achie e o e lap. The e ec o he local calib a ion is mo e impo an in he ou e egions. The size o each sub- ield is a ound 8.600 x 8.600. The panels co esponding o he di e en sub- ields o e lap wi h he speci ic sub- ield in he backg ound image. A190, page 25 o 34 Gallego-Cano, E., e al.: A&A, 689, A190 (2024) Appendix H: Mul i-laye pe cep on esul s Figu e H.1 shows he p obabili ies o he s a s ob ained by he MLP me hod in CBD-magni ude- adius space, whe e he adius is he dis ance om Sg A*. Fig. H.1. P obabili ies o he s a s ob ained by he MLP me hod in CBD-magni ude- adius space, whe e he adius is he dis ance om Sg A*. Appendix I: G adien boos ed ees esul s Figu e I.1 shows he p obabili ies ob ained by he andom o es in CBD-magni ude- adius space. Fig. I.1. P obabili ies ob ained by he andom o es in CBD- magni ude- adius space, he h ee mos impo an ea u es. A190, page 32 o 34 Gallego-Cano, E., e al.: A&A, 689, A190 (2024) Appendix J: SEDs o ea ly- ype candida es Due o disc epancies in he numbe o ea ly- ype candida es among he h ee me hods, pa icula ly in he ou e egions whe e he MLP me hod iden i ies a highe numbe o candida es com- pa ed o he o he wo me hods, his appendix del es in o he SEDs o s a s de ec ed exclusi ely wi h MLP. The goal is o assess he eliabili y o he esul s. Figu e J.1 displays he SEDs o h ee ea ly candida es loca ed in he co ne s o he image (see Fig. 13). The CBD alues, as well as he shapes o hei SEDs, sugges cha ac e is ics ypical o ea ly- ype s a s. Addi ionally, in he same egions, la e- ype candida es exhibi dis inc SED ea u es, including a no iceable dip co esponding o he CO band in wa eleng hs la ge han 2.27. This obse a ion leads us o he conclusion ha some o he s a s de ec ed only by he MLP me hod may indeed co espond o genuine young s a s. Fig. J.1. SEDs o ea ly- ype candida es de ec ed only wi h MLP me hod, loca ed in he uppe le co ne (uppe panel), lowe le co - ne (middle panel), and uppe igh co ne (bo om panel). A190, page 33 o 34 Gallego-Cano, E., e al.: A&A, 689, A190 (2024) Appendix K: On me allici y We show in Fig. K.1 he in e ac ion o p edic ed me allici y and la e p obabili y. Bo h need o be modelled a once o eliable esul s. Fig. K.1. P edic ed me allici y. Excluded a e s a s which a e spec o- scopically ea ly and s a s ou side he magni ude ange whe e he p e- dic ion wo ks. A190, page 34 o 34