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
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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.
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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). EGC and RS acknowledge inancial
suppo om he Se e o Ochoa g an CEX2021-001131-S unded by
MCIN/AEI/10.13039/501100011033, om g an EUR2022-134031 unded by
MCIN/AEI/10.13039/501100011033 and by he Eu opean Union Nex Gene a-
ionEU/PRT, and om g an PID2022-136640NB-C21 unded by MCIN/AEI
10.13039/501100011033 and by he Eu opean Union. AFK acknowledges
unding om he Aus ian Science Fund (FWF) [g an DOI 10.55776/ESP542].
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Gallego-Cano, E., e al.: A&A, 689, A190 (2024)
Appendix A: Unce ain y es ima ion
As seen p e iously, ob aining obus and eliable unce ain ies
wi hou loss o sensi i i y is c ucial o ul illing he objec i es
o ou wo k. 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).
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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.
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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.
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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).
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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