A semi-analytical perspective on massive red galaxies

As onomy
&
As ophysics
A&A, 693, A219 (2025)
h ps://doi.o g/10.1051/0004-6361/202449232
© The Au ho s 2025
A semi-analy ical pe spec i e on massi e ed galaxies
I. Assembly his o y, en i onmen , and edshi e olu ion
D. S oppache 1,2,3,⋆, A. D. Mon e o-Do a4, M. C. A ale5, A. Knebe1,6,7, N. Padilla8,
A. J. Benson9, and C. Beh ens10
1Depa amen o de Física Teó ica, Módulo 15, Facul ad de Ciencias, Uni e sidad Au ónoma de Mad id, Can oblanco, 28049 Mad id,
Spain
2Ins i u o de As o ísica, Pon i icia Uni e sidad Ca ólica de Chile, Campus San Joaquín, A da. Vicuña Mackenna 4860, San iago,
Chile
3Facul ad de Físicas, Uni e sidad de Se illa, Campus de Reina Me cedes, A da. Reina Me cedes s/n, 41012 Se illa, Spain
4Depa amen o de Física, Uni e sidad Técnica Fede ico San a Ma ía, Casilla 110-V, A da. España 1680, Valpa aíso, Chile
5Uni e sidad And es Bello, Facul ad de Ciencias Exac as, Depa amen o de Ciencias Físicas, Ins i u o de As o ísica,
A . Fe nández Concha 700, San iago, Chile
6Cen o de In es igación A anzada en Física Fundamen al (CIAFF), Facul ad de Ciencias, Uni e sidad Au ónoma de Mad id,
28049 Mad id, Spain
7In e na ional Cen e o Radio As onomy Resea ch, Uni e si y o Wes e n Aus alia, 35 S i ling Highway, C awley,
Wes e n Aus alia 6009, Aus alia
8Ins i u o de As onomía Teó ica y Expe imen al (IATE), CONICET-UNC, Lap ida 854, X5000BGR, Có doba, A gen ina
9Ca negie Obse a o ies, 813 San a Ba ba a S ee , Pasadena, CA 91101, USA
10 Ins i u ü As ophysik, Geo g-Augus Uni e si ä Gö ingen, F ied ich-Hund-Pla z 1, 37077 Gö ingen, Ge many
Recei ed 15 Janua y 2024 / Accep ed 4 Decembe 2024
ABSTRACT
Con ex . The e olu ion o galaxies wi hin a sel -consis en cosmological con ex emains one o he mos ou s anding and challenging
opics in mode n galaxy o ma ion heo y. In es iga ing he assembly his o y and a ious o ma ion scena ios o he mos massi e and
passi e galaxies, pa icula ly hose ound in he denses clus e s, will enhance unde s anding o why galaxies exhibi such a ema kable
di e si y in s uc u e and mo phology.
Aims. In his pape , we simul aneously in es iga e he assembly his o y and edshi e olu ion o semi-analy ically modelled galaxy
p ope ies o luminous and massi e cen al galaxies be ween 0.56 <z<4.15 alongside hei connec ion o hei halos as a unc ion o
la ge-scale en i onmen .
Me hods. We ex ac ed sub-samples o galaxies om a mock ca alogue ep esen a i e o he well-known BOSS-CMASS sample, which
includes he mos massi e and passi ely e ol ing sys em known oday. U ilising ypical galaxy p ope ies such as s a o ma ion a e,
(g-i) colou , and cold gas-phase me allici y (Zcold), we acked he edshi e olu ion o hese p ope ies ac oss he main p ogeni o
ees.
Resul s. We p esen esul s on galaxy and halo p ope ies, including hei g ow h and clus e ing unc ions, o each o ou sub-samples.
Ou indings indica e ha galaxies in he highes s ella and halo mass egimes a e he leas me al en iched (using Zcold as a p oxy) and
consis en ly exhibi signi ican ly la ge black hole masses and highe clus e ing ampli udes compa ed o sub-samples selec ed by such
p ope ies as colou o s a o ma ion a e. This popula ion o ms la e and e ains la ge ese oi s o cold gas. In con as , galaxies in
he in e media e and lowe s ella o halo mass egimes consume hei cold gas a a highe edshi and we e among he ea lies and
quickes o assemble hei s ella and black hole masses. In addi ion, we obse ed a clea end whe e he clus e ing o he galaxies
selec ed acco ding o hei Zcold- alues (ei he low-Zcold o high-Zcold) depends on he densi y o hei loca ion wi hin he la ge-scale
en i onmen .
Conclusions. We assume ha he galaxies in he low-Zcold and high-Zcold sub-samples o m and e ol e h ough dis inc e olu iona y
channels ha a e p ede e mined by hei loca ion wi hin he la ge-scale en i onmen o he cosmic web. Fu he mo e, hei clus e ing
dependence on he en i onmen could be an impo an a ea o u he in es iga ion.
Key wo ds. me hods: nume ical – galaxies: e olu ion – galaxies: o ma ion – la ge-scale s uc u e o Uni e se
1. In oduc ion
The mechanisms d i ing galaxy e olu ion ope a e ac oss a wide
ange o spa ial and empo al scales. These include he size
o s a - o ming molecula clouds (a ew pa secs in diame e ),
idally in e ac ing galaxies on he clus e scale, and e ec s
inco po a ing he en i e ne wo k o he cosmic web, such as
⋆Co esponding au ho ; [email p o ec ed];
[email p o ec ed]
in e -connec i i y ia ilamen s o g a i a ional collapse o la ge-
scale s uc u es. On he empo al scale, galaxy e olu ion encom-
passes bo h sho - e m s a o ma ion e en s las ing less han
one megayea and he long- e m assembly o ancien ellip i-
cal galaxies hos ed by he mos massi e da k ma e halos o
oday. Indeed, galaxy e olu ion is in luenced no only by a i-
ous in e nal physical p ocesses (Ko mendy 1979;D essle 1980;
Mannucci e al. 2010;Con oy 2013;Kalino a e al. 2021) bu also
by he e olu ion o he da k ma e halo whe e he galaxy esides
A219, page 1 o 19
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S oppache , D., e al.: A&A, 693, A219 (2025)
(Some ille & Da é 2015;Wechsle & Tinke 2018) and i s
associa ed local and la ge-scale en i onmen (Blan on & Be lind
2007;Shanda in e al. 2010;Peng e al. 2010;A gudo-Fe nández
e al. 2018;Wang e al. 2018;Con ini e al. 2020;Du a e al.
2020;Rosas-Gue a a e al. 2022).
In his con ex , he mos massi e ed galaxies, ypically li -
ing in he iches clus e s oday, a e pa icula ly in e es ing.
They no only cons i u e he backbone o he cosmic web, bu
hei o ma ion also p o ides signi ican insigh s in o he o ma-
ion and e olu ion o ou Uni e se (see e.g. Reid e al. 2010;
Zhai e al. 2023). These galaxies ep esen he inal s ages o
galaxy e olu ion and a e ex ensi ely used as ace s o he
la ge-scale s uc u e in cosmological su eys (Shanda in e al.
2010;Conselice 2014;Inagaki e al. 2015;Fa ole e al. 2016;
Sai o e al. 2016).
The e olu ion o massi e ed galaxies has been explo ed
om mul iple pe spec i es. Rega ding hei s ella mass assem-
bly his o ies, he gene al consensus is ha hese galaxies o m
he majo i y o hei s a s ea ly on (e.g. De Lucia e al. 2006;
Ma as on e al. 2009,2013;Liu e al. 2016;Johns on e al. 2022).
Howe e , he e ha e been documen ed episodes o eju ena ion
(Hawa den e al. 1979;Pandya e al. 2017;Remus & Kimmig
2023;Zhang e al. 2023).
Addi ionally, he ela ionship be ween he in e nal e olu ion
o massi e ed galaxies and hei local and la ge-scale en i on-
men s has been in es iga ed using a ious obse a ional, s a is-
ical, and nume ical ools o 90 yea s (Hubble 1936;Zwicky
e al. 1961;D essle 1980;Zeha i e al. 2005;Thomas e al.
2010;Koyama e al. 2013;Lupa ello e al. 2015;Filho e al.
2015;Schaye e al. 2015;Musso e al. 2018;Pandey & Sa ka
2020;San ucho e al. 2020;Sa ka & Pandey 2020;Su eshkuma
e al. 2021;Ala con e al. 2023). Impo an ly, he clus e ing o
massi e ed galaxies is known o be enhanced ela i e o he gen-
e al galaxy popula ion (see e.g. pionee ing wo k by Kaise 1984;
E s a hiou & Rees 1988), as hey ypically eside in he mos
massi e halos (She h e al. 2001;C o on e al. 2007). In gene al,
mo e luminous and massi e galaxies wi h edde colou s and
ea ly- ype mo phology exhibi s onge clus e ing and end o
li e in dense egions compa ed o hei less massi e, blue , and
la e - ype coun e pa s. Se e al s udies ha e p e iously explo ed
he connec ion be ween massi e ed galaxies and he so-called
assembly bias e ec , which e e s o he seconda y dependen-
cies o halo and galaxy clus e ing a a ixed halo mass (Lin e al.
2016;Mon e o-Do a e al. 2017b;Niemiec e al. 2018).
In e ms o galaxy o ma ion, he widely accep ed scena io
sugges s ha massi e galaxies in he ea ly s age o he Uni e se
unde wen an immense s a bu s phase and subsequen apid
quenching (Fo es e al. 2020). These galaxies a e hough o
belong o ei he a i s o second wa e o o ma ion, wi h hei
bulges o ming ea ly and as o la e and mo e slowly (Cos an in
e al. 2021) and whe e dis inc e en s in hei e olu ion his o y,
such as a majo me ge , helped d i e hei mass assembly (e.g.
Lackne e al. 2012;Hashemizadeh e al. 2021;Sawicki e al.
2020;Spa one e al. 2021;Dol i e al. 2023). This aligns well
wi h he wo-phase scena io p oposed by Ose e al. (2010) ha
posi s ha he build-up o a galaxy’s s ella mass is due o an
ea ly phase o in si u s a o ma ion ollowed by a la e phase o
ex si u acc e ion.
Gi en he conside a ions men ioned abo e, we can iden i y
ou majo d i e s ha con ol he e olu ion o a galaxy. These
a e i s in insic p ope ies (i.e. how many ba yons we e ini-
ially a ailable o o m a galaxy) and ba yonic p ocesses (such
as s ella eedback and ou lows, among o he s); i s galaxy-halo
connec ion ( he cha ac e is ics o he da k ma e halo in which
he galaxy esides); i s assembly his o y (including he edshi
e olu ion o bo h galaxy and halo p ope ies); and i s en i on-
men (such as he galaxy’s loca ion, whe he he galaxy is in
a less dense o dense egion o he Uni e se). I is impo -
an o no e ha hese ou elemen s a e highly co ela ed and
in e ac wi h each o he on many le els, as epea edly epo ed
in he li e a u e. Fo ins ance, he connec ion be ween in insic
p ope ies and en i onmen can be illus a ed by he g ow h o
black holes, which can acili a e he quenching o he s a o ma-
ion, gene ally known as ac i e galac ic nucleus (AGN) eedback
– a p ocess ha pa icula ly in luences he a e o massi e clus-
e galaxies (see e.g. C o on e al. 2006;Da ies e al. 2021).
Ano he example is ha quenched galaxies end o p e e spe-
ci ic en i onmen s such as he edge o ilamen s (Song e al.
2021). In addi ion, Kim e al. (2020) p oposed ha compac ellip-
icals consis o galaxies wi h wo dis inc o igins depending on
hei local en i onmen . Fu he mo e, he me ging his o y o gas
can impac galaxy e olu ion, as demons a ed o co e- o a ing
ea ly- ype galaxies, which ha e di e en assembly p ocesses
compa ed o hei co e-less coun e pa s (K ajno i´
c e al. 2020).
By examining he s ella mass assembly his o ies o simula ed
galaxies, Gup a e al. (2020) ound a apid inc ease in he ex
si u s ella mass ac ion o massi e galaxies a z<3.5, while
his ac ion emains cons an o hei low-mass coun e pa s
ac oss cosmic ime. An example o how he assembly his o y and
galaxy-halo connec ion join ly in luence in insic p ope ies has
been p o ided by Bose & Loeb (2021), who obse ed a ia ions
in he s ella eloci y dispe sion wi h age and halo concen a ion.
Finally, Ha ada e al. (2023) epo ed a s ong link be ween gas
and me al ou low in p o o-clus e s, which a e highly sensi i e o
halo mass.
U ilising obse a ional galaxy p ope ies p esen s a chal-
lenge, as i necessi a es in e ing o ma ion his o ies and halo
p ope ies ha canno be di ec ly ex ac ed om a me ge ee,
howe e his in o ma ion is eadily a ailable in simula ions.
None heless, we ind ha s udies o massi e ed galaxies can sig-
ni ican ly bene i om in eg a ing a ious aspec s o galaxy e o-
lu ion. In his con ex , we simul aneously examine he assembly
his o ies, clus e ing, galaxy-halo connec ion, and en i onmen
in his wo k. This app oach builds on he g oundwo k laid by
S oppache e al. (2019), who in es iga ed he main p ope ies
and clus e ing o luminous ed galaxies using he GALACTI-
CUS semi-analy ical model (SAM) de eloped by Benson (2012),
which esembles he selec ed BOSS-CMASS sample a z∼0.5.
Thei s udy demons a ed ha he speci ic s a o ma ion a e
and he cold gas ac ion co ela e wi h he halo mass and la ge-
scale en i onmen (less dense o dense egions). Fu he mo e,
hey obse ed a s ong bimodali y in he plane o cold gas-phase
me allici y and speci ic s a o ma ion a e (see hei Fig. 10).
In his pape , we ex end hei analysis by examining he e olu-
iona y his o y o he same galaxies in o de o illumina e hei
di e se o ma ion channels. We also in es iga e he o igins o
he bimodali y ound in he cold gas-phase me allici y and s ella
mass planes.
We u ilised modelled BOSS-CMASS galaxy p ope ies om
he a o emen ioned SAM in he edshi ange o 0.5∼
>z∼
>4
and ollowed he same selec ion p ocedu e o modelled CMASS
galaxies as in S oppache e al. (2019). Thei s udy p esen ed
a me hod o mimic he pho ome ic selec ion o luminous and
massi e galaxies ha p oduces a galaxy sample ha is bo h quan-
i a i ely and quali a i ely compa able o obse a ions. We elied
on his modelled da a because o SAM’s app oach o gene a -
ing ca alogues o galaxy p ope ies and acking he e olu ion o
s a is ically signi ican samples. These models a e usually buil
A219, page 2 o 19
S oppache , D., e al.: A&A, 693, A219 (2025)
on N-body da k ma e simula ions using me ge ees (in o ma-
ion on he hie a chical o ma ion o da k ma e halos). Unlike
o he modelling echniques, SAMs do no explici ly sol e un-
damen al equa ions o , o example, hyd odynamics bu ins ead
use simpli ied ecipes o accoun o ba yonic physics as a pos -
p ocessing s ep. This includes phenomenological ea men s o
ba yonic p ocesses and coa se-g aining he p ope ies o galax-
ies, which allows SAMs o sol e he sys em o equa ions. SAMs
a e adjus ed (o uned) o ep oduce obse ed galaxy dis ibu-
ions and a e cons ained by empi ical measu emen s. Al hough
he modelling o he physical p ocesses is simpli ied, he ad an-
age o SAMs lies in hei abili y o handle sub-g id physics
e icien ly and adap i ely, making hem an excellen ool o
explo ing a wide ange o galaxy p ope ies ac oss di e se
pa ame e spaces (Baugh 2006;Benson 2010;Baugh 2013;
Some ille & Da é 2015).
This wo k is o ganised as ollows: in Sec ion 2, we desc ibe
he pa en ca alogue used o ex ac ou SAM-CMASS mock
galaxy sample, and in Sec ion 2.3 we explain how we selec ed
sub-samples om his ca alogue and acked p ogeni o s h ough
hei me ge ees. Ou esul s a e p esen ed in Sec ion 3and ol-
lowed by a de ailed discussion o he key indings in Sec ion 4.
We summa ise ou wo k and p o ide an ou look on u u e s udies
in Sec ion 5.
The adop ed cosmology in his pape is based on a la
ΛCDM model wi h he ollowing cosmological pa ame e s:
Ωm=0.307,Ωb=0.048,ΩΛ=0.693, σ8=0.823,ns=0.96,
and a dimensionless Hubble pa ame e h=0.678 (Planck
Collabo a ion XIII 2016). He ea e , his abso bed in o he
nume ical alues o p ope ies h oughou he ex as well as in
all ables and igu es. We used ypical dependencies o he Hub-
ble pa ame e , as ou lined in C o on (2013), whe e masses om
simula ions a e ypically scaled wi h h−1.
2. Da a selec ion and sample e alua ion
2.1. Galaxy ca alogue and simula ion de ails
Ou modelled galaxy ca alogue is based on he well-known
BOSS-CMASS ca alogue om he Sloan Digi al Sky Su ey
(SDSS) (Alam e al. 2015), which is well-cons ained and ex en-
si ely s udied (e.g Cues a e al. 2016;Mon e o-Do a e al. 2016;
Chuang e al. 2016;Fa ole e al. 2016;Rod íguez-To es e al.
2016;Mon e o-Do a e al. 2017a;Ross e al. 2017;Sulli an
e al. 2017;Guo e al. 2018;Muelle e al. 2018). This galaxy
ca alogue was o iginally designed o a ge he mos luminous
and massi e galaxies in o de o p oduce a uni o mly dis ibu ed
sample o galaxies a edshi 0.43 <z<0.7. The pho ome ic
selec ion included (g-i) and ( -i) colou s (Fukugi a e al. 1996)
o isola e only he eddes and mos massi e galaxies a high
edshi s, while also allowing o an ex ension owa ds blue
colou s, meaning ha “blue-cloud”-galaxies could s ill en e he
CMASS-sample. Fo u he de ails, we e e o he BOSS a -
ge selec ion and educ ion pipeline1. We use da a om DATA
RELEASE 12, speci ically he La ge-Scale S uc u e (LSS) ca a-
logue2(Reid e al. 2016) om he SDSS Science A chi e Se e .
This was c oss-ma ched wi h he Po smou h3passi e galaxy
sample o include s ella masses, based on he s ella popula ion
models o Ma as on (2005) and Ma as on e al. (2009).
1h ps://www.sdss.o g/d 12/algo i hms/boss_galaxy_ s/
2h ps://da a.sdss.o g/sas/d 12/boss/lss/
3h p://www.sdss.o g/d 13/spec o/galaxy_po smou h/
The model we use in his s udy, he semi-analy ical galaxy
o ma ion and e olu ion code GALACTICUS, de eloped by
Benson (2012), was un on he MULTIDARK PLANCK 2 sim-
ula ion (he ea e MDPL2: Klypin e al. 2016) and eleased
as pa o THE MULTIDARK-GALAXIES (Knebe e al. 2018b).
MDPL2 is an N-body da k ma e -only simula ion wi h a
side-leng h o 1000 h−1Mpc, acking he e olu ion o 38403
da k ma e pa icles, each wi h a mass o mp=2.23 ×
109M⊙. Halos and sub-halos we e iden i ied using ROCK-
STAR (Beh oozi e al. 2013a) and me ge ees we e cons uc ed
wi h CONSISTENT TREES (Beh oozi e al. 2013b). Mo e in o -
ma ion on he model can be ound in Appendix A. This
e sion o GALACTICUS was eleased unde he name MDPL2-
Galac icus and is publicly a ailable on www.cosmosim.o g
and www.skiesanduni e ses.o g. The model adop s he
same cosmology as used in his wo k.
2.2. Selec ing modelled galaxies om he galaxy ca alogue
Fo he selec ion p ocedu e o SAM-CMASS mock galaxies we
e e o Sec ion 2 o ou companion pape S oppache e al.
(2019, he ea e S19), which ou lines how o ex ac modelled
BOSS-CMASS galaxies om he SAM galaxy ca alogue. We
adop hei app oach, applying he same selec ion algo i hm
o he galaxy ca alogue MDPL2-Galac icus (Knebe e al.
2018b). As desc ibed in Sec ion 3 o S19, he au ho s es ed a -
ious selec ion p ocedu es and ex ac ed se e al CMASS mock
galaxy samples which a e desc ibed alongside hose o he
obse ed CMASS-sample om BOSS (see hei Table 1). Fo ea-
sons de ailed in S19, hey eplica ed he pho ome ic CMASS
a ge selec ion o BOSS using a “down-sampling” app oach on
he modelled galaxies. This app oach was ho oughly assessed
and e i ied o p oduce a alid and compa able mock galax-
ies sample, as demons a ed by he s ella mass unc ions, he
galaxy-halo connec ion, and he clus e ing unc ion, all o which
show good ag eemen wi h obse a ions (see S19, Fig. 4 and
Figs. 6–8). Fo his s udy, we speci ically choose he mock
galaxy sample called Gal-dens4as ou e e ence (pa en ) sam-
ple, since he modelled sample was equi ed o ma ch he numbe
densi y o i s obse a ional coun e pa .
2.3. Me hodology o selec ing sub-samples and acking
p ogeni o s
Wi hin his wo k, we aim a s udying he s a o ma ion and
assembly his o ies o dis inc popula ions o galaxies, such as
hose exhibi ing bimodali y in he cold gas-phase me allici y
as men ioned in Sec ion 1. To achie e his, we i s needed o
es ablish selec ion c i e ia o guide ou s udy. In his sec ion,
we desc ibe his me hodology and subsequen ly apply hese c i-
e ia o ou selec ed pa en sample, Gal-dens – he modelled
CMASS-galaxies om MDPL2-Galac icus – o p oduce wha
we e e o as ‘sub-samples’. Fo cla i y, Gal-dens ep esen s
he popula ion o he mos massi e and luminous galaxies in he
Uni e se. We also speci y ha ou analysis includes only cen al
galaxies5.
We de ine ou selec ion c i e ia based on ypical galaxy
p ope ies such as obse ed colou sepa a ion (g-i), s a o -
ma ion a e (SFR), o o al cold gas-phase me allici y, Zcold.
4We adop he name con en ion o S19, whe e he label “dens” e e s
o he densi y selec ed sample.
5Fo de ails on he de ini ions o galaxy ype such as ‘cen al’ o
‘sa elli e’, we e e o Appendix 2 in Knebe e al. (2018b).
A219, page 3 o 19
S oppache , D., e al.: A&A, 693, A219 (2025)
Table 1. O e iew o sub-samples used in his wo k.
sub-sample selec ion c i e ion
name
low-SFR 20% lowes s a o ma ion a e (SFR)
passi e 20% passi e galaxies / lowes speci ic SFR (sSFR)
ed 20% eddes galaxies / highes (g-i)
low-Zcold 20% lowes cold gas-phase me allici ies (Zcold) and (g-i) >2.35
high-Zcold 20% highes cold gas-phase me allici ies (Zcold) and (g-i) >2.35
(i) (ii)
No es. This able compiles ou choice o sub-samples ex ac ed om
he modelled SAM-CMASS mock galaxy ca alogue, Gal-dens, a
z e =0.56 – he edshi o sample selec ion. In column (i), we s a e he
sub-sample’s name which is inspi ed by i s selec ion c i e ion shown in
column (ii).
Zcold ep esen s he me allici y o he cold gas a ailable o s a
o ma ion, ypically wi h empe a u es below ∼100 K (Da é
e al. 2020) Thus, his p ope y se es as an impo an diag-
nos ic o a ious p ocesses in galaxy e olu ion, including gas
in- and ou - low, and s a o ma ion in cold gas clouds (e.g.
Hughes e al. 2013;Lu z e al. 2020;Wang & Lilly 2021).
In obse a ional da a, his p ope y is o en quan i ied as he
a io o he numbe densi y o oxygen a oms o ha o hyd o-
gen a oms, 12 +log10(O/H), since oxygen is he mos abundan
hea y elemen in he cosmos. As ou model does no ou pu oxy-
gen abundances, we es ima e his p ope y using he masses o
me als and no malise hem by he Sola me allici y de ined as
8.69 +log10(MZcold /Mcold)−log10(Z⊙), whe e MZcold is he mass
o me als in he cold gas-phase. We use Z⊙=0.0134 (Asplund
e al. 2009) o he Sun’s me allici y and he ac o 8.69 o i s
oxygen abundance (Allende P ie o e al. 2001). This s anda d
p ocedu e is common in semi-analy ical models. Addi ionally,
we apply he same no malisa ion o he Oxygen abundance de e -
mined a edshi z=0 o no malise he p edic ion o ou model
a highe edshi s p ima ily o he eason o acili a e compa -
isons o me allici ies ac oss a ious sub-samples. Ou goal is
o ensu e a consis en app oach ac oss all edshi s a he han
p ecise measu emen s.
We selec i e sub-samples om he en i e popula ion o
cen als p esen in he SAM-CMASS mock galaxy sample,
Gal-dens, a edshi z e =0.56 – is ou e e ence Redshi o
sample selec ion – and name hem a e hei selec ion c i e ion.
The eby we always selec 20% o hei o al amoun o cen al
galaxies in Gal-dens (270 000) e.g. 20% wi h lowes SFR o
he sub-sample add essed as “low-SFR” o 20% o hose wi h
he eddes colou s (g-i) o he sub-sample add essed as “ ed”
as desc ibed in Table 1. This esul s in app oxima ely ∼50 000
galaxies pe sub-sample a z e =0.56.
The i s h ee sub-samples lis ed in Table 1con ain only
luminous ed galaxies (LRGs); howe e , we ind ha he
emaining wo sub-samples (low-Zcold and high-Zcold) ex ac ed
on he basis o hei cold gas-phase me allici y include bo h
“ ed-sequence” and “blue-cloud” galaxies. The la e a e massi e
galaxies wi h mild s a o ma ion, which esul s in sligh ly blue
colou s (see e.g. Eisens ein e al. 2011). To a oid con amina ion
om hese s a - o ming galaxies, we exclude he “blue-cloud”
membe s om he low-Zcold and high-Zcold sub-samples. As a
esul , we also equi e hese sub-samples o mee he classic
colou sepa a ion (g-i) >2.35 Mas e s e al. (2011). These wo
sub-samples a e pa icula ly in e es ing because hey map he
p ominen bimodali y in Zcold as ound by S19 (see hei Fig. 10).
10.8 11.0 11.2 11.4 11.6 11.8
-14
-13
-12
-11
z=0.56
log10
(
M
*
[
M
])
log10
(
sSFR
[
y
1
])
0.00
0.04
0.08
0.12
0.16
0.20
N
gal
0.00
0.04
0.08
0.12
0.16
0.20
N
gal
low
-SFR
passi e
ed
low
-
Zcold
high
-
Zcold
12.5 13.5 14.5
2.2
2.4
2.6
2.8
z=0.56
log10
(
M i
[
M
])
g i
0.00
0.04
0.08
0.12
0.16
0.20
N
gal
0.00
0.04
0.08
0.12
0.16
0.20
N
gal
low
-SFR
passi e
ed
low
-
Zcold
high
-
Zcold
Fig. 1. Sub-samples ex ac ed om he en i e da ase o he SAM-
CMASS mock galaxy ca alogue, Gal-dens, as desc ibed in Table 1
and ep esen ed by colou ed con ou s in he sSFR-M∗pa ame e space
a z e =0.56. The numbe densi y dis ibu ion o he en i e da ase
is depic ed as, loga i hmically binned hexagons in he backg ound.
The ho izon al solid ed line ma ks he classic quiescen sepa a ion,
log10(sSFR [y ]) ∼ −11 (F anx e al. 2008).
In Fig. 1we show ou de ined sub-samples as colou ed con-
ou s in he speci ic s a o ma ion a e (sSFR) e sus s ella
mass (M∗) pa ame e space oge he , wi h he en i e da ase o
SAM-CMASS mock galaxies, Gal-dens, as g ey, loga i hmi-
cally binned hexagons in he backg ound. We no e ha we use o
all ou con ou - igu es he ollowing con idence le els exp essed
as pe cen ages: [13.6, 31.74, 68.26, 95, 99.7]. Addi ionally, he
his og am panels on he op and he igh -hand ma ginal axes
show he dis ibu ion o galaxies along he binned axes, no -
malised o he o al numbe o galaxies pe sub-sample, using
35 bins. The his og ams show he same colou and line s yle keys
as he con ou s o he co esponding sub-samples. As poin ed
ou p e iously, he modelled galaxies exhibi a s ong bimodali y
in he speci ic s a o ma ion a e-s ella mass plane. The e o e,
we explici ly include he sub-samples low-Zcold and high-Zcold
selec ed on he basis o he cold gas-phase me allici y, Zcold,
in ou s udy since hey can be almos pe ec ly mapped on o
he bimodal dis ibu ion in s ella mass. In e es ingly, galaxies
selec ed based on o he p ope ies such as colou o s a o -
ma ion a e canno be assigned clea ly o ei he lowe o highe
s ella mass. We con i m ha only passi e galaxies en e ou sub-
samples since he con ou lines a e all loca ed below he quies-
cen sepa a ion ( ed solid line) as de ined by F anx e al. (2008).
In Fig. 2we show he obse ed colou (g-i) as a unc ion
o halo mass (M i ) o he same sub-samples as desc ibed in
Fig. 1. The ed solid ho izon al line indica es he ypical ed-blue
sepa a ion (g-i) >2.35 (Mas e s e al. 2011), as men ioned
be o e. As expec ed, he igu e clea ly dis inguishes be ween
he low and high me allici y popula ions, showing a simila
bimodal dis ibu ion in halo masses, analogous o he bimodal-
i y obse ed in s ella masses in Fig. 1. Speci ically, he low-Zcold
sub-sample is ound in halos o highe masses, while he high-
Zcold sub-sample occupies halos o lowe masses, a pa e n ha
was p e iously no ed by S19 and depic ed in hei Fig. 10. In
S19, au ho s concluded ha galaxies wi h ei he lowe o highe
me allici ies a e also associa ed wi h di e en en i onmen s (see
hei Table 2). This obse a ion mo i a ed he inclusion o hese
A219, page 4 o 19
S oppache , D., e al.: A&A, 693, A219 (2025)
10.8 11.0 11.2 11.4 11.6 11.8
-14
-13
-12
-11
z=0.56
log10
(
M
*
[
M
])
log10
(
sSFR
[
y
1
])
0.00
0.04
0.08
0.12
0.16
0.20
N
gal
0.00
0.04
0.08
0.12
0.16
0.20
N
gal
low
-SFR
passi e
ed
low
-
Zcold
high
-
Zcold
12.5 13.5 14.5
2.2
2.4
2.6
2.8
z=0.56
log10
(
M i
[
M
])
g i
0.00
0.04
0.08
0.12
0.16
0.20
N
gal
0.00
0.04
0.08
0.12
0.16
0.20
N
gal
low
-SFR
passi e
ed
low
-
Zcold
high
-
Zcold
Fig. 2. Sub-samples ex ac ed om he en i e da ase o he SAM-
CMASS mock galaxy ca alogue, Gal-dens, as desc ibed in Table 1
and ep esen ed by colou ed con ou s on he (g-i)-M i pa ame e space
a z e =0.56. The numbe densi y dis ibu ion o he en i e da ase is
depic ed as g ey, loga i hmically binned hexagons in he backg ound.
The ho izon al solid ed line ma ks he classic sepa a ion o ed and
blue galaxies, (g-i) =2.35 (Mas e s e al. 2011).
sub-samples in he cu en analysis o in es iga e whe he he
assembly and e olu ion o galaxies wi hin hese sub-samples
occu ed h ough sepa a e o ma ion channels, simila o he o -
ma ion pa hs o luminous ed galaxies (LRGs) in obse a ions
(e.g. Mon e o-Do a e al. 2017b). I is impo an o no e ha he
blue-cloud popula ion is explici ly excluded om bo h he low-
Zcold and high-Zcold sub-samples. Fu he mo e, o he pu pose o
na a i e con inui y, hese sub-samples a e e e ed o as “mo e”
and “less” me al-en iched. Howe e , ha does no mean ha hey
a e me al poo . All galaxies in he sample, being luminous ed
galaxies, a e me al ich wi h cold gas-phase me allici y alues
o Zcold ∼
>9, as p edic ed by obse a ions (see e.g. Maiolino &
Mannucci 2019).
A e o mula ing ou selec ion c i e ia and iden i ying i e
sub-samples o modelled CMASS-galaxies, he e olu iona y
his o y o each galaxy in he samples needs o be de e -
mined. This is achie ed by using unique iden i ica ion numbe s
(pa en Index) o cen al da k ma e halos hos ing he galax-
ies o in e es , which allow one o ace hei main p ogeni o
halos h ough hei me ge ees back in ime. This in o ma ion
is p o ided by he halo inde and co esponding ee builde
algo i hm, in ou case ROCKSTAR (Beh oozi e al. 2013a) and
CONSISTENT TREES (Beh oozi e al. 2013b), espec i ely, bo h
o which can be accessed ia he COSMOSIM-da abase6. We
no e ha ou goal is o in es iga e how each galaxy sub-sample,
de ined a a ixed edshi o z e =0.56, e ol es o e cosmic
ime. This means ha each subse is acked h ough ime using
he main b anches o hei me ge ees. While galaxies may
unde go changes in s a o ma ion a es and me allici y o e
ime, hey emain in a ixed subse in ou analysis. Fo mo e in o -
ma ion on he echnical aspec o acking halos h ough cosmic
his o y, we e e o Appendix B. This app oach allows o he
s udy o he ue edshi e olu ion o galaxy and halo p ope ies
o each galaxy ha was included in a pa icula sub-sample. I
is c ucial o no e ha , using his echnique, his wo k ocuses on
6www.cosmosim.o g
Fig. 3. Halo mass assembly his o y: in he uppe panel we show he
edshi e olu ion o median alues o he halo mass, M i , acco ding
o he selec ion p ocedu e ou lined in Fig. B.1 o ou i e selec ed
sub-samples: low-SFR (solid blue line wi h whi e do s indica ing he
edshi alues o each snapsho ), passi e (solid ligh yellow line), ed
(sho -dashed ed line), low-Zcold (solid da k magen a line), and high-
Zcold (do ed-dashed g een line). The shaded egions ep esen he ange
spanning be ween he 32nd and he 68 h pe cen ile a ound he median.
Thei co esponding mass g ow h his o y ela i e o he e e ence ed-
shi o ou s udy, z e =0.56, as z0. In his panel, Xzdeno es he alues
o M i a a speci ic snapsho / edshi compa ed o he alues a z0(Xz0).
The ho izon al dashed black line indica es he h eshold o 50% o he
o al halo mass a z e .
galaxies ha we e he eddes a z e , bu hese ha e no necessa -
ily e ol ed ou he eddes a highe edshi s. This me hod is a
common p ac ice o examining he edshi e olu ion o galaxy
p ope ies in mock ca alogues. A schema ic ep esen a ion o
his selec ion and acking me hod can be ound in Fig. B.1 in
Appendix B.
3. Resul s
We p esen esul s on he edshi e olu ion and assembly his-
o y o galaxy p ope ies om modelled massi e and luminous
ed galaxies using he CMASS mock galaxies om he semi-
analy ical model GALACTICUS. We apply selec ion c i e ia
based on ypical galaxy p ope ies such as colou o s a o ma-
ion ac i i y o selec i e sub-samples as discussed ex ensi ely
in Sec ion 2. We emind he eade ha we use only cen al
galaxies in ou analysis.
3.1. Redshi e olu ion o galaxy and halo masses
In he uppe panel o Fig. 3, we show he edshi e olu ion o
he halo mass, M i 7, o ou i e selec ed sub-samples: low-
SFR (solid blue line wi h whi e do s indica ing he edshi
7The GALACTICUS model uses he mass de ini ions p o ided by
Eq. (6) in B yan & No man (1998) o de ine he da k ma e halo mass.
Fo u he de ails, see Sec . 2.5 and Eqs. (7) and (8) in Knebe e al.
(2018b).
A219, page 5 o 19

S oppache , D., e al.: A&A, 693, A219 (2025)
alues o each snapsho ), passi e (solid ligh yellow line), ed
(sho -dashed ed line), low-Zcold (solid da k magen a line), and
high-Zcold (do ed-dashed g een line). In his igu e and he
ollowing, we show median alues o all galaxies p esen in
each sub-sample along wi h he ange spanning be ween he
32nd and he 68 h pe cen ile, shown as shaded colou ed egions
using he abo e-de ined colou and line s yle keys. The lowe
panel o he same igu e co esponds o hei halo mass g ow h
his o y (Xz/Xz0) wi h Xzbeing he halo mass a a speci ic snap-
sho / edshi and Xz0being he halo mass hey hold a he
e e ence edshi o ou s udy z e =0.56. The lowe panel
u ilises he same colou scheme, line s yle keys, and s a is ical
me hods as in he uppe panel.
Ou esul s indica e ha all de ined sub-samples exhibi
compa able e olu iona y acks bu each sligh ly di e en halo
masses a z e . The low-SFR and high-Zcold sub-samples, as well
as passi e and ed sub-samples, show e y well-aligned e o-
lu ion, eaching he lowes (M i ∼1013 M⊙) and in e media e
(M i ∼2×1013 M⊙) mass egimes, espec i ely. In con as ,
low-Zcold galaxies a e excep ions, acqui ing signi ican ly highe
halo masses o a ound M200c ∼1014 M⊙compa ed o galax-
ies om he o he ou sub-samples. Howe e , all galaxies s ill
assemble hal o hei masses a simila edshi s be ween 1.2<
z<1.4.
The edshi e olu ion o he s ella mass, M∗, mi o s he
ends obse ed o halo mass e olu ion; he e o e, a sepa a e
plo is no p o ided. Ins ead, he ollowing esul s a e epo ed:
aligned wi h esul s on he halo mass, he low-Zcold galaxies con-
sis also o he mos massi e ones in s ella mass, which assemble
hal o hei M∗a z∼1.2, while low-SFR and high-Zcold galax-
ies al eady comple ed hal o hei mass assembly a z∼1.5.
Fu he mo e, he low-Zcold (high-Zcold) galaxies show he high-
es (lowes ) s ella - o-halo mass a io, SHMR =M∗/M i . O he
sub-samples show in e media e alues, wi h low-SFR-galaxies
holding alues compa able o high-Zcold galaxies, and ed- and
passi e-galaxies alues simila o low-Zcold. In e es ingly, he
e olu ion o he SHMR as a unc ion o edshi peaks a z∼3.5
wi h SHMR ∼0.01 o he low-SFR and high-Zcold samples. A
simila peak can be ound o he es o he sub-samples bu
sligh ly la e . Fu he mo e, om z∼1.5 o lowe edshi s he
SHMR e olu ion is almos cons an ac oss all sub-samples.
3.2. Redshi e olu ion o he cold gas and black hole masses
A e examining he e olu ion o s ella and halo masses, he nex
s ep is o in es iga e he assembly his o ies o he co esponding
cold gas, cold gas ac ion (CGF), and cen al black hole masses.
In Fig. 4we show he edshi e olu ion o he cold gas mass,
Mcold, which ep esen s he gas a ailable o con e sion in o
s a s. The s eady g ow h in halo and s ella mass is suppo ed
by a consis en ly declining supply o Mcold and a dec easing
cold gas ac ion, CGF =Mcold/M∗, owa ds la e cosmic imes
o all sub-samples excep low-Zcold. low-Zcold galaxies exhibi
a cons an CGF and main ain an ex ensi e ese oi o cold
gas. No ably, du ing hei la e- ime e olu ion a e z∼2, hey
we e able o accumula e addi ional cold gas, esul ing in a la ge
ese oi a lowe edshi s compa ed o highe edshi s. This
sugges s ha hese galaxies a e gaining addi ional uel h ough
hei me ge ac i i y and smoo h acc e ion om he cosmic web.
This scena io is consis en wi h he e olu ion o hei black hole
masses, MBH, as shown in Fig. 5. In o he wo ds, he mos mas-
si e galaxies also exhibi he highes MBH and possess he la ges
M i
[
M
]
1012
1013
1014
z
X
z
/X
z
0
0.56 0.7 0.85 1 1.2 1.5 2 3 4
0.0
0.2
0.4
0.6
0.8
1.0
z
Mcold
[
M
]
0.56 0.7 0.85 1 1.2 1.5 2 3 4
107
108
109
1010
MBH
[
M
]
104
105
106
107
108
z
X
z
/X
z
0
0.56 0.7 0.85 1 1.2 1.5 2 3 4
0.0
0.2
0.4
0.6
0.8
1.0
Fig. 4. Redshi e olu ion o median alues o he cold gas mass, Mcold
– he ac ion o gas a ailable o be con e ed in o s a s – o he di e -
en sub-samples. The igu e u ilises he same colou scheme, line s yle
keys, and s a is ical me hods as in Fig. 3.
Fig. 5. Black hole mass assembly his o y: in he uppe panel he ed-
shi e olu ion o median alues o he galaxy’s supe -massi e black
hole, MBH is shown. The co esponding mass g ow h his o y ela i e o
he e e ence edshi z e =0.56 o ou s udy, is displayed in he lowe
panel, ollowing he same de ini ions as in Fig. 3. The igu e u ilises he
same colou scheme, line s yle keys, and s a is ical me hods as in Fig. 3.
ese oi o Mcold o sus ain hei con inued s a o ma ion. Con-
e sely, galaxies wi h lowe M i ,M∗, and MBH consume hei
cold gas a highe edshi s. These galaxies we e among he
i s and as es o assemble hal o hei s ella and black hole
masses (see, e.g., he high-Zcold and low-SFR samples in he
lowe panel o Fig. 5). The ollowing sec ions explo e po en ial
easons o he signi ican di e ence in e olu ion obse ed in he
Zcold sub-samples.
A219, page 6 o 19
S oppache , D., e al.: A&A, 693, A219 (2025)
3.3. Redshi e olu ion o in insic galaxy p ope ies
Un il now, he discussion has cen ed on he assembly and
g ow h his o y o mass- ela ed p ope ies. He e he ocus shi s
o addi ional p ope ies such as s a o ma ion, me allici y, and
colou . The e o e, we show in Fig. 6, om op o bo om,
he edshi e olu ion is p esen ed o : (a) he cold gas-phase
me allici y, Zcold,(b) he obse ed SDSS colou ( -i), (c) he
s a o ma ion a e, SFR, and (d) he s a o ma ion a e den-
si y, SFRD, no malised by he numbe o galaxies in each
sub-sample a a pa icula edshi . Thin e ical dashed lines
ma k he edshi s z=[0.7,1.4,2.1,3.5], highligh ing p ominen
ea u es in he ( -i) colou e olu ion in panel b.
A low edshi , high-Zcold galaxies a e he mos me al
en iched, as expec ed om hei selec ion c i e ia. Galaxies o
he low-SFR sample exhibi compa able me allici ies o high-
Zcold galaxies, while hose in he ed and passi e samples show
he second highes gas-phase me allici ies. As an icipa ed, he
low-Zcold galaxies a e he leas me al en iched a z e . In e es -
ingly, a z∼2.5, his end e e ses, wi h low-Zcold galaxies
becoming he mos me al en iched, he highes Zcold. Mo eo e ,
he high-Zcold and low-SFR samples exhibi apid me al p oduc-
ion a highe edshi , as indica ed by hei s eepe slopes in he
Zcold e olu ion be ween 2<z<3in panel a o Fig. 6, compa ed
o he o he sub-samples. A e his pe iod, he p oduc ion a e
slows down be ween z∼2and z e . In con as , low-Zcold galaxies
show a peak in Zcold be ween 2∼
<z∼
<3, ollowed by a con inuous
decline a la e imes.
In compa ison o Zcold, we ind li le a ia ion in he e o-
lu ion o ( -i)-colou wi h cosmic ime among ou conside ed
sub-samples, as shown in panel b o Fig. 6. The only excep-
ion is a sho ime in e al o 1∼
<z∼
<1.5whe e he low-SFR,
passi e, and ed samples exhibi colou s wi h ( -i) 0.25 edde
han he low-Zcold and high-Zcold samples. This is puzzling, as
hei colou e olu ion is o he wise simila be o e and a e his
pe iod. A simila beha iou in colou e olu ion has been sug-
ges ed in ano he s udy using he same galaxy o ma ion model
(p i a e communica ion wi h Tanca a, in p ep.). The cause o
his gap be ween sub-samples is cu en ly unclea , bu Tanca a
e al. discuss his aspec in mo e de ail in hei upcoming wo k.
Mo eo e , du ing his ime in e al, he colou e olu ion emains
cons an ac oss all sub-samples. I is also no ewo hy ha he ( -
i) e olu ion demons a es ou p ominen ea u es, highligh ed by
e ical dashed lines: a maximum a z∼0.7, he edge o a con-
s an colou e olu ion in e al om 1∼
<z∼
<1.5as men ioned
abo e, and wo minima a z∼2and z∼3.5, espec i ely.
The i s minimum in he colou e olu ion occu s a ound
z∼3.5as a sho , apid d op, ollowed by a p ominen min-
imum a z∼2(panel b), coinciding wi h he “cosmic noon”
– he peak o s a o ma ion in cosmic his o y (Madau &
Dickinson 2014). Du ing his pe iod, all galaxies discussed in
his s udy eached hei blues colou s. Simul aneously, he low-
Zcold sample shows a peak in Zcold (panel a). In e es ingly, un il
z∼1.5, all galaxy samples exhibi he same median colou
e olu ion and minima in bo h ( -i) and (g-i) colou s. Howe e ,
hei median s a o ma ion a es (SFRs) di e , as shown in
panel c. The low-Zcold, passi e, and ed samples display highe
SFRs o app oxima ely sim3–5 M⊙y −1, compa ed o he lowe
a es seen in low-SFR and high-Zcold galaxies. A e z∼2, he
galaxies unde go cons an eddening un il z∼1.5, ollowed by a
pe iod o no signi ican e olu ion un il z∼1. This epoch aligns
wi h he ime when hal o he s ella and halo masses we e
assembled in all samples, excep o low-Zcold. Fu he mo e, hei
co esponding mass g ow h unc ions e e se hei cu a u es
low-SFR passi e ed low-ZCold high-ZCold
Zcold
(a)
8.8
9.0
9.2
9.4
9.6
9.8
10.0
10.2
i
(b)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
SFR [
M
y
1
]
(c)
0
5
10
15
20
25
z
SFRD/N
gal
[
M
y
1
Mpc
3
]
(d)
0.56 0.7 0.85 1 1.2 1.5 2 3 4
10 11
10 10
10 9
10 8
Fig. 6. F om op o bo om, we p esen he edshi e olu ion o he
ollowing galaxy p ope ies: (a) he cold gas-phase me allici y, Zcold;
(b) he obse ed colou , ( -i); (c) he s a o ma ion a e, SFR; and (d)
he s a o ma ion a e densi y, SFRD, no malised by he numbe o
galaxies in each sub-sample a a pa icula edshi . The e ical hin
dashed lines ma k edshi s o p ominen line ea u es in ( -i). The igu e
u ilises he same colou scheme, line s yle keys, and s a is ical me hods
as in Fig. 3.
A219, page 7 o 19
S oppache , D., e al.: A&A, 693, A219 (2025)
– om g owing mo e apidly o mo e slowly – a his edshi
(see he lowe panel in Fig. 3).
A he las ea u e, a p ominen peak in ( -i) a z∼0.7, all
galaxies eached hei eddes colou s in ( -i) independen ly o
hei sub-sample assignmen . A simila e olu ion om blue o
edde colou s un il z∼0.7was also epo ed by Ma as on e al.
(2009) o modelled luminous ed galaxies. In addi ion, he same
peak can be obse ed in he (g-i) colou a he same edshi o
he low-Zcold and high-Zcold samples, while o he es o he
sub-samples, his peak occu s sligh ly ea lie in cosmic ime, a
z∼0.85.
The s a o ma ion a e densi y (SFRD), no malised by he
galaxy numbe coun (Ngal) in each sub-sample, is shown in he
panel d o he same igu e and does no indica e s ong a i-
a ions be ween he samples a cosmic noon. Howe e , sligh ly
highe SFRD/Ngal alues a e measu ed o he high-Zcold galax-
ies a ound z∼1.5, coinciding wi h he edge o he no-e olu ion
pe iod in colou seen in panel b. This end is also e lec ed in
he speci ic s a o ma ion a e (sSFR), whe e high-Zcold galax-
ies consis en ly show highe , o a leas simila , median sSFRs
as o he sub-samples a z>0.85. In e es ingly, he SFRD/Ngal
o ou sub-samples does no show he expec ed peak a ound cos-
mic noon. I is impo an o no e ha we no malised he SFRD
by he como ing olume and he numbe o galaxies in each sub-
sample o ensu e an unbiased compa ison ac oss sub-samples.
This esul s in lowe alues han he cosmic s a o ma ion a e
densi y p esen ed by Madau & Dickinson (2014). As shown in
he igu e, he cu es o all sub-samples indica e a mode a e
inc ease in e olu ion a highe edshi . Un o una ely, ou abil-
i y o explo e his u he is limi ed by he a ailable me ge ee
da a, which only acks galaxies consis en ly up o z=4.15.
None heless, an ea lie peak in he cosmic s a o ma ion a e
densi y8o all galaxies in he GALACTICUS model, as shown
in Fig. 4 o he THE MULTIDARK-GALAXIES elease pape
(Knebe e al. 2018b), be ween z∼3–4suppo s his hypo hesis
and may explain why we do no obse e a peak a cosmic noon.
To summa ise his sec ion, ou esul s indica e ha low-Zcold
galaxies consis en ly exhibi signi ican ly highe M∗,M i , as
well as he la ges black hole mass MBH in compa ison o o he
sub-samples, including high-Zcold galaxies, as shown in Figs. 3–
5. These galaxies also accumula e la ge ese oi s o cold gas
mass, Mcold, (unlike all o he sub-samples) and e mina e hei
e olu ion wi h mo e Mcold han hey possessed ini ially a high
edshi . Fu he mo e, hey assemble hei mass la e and mo e
apidly, and p oduce s a s mo e e icien ly due o hei abundan
supply o Mcold compa ed o high-Zcold galaxies.
The high-Zcold galaxies, on he o he hand, si on he
lowe -mass end o he spec um o M i ,M∗as well as MBH
and he e o e comple ed hei mass assembly ea lie and mo e
con inuously han hei low-Zcold coun e pa s. This is e lec ed
in hei lowe cold gas ac ion in compa ison o low-Zcold galax-
ies. In ou companion pape S19 i was no ed ha he e is
a p ominen bimodali y in Zcold a he ini ial edshi o ou
s udy z e =0.56. As discussed abo e, he au ho s could map
his bimodali y in low-Zcold and high-Zcold galaxies on speci ic
galaxy and halo p ope ies. We con i med hei hypo hesis ha
high-Zcold and low-Zcold galaxies o m ia dis inc pa hways and
co espond o wo sepa a e and dis inguishable samples o galax-
ies ha p esen he o e all popula ion o luminous and massi e
8We no e ha he cosmic s a o ma ion a e densi y is he cumula i e
sum o s a o ma ion a es no malised by he physical olume, bu no
addi ionally no malised by he numbe densi y o galaxies in each sub-
sample.
low-SFR passi e ed low-ZCold high-ZCold
log10
(
2
(
)
[
Mpc
2]
)
z=0.56
Gal-dens
1.0
1.5
2.0
2.5
[
Mpc
]
(
)/ (
)
e
- 1
1 2 5 10 25 50 95
-1.0
0.0
1.0
Fig. 7. Galaxy clus e ing unc ions: in he uppe panel, we show he eal-
space wo-poin co ela ion unc ion, ξ( ), a edshi z e =0.56 o all
sub-samples (using hei espec i e colou scheme and line s yle keys as
in Fig. 3) and he pa en sample o he SAM-CMASS mock galaxies,
Gal-dens (sho -dashed black line). In he lowe panel we display he
ac ional di e ence be ween he clus e ing unc ion o each sub-sample
(ξ( )) and ha o Gal-dens (ξ( ) e ).
galaxies a z e . We aim a unde s anding wha d i es hei dis-
inc e olu ion ia s udying hei clus e ing and loca ion in he
la ge-scale en i onmen o he cosmic web.
3.4. Galaxy clus e ing
In his sec ion, we s udy he galaxy clus e ing o ou di e -
en sub-samples o galaxies h ough he eal-space wo-poin
co ela ion unc ion (2PCF), ξ( ). We use he CORRFUNC so -
wa e package9 om Sinha & Ga ison (2017) and he s anda d
Landy & Szalay (1993) es ima o . We calcula e 2PCFSwi h 25
loga i hmic-spaced bins in he ange o 0.5< (Mpc) <150
assuming pe iodic bounda y condi ions. As s a ed p e iously,
he galaxy samples ha e he same numbe densi y bu di e en
mean alues o he s ella and halo masses, which is e lec ed in
he clus e ing.
In he uppe panel o Fig. 7we show he 2PCF o cen al
galaxies a edshi z e =0.56 o all sub-samples (using he
same colou and line s yle choices as in p e ious sec ions). We
also include he esul om he en i e sample o SAM-CMASS
mock galaxies, Gal-dens, as a e e ence (sho -dashed black
line). In he lowe panel o he same igu e, we plo he ac-
ional di e ence o ξ( ) o each sub-sample wi h espec o he
unc ion o Gal-dens,ξ( ) e .
As ou esul s indica e, he low-SFR sample and he en i e
sample o SAM-CMASS mock galaxies, Gal-dens, ha e nea -
iden ical co ela ion 2PCFS. This means ha he 20% o low-
s a o ming galaxies can mimic he clus e ing o he en i e
popula ion o SAM-CMASS mock galaxies. As we p e iously
desc ibed, Gal-dens is he pa en sample om which all sub-
samples we e ex ac ed ollowing a ce ain selec ion c i e ion
9h p://co unc. ead hedocs.io/en/mas e /index.h ml
A219, page 8 o 19
S oppache , D., e al.: A&A, 693, A219 (2025)
log10
(
2
(
)
[
Mpc
2]
)
z=0.56
Gal-dens
all
kno s
ilamen s
1.0
1.5
2.0
2.5
z=0.56
low-
Zcold
z=0.56
high-
Zcold
[
Mpc
]
(
)/ (
)
e
- 1
1 2 5 10 25 50 95
-1.0
0.0
1.0
[
Mpc
]
2 5 10 25 50 95
[
Mpc
]
2 5 10 25 50 95
Fig. 8. Galaxy clus e ing unc ions in di e en en i onmen s: in he uppe panels, we show he eal-space wo-poin co ela ion unc ion, ξ( ), a
z=0.56 o galaxies in he pa en sample, Gal-dens (le panel), and o sub-samples low-Zcold (middle panel) and high-Zcold ( igh panel). In each
panel we show he clus e ing o all galaxies in he sample (dashed black line), kno galaxies (solid yellow line), and ilamen galaxies (solid blue
line wi h whi e do s). In he lowe panel, we p esen he ac ional di e ence in he clus e ing unc ion o he ilamen and kno popula ions (ξ( )),
espec i ely, wi h espec o he clus e ing o he en i e sample (‘all’, ξ( ) e ).
lis ed in Table 1. This may la gely be coinciden al, as p edic-
ions o galaxy and halo p ope ies om bo h he pa en sample
and he low-SFR sub-sample a z e as well as hei subsequen
e olu ion show no compa able ends.
Addi ionally, he clus e ing unc ions o ou passi e and ed
samples exhibi e y simila 2PCFS, while low-Zcold galaxies
show a signi ican ly highe clus e ing ampli ude. In con as , he
leas clus e ed sample is high-Zcold, which displays he lowes
ampli udes excep o e y small sepa a ions. A sligh u no e
in he clus e ing s eng h is obse ed a scales smalle han
<2 Mpc, whe e high-Zcold (low-Zcold) galaxies clus e mo e
(less) s ongly. In e es ingly, he low-Zcold and he high-Zcold
samples ep esen he uppe and lowe limi s in he o al clus-
e ing s eng hs. These di e ences in he clus e ing a e d i en
by he mean halo masses, wi h passi e, ed, and low-Zcold galax-
ies ypically esiding in he mos massi e and consequen ly he
mos clus e ed halos.
We also in es iga e he edshi e olu ion o he eal-space
clus e ing unc ion, hough we do no dedica e a sepa a e plo
o i , as he clus e ing s eng h shows only mild a ia ion wi h
edshi . Galaxies in he low-Zcold (high-Zcold) sample a e always
mo e (less) s ongly clus e ed while he low-SFR sample shows
an in e media e s eng h be ween low-Zcold and high-Zcold. As
expec ed, hese indings wi h he cosmic e olu ion o he halo
masses o each galaxy sub-sample. A smalle sepa a ions, he
clus e ing signal o low-Zcold galaxies dec eases apidly wi h
inc easing edshi , whe eas low-SFR and high-Zcold galaxy pai s
emain de ec able a <2 Mpc o <5 Mpc a z=0.7o
z=3.51, espec i ely. Due o he gi en limi a ion in pa icle
esolu ion and simula ion box side-leng h, he 2PCFSexhibi
g owing unce ain ies a la ge sepa a ions.
3.5. Galaxy p ope ies and he la ge-scale en i onmen
We ha e shown ha he low-Zcold and high-Zcold galaxy samples
ep esen he uppe and lowe limi s o he pa ame e space o
a ious galaxy p ope ies (see e.g. Figs. 1,2,3,o 5). In his
sec ion, we e isi ou analysis by classi ying he galaxies in ou
de ined sub-samples acco ding o hei la ge-scale en i onmen-
al a ilia ion o he cosmic web, ca ego ised as “mo e-dense” o
“less-dense” egions. To his ex en , we apply he VWEB code
(Ho man e al. 2012;Libeskind e al. 2012,2013;Ca lesi e al.
2014;Cui e al. 2018,2019) applying i o he da k ma e ca -
alogue ha unde pins ou galaxy o ma ion model. The code
de e mines he en i onmen al a ilia ion o he da k ma e halos
in which he galaxies eside acco ding o “kno s”, “ ilamen s”,
“shee s”, and “ oids” as al eady discussed in ou companion
pape S19 (see Appendix A o de ails). In his analysis, we
adop he ca ego ies kno s as “mo e-dense” and ilamen s as
“less-dense” egions.
The uppe panels o Fig. 8show he 2PCF om le o
igh o Gal-dens, low-Zcold, and high-Zcold galaxies in kno s
(da k blue lines wi h whi e do s) and ilamen s (ligh yellow
lines) as well as o all galaxies ega dless o he en i onmen
(sho -dashed black lines). The lowe panels show he ac ional
di e ence be ween he kno and ilamen popula ions ela i e o
he co esponding ull sample. As expec ed, we obse e a a i-
a ion in clus e ing s eng h depending on sepa a ion leng h and
la ge-scale en i onmen , as demons a ed o he en i e SAM-
CMASS mock galaxy sample (le panel). Speci ically, a smalle
sepa a ions, <10 Mpc, kno galaxies ( ilamen galaxies) clus-
e mo e (less) s ongly, while a la ge sepa a ions, he clus e ing
s eng h becomes simila ac oss bo h en i onmen s. The same
beha iou is obse ed o high-Zcold galaxies up o <25 Mpc.
Howe e , unexpec edly, low-Zcold galaxies do no ollow he
same end; ins ead, he clus e ing s eng h o kno , ilamen ,
and he o e all popula ion o low-Zcold galaxies is ela i ely sim-
ila . No ably, a he sepa a ion leng h o ∼10 Mpc, we ind a
dip in he clus e ing o kno galaxies, bu his ea u e is absen
o ilamen s galaxies. Mo eo e , his dip is mo e p onounced in
high-Zcold galaxies compa ed o low-Zcold ones.
To complemen ou galaxy clus e ing analysis, we com-
pu e he median alues o he galaxy and halo p ope ies o
low-Zcold and high-Zcold galaxies in ilamen s and kno s shown
in Table 2. As p e iously epo ed by S19, we ind a clea
endency o he halo mass, M i , o co ela e wi h he en i on-
men . In mo e de ail, he kno ( ilamen ) popula ion o high-Zcold
galaxies exhibi s median halo masses wi hin he 32nd and he
68 h pe cen ile o log10(M i [M⊙]) = 13.09+0.17
−0.17 (log10(M i
[M⊙]) = 12.97+0.15
−0.15) compa ed o he low-Zcold galaxies o
log10(M i [M⊙]) = 3.93+0.15
−0.14 (log10(M i [M⊙]) = 13.70+0.14
−0.12),
A219, page 9 o 19
S oppache , D., e al.: A&A, 693, A219 (2025)
Acknowledgemen s. We hank he anonymous e e ee o hei cons uc i e and
insigh ul commen s, which ha e signi ican ly imp o ed he quali y o his a i-
cle. DS is unded by he Spanish Minis y o Uni e si ies and he Eu opean Nex
Gene a ion Fond unde he Ma ga i a Salas Fellowship CA1/RSUE/2021-00720.
DS also wan s o hank B an Robe son o g an ing he ime o wo k on his
p ojec and José Oño be o his guidance and suppo on bu eauc a ic issues as
well as as he eam om Koblischek-byKa in o se ing excellen co ee in an
amazing a mosphe e in Weiz and u he D . Rosa Ma ia Laßnig o he kind and
p o essional suppo du ing he las yea s. The COSMOSIM-da abase used in his
pape is a se ice by he Leibniz-Ins i u e o As ophysics Po sdam (AIP). The
Mul iDa k da abase was de eloped in coope a ion wi h he Spanish Mul iDa k
Consolide P ojec CSD2009-00064. In addi ion, his wo k has bene i ed om
he publicly a ailable so wa e ools and packages: MATPLOTLIB (Hun e 2007);
Py hon So wa e Founda ion (h ps://www.py hon.o g) 1990–2023, e sion
2.7 and 3; ANACONDA (h ps://www.anaconda.com); PYENV (h ps://
gi hub.com/pyen /pyen ); SEABORN (h ps://seabo n.pyda a.o g/)
and STATSMODELS (Seabold & Pe k old 2010); ASTROPY(h ps://www.
as opy.o g/) (As opy Collabo a ion 2013,2018); JUPYTER NOTEBOOK
(h ps://jupy e -no ebook. ead hedocs.io/en/la es /); The Cen-
OS P ojec (h ps://www.cen os.o g), The Fedo a P ojec (h ps://
edo ap ojec .o g/), TOPCAT (Taylo 2013). We used OpenAI’s GPT-4 lan-
guage model o assis ance wi h language e inemen and d a ing pa s o he
manusc ip . ADMD hanks Fondecy o inancial suppo h ough he Fonde-
cy Regula 2021 g an 1210612. AK is suppo ed by he Minis e io de Ciencia
e Inno ación (MICINN), Spain unde esea ch g an PID2021-122603NB-C21
and u he hanks The Me In You o gi l in amou . NDP acknowledges suppo
om a RAICES g an om he Minis e io de Ciencia, Tecnología e Inno ación,
A gen ina.
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A219, page 17 o 19
S oppache , D., e al.: A&A, 693, A219 (2025)
Appendix A: In o ma ion on he adop ed galaxy
ca alogue: MDPL2-Galac icus
As GALACTICUS is p ima ily desc ibed in Benson (2012), wi h
addi ional ea u es ou lined in Knebe e al. (Sec. 2.2 and Tab. 1
2018b) as pa o he THE MULTIDARK-GALAXIES ca alogues,
we summa ise only i s aspec s mos ele an o his wo k. The
GALACTICUS semi-analy ic model inco po a es a s ella popu-
la ion syn hesis model om Con oy e al. (2009), an ini ial mass
unc ion om Chab ie (2003), and a dus model o Fe a a e al.
(1999). The de ini ion o he da k ma e halo mass is gi en by
M e (<R e )= ∆ e ρc
4π
3R3
e ,(A.1)
whe e ∆ e = ∆BN98 o MBN98 wi h ∆BN98 being he i ial ac o
as gi en by he Eq. (6) o B yan & No man (1998); ρcdeno es
he c i ical densi y o he Uni e se, and R e is he co espond-
ing halo adius a which he in e io mean densi y ma ches he
desi ed alue as speci ied on he igh -hand side o Eq. (A.1).
We no e ha ROCKSTAR o e s a ious halo mass de ini ions;
howe e , his e sion o GALACTICUS was un using his one.
The pa ame e s o galaxy o ma ion physics in GALACTI-
CUS we e de e mined h ough a manual sea ch o he pa ame e
space, aiming o ma ch a a ie y o obse a ional da a. These
include he z=0s ella mass unc ion o galaxies (Li & Whi e
2009), z=0K and bJ-band luminosi y unc ions (Cole e al.
2001;No be g e al. 2002), he local Tully-Fishe ela ion (Piza-
gno e al. 2007), he colou -magni ude dis ibu ion o galaxies
in he local Uni e se (Weinmann e al. 2006), he dis ibu ion
o disc sizes a z=0(de Jong & Lacey 2000), he black hole
mass o bulge mass ela ion (Hä ing & Rix 2004), and he s a
o ma ion his o y o he Uni e se (Hopkins e al. 2014).
This e sion o GALACTICUS employs a simple acc e ion
model whe e gas acc e es om he in e galac ic medium on o
he da k ma e halo, as ou lined by Benson e al. (Eq. (35)
in 2002). Cooling a es om he ho halo a e compu ed using
he adi ional cooling adius app oach om Whi e & F enk
(1991). Me allici y-dependen cooling cu es a e calcula ed wi h
CLOUDY ( 13.01, Fe land e al. 2013). The disc is modelled as
ei he a adia i ely e icien , geome ically hin, Shaku a & Sun-
yae (1973)- ype disc (i he acc e ion a e being be ween 0.01
and 0.3 ˙
MEdd, whe e ˙
MEdd being he Edding on acc e ion a e) o
o he wise as an ad ec ion-domina ed low-acc e ion hick disc,
ollowing (Begelman 2014). The model dynamically swi ches
be ween hese wo modes.
S a o ma ion is modelled using he p esc ip ion o
K umholz e al. (2009, i.e. hei Eq. (1) o he s a o ma ion a e
su ace densi y, and Eq. (2) o he molecula ac ion), assuming
ha he cold gas o each galaxy ollows an exponen ial adial dis-
ibu ion. The scale leng h o his dis ibu ion is de e mined om
he disc’s angula momen um by sol ing o he equilib ium
adius wi hin he g a i a ional po en ial o he disc+bulge+da k
ma e halo sys em (Gnedin e al. 2004). Me al en ichmen is
acked using he ins an aneous ecycling app oxima ion, wi h a
ecycled ac ion o 0.46 and yield o 0.035. Me als a e assumed
o be ully mixed in all phases, he eby acing all mass lows
be ween phases.
The supe no a eedback is implemen ed using a wind mass
loading ac o , β, compu ed as β=(Vdisc/250km/s)−3.5whe e
Vdisc is he ci cula eloci y a he disc’s scale adius. Gas
expelled om he galaxy by winds is e ained in a ese oi o
ou lowed gas, which g adually leaks mass back in o he ho halo
on a imescale o dyn/5, whe e dyn is he dynamical ime o he
halo a he i ial adius. Ma e ial is ans e ed om he disc o
he sphe oid on an ins abili y imescale, which is de ined by an
ins abili y pa ame e as desc ibed in E s a hiou e al. (1982) (see
also Eq. (1) in Knebe e al. 2018b).
GALACTICUS does no include a speci ic s a bu s mode.
Ins ead, s a o ma ion in he sphe oid occu s a a a e ˙
M⋆=
0.04Mgas/ dyn(V/200km/s)−2, whe e dyn is he dynamical ime
o he sphe oid a i s hal mass adius, and Vi s ci cula eloci y
a he same adius. The model acks he mass and spin o black
holes in de ail, assuming an ini ial seed mass o 100 M⊙. AGN
eedback is inco po a ed in bo h he “ adio” mode (see Benson
& Bowe 2010) and he “quasa ” mode (see Os ike e al. 2010)
wi h a black hole wind e iciency o 0.0024 being implemen ed.
The model uses he s anda d sphe oid implemen a ion adop ing
a sphe oid densi y p o ile (He nquis -p o ile (He nquis 1990)),
which is desc ibed by a single-leng h scale whe e s a s ace he
gas densi y.
I he (ba yonic) mass a io o wo me ging galaxies exceeds
1:4, a “majo ” me ge is assumed. In his scena io, he me ging
galaxies a e ans o med in o a sphe oidal emnan . O he wise, a
”mino “ me ge occu s, whe e he less massi e galaxy is inco -
po a ed in o he sphe oid o he mo e massi e galaxy, lea ing he
disc o he la ge galaxy una ec ed.
Appendix B: T acing modelled galaxies ac oss
cosmic his o y
Fig. B.1 p o ides a schema ic ep esen a ion o he selec ion
p ocedu e and acking o p ogeni o halos. This is achie ed
by using he unique iden i ica ion numbe s – pa en Index –
o cen al da k ma e halos hos ing he galaxy o in e es o
ace hei main p ogeni o halos on hei me ge ees back in
ime. This in o ma ion is p o ided by he halo inde and he
co esponding ee builde algo i hm. By de ini ion, he me ge
ee main b anch o he algo i hm applied o he da a used in
his s udy (e.g. ROCKSTAR and CONSISTENT TREES), is he
mos massi e p ogeni o b anch and can be aced on he le -
mos side o each sub- ee – he lowes mainLea Id – in he
iend-o - iends (FoF) g oups. Tha means in p ac ice ha he
main p ogeni o halo, he one o in e es , always has he low-
es ID (deno ed by he sa elli eNodeIndex) o he same
pa en Index and is also he mos massi e p ogeni o . Tha is
pa icula ly use ul gi en ha he MDPL2-Galac icus ca a-
logue includes millions o galaxies and sa elli e galaxies ha
need o be il e ed and aced o ind he speci ic one o in e es . I
is impo an o no e ha while he GALACTICUS model uses he
same IDs, i employs a di e en naming con en ion ha may no
be immedia ely ecognisable o hose amilia wi h ROCKSTAR
e minology. Fo addi ional in o ma ion, eade s a e e e ed o
he COSMOSIM-da abase.
I is no ed ha while i may seem excessi e o dedica e
an addi ional igu e solely o he acking o p ogeni o halos,
he companion pape in p epa a ion will demons a e ha he
sub-sample selec ion p ocedu e does no necessa ily need o be
conduc ed a a speci ic edshi . This lexibili y will lead o a
di e en app oach o a ge selec ion.
Appendix C: Illus a ion halo mass dependency on
en i onmen
In his appendix, we illus a e and assess he s a is ical simila i y
o galaxies in he low-Zcold and high-Zcold sub-samples based on
hei la ge-scale en i onmen s ( ilamen s o kno s). As shown in
A219, page 18 o 19
S oppache , D., e al.: A&A, 693, A219 (2025)
z
p ogeni o s
o S1x
a zx>zx-1
p ogeni o s
o S2x
a zx>zx-1
p ogeni o s
o S1
a za>z e
CMASS
S1 S2
S-1 S2aS1a
sample
S1
a z e
S1b
S2a
S2b
Z e = 0.56
(sample selec ion)
S1x S2x
p ogeni o s
o S1a
a zb>za
p ogeni o s
o S2a
a zb>za
p ogeni o s
o S2
a za>z e
sample
S2
a z e
high-
Z
cold
low-
Z
cold
sample
12.0
12.5
13.0
13.5
14.0
14.5
15.0
log10 (
M
i
[
M
])
ilamen s
kno s
Fig. B.1. Schema ic ep esen a ion o he selec ion p ocedu e and ack-
ing o p ogeni o halos. The selec ion c i e ia we e applied only once a
he z e =0.56, esul ing in he S1 and S2 om he en i e popula ion o
CMASS mock galaxies ca alogue. The p ogeni o s o hese samples a e
hen iden i ied a he subsequen simula ion snapsho using hei unique
iden i ica ion numbe , esul ing in he p ogeni o sub-samples S1a co -
esponding o S1-sample and S2a o S2-sample. This s ep is epea ed
and we subsequen ly mo e owa ds highe edshi s (S1x and S2x). This
p ocess is epea ed as we p og ess o highe edshi s, gene a ing S1x
and S2x. This app oach ep esen s he con en ional me hod o ex ac -
ing in o ma ion on he edshi e olu ion o galaxies in simula ions.
Fig. 8high-Zcold ilamen and kno galaxies exhibi dis inc clus-
e ing unc ions, e en hough he median halo masses o hese
galaxies di e by only 0.13 dex in M⊙. Con e sely, he median
halo masses o low-Zcold ilamen and kno galaxies a e sep-
a a ed by 0.23 dex in M⊙, ye hey show simila clus e ing
unc ions in bo h shape and ampli ude a z=0.56. In Fig. C.1,
we p esen iolin plo s showing he dis ibu ion o halo mass
(M i ) o high-Zcold and low-Zcold galaxies, wi h o e laid box
plo s in g ey. This plo isually con i ms ha he kno popula-
ion (displayed in blue by he le hal o he iolin) and he
ilamen popula ion (shown in yellow by he igh hal o he
iolin) beha e consis en ly wi h he indings om he clus e ing
analysis.
Thei median alues a e mo e sp ead ou , close o he edges
o he in e qua ile ange. high-Zcold galaxies, on he o he hand,
ha e median alues ha a e mo e closely aligned. Al hough he
median halo masses o high-Zcold galaxies in bo h kno s and il-
amen s a e simila , hei clus e ing beha iou di e s (Fig. 8).
Con e sely, low-Zcold galaxies clus e simila ly in bo h kno s and
ilamen s, despi e hei s a is ical dis ibu ions di e ing. To sup-
po hese obse a ions, we conduc ed a Kolmogo o -Smi no
(KS) es using he Py hon package SciPy.s a s o compa e
he ilamen and kno popula ions in bo h sub-samples.
The KS es is a obus me hod o assess whe he hei dis i-
bu ions a e s a is ically simila . The KS s a is ic ou pu s a alue
high-
Z
cold
low-
Z
cold
sample
12.0
12.5
13.0
13.5
14.0
14.5
15.0
log10 (
M
i
[
M
])
ilamen s
kno s
Fig. C.1. Violin plo isualising he dis ibu ion o halo mass (M i ) o
he sample. The high-Zcold galaxies a e shown on he le , and he low-
Zcold galaxies a e on he igh . Each iolin displays he dis ibu ion o
ilamen and kno galaxies. The le side o each iolin ep esen s he
ilamen galaxy dis ibu ion, while he igh side shows he kno galaxy
dis ibu ion. We ha e also o e layed box plo s in g ey, wi h he median
alues ma ked in whi e. This isual ep esen a ion con i ms he esul s
o ou KS es : ilamen and kno galaxies in he high-Zcold sub-sample
a e s a is ically close , while ilamen and kno galaxies in he low-Zcold
exhibi g ea e di e ences.
be ween ze o and one, which ep esen s he maximum dis ance
be ween he cumula i e dis ibu ion unc ions (CDFs) o he
compa ed samples. The KS s a is ic alues close o ze o indi-
ca e ha he dis ibu ions a e mo e simila , while alues close
o one sugges g ea e di e gence be ween he dis ibu ions. Fo
he high-Zcold sample, he KS es e u ned a alue o 0.15 (wi h
a p- alue <0.0515) when compa ing ilamen and kno galax-
ies. This esul indica es ha he wo dis ibu ions a e ela i ely
simila , wi h a mode a e di e ence o 0.15 be ween hei CDFs.
In he low-Zcold sub-sample, he KS es e u ned a alue o 0.3,
double ha o he high-Zcold sample. This la ge alue signi ies a
g ea e disc epancy be ween he dis ibu ions, meaning hey a e
less simila . We also conduc ed simila es s in na ow halo mass
bins and ound consis en esul s.
15 The p- alue indica es he s eng h o e idence agains he null
hypo hesis, wi h a lowe p- alue sugges ing ha he obse ed esul s
a e less likely o ha e occu ed by chance, he eby lending mo e c edi-
bili y o he ob ained s a is ics. Typically, p- alues smalle han 0.05 a e
conside ed o indica e s a is ical signi icance.
A219, page 19 o 19