Title: Structure and substructure in the stellar halo of the Milky Way

Cover Page

The handle http://hdl.handle.net/1887/33295 holds various files of this Leiden University dissertation.

Author: Pila Díez, Berenice

Title: Structure and substructure in the stellar halo of the Milky Way

Issue Date: 2015-06-16

halo of the Milky Way

Proefs hrift

terverkrijging van

degraadvanDo toraan deUniversiteitLeiden,

opgezagvanRe torMagni usprof.mr. C.J.J.M.Stolker,

volgensbesluitvanhetCollegevoorPromoties

te verdedigenopdinsdag16juni2015

klokke11.15uur

door

Bereni e PilaDíez

geborente Logroño,Spanje

in1986

Promotor: Prof. dr. K.H.Kuijken

Referent: Prof. dr. E.Tolstoy UniversityofGroningen

Overigeleden: Prof. dr. H.J.A.Röttgering UniversityofLeiden

Prof. dr. S.F.PortegiesZwart UniversityofLeiden

Dr. A. G.A. Brown UniversityofLeiden

Dr. H. Hoekstra UniversityofLeiden

ISBN978-90-9029080-5

Anele troni versionofthisthesisisavailableathttp://opena ess.leidenuniv.nl

Its ontent anbe opied anddistributed providedthatpermissionisgrantedfor

alljournal-published material. Creditshould begiven to theauthorfor original

ontentortotheauthorsofanyreferen edmaterial.

Theworkdes ribedin thisthesisispartoftheNetherlands'Resear hS hool

forAstronomy(NOVA).

The overshowsanimageofM54,aglobular lusteroftheSagittariusdwarf

galaxy(Credit:ESO/VLT,ID:eso1428a). The foregrounddisplaysanedited pi -

tureof Leiden's Observatory (Oude Sterrewa ht). Both theforeground and the

graphi design are opyrightof the thesisauthor. The fontis CharterBold, by

BitstreamIn . (designer: Matthew Carter).

(AndréGide, 1952)

1 Introdu tion 7

1.1 A Universeofgalaxies . . . 7

1.2 Stellar tra ersforGala ti stru ture . . . 12

1.3 TheMilkyWay . . . 18

1.4 Thisthesis. . . 22

2 Askewersurvey ofthe Gala ti halo fromdeep CFHTand INT images 23 2.1 Introdu tion. . . 24

2.2 Observationsanddatapro essing . . . 24

2.3 Stellar radialdensityproles . . . 31

2.4 Dis ussion . . . 40

2.5 Con lusions . . . 47

3 A KiDSview on the stru ture ofthe Gala ti halo 49 3.1 Introdu tion. . . 50

3.2 Surveyandstellar atalogues . . . 50

3.3 Stellar radialdensityproles . . . 53

3.4 Dis ussion . . . 66

3.5 Con lusions . . . 72

4 Findinghalo streams with a pen il-beamsurvey new wrapsin the Sagittarius stream 75 4.1 Introdu tion. . . 76

4.2 Observationsanddatapro essing . . . 77

4.3 TheSagittariusstream. . . 85

4.4 ThePalomar5streamandtheOrphanstream . . . 96

4.5 Con lusions . . . 100

5 Asear hforstellar tidaldebrisofdefun tdwarfgalaxiesaround globular lusters in the innerGala ti halo 103 5.1 Introdu tion. . . 104

5.3 Methodology . . . 112

5.4 Results. . . 124

5.5 Dis ussion . . . 129

5.6 Con lusions . . . 144

6 Sear hfor halo substru turein KiDS 147 6.1 Introdu tion. . . 148

6.2 Observationsanddatapro essing . . . 149

6.3 Sear hforoverdensities . . . 149

6.4 Dis ussion . . . 167

6.5 Con lusions . . . 169

Bibliography 171

Samenvatting 179

Summary 183

Curri ulumVitae 187

A knowledgements 189

BHB BlueHorizontal Bran h

CMD ColourMagnitudDiagram

EBS EasternBandStru ture

MSTO MainSequen e TurnO

Pal 5 Palomar5

RC RedClump

RGB RedGiantBran h

Sgr Sagittarius

a knowledgements

This thesisis based on observations made with ESO Teles opes at the La Silla

ParanalObservatory aspart oftheKiDS publi survey.

ItisalsobasedonobservationsmadewiththeIsaa NewtonTeles opethrough

programIDs I10AN006, I10AP005, I10BN003, I10BP005,I11AN009, I11AP013

and MegaPrime/MegaCam, a joint proje t of CFHT and CEA/IRFU, at the

Canada-Fran e-Hawaii Teles ope (CFHT).The Isaa Newton Teles ope isoper-

atedontheislandofLaPalmabytheIsaa NewtonGroupintheSpanishObser-

vatoriodel Roquede losMu ha hosof theInstituto deAstrofísi a deCanarias.

TheCFHTisoperatedbytheNationalResear h Coun il(NRC)ofCanada,the

InstitutNationaldesS ien edel'UniversoftheCentreNationaldelaRe her he

S ientique(CNRS)ofFran e,andtheUniversityofHawaii.

Most of the data pro essing and analysis in this work has been arried out

using Python and, in parti ular, the open sour e modules S ipy, Numpy, As-

troAs iiData and Matplotlib. Top at and Stilts have been used for o asional

tablemanipulation.

Introdu tion

1.1 A Universe of galaxies

Galaxiesarethefundamentalblo ksoftheUniverse'slarges alestru ture. Galax-

ies are gravitationally bound entities that reside at the entre of dark matter

(sub)haloes, and ontainsu ientbaryoni matter totrigger starformation,lo-

alized hemi al and nu lear rea tions that produ e ele tromagneti radiation.

Galaxies onsist of gas, dust, i y mole ules, stars, planets and dark matter in

varying proportions. Gas, dust and i e mole ules together with planets'interi-

ors, surfa es and atmospheres are involved in hemi al rea tions, and thebasi

elements of the Periodi Table ranging from hydrogen to ironare involved

in the nu lear rea tions that take pla e in the stellar interiors. Be ause of the

dierentenergiesat whi hthese pro essestakepla e,theyshowtheirsignatures

inele tromagneti radiationovera widerangeofwavelengths.

Galaxies omeinawiderangeofsizes,masses,andshapes,whi harearee -

tionoftheirevolutionarystageandpasthistory,andthey anbe lassiedinthe

Hubblediagram(seeFigure1.1). Irregulargalaxieshoststarsthatfollow omplex

orbits without a well dened rotation entre, and may be abundantin gas and

dust (with the ex eption of dwarf irregulars). Spiral galaxies are also gas-ri h

star-formingsystems but,unlikeirregulargalaxies, theyare rotationsupported,

resultingin a well-dened set of stru tural omponents: an inner bulge, a disk

withspiralarms,anellipsoidalhaloand, sometimes,a entralbar. Itisbelieved

that thepresen e or absen eof a baris dependent onthe massavailable in the

galaxyespe iallythe entral massofthegalaxy andonthegas+stars todark

mattermassratio,aswellasonitsintera tionhistory. Thesetwotypesofgalaxies

ontain louds of oldgas dense enough to undergo gravitational ollapses and

keepprodu ingstars. By ontrast, ellipti algalaxiesarenostar-forming andel-

lipsoidal,withtheir starshavingmetastableorbits arounda welldened entre.

Ellipti algalaxies,however,havealsobyandlargeexhaustedorheatedtheir old

mole ulargas,and annotformanynewgenerationofstars. Forthisreasontheir

Figure1.1: Hubble's lassi ation diagram, as builtbytheGalaxyZoo proje t.

Eindi ate ellipti algalaxies,S andSBindi ate spiralandspiral-barred galaxies

respe tively,andIrrindi atestheirregulartype.

spe traaredominatedbyoldlow-massstars. Thesetwo hara teristi s(stellaror-

bitsand oldgas ontent)thusleadtomorphologi aldieren esbetweentypesof

galaxiesandafundamental dieren eintheirstellarpopulationmake-up,whi h

isree tedin theirspe tralenergydistributions (SED).

Galaxies over a large range of total luminosities, from

10 ³ L ⊙

^to

10 ¹² L ⊙

^,

giving riseto a relative lassi ation of galaxies into (ultra-)faint, intermediate,

bright or ultra-luminousgalaxies. They an alsohavea variety ofmasses, from

10 ⁵ M ⊙

^to

< 10 ¹³ M ⊙

^{intotalmass,leadingtoa} lassi ationintodwarf,medium andgiantgalaxies. Irregularandspiralgalaxiesaretypi allyasso iatedwiththe

intermediateand smaller massranges, whereasellipti al galaxies are asso iated

withallmassranges. The urrenttheoryforgalaxyformationlinksthisobserved

distributiontotheirassemblyhistory andevolutionthrough thepro ess ofgrav-

itationala retion(Coleet al.1994),aswewill seeinthefollowingse tion.

1.1.1 Galaxy formation and evolution

It is well known that a losed, isolated, isotropi and perfe tly uniform system

an be onsidered in equilibrium, and therefore will not undergo any evolution

in the absen e of external for es. To the best of our knowledge, the Universe

is a losed, isolatedand isotropi system, but itis notand was nota perfe tly

uniform system at the Epo h of Re ombination and photon de oupling, as the

Cosmi Mi rowaveBa kgroundshows. This la kofuniformityisthereasonwhy

weobserveadynami andevolvingUniverse, insteadofa simplehomogeneously

expanding Universe. However any theory of galaxy formationneeds to explain

howthese inhomogeneitiesoriginatedandhowtheyevolvedinto anin reasingly

lusteredandinhomogeneousstate.

Thetheoryof theBig Bangstatesthat theUniversewasbornfrom a singu-

larityin a very high densitystatethat underwent a brief exponentialexpansion

earlyon(theInation). It has ontinuedto expandand oolsin e. The urrent

paradigm for the early Universe is that primordial quantum u tuations were

ampliedbytheInationand lefttinydensityvariationsspread throughoutthe

Universe,whi h grewthrough gravitational instability. These densityvariations

weretheseeds for urrentgalaxies. Asa smalloverdensitystartstogravitation-

allyattra tmatter,themorematterita retes,be ominganin reasinglystrong

gravitational well. Eventually these density seeds a reted enough gas to form

loudsthat ould(gravitationally) ollapseandprodu etherststarsandgalax-

ies. Theseprotogalaxiesinturnmergedwithea hotherintoin reasinglymassive

galaxies. Thismerging growthme hanismknownas thehierar hi alformation

s enario omprises, together with the Big Bang theory, gravity and the early

Universeobservations,the urrentparadigmforgalaxyformation(White&Rees

1978).

Gravitationalintera tionsbetweengalaxies aninvolvepro essesoffourtypes.

They anleadtomassgrowthormassloss,aswellasmorphologi alanddynami al

hanges. Thesepossiblepro essesarehigh-speeden ounters,galaxymergers,tidal

strippinganddynami alfri tion. Simplyput,high-speeden ountersarethosein

whi hthedieren einvelo itybetweenthetwogalaxiesisenoughin omparison

to their gravitational pull to prevent them from slowing down and be oming

orbitallyboundobje ts(i.e.,theirintera tionislimitedtooneevent),andtheyare

hara terizedbyhigh-speedpro essesthat perturbthegalaxies. Oftenthistype

ofintera tionsrequire numeri alsimulations in order to beunderstood, but,in

thesimpler aseinwhi htheinternalvelo itydispersionoftheperturbedgalaxies

ismu hsmallerthantheen ountervelo ity,theintera tion anbeapproximated

asa tidalsho k,whi h auses oolingandexpansionofthesystem,andpotential

massloss.

Galaxymergersarethedire tresultofa loseen ounterinwhi htwosystems

haveasu ientlyloworbitalenergytomakethemslowdownandmixwithea h

other,eventuallylosingallmorphologi al signsofoneor bothof theprogenitors

andbe omingoneintegratedsystem. "Anyboundorbitwill eventuallyleadtoa

mergerbe ausethetidalintera tionbetweentwogalaxiesalwaystransfersorbital

energy into internal energy", but "if the angular momentum is high and if the

orbitalenergyisnotlowenough,themergerwillnothappenina Hubbletime 1

"

(Moetal.2010). Additionally,mergers analsohappenbetweeninitiallyunbound

galaxies, provided that the tidal intera tions of the en ounter drain su ient

orbital energy from the system. Mergingevents an be roughly separated into

two typesbasedontheirprogenitorsmassratio: majororminor. Majormergers

arethose involving two galaxiesof similarmasses (witha massratiolower than

a fa tor of

4

), whereas minor mergers are those involving two galaxies of quite

dierent masses. Major mergers ause the violent relaxation of the resulting

remnant, and oftenlead to thequi k onsumption or expulsion of the old gas.

Thiseventually turnsthe resultingsystem into a galaxy populated byold stars

withareddominatedspe trum. MinormergersinvolvephasemixingandLandau

damping,andoftenresultinasystemthatresembles(morphologi allyspeaking)

themostmassiveprogenitor.

Tidal stripping entails the removal of material from the outer regions of a

ollisionlesssystemas a resultof tidalfor es. Thispro ess istypi alin orbitally

bound systems (metastable) or in systems that are onthe way to be omingor-

bitallyboundorfullya reted(unstable). Thekeyelementofthispro essisthat

the tidal for es, in ombination with the rotation entrifugal for es of the sys-

tem,ex eedthebindingfor esforsomeofthematerialinthesatellitebodythe

materialsituatedfurther thana riti aldistan e fromthe entre ofthesatellite,

a distan e alled the tidal radius. As a result of tidal stripping, tidal streams

andtails formoutof thestripped material,leading andtrailing thesatelliteap-

proximatelyalongitsorbit. Tidaltails analso beobservednotonlyin satellite

galaxiesor globular lusters (Mateoet al.(1996),Odenkir hen etal. (2001))but

alsointhemergingof(disk)galaxies(Toomre &Toomre1972).

Finally,dynami alfri tionisthepro essbywhi hagalaxymovinginamu h

lessdenseenvironmentexperien esadragasittransfersenergyandmomentumto

theparti lesintheenvironment. This ausesorbitstode aywithtime,bringing

thegalaxyexperien ingthefri tiontowardsthe entreofthehost'spotentialwell.

Sin ethedragfor eisproportionaltothesquareofthemassofthegalaxy,there

isa masssegregation intheorbital de ay,bringingmoremassivegalaxiesdeeper

intothegravitationalwell,andleavingthemmoresus eptibletomergersortidal

stripping.

There is abundantobservationaleviden e for allthese pro esses in thelo al

Universe: stripped gas and stellar streams aroundgalaxies (Figure 1.2), galaxy

ollisions(Figure 1.3)or even rampressure stripping in galaxiesfalling through

a galaxy luster (Figure 1.4). However there is also ample eviden e of these

pro esses having o urred earlier in the Universe's history. Medium and high-

redshiftresear hshowsstatisti aleviden eforthemerger,massgrowthandtype-

evolutionofgalaxies(fromstar-formingtoquies ent),assummarizedinFigure1.5

(Muzzinetal.2013). Thisgureillustrateshowthenumberdensityofquies ent

galaxieshasbeenin reasingovertimeforallmassranges,andthatthehigh-mass

ut-o has grown with time (indi ating mergers). Simultaneously, the number

densityofhighmassstar-forminggalaxieshasbeenvirtually onstant,whilelow-

massstar-forminggalaxiesoutnumberthequies entones(indi atingmergersand

aneventualquen hing of star-forming galaxies). This, in ombination with the

typi alspe tralenergydistribution(SED)ofquies entandstar-forminggalaxies,

supports the hierar hi al formation s enario and the morphologi al and mass

1

TheHubbletimeisanestimatefortheageof theUniverse,basedon theapproximation

thattheUniversehasalwaysbeenexpandingatthesamerateitdoestoday.

Figure 1.2: Faint stellar tidal streams around the edge-on galaxy NGC 5907.

Image redit:R.J.Gabanyin ollaborationwithMartínez-Delgadoetal.(2010a).

evolutionofgalaxies.

Numeri al osmologi alsimulationshaveprovideda ontextfortheseobserva-

tions,andhaveshownthattheunderlyingme hanismsforhierar hi alformation

(theprimordial small density variations, in ombination with old dark matter

and gravity) an a tually reprodu e the observed history and mat h (most of)

the urrentobservations. On ethesimulations ompletethe( urrentlyongoing)

transitionfrom dark matter-onlyto ones that in lude hydrodynami s (gas) and

stellarpro esseslikefeedba k,stellarwinds,or entralAGNs,andover ome ur-

rentresolutionlimitations,these omparisons angrowfurtherin sophisti ation.

Togetherwithimprovementsin theobserved ensusofthepropertiesofgalaxies,

su h resear h will further rene our understanding of the pro esses that drive

galaxyformation.

1.1.2 A unique test ase: the Milky Way

TheMilkyWaya medium-sized, modestly star-formingspiral galaxyposesa

unique asestudyofgala ti stru ture,evolutionandminormergingintheLo al

Universe. Asobserverslo atedwithin theMilkyWay,wehavea

360 deg

^{view of}

theGalaxy,in ontrastwith theone-dire tionalview (eitherfa e-on oredge-on)

we have of any other galaxy. Additionally, as opposed to what happens with

mostothergalaxiesex eptthoseinour losestvi inity,intheMilkyWaywehave

a esstospatially resolvedstellarpopulationsandspatially resolvedkinemati s.

This means that the disk, bulge, spiral arms and halo an be studied not just

asbulk omponentswithmajorfeatures, butasresolvedstellarsystems. Finally

Figure 1.3: The Mi e galaxies (NGC 4676) in the pro ess of merging. Tidal

tails an be observed. Image redit: NASA, H. Ford (JHU), G. Illingworth

(UCSC/LO), M.Clampin (STS I), G. Hartig (STS I), the ACS S ien e Team,

andESA APOD2004-06-12.

our proximity allows us to probe intrinsi ally fainter stars and therefore study

obs ured or distant regions. Similarlyit givesus the possibility to build a very

a urate ensus of satellite galaxies, potentially omplete at the ultra-faint end

savethezoneofavoidan edeterminedbytheGala ti disk.

Thestudy of the MilkyWay through detailed analysis of its resolved stellar

populations isknownas"Gala ti Ar haeology".

1.2 Stellar tra ers for Gala ti stru ture

Asstarsorbittheirhostgalaxy,theysuertheperturbativeinuen eofmole ular

louds,star lusters, dark matter,spiralarmsor nearbymassiveobje ts,evenif

overallthegravitationalpotentialis losetoasteadystate. Spiralgalaxies onsist

ofa entral stellarbulge,a stellarthindisk and(potentially) athi kdisk,anda

stellarhalo. The starsin the diskare ae ted bytransient spiraldensitywaves

thata elerateandde eleratethemintheirorbits,butonthewholestellardisks

an be onsidered to be in a quasi-steady state. This may not be true for the

stars in the halo, however: at largeradii dynami al times are long, and hen e

perturbations and a retions due to minor mergers and subhaloes persist over

manyGyr. Studyingthedistribution,kinemati s, hemi al ompositionandage

ofstars in theintermediate andouter halo an therefore providesigni antun-

derstandingonthestru ture,evolutionanda retionhistoryoftheGalaxy. This

task anbe arriedoutusingphotometri data,spe tros opi dataorsimulations.

Parti ularly, when using onlyphotometri te hniques, ombining measurements

of dierenttypes of stars at distin t evolutionary stages, with diverse ages and

Figure1.4: AgasstreaminX-rays(Chandra X-RayObservatory), rampressure

stripped from galaxy ESO 137-001 as it falls through the galaxy luster Abell

3627(HubbleSpa eTeles ope). Credit: NASA,ESA,CXC.

Figure1.5: Galaxynumber densitydistribution alongdierentstellarmassesfor

dierentredshifts. Thedierentpanelsrepresentthe generaldistribution (left),

thequies entpopulation( entre)andthestarformingpopulation(right). Credit:

Muzzinet al.(2013).

metalli itiesand lo ated in dierentregions an help build a full pi tureof the

present-dayGalaxyas wellasitsformationanda retionhistory.

1.2.1 The H-R diagram

Oneof the fundamental photometri toolsfor resolved gala ti Astrophysi s or

resolvedstellarpopulationsistheHertzsprungRusselldiagram (H-Rdiagram).

ThestrengthoftheH-Rdiagram(leftpanelonFigure1.6)liesinitsdes riptive

and lassifyingpower,appli ablebothto fundamentaland observableproperties

of stars. The H-R diagram lo ates stars in a 2-dimensionalparameter spa e of

surfa e temperatureand intrinsi brightness,in whi h starsni ely separateinto

several evolutionary stage lo i. From an observational point of view, the H-R

diagramis onstru tedfromthespe traltypeor photometri olourofthestars

andtheirabsolutemagnitude,whi h requiresto haveanestimateforea h star's

distan e.

Stars in the H-R diagram an be grouped along iso hrones (right panel on

Figure1.6). These,astheirnameindi ates,arethelo iforstarsofequalage(and

equal omposition)butdierentmassintheH-Rdiagram. Iso hrones hara terize

starsthathavebeenbornfromthesameparent loudandareparti ularlyuseful

totra egroupsofstarsthathavesimilarageandarelo atedatsimilardistan es.

Figure1.6: Left: theHertzsprungRusselldiagramofstars. They-axesrepresent

absolutemagnitude(left)andluminosity(right)adthex-axesrepresentee tive

temperature (top) and spe tral lass (bottom). Right: The olour magnitude

diagramforglobular lusterM55;atheoreti aliso hroneforM55isshown(bla k

line). The y-axes represent absolute magnitude (left) and luminosity (right),

whereas the x-axes represent ee tive temperature (top) and olour (bottom).

Credits: CristopherS hneider (left),andB.J.Mo hejska andJ.Kaluzny(right).

Figure 1.7: Left: Colour magnitude diagram (CMD) in the dire tion of galaxy

lusterAbell990;starsatdierentevolutionarystagesarenotdistin tlygrouped

mainly be ause of the distan e ee t on apparent magnitudes. Right: Colour

olour diagram for a set of CFHT-INT elds ( hapter 3). The green dashed

lineindi ates thetheoreti al lo ationofthe mainsequen e stars; thebla kdots

indi atetheobserved oloursforpoint-likesour es.

1.2.2 Observational hara teristi s of stellar populations

Inpra ti e,theobservationalequivalentof anH-R diagram is onstru tedfrom

theapparentmagnitudeanda photometri olour(theratiooftheuxofa star

measuredthroughtwolters),andis alleda olourmagnitudediagram(CMD).

Insu h a diagram, thedierentevolutionary stages an mix severely along the

y-axiswhenthere isadistribution ofdistan esalongtheline ofsight. Similarly,

varyingmetalli itiesandagesbringsmallvariationsintemperatureforstarswith

thesamemassandevolutionarystage,moderatelybroadeningin olourthestellar

lo iandevolutionarytra ks. Theseee tsmakeitimpossibletodire tlyre ognize

typesof stars(see Figure 1.7, left panel) unless anoverdense stellar population

withawelldeneddistan e ispresentin theobservedeld. Conversely,be ause

photometri olours are distan e-independent, it is possible to some extent to

re over the information ontained within the H-R diagram by onstru ting an

observation olour- olourdiagram(Figure1.7,rightpanel). Thistypeofdiagram

an be su essful in re overing a main sequen e lo us, forinstan e; but,on the

other hand and depending on the set of lters, might be unsu essful in fully

separatingthe main sequen efrom the supergiantsat the redend (Coveyet al.

2007).

Stellar populationsen odepart of theformationhistory of anygalaxy, sin e

they ontainsibling starsformed at thesame time from thesame parent loud.

If stars from a given stellar population are still onned to a small region (in

youngopen lustersthat havenothadtimeto dissolveyet orin thehalo,where

dynami times alesarelonger),a learoverdensity anbeidentied intheform

ofaniso hronein a CMD,and a statisti al approa h an beused to a urately

hara terize its age and metalli ity by tting theoreti al iso hrones. Hen e de-

termining the birth-epo h of the stars and their ontribution to the Galaxy's

stru ture.

Theparti ularrelevan eoftheoreti aliso hronesforGala ti Ar haeologylies

notonlyintheirpowerto hara terizetheageandthemetalli ityofagivenstellar

population, but also onthe possibility of estimating itsdistan e to us provided

thattheothertwoparameters(metalli ityandage)areknown. Themetalli ityof

astar anbea uratelymeasuredthroughspe tros opy,anditsage anbederived

withreasonablea ura yassumingadistan eoramassisknown. However,with

justphotometri datatheseparameters anonlybeestimatedprovidedthatvery

a urate oloursareknown. Insu ha asethestar analsobe lassieda ording

toitsspe traltypeandevolutionarystage.

Thorough models of stellar interiors and stellar atmospheres have been de-

veloped in the last de ades to derive expe ted absolute magnitudes for spe i

evolutionarystagesandbuildrobustsetsoftheoreti aliso hrones(Girardi etal.

(2010);Marigoetal.(2008);Dotteretal.(2008a),forinstan e). However,ontop

ofobservationalun ertainties anddespitetheverypre isetheoreti aliso hrones,

some intrinsi hallenges remainsin e anage-metalli itydegenera y in absolute

magnitude and olour is present for some evolutionary stages. The reason for

thisis, ontheone hand,thatan in reasingmetal ontentalways oolsthetem-

perature of stellar atmospheres and de reases their luminosity be ause of the

asso iatedphoton absorption. This movesthe starsredwards andfaintwardsin

theH-Rdiagram. Ontheotherhand,theageofstarsalso ae tstheiree tive

temperature,withdierentevolutionarystagesbeingmoresensitivetoagethan

others(someexamplesareprovided inse tion1.2.3).

1.2.3 Stellar evolution stages suitable for Gala ti studies

Espe ially relevant to Gala ti Ar haeology are those stars that, be ause of a

small s atter in their intrinsi brightness, a brightevolutionarystage or a high

number density, an be used as distan e tra ers, age tra ers or spatial density

tra ers (respe tively). A brief des ription and hara terization of those types

nowfollows.

Mainsequen e starsare byfar themost abundanttypeof stars, be auseall

starsmustundergothisphaseatthebeginningoftheirlivesandthelessmassive

stars an spend many Gigayears in this stage. However, pre isely these most

abundantlow-massmainsequen estarsareintrinsi allyfaint,andmainsequen e

stars overa ontinuousrangeofabsolutemagnitudes. Bothfa tsmakethempoor

distan eandspatialdensitytra ers. However,there isoneex eption,thatofthe

so alledmainsequen eturno point(MSTO),whi hfora givenpopulation of

starswiththesameagerepresentsthemassorspe traltypeforwhi hstarsare

urrentlyabandoningthe orehydrogen-burningphase.Providedthatanestimate

forthedistan etothestellarpopulationexists(fromCepheidorRRLyraestars,

fromhorizontal bran h starsor fromthetip ofthered giantbran h stars),a t

totheMSTO anbeusedtodeterminetheageandmetalli ityofthepopulation.

Onthe otherhand, ifthe ageand metalli ityof a stellar population areknown

from spe tros opi works, a theoreti al iso hrone an be used, in ombination

withthedistan emodulus,toestimatethedistan e.

Thered giantbran h (RGB) stars arelow-to-intermediate massstars (

0 .3 − 8 M ⊙

^{)that havenishedfusing hydrogeninto helium in their ores but are still}

fusingitin ashellsurroundingthehelium ore. Theyareintrinsi allybrightand

relativelynumerous,whi hmakesthemgoodspatialdensitytra ers. Furthermore

thetipofthebran h(TRGB)hasanintrinsi absolutemagnitude(

M I = −4.0 ± 0 .05

^{, Madore &Freedman (1993), Frayn & Gilmore (2003)), whi h also makes}

thema uratedistan etra ers whena singlepopulation anbeidentiedin the

CMD.

Thered lump(RC)isanoverdensityin theH-R diagram onsisting of old

(eithermetal-ri horyoung)horizontal bran hstars,andthereforealreadyfusing

heliuminto arbon in their ores. The RChas anintrinsi absolute magnitude

thought to be independent of age and metalli ity (

M r = 0 .6

^{, Bellazzini et al.}

(2006 )),a verynarrow olourrange(avery spe i temperature,Correntietal.

(2010)), it is easily identied in the CMD and it indi ates an intermediate age

population.

Thebluehorizontalbran h(BHB)starsarealsohelium-burningstars,lo ated

bluewardoftheRRLyraestars. Theyaretheleastmassiveandoldestamongthe

horizontal bran h stars, andvery metalpoor. They areintrinsi ally bright and

blueandthereforeoneofthemostpra ti aldistan etra ersinthehalo,provided

that theBHB tailis avoided. Theyhavea spe i olour- olourrange (Deason

etal.2011)andalsoaspe i absolutemagnitude(

M g = 0 .5 ± 0.1

^{),whi hmakes}

thema uratedistan etra ers. Nonetheless,RRLyraestars,whi harepulsating

HB stars in the instability strip, are optimal distan e indi ators owing to the

relationbetweentheirpulsatingperiodandtheirabsolutemagnitude.

Substantialand ontinuedeortsbytheastronomi al ommunityhaveyielded

a uratephotometri sele tion riteria forthese typesofstars andredu ed on-

tamination by stellar types with similar olours. This onveniently allows for

pra ti almulti-bandanalyti starsele tionanddire t distan ephotometri par-

allax al ulationsofBHB,RC,TRGB andMSTOstars.

1.3 The Milky Way

Asbriey statedabove,the MilkyWay isa disk spiralgalaxy, moderatelystar-

formingandmediumsized. Itisoneoftwodominantgalaxiesintheso alledLo al

Group halo, together with the Andromeda Galaxy. Both galaxies are heading

towardsea hotherandwill ollideinapproximately4Gyr,eventuallyprodu ing

amergerremnant.

Thedynami onstraintsfromsatellitegalaxiesandglobular lustersindi ate

that the dark matter ontent of the Galaxy (that of the dark matter halo) is

1 − 3 · 10 ¹² M ⊙

^{(Battaglia et al. 2006), whereas the baryoni mass is estimated}

to be less than

∼ 10 ¹¹ M ⊙

^{. About}

75%

^{of the baryoni mass is lo ated in the}

disk,andmostoftheremainingbaryoni massresidesinthebulge. Ontheother

hand,thedark matter mass ontainedwithin 50kp (thedistan e to theLarge

Magellani Cloud) is only about one quarter of the estimated total (Sakamoto

etal.2003).

1.3.1 The stru ture of the Milky Way

The entral 3 kp of the Milky Way are dominated by a bulge, with a peanut

shape and mat hing kinemati s, indi atingthe presen e of a bar. The bulge is

mainly omposed of an old population of stars, with a small range of ages but

a largedispersion in metalli ity and a metalli itygradient alongtheminor axis

ofthebulge(Zo alietal.2008). This suggeststhat theMilkyWay'sbulgeisa

mixturebetweena lassi al bulge(originatedearlyin thehistoryof theGalaxy)

andapseudo-bulgeoriginatedfromabu kleddis ,but thetimeofthisbu kling

andthereforetheageofthebulgeas astru tureisyetun lear.

Thediskhostsmostofthe oldgasanddustoftheGalaxy,andthereforemost

ofthestarformation. Itisoftendes ribedasa ombinationoftwosub omponents:

a thindisk with a verti als ale height

∼ 300

^{p and extending notfurther out}

than

R GC ≤ 15

^{kp , and a thi k disk with s ale height}

∼ 900

^{p and only old}

stars. Additionally, thedisk is warpedin its outerregions. The a tualorigin of

thethi k disk is stillun lear. Possible explanations are thindisk heating, early

low-in linationsatellitea retionsandanearlyturbulentgasdiskthat givesrise

tostarformationandeventuallysettlesintoathindisk. Moreover,thepresen eof

thea retionsubstru turedenominatedtheMono eros ring onfusestheproper

delimitationofthethi kdisk. Oneofthemain hallengesforthefuture onsistsof

ndingaproperandrobustdenitionforthesetwo omponents,beitkinemati al,

hemi al,stru turalor,preferably,dynami al.

Thestellarhaloisaspheroidal omponentthatspansallradiifromthe entral

partsofthebulgeouttoprobably

100

^{kp . It ontainsglobular lustersandstellar}

debris,aswellassomeofthesatellitegalaxies. Thestellardebris antaketheform

ofshellsand louds(whenthematerialhaslongagodepartedfromtheprogenitor

anditispopulatingtheapogala ti oninwide, heating-uporbits) ortheform of

streams (elongated strips of stars in relatively round orbits or still lose to the

progenitorortheperigala ti on). Additionally,therearealsoan ientdebris,but

these are only re ognizable in the phasespa e sin e by now they have already

spatiallymixedup(phasewrapped)withtherestofthehalo. TheESAsatellite

Gaia, urrently in operation, is expe ted to help unravel the halo phase spa e

with unpre edented a ura y and rea h the old heated debris ontained within

thedisk and theinner halo. Current al ulations indi ate that only

60%

^{of the}

halo'stotal luminositydensity an beexplainedby a smoothan ientspheroidal

omponent(Bellet al.2008);theother

40%

^{mostlikelyhasbeena reted.}

Figure1.8: Satellitegalaxies ir atheMilkyWay(in ompletelist). Credit: J.T.A.

deJong, afterJ.Bullo k.

1.3.2 The satellites of the Milky Way

Thehaloisdimandnotverydenselypopulatedbystars,butinterestinga retion

phenomenatakepla einit. Assoonasa urateextragala ti distan eindi ators

be ameavailable, two prominentSouthernskyobje ts,theSmallandtheLarge

Magellani Clouds,werequi klyidentiedassatellitegalaxiesorbiting theMilky

Way. Lateron,withtheadventofradioobservations,theirtidalintera tionwith

theMilkyWaywasdis overedintheformofagasbridge. However,onlyin1996

thersteviden e was gathered fora urrentdisruptionand annibalizing event

in the Milky Way: the Sagittarius dwarf galaxy (dis overed in 1994) is being

tornapart andassimilated bythe MilkyWay,in a stripping pro ess thatwraps

two tails at least

180 deg

^{aroundtheMilkyWay. Sin e then,with theadventof}

deeplarge-areasurveys,manymoresatellitegalaxieshavebeendis overedwithin

∼ 400

^{kp oftheGala ti entre,aswellasseveralnarrowandwidestreams. The}

ensusof satellitegalaxies (over 30, with8 to 9 newadditions justin 2015 and

only8 additions betweenthe '30s andthe '90s)and the ensusof stellar debris

(inauguratedin 1996 andpopulated sin e 2006)havegenuinely exploded in the

last de ade. It seems that, for now, the nextdis overy or improvement in the

hara terizationis alwaysone photometri tra er, one surfa emagnitude orone

magnitudedeeperawaythanallowedbythe urrentteles opes.

In the years between the lassi ation of the Magellani Clouds as satellite

galaxies and the dis overy of su h a ri h population of satellite dwarf galaxies,

many Globular lusters lustered groupsof oldstars andmetalli ities dierent

from that of theeld halo starshavebeendis overed and added to thelist of

haloobje ts. Theyaresystems with onlyone or two stellarpopulationsand no

dete teddark matter ontent. Someof themare onsidered to be nativeto the

MilkyWay,whileothersare urrently ataloguedasnativesofdwarfgalaxyhaloes

a retedintotheMilkyWay'shalo. The onne tionbetweenglobular lustersand

thelowest-massdwarf galaxies, theirrole in the galaxy formations enario, and

theirdieren eswiththeeldstarsofthehaloareyettobefullyunderstoodand

pla edwithin asinglepi tureoftheformationand evolutionofthehalo.

1.3.3 Stars in the halo

Halostars aretypi allyfound atvery largehelio entri distan es, making them

hard to dete t. However, their distan es and their presen e in lines of sight

away from the disk makes them mu h easier to identify, both spatially and on

CMDs. With CCD astronomy and the state-of-the-art

4 − 8

^meter teles opes, wehaverea hedenoughsensitivitytonallysurveythehaloinasystemati and

statisti allysigni antway,bothphotometri allyandspe tros opi ally.

Thehalo ismainly populated byold, metal-poor stars. Themain reasonfor

thisisthatitisnotana tivelystar-formingregioninanygalaxy. Coldmole ular

loudsare absent from ourhalo, sin ethis typeof gas easily sinks towardsthe

disk, and only there a quires high enough densities to undergo a star-forming

Jean'sinstability ollapse. Therefore thehalo is formed by oldstars from early

generations, whose parental louds were barely enri hed with outowingmetals

frompreviousgenerations.

Sin ehalostarsareoldstars,allofitsmostmassivestars(O,BandAspe tral

types) haveby now nishedtheir lives, and onlythe least massiveof them an

be observed as white dwarves. Typi al halo main sequen e turno point stars

are of spe tral type F, with early F and late A stars having already evolved

into red giants and horizontal bran h giants. As stated earlier, the brightness

ofredgiantsand horizontal bran hstars makesthem good distant halotra ers.

And both the main sequen e turno point and the white dwarf sequen e are

parti ularlyinterestingtophotometri allydeterminetheageofagivenequidistant

halopopulation.Howeverthewhitedwarfsequen eisevenmore ostlytoobserve

thanthe main sequen e due to its intrinsi faintness. Therefore, theuse of red

giants and horizontal bran h giants has been wide-spread and main sequen e

turnopointstarshavebeenexploitedto some extent,but theuse ofthewhite

dwarf sequen e has been limited to spe i targets (like globular lusters) or

extremelydeepHubbleSpa eTeles opear hivaldata(Hansenetal.2002,2013).

The starsin thehalo havespe i hemi al abundan esthat separate them

fromthediskstarsandfromtheoldbulgepopulation. Similarly,spe i hemi al

abundan es an beused to separateaverage halo eld starsfrom a reted stars

born in satellite galaxies or globular lusters with a dierent metal enri hment

history. The urrent and re ent spe tros opi surveys are only the rst wave

leadingtowardsa fulltaxonomyofthestellar haloand a omplete pi tureofits

formationhistory.

Overallthehierar hi alformations enariooersaframeworktointerpretthe

minormerger history ofthe MilkyWay, and itmeansthat we an dynami ally,

spatiallyand hemi allydistinguishtwo broadgroups ofstarsinthehalo: those

belonging to the smooth eld omponent and those a reted, whi h an be dy-

nami ally oldoralreadyspatially-mixed.

1.4 This thesis

In this thesis we target the stellar halo of the Milky Way with the aim of un-

derstanding its stru ture, stellar populations and urrent a retion history. In

hapters2and3weaddressthestru turalpropertiesofthesmooth omponentof

thestellarhalo. Inparti ularwesele tnearmainsequen eturnopointstarsand

usethemtobuildstellardensityprolesalongseverallinesofsight. Wetstellar

halomodelstothesedensityproles,derivethestru turalparametersforthebest

tsanddeterminethemostplausiblemodel. In hapter4wedevelopanalgorithm

tore overhalooverdensitiesintheformofmainsequen esignaturesfromColour

MagnitudeDiagramswhere a foregroundandba kgroundstatisti al subtra tion

to enhan e the signal is not possible be ause of the absen e of nearby ontrol

elds. Weapplythismethodto severaleldsandsu essfullymeasure distan es

to theOrphan stream, the Palomar5 streamand the Sagittariusstream, while

ndingpotentiallynewweakoverdensities. In hapter5weapplythismethodto

thesear hforstreamsandunderlying adja entstellarpopulationsaroundglobu-

lar lusters. And,nally, in hapter6 weexplore theKiDSdata release1 and2

footprintsin sear h forhalo substru tureandoverdensities. Wetra e theSagit-

tarius stream in the southernsky using main sequen e turno point stars, and

we also identify the Virgo Overdensity, the Eastern Band Stru ture, the Sagit-

tarius stream and a Palomar 5 tail in the northern hemisphere. Wesear h for

potentiallynew overdensities su h as oldstreams, satellite galaxies or globular

lusters but ndnone in the area so far probed. We on lude by reporting the

futureexpe tationsforup- omingKiDS datareleases.

A skewer survey of the

Gala ti halo from deep

CFHT and INT images

Authors

B.Pila-Díez,J.T.A.deJong,K.Kuijken,R.F.J.vanderBurgandH.Hoekstra

Abstra t

We study the density prole and shape of the Gala ti halo using deep multi-

olour images from the MENeaCS and CCCP proje ts, over 33 elds sele ted

to avoid overlap with the Gala ti plane. Using multi olour sele tionand PSF

homogenizationte hniques we obtain ataloguesof Fstars (near-main sequen e

turnostars)outtoGala to entri distan esupto60kp . Groupingnearbylines

ofsight,we onstru tthestellardensityprolesthroughthehaloineightdierent

dire tionsbymeansofphotometri parallaxes. Smoothhalo modelsarethent-

tedtotheseproles. Wend leareviden eforasteepeningofthedensityprole

power law index around

R = 20

^{kp , from}

−2.50 ± 0.04

^to

−4.85 ± 0.04

^{, and}

foraattening ofthehalo towardsthepoles withbest-taxis ratio

0 .79 ± 0.02

^.

Furthermore,we annotruleoutamildtriaxiality(

w = 0.88 ± 0.07

^{). Were over}

thesignaturesofwell-knownsubstru tureandstreamsthat interse tourlinesof

sight. These results are onsistent with those derived from wider but shallower

surveys,andaugurwellforup oming,wide-eldsurveysof omparabledepth to

ourpen ilbeamsurveys.

A eptedforpubli ationinAstronomy&Astrophysi s

PreprintinarXiv:1502.02460[astro-ph.GA℄

2.1 Introdu tion

ThestellarhalooftheMilkyWayonly ontainsatinyfra tionofitsstars,yetit

providesimportant luesabouttheformationoftheGalaxyandgalaxyformation

in general. Within the paradigm of hierar hi al stru ture formation, galaxies

evolveovertime, growingbymeansof mergersanda retionof smallersystems.

Whilein the entral parts of galaxies the signatures of su h events are rapidly

dissipated, thelong dynami al times alesallow a retion-indu edsubstru tures

tolingerfor Gigayears in theiroutermostregions. Thus, thestellarstru ture of

theouterhalosofgalaxiessu hastheMilkyWay anhelp onstrainnotonlythe

formationhistoryofindividualgalaxies,butalso osmologi almodelsofstru ture

formation.

Owing to the intrinsi faintness of stellar halos, the Milky Way is our best

bet fora detailedstudyof su h stru tures. However,even studyingtheGala ti

stellarhalo is fraught withdi ulties; very sensitive dataare requiredto probe

starsatthese largedistan es(outto 100kp ),andspread over su ientlylarge

areas to onstrain the overall stru ture as well as lo alized substru tures. In

re entde adestheadventofCCD-basedall-skysurveyssu hastheSloanDigital

Sky Survey (SDSS York et al. 2000; Ahn et al. 2014) in the opti al and the

2 Mi ron All Sky Survey (2MASS Skrutskie et al. 2006) in the infrared have

unlo ked unpre edented views of the outer regions of the Galaxy. This has led

tothedis overy ofmanypreviouslyunknownsubstru tures (e.g. Newberget al.

2002;Belokurovetal.2006b;Grillmair2006b;Belokurovetal.2007b;Juri¢etal.

2008;Belletal.2008)andtoimprovedknowledgeoftheoverallstru tureinthese

outskirts(e.g.Chenetal.2001;Juri¢etal.2008;deJongetal.2010;Sesaretal.

2010a,2011;Fa iolietal.2014). Nevertheless,mostofthesere entanalysesare

still limited to either the inner parts of the stellar halo (

R GC ≤ 30

^{kp ) or to}

parti ular,sparsestellartra ers(e.g. K-giantsorRRLyrae).

In this paper we use deep photometry obtained with the Canada-Fran e-

HawaiiTeles ope(CFHT)MegaCamandtheWide FieldCamera(WFC)atthe

Isaa Newton Teles ope(INT),s atteredovera largerangeofGala ti latitudes

and longitudes to probe main sequen e turn-o (MSTO) stars outto distan es

of60kp . Combiningourdataintoeightindependentlines ofsightthrough the

Gala ti halo,weareableto onstraintheoverallstru tureoftheouterhalo,and

toprobethesubstru tureintheseoutermostregions. Inse tion2wedes ribethe

dataset used forthis analysis andthe onstru tion ofourdeep star atalogues.

Se tion3presentsthederivedstellardensityprolesandsmoothGala ti model

ts. Wedis ussourresultsin se tion4andpresentour on lusionsinse tion5.

2.2 Observations and data pro essing

2.2.1 Survey and observations

Weuse

g

^and

r

^{images from theMENeaCSand theCCCPsurveys(Sand et al.}

2012; Hoekstra et al. 2012; Bildfell et al. 2012) together with several ar hival

−50 0

50 100

150 200

250 RA (degrees)

−40

−20 0 20 40 60 80

D EC ( de gr ee s) A

B C

D

E

G F H

Figure2.1: Equatorialmapshowingthepositionofalltheeldsusedinthiswork.

Thedierent oloursand symbols indi ate how theelds havebeengrouped to

al ulatethedierentdensity proles. The ba kgroundimage isthe SDSS-DR8

map from Koposov et al. (2012), whi h shows the footprint of the Sagittarius

stream and the lo ation of the Sagittarius dwarf galaxy. When grouping the

elds,wehavealsotakenintoa ountthepresen eofthisstream,theTriangulum-

Andromedaoverdensity,andtheanti entresubstru tures(ACS,EBS,andMono-

eros),intrying to ombine theiree t in ertainprolesandavoiditin others.

lustereldsfromtheCFHT-MegaCaminstrument. We ombinethesedatawith

U

^and

i

^{imagesfrom a follow-up ampaign withtheINT-WFC instrument(van}

derBurgetal.,inprep.). Whereasthesesurveystargetedapresele tedsampleof

galaxy lusters,thepointings onstitutea"blind"surveyoftheMilkyWaystellar

halosin etheirdistribution is ompletelyindependentofanypriorknowledgeof

thehalo's stru tureandsubstru ture.

Our pointings are distributed over the region of the sky visible to both the

CFHT and the INT (see Figure 2.1). To optimize the star-galaxy separation

(see se tion 2.2.2) we restri t our analysis to exposures with image quality of

subar se ond seeing, typi ally

<≈ 0.9 arcsec

^{in the}

r

^{band. This} limitation, ombinedwith thevarying elds of view and observing onditions between the

datasets,leadstopointingfootprintsizesthatrangebetween

0.24

^and

1.14 deg ²

^.

2.2.2 Image orre tion of the PSF distortion [and impli a-

tions for the star-galaxy separation℄

Previousresear hbyourgrouphasshownthattheperforman eofstandardstar-

galaxyseparationmethodsbasedonthesizeandellipti ityofthesour es anbe

improvedbyhomogenizingthepoint-spreadfun tion(PSF)a rossanimageprior

toitsphotometri analysis(Pila-Díezet al.2014). Inaddition,su h a orre tion

alsoprovidesthebenetofallowingustoperformxedaperturephotometryand

olourmeasurements.

InordertohomogenizethePSFofourimages,weusea ode(Pila-Díezetal.

2014)that,asarststep,takestheshapeofthebrightstarsinagivenimageand

usesittomapthevaryingPSFand, asase ondstep, onvolvesthismapwitha

spatiallyvariable kerneldesignedto transformeverywheretheoriginalPSFinto

agaussianPSF.

2.2.3 Catalogues

From the PSF-homogenized exposures we reate photometri atalogues using

Sour eExtra tor (Bertin &Arnouts 1996). For the

g

^{and the}

r

^{data, we sta k}

thedierentexposures in ea h band to reatea single alibratedimage, and we

extra t the band atalogues from them. We perform a star-galaxy separation

based on the brightness, size and ellipti ity of the sour es and we mat h the

surviving sour es in the two atalogues to produ e a

gr

^{- atalogue of stars for}

ea held ofview (seePila-Díezetal.(2014)). Thelimitingmagnitudesof these

gr

^{star atalogues rea h}

m AB ∼ 25.0

^atthe

5 .0σ

^{levelin the}

r

^band.

Forthe

U

^andthe

i

^{eldsofview,weprodu eseveral}photometri atalogues, oneforea hindividualexposure. We orre tthemagnitudesinthe

i

^ataloguesfor

thedependen yoftheilluminationonpixelposition. Forea hpointingandband,

theexposure ataloguesare alibratedto a ommonzeropointand ombinedto

produ e a single-band atalogue. Inthese single-band atalogues, the resulting

magnitudeforea h sour eis al ulatedas themedianof the ontributionsofall

theindividualexposures. Atthispointthe

U

^andthe

i

^{magnitudesare onverted}

from the INT to the CFHT photometri system using the following equations,

whi hwederiveby alibratingourmixedINT-CFHT olourstothe olourstellar

lo ioftheCFHTLega ySurvey(Erbenetal.(2009),Hildebrandt etal.(2009)):

i M egaCam = i IN T − 0.12 ∗ (r M ega − i IN T )

(2.1)

u M egaCam = u IN T − 0.15 ∗ (u IN T − g M ega ) .

^(2.2)

Finallyweposition-mat hthesour esfromthe

U

^-,the

i

^-andthe

gr

- atalogues to reateanal atalogueofstellarsour esforea heldofview. Thesenal

ugri

^-

ataloguesareshallowerthanthe

gr

- ataloguesbe auseofthelesserdepthofthe

i

^andthe

U

observations(seeTable2.1). Figure2.2showsthe olour-magnitude diagrams (CMDs) for the nal

ugri

^and

gr

^{atalogues (top and entre, respe -}

tively),andthedieren ebetweenthem(bottom). Thebottompanelhighlights

that,inthe olourregimeofthehalo(

0 .2 < g − r < 0.3

^),the ombinationofthe fourbandsremovesmainlyveryfaint,unresolvedgalaxies.

We orre tforinterstellarextin tionusingthemapsfromS hlegeletal.(1998)

andtransform themagnitudes in the

ugri

^{-stellar atalogues from theCFHT to}

theSDSS photometri system. For this we use the equations on the Canadian

Table2.1: GroupsofpointingsasshowninFigures2.1,2.5,2.6and2.8. Thetable

showsthe entral oordinates for ea h group,the number of individual elds of

view ontributingto it, itstotalarea and thestellar ompleteness limitin ther

band.

Group RA(deg) De (deg)

l

^(deg)

b

^(deg)

n fields Σ

^(deg

²

^{) mag}

_lim,r,∗

A 160.654338 43.98310 171.335811 59.15040 8 5.60 22.8

B 231.593130 29.13513 45.577138 55.93598 5 3.98 22.7

C 229.347757 6.91624 9.425402 49.92775 4 3.44 24.1

D 210.062933 51.67173 99.735627 62.24580 2 0.64 23.4

E 121.918411 41.20348 179.233500 31.26694 5 2.73 22.7

F 342.735895 17.09581 86.019738 -36.99391 3 2.17 23.2

G 157.028363 17.15674 222.142793 55.48268 3 2.02 23.1

H 220.659749 2.00187 354.337092 53.38989 3 2.04 24.2

AstronomyData CenterMegaCamwebsite 1

u M egaCam = u SDSS − 0.241 · (u SDSS − g SDSS )

(2.3)

g M egaCam = g SDSS − 0.153 · (g SDSS − r SDSS )

(2.4)

r M egaCam = r SDSS − 0.024 · (g SDSS − r SDSS )

(2.5)

i M egaCam = i SDSS − 0.003 · (r SDSS − i SDSS )

(2.6) andinvertthemtoturn ourmeasurementsintoSDSSmagnitudes. Subsequently

we alibrate ea helddire tlytoSDSSusingstellarphotometryfromDR8. The

resultingphotometrymat hesthe olour- olourstellarlo iofCoveyetal.(2007)

asshownin Figure2.3. Unlessexpli itlystatedotherwise,allmagnitudesin this

paper areexpressedin theSDSSsystem.

Inordertoredu ethenoisewhenanalysingtheradialstellardensitydistribu-

tionofthehalo,we ombinethe ataloguesfromnearbypointings,groupingthem

a ordingto theirposition in thesky. Thisstepisimportantbe auseofthena-

tureofoursurvey,whi his omposedofrelativelysmall,s atteredeldsofview.

Weusea friends-of-friends(FoF)algorithmto groupthedierentpointings. We

requesttwofriendsnotto beapartbymore than20degrees,andin a few ases

we leanorsplitaresultinggroup(redpentagonsorblueandorangetrianglesin

Figure2.1) or ombineothers (purple diamonds)to a ountforthepositions of

thegala ti diskor majorhalosubstru tures. Be ause thedierentpointingsin

oursurveys havedierent ompletenesslimits,these groupedor ombined ata-

logueswhi hwenameA,B,C,... Harenallylteredtomeetthe ompleteness

magnitudethresholdoftheirmostrestri tive ontributor 2

.

1

www2. ad - da.hia-iha.nr - nr .g . a/megapipe/do s/lters.html

2

Todeterminethe ompletenesslimitofea heldofview,wetitsmagnitudedistribution

to a gaussian representing thepopulation of faint galaxies and another variable fun tion

representingthe stellar distribution alongthe whole magnituderange. We hoose as the

ompletenesslimiteitherthetransitionpointbetween thetwodistributions(thevalley)or,if

insteadthereisaplateau,theturningpointofthewholedistribution(theknee).

Figure2.2: Hessdiagrams showingthe number ofsour esper olour-magnitude

binin the

ugri

^{atalogue (top), in the}

gr

^{atalogue ( entre) and the dieren e}

betweenboth(bottom)foreld A1033. Mostofthesour eslostwhen ombining

the atalogues orrespondtofaintmagnitudes,be ausethe

i

^andthe

U

^observa-

tionsareshallower. Theee tistheremovalofmostofthefaintgalaxies(lo ated

in the

−0.2 < g − r < 0.7

^and

r > 23

^{region in the entral panel), mostof the}

faintestdiskMdwarves(

1 .1 < g − r < 1.3

^{)andanumber offaintobje ts(inthe}

i

^orthe

U

^{bands)s atteredthroughoutthe}

( g − r, r)

^diagram.

Figure2.3: Colour- olourdiagrams(CCDs) orrespondingto theelds ingroup

A(pointingsmarkedaslightgreen ir lesinFigure2.1). Thesour esinthe

ugri

atalogues(bla k)andthesubsetofnear-MSTOstars(red)havebeen alibrated

to SDSS using DR8 stellar photometry. The main sequen e stellar lo i (green

dashedlines)aretheonesgiveninTables3and4ofCoveyetal.(2007). Quasars

andwhitedwarf-Mdwarfpairsareabundantinthe

u − g < 1

^,

−0.3 < g − r < 0.7

spa e.

0.0 0.2 0.4 0.6 0.8 1.0

g - i

−10

−5 0 5 10

M ag r

−7 −6 −5 −4 −3 −2 −1 0 1

[Fe/H]

−10

−5 0 5 10

M ag r

Figure 2.4: Estimated absolute magnitude in the

r

^{band (}

M r

^{) and estimated}

metalli ity(

[ F e/H]

^{)forgroupAforthesour estypi ally onsideredashalostars}

(blue)and those that we havesele ted as near-MSTO stars(red). The sour es

sele tedas halo members meet

0 .2 < g − r < 0.3

^and

g, r, i > 17

^{. The subset}

of near-MSTO stars, additionally meets

M r > −2

^,

−2.5 ≤ [F e/H] ≤ 0

^and

0 .1 < g − i < 0.6

^.

2.3 Stellar radial density proles

2.3.1 Star sele tion and onstru tion of the radial stellar

density proles

The oordinatesandthe ompletenesslimitsofthegroupsaregiveninTable2.1.

Weusehalomainsequen eturnostarsinoureldsastra erofthestellarhalo:

atthe ompletenesslimitsofthedatasu hstars anbeidentiedasfaroutas

60

kp fromtheGala ti entre. WetseveralGala ti stellardistributionmodelsto

thesedensityprolesandderiveanumberofstru turalparametersforthestellar

halo. Previous works have already used main sequen e turno point (MSTO)

stars, near-MSTO stars, BHB and blue stragglers of type A and RRLyrae as

stellartra ersfortheGala ti stellarhalo. We ompareanddis ussourndings

totheirsin se tion2.4.2.

In order to sele t the near main sequen e turno stars we make use of two

empiri al photometri variables. The ratio

[ F e/H]

^{is al ulated following the}

photometri metalli ityrelationbyBondetal.(2010),andtheabsolutemagnitude

M r

^{is al ulated following the} photometri parallax relation from Ivezi¢ et al.

(2008):

[ F e/H] = −13.13 + 14.09x + 28.04y − 5.51xy − 5.90x ²

− 58.68y ² + 9 .14x ² y − 20.61xy ² + 58 .20y ³ ,

^(2.7)

where

x = u − g

^and

y = g − r

^{. This relation is valid in the}

g − i < 0.6

^and

−2.5 ≤ [F e/H] ≤ 0

^{range,whi his ompatiblewiththeregimeofournear-MSTO}

starsele tion.

M r = −0.56 + 14.32z − 12.97z ² + 6 .127z ³ − 1.267z ⁴

+ 0 .0967z ⁵ − 1.11[F e/H] − 0.18[F e/H] ² ,

^(2.8)

where

z = g − i

^{. The tested validity regime of this equation} en ompasses the

0 .2 < g − i < 1.0

^{range, meaning that the absolute} brightnesses of our near- MSTO starshave been properlyestimated. We extrapolatethe relationfor the

0 .1 < g − i < 0.2

^{range, whi h isjustied owingtothesmoothandslow hange}

of

M r

^with

z

^.

Wesele tthehalo near-MSTOstarsbyrequiring

0 .2 < g − r < 0.3 ;

^(2.9)

g, r, i > 17 ;

^(2.10)

0 .1 < g − i < 0.6 ;

^(2.11)

5 .0 > M r > −2 ;

^(2.12)

−2.5 ≤ [F e/H] ≤ 0 .

^(2.13)

Thersttworestri tions(2.9and2.10)retrievestarstypi allyasso iatedwith

thehalo,inparti ulardistantmainsequen eFstars(seeTable3fromCoveyetal.

(2007)). This sele tion however, an be signi antly ontaminated by quasars

and white dwarf-M dwarf pairs, whi h are abundant in (but not restri ted to)

the

−0.2 < g − r < 0.3

^{range (seeFigure 2.3). To redu e thepresen e of these}

interlopersandsele tthebulkoftheFstarspopulation,weapplyrestri tions2.11

(basedonTable4in Coveyetal.(2007))and2.12. Constraint2.13ensuresthat

the nal sour es are at most as metal ri h as the Sun (to a ount for possible

ontributionsfrommetal-ri hsatellites)andnotmoremetal-poorthan0.003times

theSun.

The de rease in interlopers attained by applying restri tions 2.11, 2.12, and

2.13 omparedtoonlyapplyingrestri tions2.9and2.10isillustratedinFigure2.3,

wherethered dots indi ate thenalsele tion ofhalo near-MSTOstarsand the

bla k dots represent the whole atalogue of star-like sour es. It is lear that

thenalsele tionof near-MSTOstars doesnotspanthewhole rangeofsour es

en ompassedbetween

g − r = 0.2

^and

g − r = 0.3

^{. Theee t ofthe}

[ F e/H]

^and

M r

^{sele tionisfurther} illustratedin Figure2.4.

Using the estimated absolute brightness, we al ulate the distan e modulus

and the helio entri distan e for all the near-MSTO stars. We dene distan e

modulusbinsofsize

∆ µ = 0.2

^magand

∆ µ = 0.4

^{mag,and ountthenumber of}

near-MSTOstarsper binforea hgroup of elds (A,B,C,...). The hoi e ofdis-

tan ebinsismotivatedbya ompromisebetweenmaximisingtheradial distan e

resolutionandminimisingthePoissonnoiseinthestellarnumber ounts. Wetest

this ompromise byexploring two distan emodulusbinsizes, whi h orrespond

todistan ebinsizesoftheorderof

10 ²

p and

10

kp ,respe tively.

Wethen al ulatethenumberdensityper binanditsun ertaintyasfollows:

ρ l,b,D = N l,b,∆µ

0 .2 · ln(10) · D hC ³ · ∆Ω · ∆µ ,

^(2.14)

E ρ =

r ( ρ

√ N

) ² + ( ρ

√ n f ields

) ² ,

^(2.15)

where

∆Ω

isthearea overed byea h group,

D hC

^{is the}helio entri distan e,

l

and

b

^{arethegala ti} oordinatesand

N l,b,∆µ

^{isthenumberofstarsper binina}

givendire tionofthesky. Parti ularly,

∆Ω = 4 π

41253 Σ(deg ² )

(2.16)

and the area of ea h group (

Σ

) depends on the individual area of ea h eld ontributingtoit(Table2.1).

The resultsfor these number density al ulations an beseen in Figure 2.5,

whereweplotthelogarithmi numberdensityagainstthegala to entri distan e 3

,

R GC

^{, forea h group (orline of sight). For thisand thesubsequentanalysis, we}

only onsiderbinswith

R GC > 5kpc

^,

|z| > 10

^{kp (toavoidtheinner regionsof}

theGalaxy)andadistan emodulusof

µ ≤ mag lim −4.5

^{(toguaranteea omplete}

sampleofthefaintestnear-MSTOstars 4

).

Figure2.5showsthat thedensityprolesde reasequitesmoothlyfor

40 − 60

kiloparse sandformostofthelinesofsight.

2.3.2 Fitting pro edure

Wet several models of theGala ti stellar number density distribution to the

data,rangingfromabasi axisymmetri powerlawtomore omplexmodelswith

triaxiality and a break in thepower law. Themodels take the following math-

emati alforms, with

x

^,

y

^{, and}

z

^{being the artesian} gala to entri oordinates withtheSunat(8,0,0) kp (Malkin2012):

- Axisymmetri model

ρ(x, y, z) = ρ 0 ·



x ² + y ² + z ² q ²



n/2 ,

^(2.17)

where

q = c/a

^{isthepolaraxis ratioortheoblatenessofthehalo;}

- Triaxial model

ρ(x, y, z) = ρ 0 ·

 x ² + y ²

w ² + z ² q ²



n/2 ,

^(2.18)

where

w = b/a

^{istheratiobetweentheaxesintheGala ti plane;}

- Brokenpower law,withvaryingpower indexat

R break

ρ(x, y, z) =

 ρ 0 · (R ellip ) ^{n in} , R ellip < R break

ρ 0 · (R ^ellip ) ^{n out} · R ⁿ break ^{in −n out} , R ellip ≥ R ^break

^(2.19)

R ellip =



x ² + y ² + z ² q ²



1/2 ;

3

R GC = p R ² + z ²

where

R

^and

z

^{aretheradialandverti al} oordinatesonthe ylindri algala to entri referen e system.

4

This onstraintguaranteesthattherearenodistan e ompletenessissuesduetoourspe i

typeofstellartra ersandduetothedierentdepthsofourelds. Theonlysubsetae tedby

in ompletenessisthatof

mag lim − 5.0 < µ < mag lim − 4.5

^{forthestarsinthe}

4.5 < M r < 5.0

range;anditsaveragelossisof

20%

overthetotalnumberofnear-MSTOstars(

−2.0 < M r <

5.0

^{)inthesamedistan e range. Several testson dierentupperdistan ethresholds forthe}

density proles show that thedistan e modulus onstraint of

µ ≤ mag lim − 4.5

^isenough

toguaranteethatallthelinesofsight ontributerobustdensitymeasurementsatthefurthest

distan esandthatthein ompletenessin

mag lim −5.0 < µ < mag lim −4.5

^forthe

4.5 < M r < 5.0

near-MSTOstarshasnostatisti allysigni antee tonthebesttparameters.

Figure2.5: Logarithmi stellardensityprolesversusdistan e forthenearMain

Sequen e turno point stars (near-MSTO) from the elds in groups A (green

ir les),B( yansquares),C(bluedownwardtriangles),D(yellowupwardtrian-

gles),E(redpentagons),F(pinkhexagons),G(purplediamonds)andH(orange

leftwardtriangles). Theirsymbolsmat h thoseinFigure2.1.

- Brokenpower law,withvaryingpower indexandoblatenessat

R break

ρ(x, y, z) =







ρ 0,in · 

x ² + y ² + ^{z 2}

q ² _in

 n in /2 , R GC ≤ R break

ρ 0,out · 

x ² + y ² + ^{z 2}

q _out ²

 n out /2 , R GC > R break ,

(2.20)

wheretheinner power lawistto datathat meets

R GC ≤ R break

^andthe

outerpower lawisappliedtodatathat meets

R GC > R break

^.

Wetallthesemodelstothedatausingthe" urve-t"methodfromPython's

S ipy.optimize, whi h uses the Levenberg-Marquardt algorithm for non-linear

least squares tting. The obje tive fun tion takes the form of a

χ ²

^{, and we}

also al ulatearedu ed

χ ²

^{foranalysispurposes,}

χ ² =

N data

X

i=1

 ρ data,i − ρ ^model,i E ρ,i

 2

,

^(2.21)

χ ² _red = χ ² N data − N params

,

^(2.22)

where

N data

^and

N params

^{arethenumber ofdata pointsandthenumber offree}

parameters,respe tively.

The inuen e of the photometri un ertainties on the density proles and

the best t parameters is evaluated through a set of Monte Carlo simulations

that randomly modify the

g

^,

r

^,

i

^,

u

^{magnitudes of ea h star within the limits of}

thephotometri un ertainties. Through this method wend that the variation

oftheMonte Carlo bestt parameters aligns with theun ertainties of ourbest

t parameters (derived from the se ond derivative of thets by the " urve-t"

method). The entre ofthesevariationsiswithin

1 σ

^{ofourdire t ndings.}

Wet all models tofour data sets: with and without[known℄ substru tures

andbinnedin

0 .2

^and

0 .4

^{magnitude ells.Inthiswaywe an he ktherobustness}

ofourresultstodierentbinningoptionsandweareableto omparewhatwould

betheee tofsubstru tureonourunderstandingofthesmoothhalo ifwewere

to ignore it or unable to re ognize it as su h. Spe i ally, we ut the distan e

binsat

R GC < 25

^{kp in groupEto avoid} ontributionsbythestru turesinthe dire tionofthegala ti anti entre(theMono erosring,theAnti entreStru ture

andtheEasternBandStru ture),thedistan ebinswithin

15 < D hC < 40

^{kp in}

groupGto avoid ontributionsbytheSagittariusstream, and thedistan ebins

within

20 kpc < D hC < 60

^{kp in group H to avoid} ontributions againby the Sagittariusstream.

2.3.3 Results

Thebesttparametersforea hmodelresultingfromttingthesefourdatasets

aresummarizedin Tables 2.2to2.5. Table2.2 ontainstheresultsofttingthe