andthe hemi alsignatures from re ent spe tros opi observationsasso iateits
progenitor with a dwarf galaxy (Casey et al. 2013b,a). A number of plausible
progenitorshavebeensuggested(Zu keretal.2006;Fellhaueretal.2007b;Jin&
Lynden-Bell2007;Salesetal.2008),butitisstillpossiblethatthetrueprogenitor
remainsundis overed inthesouthernhemisphere(Caseyet al.2013b).
Ingeneral,thedis overyofmostofthesubstru tures inthehalooftheMilky
Wayhasbeenpossiblethankstophotometri multi- olourwideareasurveys. Su h
surveysposeseveraladvantagesforthiskindofsear h. First,theirmultiple-band
photometryallowsforstellarpopulationsele tions(haloorthi kdisk;red lump,
main sequen e turno point, et .) based on olour- olour stellar lo i. These
sele tion riteria anbeusedtomakestellardensitymapsthattra kthestreams
all through the survey's overage area (Majewski et al. 2003; Belokurov et al.
2006b). Se ond,their ontinuous overageofalargeareaallowthe eldsadja ent
to the substru ture to a t as ontrol elds. In this way, the olour-magnitude
diagrams (CMDs) of the ontrol elds an be used to statisti ally subtra t the
foreground and the ba kground stars from the elds probing the substru ture.
Thisenhan esthesignatureofthestellar population belongingtothestreamor
satellite(byremovingthenoise),andmakesitpossibletoidentifyageanddistan e
indi atorssu has the red lumpor themain sequen e turno point(Belokurov
etal.2006b;Koposovetal.2012;Slateret al.2013).
Inthispaper weexplorethepossibilitiesofusingdeeptwo-bandpen il-beam
surveys instead of the usual wide-area multi- olour surveys in order to dete t
and hara terize stellar streams of the halo and, in parti ular, we revisit the
Sagittarius, the Palomar 5 and the Orphan streams. We derive photometri
distan esusingpurelythemainsequen eturnopointandunlikeotherworks
regardlessofthegiantbran h anditsred lump.
−50 0
50 100
150 200
250 RA (degrees)
−60
−40
−20 0 20 40 60 80
DE C ( de gre es )
Sgr dwarf survey fields
Sgr stream fields, faint branch Sgr stream fields, bright branch Pal5 and Orphan fields
Figure4.1: Equatorialmapshowingthepositionofallthe eldsfromoursurvey
(white hexagons) and highlighting the ones that lay on the Sagittarius stream
(green ir lesforthefaintbran handgreensquaresforthebrightbran h),onthe
Palomar5streamandontheOrphanstream(orangediamonds). Theba kground
imageistheSDSS-DR8mapoftheSgrstreamfromKoposovetal.(2012),where
thelo ationoftheSagittariusdwarfgalaxyhasbeenmarked(redstar).
Bona a et al. 2012b) (see Figure 4.1). Further away from the plane of the Sgr
stream,wealso ndthree eldstobe oin identwiththeTriangulum-Andromeda
stru ture(Ro ha-Pinto et al.2004; Bona a et al. 2012a), two to three with the
Pis esOverdensity(Watkinsetal.2009;Sesaret al.2010b; Sharmaetal.2010),
onetransitionalbetweentheTriangulum-AndromedaandthePis esOverdensity,
fourwith theAnti enter Stru ture (Grillmair2006b) and two tothree with the
NGC5466stream (Grillmair & Johnson 2006; Fellhauer et al. 2007a). We also
nd two elds on the Lethe stream (Grillmair 2009), four on the Styx stream
(Grillmair2009), one ona region apparently ommon to the Styxand Co ytos
streams(Grillmair2009)andtwoontheCanisMajoroverdensity(Martinet al.
2004).
In this paper we on entrate on the learest stru tures (those where the
ontrast-to-noisein the CMD is higher)in order to test the apabilities of our
method. Inparti ular, we address theSagittariusstream, thePalomar5 stream
andtheOrphanstream.
4.2.2 Corre tion of the PSF distortionand impli ations for
the star/galaxy separation
Beforebuilding atalogues andin orderto performana uratestar/galaxy
sep-aration,itisne essary tore tifythevaryingPSF a rossthe elds oftheCFHT
images.
Inorderto orre tforthisee t,wemakeuseofa 'PSF-homogenizing' ode
(K.Kuijkenet al.,in prep.). The ode usestheshapesofbright obje ts
unam-biguously lassi edasstarstomapthePSFa rosstheimage,andthen onvolves
itwithanappropriatespatiallyvariablekerneldesignedtorenderthePSF
gaus-sianeverywhere. WithaviewtoobtainingaPSFashomogeneousaspossible,we
treatthedataasfollows(vanderBurgetal.2013): i)weimplementana urate
sele tionof su iently brightstars basedonan initial atalogue, ii)werun the
ode ontheindividual exposures forea h eld,and iii) wereje t bad exposures
basedonaseeing riterion 1
beforesta kingtheminto one nalimage,onwhi h
weperformthe nalsour eextra tionandphotometry.
The advantages of this pro edure are twofold. First, be ause the resulting
PSFforea hexposureis gaussian,all thestarsbe omeround. Se ond, be ause
thePSFanisotropyisremovedfromallexposuresbeforesta king,thedispersion
in size for the point-sour e obje ts be omes smaller, even if the average value
in reases after sta king the individual exposures (see Figure 4.2). These two
improvementssigni antlyredu ethegalaxy ontaminationwhenperformingthe
starsele tion(illustratedinFigure4.3). Additionally,homogenizingthePSFalso
allowstomeasure oloursin xedapertures.
Fromthe nalimages, weextra tthesour esand produ ephotometri
ata-loguesusingSExtra tor(Bertin&Arnouts1996). Toderivethestellar atalogues,
weusea odethat ltersthesour e ataloguesas follows: i) ndsthesaturated
starsandremovesthemfrom thestellar atalogue;ii)evaluatesthedistribution
of bright sour es (
r ′ = [18.0, 20.0] mag
) in the brightness-size parameter spa e, assumesa gaussian distribution inthesize and inthe ellipti ityparameters (e 1
,e 2
)2 of stars, and uses this information to de ne the boundaries of the stellar lo us along the bright range; iii) evaluates the dependen e of the width of thestellar lo us on brightness and extrapolates the relation to fainter magnitudes;
iv)appliestheextendedstellarlo usand anellipti ity riterionto dropgalaxies
fromthestellar atalogue.
For the starsresultingfrom thissele tion (Figure4.3), we orre t their
pho-tometryfromgala ti reddeningbyusingtheextin tionmapsfromS hlegeletal.
(1998). The nalstellar ataloguesareusedtobuildtheCMDsemployedforour
analysis. ThePSF- orre ted ataloguesyieldmu h leanerCMDsthanthe
ata-logueswithsimilar star/galaxyseparation butnoPSF- orre tion(Figure4.4).
1
Thereje tionofexposuresderivesfromtryingtooptimizetheimagequalitywhilea hieving
thedesiredphotometri depth. Thusourseeing riterionisavariablenumberdependentonthe
elditself,theseeingdistributionforindividualexposuresandtheindividualplustotalexposure
time.Ingeneralittakesvalues
<≈ 0.9 ′′
.2
e 1 = 1 − q 2
1 + q 2 cos 2θ , e 2 = 1 − q 2 1 + q 2 sin 2θ ,
where
q =
axisratio,θ =
positionangleofthemajoraxis.Figure4.2: Brightnessversussizediagramofallthesour esinoneofourpointings.
Thestellarlo uspriortothePSF-homogenization (bla k)iswiderandtherefore
subje t to greater galaxy ontamination at the faint end than the stellar lo us
posteriortothe orre tion(blue)be ausethePSFinitiallyvariesa rossthe eld.
The sour es more ompa t than the stellar lo us are artefa ts from the sour e
extra tion;theyholdnorelevan eforouranalysissin etheydonotpassthestar
sele tion(seeFigure 4.3).
Figure4.3: BrightnessversussizediagramshowingallthePSF- orre tedsour es
(blue)and thesubset ofsour es sele tedas stars through ourstar/galaxy
sepa-rationalgorithm(red) forone ofourpointings. Althoughthestarsele tionmay
notbe omplete at the faint end due to in reasing s atter, our algorithm
mini-mizesthegalaxy ontamination, whi hotherwisewouldbethemain obsta lefor
dete tingfaintstru turesin theCMD.
Figure4.4: Colour-MagnitudeDiagram(CMD)displayingthesele tionofsour es
onsideredstars(sele tedasexplainedinse tion2.2). Theplumeontheredside
(
g − r ≈ 1.2
)is omposedofthenearbyM-dwarfs,whereasthemainsequen eonthebluer side(
0.18 < g − r < 0.6
) orrespondsto a halo overdensitylo ated at a parti ularwell-de ned distan e. The loudof sour esat faintmagnitudes arefaintgalaxiesthatenterthestarsele tion. Left: CMDderivedfromanimagethat
hasnotbeenPSF- orre ted. Right: CMDderivedfrom a PSF- orre tedimage.
AfterhomogenizingthePSF,thegalaxy ontaminationde reasesmarkedlybelow
r ≈ 22
.4.2.3 Identi ation of the main sequen e turno point
Thephotometri depthofourdataallowsustodete tanumberofhalo
substru -tures several magnitudes below their main sequen e turn-o point. However,
be auseoursurveyisapen il-beamsurveyla king ontrol eldsadja enttoour
target elds, wehavenoreferen e-CMDsrepresentinga lean foregroundplusa
smoothhalo, and thus a simpleforeground subtra tion is notpossible. Instead
thehalosubstru turesinoursurvey anonlybedete tedinthose eldswherethe
ontrastin densitybetweenthemain sequen e stream starsand the foreground
andba kgroundstarsissigni antin theCMD.
Thus, in order to sear h for main sequen es in theCMDs, we build a
ross- orrelationalgorithmthatruns a rossaregionoftheCMD(the'sear hregion'),
fo usedonthe olourrangeasso iatedwiththehaloturnostars(
0.18 ≤ g − r ≤ 0.30
). Within the boundaries of this sear h region, we slide a template mainsequen e-shaped2Dfun tionthatoperatesoverthenumberofstarsand,forea h
step,yields anintegral representingtheweighteddensityofstars insu h amain
sequen e-shapedarea. Whenthetemplatemainsequen efun tion oin ideswith
a similarly shaped overdensity in the CMD), the value of the ross- orrelation
(theweighteddensity)ismaximized,andavaluefortheturnopointisassigned.
Thispro essisillustratedin Figure4.5.
Insome asesa CMD presentsmore than one main sequen esignature with
su ient ontrast to noise. When this happens we use the dete tion of the
primary main sequen e (the position of its turno point and its hara teristi
width-fun tion)to randomlysubtra t a per entage of the stars asso iated with
it (lowering its density to the foreground level) and dete t the next prominent
mainsequen efeature. Wenamethesemainsequen edete tionsasprimary,
se -ondary, et ., ranked by their signal to noise. We require the signal to noise to
be
> 3.5σ
for primary MSs and> 4σ
for the se ondary or tertiary MSs afterpartiallyremovingtheprimaryone.
Shape ofthe template main sequen efun tion
When onstru tingthetemplatemainsequen e-shaped2Dfun tion(fromnowon,
'template-MS'),weusetwoingredients. The rstoneisatheoreti aliso hrone 3
of
age
t = 10Gyr
andmetalli ity[F e/H] = −1.58
,whi hisusedtode nethe entralspineofthetemplate-MS.Thepositionofthis entralspineislatershiftedin
mag-nitudeand olourstepsduringthe ross- orrelation. Sin eweareonlyinterested
intheshapeofthisiso hrone(itsabsolutevaluesareirrelevantbe auseitwillbe
shifted)andsin ewearesear hingforhalosubstru tures,we hoosetheaboveage
andmetalli ityvaluesbe ausetheyyieldaniso hroneshaperepresentativeofold
metal-poorstellarpopulations. These ond ingredientisa magnitude-dependent
olour-width, whi h is used to broaden the iso hrone template as illustratedin
theleftpanelof g.4.5).
3
Through all this work we use a subset of theoreti al iso hrones from
http://stev.oapd.inaf.it/ md. The theoreti al iso hrones (Marigo et al. (2008), with the
Figure 4.5: Left: Dereddened CMD (bla k dots) with the sear h region (pink
solid-line re tangle) for the ross- orrelation and the template main
sequen e-shaped fun tion(green solid line) at theposition of maximum density(peak of
the ross- orrelation). Right: Binned diagramrepresentingtheweighteddensity
of stars resulting from the ross- orrelation pro ess. The density in ea h bin
orrespondsto theintegral ofthe templatemain sequen e-shaped fun tionwith
topleft ornerinthepositionofthebin.
Thewidthisingeneraldire tlyderivedfromthewidthofthelo usofnearby
M-dwarfs (
1 .0 < g − r < 1.4
). The width of this feature is al ulated for anumber of magnitude bins as three times the standard deviation in olour for
ea h bin. Then a fun tional form dependent on magnitudeis obtained through
polynomial tting. Ina few ases, minor tweaking isneeded to ompensate for
extremelylargewidths ( olourshiftsbe omeinsensitiveto any substru ture)or
forextremelysmallwidths(densityvaluesbe omemeaninglessduetothebuilt-in
weight[seebelow℄). Thiswayofde ning thewidthofthetemplate-MSa ounts
for the observational broadening of intrinsi ally well de ned stellar lo i due to
in reasingphotometri un ertainties atfaintmagnitudes.
Weights within the templateMS-fun tion
Inadditiontoatheoreti allyandobservationallymotivatedshapeforthe
template-MS,wealso givea dierentweightto ea h region ofthe template. This means
that,for ea h step of the ross- orrelation, the stars ontained within will
on-tributedierently tothe en losedstellar density dependingon howfar theyare
fromthespineofthetemplate-MS.
orre tionsfrom Case Ain Girardi et al. (2010) and the bolometri orre tionsfor Carbon
starsfromLoidletal.(2001))areprovidedasobservablequantitiestransformedintotheCFHT
photometri system.
Theweightin olour(starsnearthespineofthetemplate-MSaremorelikely
to belong to the main sequen e than stars lose to the boundaries) is assigned
throughtheexponentialtermina gaussianweightfun tion. Wemat hthe
stan-darddeviationofthegaussianweighttothestandarddeviation ofthe
template-MSwidth(
3 σ = ω M S
)sothatallthestars ontainedwithinthetemplate-MSare assignedaweight. To guaranteethat theweightdoesnotfavourbrightfeatures,we hoosetheamplitudeofthegaussian fun tionto besu hthat theintegral of
theweight fun tionbetween theedges of thetemplate-MS fun tionis thesame
forallmagnitudes.
Theresultingweightfun tionfora givenstarinthetemplate-MSata
parti -ularstepofthe ross- orrelationthenfollows:
W ∗ ( mag, colour) = A
√ 2 πσ(mag) · exp
− [ colour − η CC ( mag)] 2 2[ σ(mag)] 2
(4.1)
where
mag
andcolour
arethemagnitudeand olouroftheweightedstar,η CC ( mag)
representsthetheoreti aliso hroneatthatparti ularstepofthe ross- orrelation,
and
σ(mag) = 1 3 ω M S ( mag)
isproportionaltothewidthofthetemplate-MS fun -tionforthatparti ularCMD.4.2.4 Un ertainties in the turno point
The olourandmagnitudevalues fortheturno pointofagivenmain sequen e,
(
c T O
,mag T O
),arederivedfrom theposition ofthetemplateatwhi htheross- orrelationpeaks. Thereforetheun ertaintiesfortheseturnopointvaluesderive
from the ontribution of individual stars to theposition and shapeof themain
sequen e(theun ertaintyfromtheCMDitself). Toevaluatethisun ertainty,we
arryout a bootstrappingpro ess. In this pro ess rstwegenerate re-sampled
stellar ataloguesbyrandomlywithdrawingstarsfromoneofourtrue atalogues.
Se ond we run the ross- orrelation and obtain the turno points for ea h of
thesere-samples. Third we onsidertheosets betweentheseturno pointsand
theoriginal turno point and derive thestandard deviation of thedistribution.
The ontributionofanyCMDtotheun ertaintyofitsturnopoint anthenbe
al ulatedasa fun tionofa referen e(bootstrapped)standarddeviation,
s
:E mag,CMD = f mag,BS · ( s mag,BS )
∂ 2 ρ CC
∂ 2 mag
TO
, E c,CMD = f c,BS · ( s c,BS )
∂ 2 ρ CC
∂ 2 c
TO
,
where, in pra ti e,
s mag,BS
ands c,BS
are the standard deviations al ulatedforanumberofrepresentative elds,
f mag,BS
andf c,BS
ares alefa torsthatallowtoobtain the un ertainty forany eld from thestandard deviation of the
boot-strapped elds, and
∂ 2 ρ CC
∂ 2 mag
and∂ 2 ρ CC
∂ 2 c
evaluatethe prominen eofthe parti ularoverdensity as a fun tionof magnitude or as a fun tionof olour. In pra ti e,
E mag,CMD = s mag,BS
andE c,CMD = s c,BS
for the bootstrapped elds used as a referen e.Thephotometri turno pointdistan esarederivedfromthedistan e
modu-lus. Thereforetheun ertainties inthedistan es an be al ulatedasa
ombina-tionoftwosour esoferror: theun ertaintyderivedfromtheobservedbrightness
of the turno point (
E mag,CMD
, dis ussed above) and the un ertainty derived fromtheabsolutebrightnessoftheturnopoint,whi hdependsonthe hoi eofiso hrone(andthusontheun ertaintyintheageor inthemetalli ity).