Dis ussion

Italsoin reasesthe entralvalueofthepolaraxisratio

q

^withintheun ertainties, fromaweighted

q = 0.77 ± 0.04

^{toa weighted}

q = 0.79 ± 0.02

^{. Globally,thedisk}

axisratioseemsto bethemoststableparameterthroughout thedierentmodel

tstoourdata, returninga moderatelyoblatehalo.

Finally we x the break distan e at the best t value found by the broken

power law model (

R break = 19

kp and

20

kp for the

0 .2

^and

0 .4

^{mag binned}

data,respe tively)andaddanotherparametertoit,allowingnotonly

n

^,butalso

q

^{to hangeatthebreakdistan e. Wendthatthebesttstothismodelreturn}

su h largeerrorbarsfortheinner halo that,inpra ti e, ityieldsun onstrained

measurements:

∆ ρ 0 ≤ ρ 0

^,

∆ n in

^{is12-18% of}

n in

^and

∆ q in

^is30%of

q in

^.

Weexplore ea h modelto investigatepossible parameter degenera ies,

toler-an e rangesand potentiallo al minima in our best ts. For this we x all the

parametersinthefourmodelsex eptthedensitys alefa tor

ρ 0

^,andwerunthe

tsa rossa gridofparameter values. Inparti ular, thegridsarebuiltfollowing

q ² , w ² ∈ [0.1, 2.0; δ = 0.05]

^,

n ∈ [−5.0 − 1.0; δ = 0.1]

^,

n in ∈ [−4.0, −1.0; δ = 0.1]

^,

n out ∈ [−7.0, −3.0; δ = 0.2]

^and

R br ∈ [15, 50; δ = 1]

^{, where}

δ

^{is the}in remental stepforea hparameter. Wendthatthereisadegenera ybetween

R br

^and

n in

forthesimplebrokenpowerlawmodelforbothbinnings(seeFigure2.7).

Finallyourmeasurementsforthedensitys alefa tor

ρ 0

⁽

ρ

^at

R GC = 1

kp ) aretheresultoflargeextrapolationsandmerelyserveas normalizationsforour

ts. Forthat reasonwedonotdis ussthese valuesin detail.

(a)

χ ² _red

^{mapfortheltered}

0.2

^{magbinneddataset.}

(b)

χ ² _red

^{mapfortheltered}

0.4

^{magbinneddataset.}

Figure2.7:

χ ² _red

iso ontoursmapsfor

n in

^and

R br

^{fromthesimplebrokenpower}

law model. The minimum is indi ated with a white star. The bla k solid

iso- ontours rangefrom

min(χ ² _red ) + 0.1

^{to the maximumvalue, whereasthewhite}

dashediso ontours rangefrom

min(χ ² _red ) + 0.01

^to

min(χ ² _red ) + 0.05

^{. Themaps}

illustrateadegenera ybetweenbothparametersin thebest ts.

alsoinuen e the measurementsof the dierentparameters, but havea smaller

inuen e on thegeneral pi ture we would derive. Overall wesee that the lines

of sight we use an havea drasti ee t on the

w

^{resultsand a signi ant but}

moderateee ton

q

^and

n

^{. Thismeansthataglobalviewofthehaloisessential}

owingto its omplexstru ture.

2.4.2 Comparison to previous studies

Previousinvestigationsusingnear-MSTOstarshaveexploredboththeinnerand

the outer halo out to moderate distan es (

30 − 40

^{kp ), and similar regimes}

have been probed with blue horizontal bran h stars and blue struggler stars,

MSTO stars or multiple stellar halo tra ers. Studies involving RRLyrae stars

haverea hed furtheroutto

50

^{kp . Remarkably, thedepthof ourdataallowsus}

to probe further than any previous study (out to

60

^{kp ) in several} dire tions, independentlyofthestellartra er.

In this se tionwe ompare our ndingsregarding thestru tural parameters

ofthestellarhalo tothoseofthefollowingresultsin theliterature:

- Juri¢et al. (2008) use near-MSTOstars from theSDSS-DR3 and DR4as

stellartra ers, and over the

5 kpc < R GC < 15

^{kp range. They omprise}

5450

^deg

²

^{inthenorthernGala ti hemisphereand}

1088

^deg

²

^inthesouth.

- Sesar et al. (2011) use as well near-MSTO stars from the CFHT Lega y

Survey, and explore the

5 kpc < R GC < 35

^{kp range. Two of their four}

eldsexploretheSouthGala ti Cap.

- Deason et al. (2011) use type A blue horizontal bran h (BHB) stars and

bluestragglers (BS),rea hingoutto

R GC = 40

^{kp .}

- deJongetal.(2010)useCMDttingofSEGUEstellarphotometrytoprobe

thetotalstellarmassdensityfrom

R GC = 7

^{kp to}

R GC = 30

^{kp alonga}

"pi ketfen e"of

2.5

^{degreewidestripsatxedGala ti longitudespanning}

alargerangeofGala ti latitudes.

- Chen et al. (2001) use more general MSTO stars from two high latitude

regionsofSDSStotheNorthandtheSouthoftheGala ti plane(

49 deg <

|b| < 64 deg

^{). Theyexploretheinner haloregime(}

R GC . 30

^{kp ).}

- Bellet al.(2008) usealsomoregeneralMSTOstarsfromSDSS-DR5

span-ning

5 < R GC < 40

^{kp .}

- Fa ioli et al. (2014) use RRLyrae in the

9 kpc < R GC < 49

^{kp range.}

Theirmultiepo hdata omesfromtheXuyiS hmidtTeles opePhotometri

Survey(XSTPS)in ombinationwithSDSS olours,and overs

376.75

^deg

²

at

RA ≈ 150

^{deg and}

Dec ≈ 27

^deg.

- Sesaretal.(2010a)useRRLyraestarsfromSDSS-IIinthestripe82region.

Althoughtheirdataoriginallyspans

5 kpc < R GC < 110

^{kp ,thereanalysis}

performedbyFa iolietal.(2014)toderivestru turalparameterstrun ates

thesampleat

49

kp .

- Watkinset al.(2009) useaswellRRLyraefromSDSSinstripe82,andthe

omparative derivation of stru tural parameters by Fa ioli et al. (2014)

alsotrun atesitat

49

kp . Stripe82islo atedintheSouthGala ti Cap.

Theresultof this omparisonis summarized in Table2.6. Wenote that the

oblatenessvaluesforFa iolietal.(2014),Sesaretal.(2010a)andWatkinsetal.

(2009) are not the result of absolute best ts to a set of free parameters, but

thebest ts to free

R br

^,

n in

^and

n out

^{with xed priorvalues for a quite oblate}

(

q = 0.59 ^+0.02 _−0.03

^{)anda moderatelyoblatehalo(}

q = 0.70 ± 0.01

^).

Allsurveysthatrea hbeyond

R GC = 30

kp oin ideintheneedforabreakin thepower-lawindexofthehalodensity. Regardingpossibletriaxiality,onlyafew

ofthestudiesreport onstraintson

w

^{. Thosethatdo,haveeitherreported'nding}

unreasonable values' (Sesar et al. 2011) or have obtained limits on triaxiality

similartoours(

w > 0.8

^{,Belletal.(2008)).}

On thebreak radius, there is a general onsensus towards

R break ≈ 27

^{kp .}

Theonlyex eptionisthatofBelletal.(2008),whondavaluevery losetoour

measurement(

∼ 20

^{kp ). These}dis repan ies,however, anbeexplainedbythe ee tofthe

R break

^-

n in

^{degenera ydis ussedinse tion2.3.3.}

Theinnerandouterhalopowerlawindi esmostlyfallinthe

[ −2.3, −3.0]

^and

[ −3.6, −5.1]

^{ranges. Ourinnerpower lawindex}

n in = −2.50 ± 0.04

^{is onsistent}

with these results, parti ularly with the lower end. In the ase of the outer

halo power index (

n out = −4.85 ± 0.04

^{), the omparison is less trivial. First,}

only Sesar et al. (2011) and Deason et al. (2011) have provided measurements

for

n out

^{basedonts with a free}

q

^{parameter (}

n out = −3.8 ± 0.1

^and

−4.6 ^+0.2 −0.1

^,

respe tively). Se ond,onlyone work with

n out

measurements(Sesaretal.2011) uses a stellar tra er similar to ours (the others use A-BHB and BS stars, or

RRLyraestars). Most important, a good onstraint on

n out

^{requiresdeep data,}

andnoneofthese earliersurveys rea h asdeepas ourdataset. Oursteep outer

index,although well in therangeofprevious measurements, might wellindi ate

aprogressivesteepeningofthehalodensity,thoughitwouldbegoodtotestthis

with additional sight lines of omparable depth. In any ase, it seems safe to

on ludethat

n out < −4.0

^.

Thebest t values forthe polaraxis ratioor oblateness

q

^{range from}

0 .5

^to

0 .9

^{,withmostofthe}measurements on entratedwithin

(0 .55, 0.70)

^{. Thevalues}

of

q

^{donotseemtodepend onwhethera break was dete tedor not,noronthe}

limitingdistan eofthesurveyoronthestellartra er. Thedis repan ies anthus

beattributed either tomethodologi al dieren esorto dieren esin thespatial

overage of the data samples. However, it is di ult to determine the a tual

ause. Our results(

q = 0.79 ± 0.02

^{)do nott well within themost} onstri ted rangebut rathermat htheupperpart ofthebroaderrange.

Finally it is noteworthy that the hoi e of stellar tra er a ross the dierent

worksdoesnotseemto auseanysigni antbiasonthebest tparameters.

Dis ussion

ofthe

0 .2

^and

0 .4

^{mag datasets)and thosereported byothergroups inprevious works. Thedierent workshavebeen}

labelledasfollows: J08(Juri¢et al.2008),S11(Sesaret al.2011),D11 (Deasonetal.2011),dJ10(deJonget al.2010),

Ch01(Chenetal.2001),B08(Belletal.2008),F14(Fa iolietal.2014),andS10(Sesaretal.2010a)andW09(Watkins

et al.2009) as reanalysedin F14. Thettedmodelsin F14,S10 and W09 havexed oblatenessand testtwo dierent

valuesmotivatedbythepreviousndingsinS11 andD11.

Work stellartra er dist.range(kp )

χ ² _red R br (kpc) n n in n out q w

thiswork-axisym. near-MSTO

[10, 60]

^{1.9 }

−4.28 ± 0.06

^{ }

0.78 ± 0.04

^

thiswork-triax. near-MSTO

[10, 60]

^{1.9 }

−4.26 ± 0.06

^{ }

0.77 ± 0.04 0.88 ± 0.07

thiswork-broken near-MSTO

[10, 60]

^1.5

19.5 ± 0.4

^

−2.50 ± 0.04 −4.85 ± 0.04 0.79 ± 0.02

^

J08 near-MSTO

[5, 15] [2, 3]

^{ }

−2.8 ± 0.3

^

0.65 ± 0.15

^

S11 near-MSTO

[5, 35] 3.9 27.8 ± 0.8

^

−2.62 ± 0.04 −3.8 ± 0.1 0.70 ± 0.02

^{ex luded}

D11 A-BHB,-BS

[−, 40]

^

27.1 ± 1

^

−2.3 ± 0.1 −4.6 ^+0.2 _−0.1 0.59 ^+0.02 _−0.03

^

dJ10 multiple

[7, 30] [3.9, 4.2]

^

−2.75 ± 0.07

^{ }

0.88 ± 0.03

^

Ch01 MSTO

[−, 30]

^{ }

−2.5 ± 0.3

^{ }

0.55 ± 0.06

^

B08 MSTO

[5, 40] 2.2 ∼ 20 −3 ± 1

^{ }

[0.5, 0.8] ≥ 0.8

F14 RRLyrae

[9, 49] 0.8 28.5 ± 5.6

^

−2.8 ± 0.4 −4.4 ± 0.7 q f ix = 0.70 ± 0.01

^

" RRLyrae

[9, 49] 1.04 26.5 ± 8.9

^

−2.7 ± 0.6 −3.6 ± 0.4 q f ix = 0.59 ^+0.02 _−0.03

^

S10 RRLyrae

[9, 49] 1.1 34.6 ± 2.8

^

−2.8 ± 0.2 −5.8 ± 0.9 q f ix = 0.70 ± 0.01

^

" RRLyrae

[9, 49] 1.52 26.2 ± 7.4

^

−3.0 ± 0.3 −3.8 ± 0.3 q f ix = 0.59 ^+0.02 _−0.03

^

W09 RRLyrae

[9, 49] 1.1 27.6 ± 3.3

^

−2.5 ± 0.3 −4.3 ± 0.4 q f ix = 0.70 ± 0.01

^

" RRLyrae

[9, 49] 0.69 26.9 ± 3.1

^

−2.1 ± 0.3 −4.0 ± 0.3 q f ix = 0.59 ^+0.02 _−0.03

^

2.4.3 Dete tion of overdensities and identi ation

We analyse the data-to-models residuals for the dierent lines of sight in

Fig-ure 2.6b in sear h for overdensities. We nd that, in general, all the lines of

sightpresentregionswithdata-to-modelsdeviationsofamaximumfa toroftwo.

Additionally, ertainlinesof sightC,D, G,andHpresentmoresigni ant

de-viations spanning from a few kiloparse s to tens ofkiloparse s in distan e. We

dis ussthese overdensitiesin greater detailbelow, and wealso dis uss expe ted

overdensitiesthat shownosignaturein ourdata.

Themost prominentoverdensities in thedata-to-modelresiduals orrespond

to the northern wrap of the Sagittarius (Sgr) stream. This stream overlaps in

proje tion with groups G and H (see Figure 2.8). For group G, the residuals

indi ateoverdensitiesin thedistan erangewhereweexpe ttondboththeSgr

andthe Orphanstream (

20 < D hC . 40

^{kp or}

25 < D GC . 44

^{kp ,Pila-Díez}

et al. (2014)). The overdensities indeed peak between

R GC = 25

^{kp and}

45

kp , rea hing

ρ/ρ M = 7 ± 2

^{,and drop sharply}afterwards. GroupH probesthe Sgrstream losertotheGala ti entrebut alsoforlarger distan esthangroup

G. Based both on extensive data (summarized in Pila-Díez et al. (2014)) and

in models (Law & Majewski (2010b) and Peñarrubia et al. (2010)), we expe t

this stream to span the

20 < D hC < 60

^{kp or}

16 < R GC < 55

^{kp range at}

these oordinates. Thisexpe tation ismetallalong: theysteadily in reasefrom

R GC ≈ 15

^{kp ,departfrom}

ρ/ρ M = 3 ± 1

^at

R GC = 30

^{kp ,rea h}

ρ/ρ M = 6 ± 2

at

R GC = 40

^{kp and peak at}

R GC = 45

^{kp with}

max(ρ/ρ M ) = (12 , 15) ± 2

^.

However,theydonotde reasenear

R GC = 55

^{kp but seemtostaystable with}

a signi ant

ρ/ρ M > 7 ± 2

^{). This suggests a thi ker bran h than predi ted by}

themodels,butin agreementwithpreviousRRLyraemeasurements(Ibataetal.

(2001 ),Totten&Irwin(1998)andDohm-Palmeretal.(2001)assummarizedin

Figure17ofMajewskietal.(2003)).

Twomoremodestoverdensitiesthatdonotappearintheliteratureseemtobe

presentingroups CandD.Ingroup C,a weakbut onsistentoverdensityspans

adistan e rangeof

R GC ≈ 35

^{kp to}

R GC ≈ 60

^{kp . Ingroup D,asharpbump}

extendsoverafewkiloparse s around

R GC ≤ 20

^{kp .}

Wehavelookedforotherknownoverdensitiesthatposition-mat hourlinesof

sight(seeFigure2.8),butfoundnoindi ationofthemintheresiduals. Therst

one orresponds to the tidal tails of the NGC5466 globular luster (Belokurov

etal. 2006a),whi h overlap withone eld in groupA and anotherone ingroup

B (A1361 entred at

(RA, Dec) = (176.09, 46.39)

^{and A1927 at}

(RA, Dec) = (217.92, 25.67)

^{). Thisisaveryweak old}substru turelo atedat

R GC ≈= 16

^kp

andextending for

45 deg

^{with anaverage widthof}

1.4 deg

^{(Grillmair&Johnson}

2006). Assu h,itisnotsurprising tondnosignaturein thedensityproles.

These ondone istheensembleof threeknown overdensities inthedire tion

ofgroupE:theAntiCenterStream(

R GC = 18 ± 2

^{kp ,}Ro ha-Pintoetal.(2003) andLietal.(2012)),theMono erosring(

R GC ≈ 18

^{kp ,Lietal.(2012))andthe}

EasternBandStru ture(

R GC = 20 ±2

^{kp ,Lietal.(2012)). These}substru tures

Dis ussion

−50 0

50 100

150 200

250 RA (degrees)

−40

−20 0 20 40 60 80

D EC ( de gr ee s)

EBS G&D ACS

Pisces NGC5466

Orphan

Tri-And A

B

C D

E

G F H

Figure2.8: Equatorialmapshowingthepositionofalltheeldsusedinthisworkandthe losest oldstellaroverdensities

tothem. Theseoverdensitiesareusedfor omparisonanddis ussionofthestellardensityproledata-to-modelresiduals

throughout se tion 2.4.3. The labels in the gure orrespond to the Anti entre Stru ture (ACS), the Eastern Band

Stru ture (EBS),theNGC5466stream, theGrillmair &Dionatosstream (G&D),theOrphanstream, the

Triangulum-Andromedaoverdensity(Tri-And)andthePis esoverdensity. Theba kgroundimageistheSDSS-DR8mapfromKoposov

et al. (2012), whi h shows the footprint of the Sagittarius stream. The Mono eros ring also appears partially in this

ba kgroundimage,as adarkregionoverlappingthewesternpartoftheGala ti diskintheanti entreregion,eastwards

oftheACS.

aremaskedfrom ourtsandresidualswhenweimpose

|z| > 10

^{kp toavoidthe}

inuen eofthethi kdisk,andtherefore,they annotbedete ted.

TheTriangulum-Andromeda overdensity((Martin et al. 2007)) falls lose to

oneoftheeldsingroupF.Despitethisproximity,theresidualsshownoeviden e

foranoverdensityattheexpe teddistan eof

R GC ≈ 30

^{kp ,indi atingthatthe}

overdensitydoesnotextendfurtherin thisdire tion.

In document Title: Structure and substructure in the stellar halo of the Milky Way (pagina 47-54)