Constraining the distribution of dark matter in dwarf spheroidal galaxies with stellar tidal streams

3.6 MB·English

by  Raphaël Errani

preprintofletterMNRAS449,L46-L50(2015),arXiv:1501.04968[astro-ph.GA](compiledusingMNLATEXstylefilev2.2)
Constraining the distribution of dark matter in dwarf spheroidal
galaxies with stellar tidal streams
Raphaël Errani1,2,(cid:63), Jorge Peñarrubia2 & Giuseppe Tormen1
1DipartimentodiFisicaeAstronomia‘GalileoGalilei’,UniversitàdegliStudidiPadova,VicoloOsservatorio3,35122Padova,Italy
2InstituteforAstronomy,UniversityofEdinburgh,RoyalObservatory,BlackfordHill,EdinburghEH93HJ,UK
5
1
Accepted2015January20.Received2015January14;inoriginalform2014November20
0
2

r ABSTRACT
a
M
Weusehigh-resolutionN-bodysimulationstofollowtheformationandevolutionoftidal
streams associated to dwarf spheroidal galaxies (dSphs). The dSph models are embedded
1
in dark matter (DM) haloes with either a centrally-divergent ‘cusp’, or an homogeneous-

] density ‘core’. In agreement with previous studies, we find that as tides strip the galaxy the
A evolution of the half-light radius and the averaged velocity dispersion follows well-defined
G tracksthataremainlycontrolledbytheamountofmasslost.Crucially,theevolutionarytracks
behavedifferentlydependingontheshapeoftheDMprofile:atafixedremnantmass,dSphs
.
h embeddedincoredhaloeshavelargersizesandhighervelocitydispersionsthantheircuspy
p counterparts. The divergent evolution is particularly pronounced in galaxies whose stellar
- component is strongly segregated within their DM halo and becomes more disparate as the
o
remnantmassdecreases.OuranalysisindicatesthattheDMprofileplaysanimportantrolein
r
t definingtheinternaldynamicsoftidalstreams.Wefindthatstellarstreamsassociatedtocored
s
a DMmodelshavevelocitydispersionsthatliesystematicallyabovetheircuspycounterparts.
[ OurresultssuggestthatthedynamicsofstreamswithknowndSphprogenitorsmayprovide

strongconstraintsonthedistributionofDMonthesmallestgalacticscales.
2
v
Keywords: galaxies:dwarf,kinematicsanddynamics,evolution,LocalGroup–cosmology:
8
darkmatter–methods:numerical
6
9
4
0
. 1 INTRODUCTION limit the number of stellar tracers for which kinematic informa-
1
tioncanbeobtainedandalsoreducethephase-spaceinformation
0 Itiswidelybelievedthatthemicroscopicpropertiesofdarkmat-
5 toquantitiesprojectedalongthelineofsight.Inaddition,asfore-
ter(DM)particlesarereflecteduponthedistributionofDMonthe
1 groundcontaminantstendtodominateinnumberintheoutskirts
smallestgalacticscales(e.g.Tremaine&Gunn1979;Gilmoreetal.
: of these galaxies most spectroscopic surveys suffer from strong
v 2007).Beingthesmallestandmostdarkmatter-dominatedgalax-
sampling biases that severely complicate the dynamical analysis
i iesintheknownUniverse,dwarfspheroidalgalaxies(dSphs)place
X of these objects. Given the number and graveness of these short-
strong constraints on the DM particle mass (e.g. Boyarsky et al.
r comingsitisperhapsnotsurprisingthatdifferentmethodsthataim
2009;Macciòetal.2012;Lovelletal.2014)aswellasonitscross
a tomeasurethemassprofileofMilkyWaydSphsyieldcontradic-
section (Burkert 2000; Loeb & Weiner 2011; Vogelsberger et al.
toryresults.Forexample,whereassomestudiesfindevidencefor
2012,2014;Rochaetal.2013).Furthermore,withluminositiesin
constant-densityDMcores(Battagliaetal.2008;Walker&Peñar-
therangeof104−108L(cid:12)(McConnachie2012),thesegalaxiessam- rubia2011;Amorisco&Evans2012),othermethodsoftenapplied
plethefaintestendofthegalaxyluminosityfunction,providinga
tothesamedatasuggestcentrally-divergent‘cusps’(Richardson&
testbedfortheoreticalmodelsthataimtounderstandthedynamical
Fairbairn2014)orremaininconclusive(Breddels&Helmi2013;
interplaybetweenbaryonsandtheDMhaloes(e.g.Navarroetal.
Strigarietal.2014).
1996; Pontzen & Governato 2012, 2014; Peñarrubia et al. 2012;
Brooks & Zolotov 2014; Di Cintio et al. 2014; Nipoti & Binney Recentnumericalstudieshaveshownthatthedynamicalprop-
2015). erties of tidal streams are sensitive to the internal mass distribu-
However, measuring the distribution of DM from the inter- tionoftheprogenitorsystem(Küpperetal.2008,2012;Peñarrubia
nal kinematics of dSphs has proven to be challenging. Their low etal.2006,2010;Eyre&Binney2011).Usinghigh-resolutionN-
surfacebrightnessplustheirrelativelylargeheliocentricdistances bodysimulationsweshowinthispaperthatthedistributionofdark
matter in dSphs plays an important role in defining the orbits of
tidallystrippedstars,andthatthedynamicsofstellarstreamspro-
(cid:63) E-mail:[email protected] videconstraintsonthedarkmatterhaloprofileofdSphswhichare
©2015RAS
2 RaphaëlErrani,JorgePeñarrubia&GiuseppeTormen
5 cusp,core; r(cid:63)/a=0.1(open),0.2(filled) 1990)withscaleradiusab=1.2kpcandmassMb=1.3·1010M(cid:12),
and an axis-symmetric disk (Miyamoto & Nagai 1975) with ra-
0 dialandverticalscalelengthsad=3.5kpc,bd=0.3kpcandmass
r/h, Md=7.5·1010M(cid:12).
rh To generate N-body models of dSphs in dynamical equilib-
riumwedraw2×107particlesfromaDehnen(1993)distribution
1
function.Thesemodelsfollowananalyticaldensityprofile
1
M(3−γ)a
ρ(r)= , (1)
h,0 4πrγ(r+a)4−γ
σ
/
σh whereγ≡−limr→0dlogρ/dlogrdefinestheslopeoftheinnerden-
sity profile. In this work we consider two values, namely γ =1
0.2
(cusp)andγ =0(core),andseta=1kpc.OurdSphsmodelsare
1
builtundertheassumptionthatstarsbehaveasmasslesstracersof
theunderlyingDMpotential.Togenerateastellarcomponentem-
0
(cid:63), beddedintheDMhaloinequilibriumwefollowtheapproachde-
m
/ scribedbyBullock&Johnston(2005),whereeachindividualDM
(cid:63) 0.2 5kpc 15kpc
m 7.5kpc 20kpc particle is assigned a probability, or mass-to-light ratio, of repre-
10kpc senting a ’star’ in such a way that the overall stellar density pro-
filefollowsaPlummerspherewithsegregationr(cid:63)/a(cid:39)rh/(1.3a),
1 0.5 0.2 0.1
where rh and r(cid:63) are the half-light and core radii of the Plum-
mh/mh,0 mermodel,respectively.Tofacilitateacomparisonbetweencored
and cuspy models the dSph parameters are chosen such that for
Figure1.EvolutionarytracksforcuspyandcoreddSphgalaxies.Allquan- agivenspatialsegregationbothcoredandcuspyDMhaloeshave
titiesaremeasuredatapocentre(seetext).ThedashedlinesarefitsofEqua- thesamemassenclosedwithinthehalf-lightradiusm ≡m(<r )
h h
tion2.Thehalf-lightradiusrh,theluminosityaveragevelocitydispersion att =0. Since the mass profile of a Dehnen model is m(<r)=
σhwithinrhandthetotalstellarmassm(cid:63)arenormalisedtotheinitialvalue M[r/(r+a)]3−γ,imposingm =m requireschangingthe
artihna.dlTsathreeellaptrrlaosctektgesdreagaresataiionfnduenrp(cid:63)ce/tniaodnaennodtfostihfgetnhciefiucrorarenbntiltty,msdlaeisgpshetnmldyhe/dnmetpho,e0nnetdhneecnltsohosaenpdethwoeiftihtnhiine- itnogtalMmcuassps=of1th0e8Mdw(cid:12)aryfiemldosdeMlhsc,coburyesp=Mc8u.s6ph6/,cM·or1ec0or8eM=(cid:12)rhf/o(rrrh(cid:63)+/aa=).F0i.x1-,
massprofile(cuspy/cored)ofthedSphgalaxy. andMcore=4.83·108M(cid:12) forr(cid:63)/a=0.2.Ourmodelsarepurely
gravitational, thus they are scale free, and physical units are just
givenforclarity.
Table1.EmpiricalFitParameterstotheTidalEvolutionaryTracks Weusetheparticle-meshcodeSUPERBOX(seeFellhaueretal.
2000),whichsamplesthedensityinthreegridswithdifferentreso-
r(cid:63)/a rh/rh,0 σh/σh,0 m(cid:63)/m(cid:63),0 lutionandperformsaleapfrogintegrationtosolvetheequationof
motion.Inourmodelseachgridconsistsof1283cubiccells.Grids
α 1.49 -0.88 3.43
0.1 1 and 2 move with the centre of density of the progenitor, while
P β 0.35 0.24 1.86
CUS 0.2 α 1.22 -0.68 3.57 gprriodge3niistocrenwtirtehdaonretshoeluhtoiosntgoafla2xay/.1G26rid≈11r6epsocl,vweshitlheegcroidreso2fatnhde
β 0.33 0.26 2.06
3haveresolutionsof20a/126≈160pcand400a/126≈3.2kpc,
0.1 α 2.91 -2.56 1.43 respectively.Weuseafixedtimestepof1Myrandstoresnapshots
E β 0.15 0.05 0.69
R every200Myrs.Allmodelsareruninisolationfor14Gyrsinorder
O α 1.63 -1.39 0.82
C 0.2 totestthestabilityofournumericalset-up.
β 0.03 0.29 0.82
The dSph models are placed on highly eccentric orbits with
a fixed apocentre distance ra = 150kpc and pericentres rp =
complementary to those inferred from the internal kinematics of 5,7.5,10,15and20kpc.Theseorbitsareconfinedtotheplaneper-
theprogenitorgalaxy.TheLetterisorganisedasfollows:Section pendiculartothesymmetryaxisofthehostdiscinordertofacil-
2describestheN-bodydSphandanalyticalhostgalaxymodelsas itatetheanalysisoftheassociatedtidalstreams.Astidesstripthe
wellasthenumericalsetup.InSection3weanalysehowcuspyand dSphmodelswefollowtheevolutionofthehalf-lightradiusrh,the
coreddSphsevolveundertidalstrippingandintroducetheevolu- luminosity-averagedvelocitydispersionσhandthestellarmassm(cid:63)
tionarytracks.InSection3wepresentourresultsregardingthedif- asafunctionofthemassmhwithinrh.Allquantitiesreportedinthis
ferencesoftidalstreamoriginatingfromcuspyandcoredmodels. paperarenon-projected.Notethatmhcanbeinprinciplemeasured
Section4describeshowthesedifferencescanbeusedtoconstrain withrelativelyhighaccuracyinisolatedsystems(seee.g.Walker
theDMprofileofdSphswithassociatedtidalstreams. et al. 2009; Wolf et al. 2010), but the calculation of σ requires a
luminosity-averaged integral over the entire dSph, which in case
ofthedSphundergoingtidalstrippingmaybedifficulttoestimate
owingtothepresenceoftransient‘extra-tidal’features.Tocompute
2 NUMERICALMETHOD
thehalf-lightradiusrh andthestellarmassm(cid:63),wefitaPlummer
The host galaxy is modelled as a Milky Way-like static potential profiletotheDMparticlesweightedbythecorrespondingmass-to-
composed of a spherical NFW halo (Navarro et al. 1997) with light ratio. To avoid contamination with ‘extra-tidal’ particles we
virialradiusrvir=258kpc,massMvir=1012M(cid:12) andconcentra- followaniterativeapproach,whereonly3/4oftheparticleswithin
tion c =12 (Klypin et al. 2002); a spherical Bulge (Hernquist aradiusof5kpctothedSpharefittedatatime.Thenusingthefit-
©2015RAS,MNRAS
ConstrainingDMindSphswithstellarstreams 3
0
100 CUSP y(kpc)p -055 50 -2pylg()⋆
y(kpc) 0 -5xp(0kpc)5 z(kpc) 0 --64probabilit
d
-100 -50 -8ojecte
1stapo 2ndapo 3rdapo 4thapo 4thapo pr
-10
CORE
100 50
kpc) 0 kpc) 0
( (
y z
-100 -50
1stapo 2ndapo 3rdapo 4thapo 4thapo
-100 0 100 0 100 200
x(kpc) R(kpc)
Figure2.Snapshotsoftheevolutionoftidalstreamsassociatedtocuspy(toprow)andcored(bottomrow)models.Bothmodelshavera=150kpc,rp=
20kpc,a=1kpcandr(cid:63)/a=0.2.Oneorbitalperiodequalsroughly2.4Gyrs.Themasseshavebeenrescaledtoensurethattheluminosity-averagedvelocity
dispersionwithinrhisthesameforbothprogenitorsatt=0.Smallboxesineachpanelshowadetailviewoftheprogenitor.Therightmostcolumnshowsthe
projectionoftidalstreamandprogenitoronthe(R,z)plane,whereRisthecylindricaldistancefromthegalacticcentreandzisthedistanceabovetheorbital
planeoftheprogenitor.DMparticlesarecolour-codedaccordingtotheirprobabilityoftaggingstars.SeeArXivancillaryfilesforanimations1.
tedPlummerparameterswederivetheradiusthatcontains3/4of coldervelocitydispersionsthantheircuspycounterparts.Thisdif-
thestellarmassandrepeatthefitagain.Thesestepsarere-iterated ferencecanbeeasilyunderstoodintermsofthedynamicaltimeof
untilconvergenceisreached.Thestellarvelocitydispersionσhand theprogenitorgalaxies,whichscalesastdyn∝(Gρ)−1/2.Because
massmh arecomputedfromthevelocitiesoftheparticleslocated ρcusp(cid:29)ρcore atr(cid:28)awefindthatstarsembeddedinDMcusps
withinthehalf-lightradius. reactadiabaticallytoexternalperturbations.Incontrast,starsem-
BecausetheinternaldynamicaltimeofthedSphmodelsare beddedincoredDMhaloestendtoabsorbarelativelylargeamount
much shorter than the period of the orbit, the progenitor reaches ofenergyduringtidalencounters,whichleadstoanoverallexpan-
anequilibriumconfigurationshortlyaftereachpericentrepassage. sionandalowkinematictemperatureoncedynamicalequilibrium
Todecreasestochasticfluctuationsparametersareaveragedover7 isreached.
snapshotschosensymmetricallyaroundeachapocentre. A second interesting point can be gleaned from the lower
panelofFig.1,whichshowsthefractionofstarslosttotidesver-
sustheremnantmass.Wefindthatatagivenremnantmasscored
dSphmodelslostlessstarsthantheircuspycounterparts.Thisap-
3 TIDALEVOLUTIONARYTRACKS
parentlycounter-intuitiveresultarisesfromthedichotomybetween
Previousstudies(e.g.Peñarrubiaetal.2008,2010)haveshownthat theshapesofthestellarandDMdensityprofiles.Whereasstarsin
tidaleffectstendtolowerthevelocitydispersionandincreasethe incoredDMhalomodelstendtobeassociatedtothemost-bound
half-lightradiiofstarsembeddedwithinNavarroetal.(1997)ha- DMparticles,incuspyDMhaloesalargefractionofparticleswith
los,andthatthestructuralchangesinthestellarcomponentofthese highbindingenergyarelocatedwithinthedensitycuspandhave
galaxies follow well-defined evolutionary tracks that are mainly alowprobabilityoftaggingastar,i.e.ahighmass-to-lightratio.
controlledbyhowmuch(andnothow)themassmhenclosedwithin E.g.forcuspymodelswithr(cid:63)/a=0.2,onefindsthat90%ofthe
thehalf-lightradiusr varies.Fig.1showsthatthisresultalsoholds stellarparticlesareassociatedtothe14.5%most-boundDMparti-
h
for galaxies embedded in cored DM haloes. However, while the cles,whileincoredmodelsthisfractionfallstoamere5%.Note,
tidaltracksassociatedtocuspyDMhaloesscarcelydependonthe however,thatbecausedSphsembeddedincoredDMhaloesarein
spatialsegregationofthestellarcomponentwithintheDMhalo,as generallessresilienttotidalstripping,thesemodelstendtoevolve
shownbyPeñarrubiaetal.(2008),thoseassociatedtocoredDM atafasterpacealongtheevolutionarytracksthanthoseembedded
haloesappeartobesensitivetotheinitialvalueofr(cid:63)/a.Inparticu- incuspyhaloes(e.g.Peñarrubiaetal.2010).
lar,wefindthatthehalf-lightradiusincreasestoalargerextentthe
moredeeplysegregatedthestarsarewithintheDMcore.Forthe
remainderofthispaper,itisusefultoparametrizetheevolutionary 4 STREAMEVOLUTION
tracksusingtheempiricalformulaofPeñarrubiaetal.(2008)
Inthissectionwecomparethepropertiesofstellarstreamsassoci-
2αxβ atedtocoredandcuspyprogenitors.Asexpected,Fig.2showsthat
f(x)= where x=m /m . (2)
(1+x)α h h,0 tides are strongest at pericenter and trigger recurring episodes of
mass loss at every pericentric passage. Comparison between the
The best-fitting parameters are listed in Table 1 and the resulting
tracksareplottedwithdottedanddashedlinesinFig.1.Fig.1also
shows other points of interest. First, note that at a fixed remnant 1 dSph_stream_brightness.avi:colour-codedbysurfacebrightness
mass mh/mh,0 cored progenitors have larger half-light radii and dSph_stream_dispersion.avi:colour-codedbyvelocitydispersion
©2015RAS,MNRAS
4 RaphaëlErrani,JorgePeñarrubia&GiuseppeTormen
Core 20kpc
Cusp
40kpc
10 1stperiwrap
60kpc
2ndperiwrap
80kpc
3rdperiwrap 4thapo
h 100kpc p
σ s
/ cu
z ˜σ
σ
/
= e intrinsicoffset
or 3rdapo
˜σ ˜σc
2ndapo
1 1stapo Progenitor
t=0
1 1stperiwrap
2ndperiwrap
4th apo
3rdperiwrap
1 10
1
w˜ =w/r
h w˜ /w˜
core cusp
Figure3.Widthw˜ andvelocitydispersionσ˜ ofthestreamsnormalizedto
Figure4.Timeevolutionofthewidthandvelocitydispersionratiosbe-
thehalf-lightradiusandluminosity-averagedvelocitydispersionofthepro-
tweenstreamsassociatedtodSphsembeddedincoredandcuspydarkmat-
genitordSph,respectively.Weshowdataatafixedsnapshot(4thapocentre)
terhaloesofthesimulationshowninFig.2.Symbolsdenoteparticleslostat
ofthesimulationshowninFig.2.WedistinguishbetweendSphmodels
differentpericentricpassages(wraps),whereascoloursdistinguishbetween
embeddedincuspy(opensymbols)andcored(filledsymbols)DMhaloes.
differentsnapshots.Thewidthandvelocitydispersionratiosroughlyfollow
Symbols are colour-coded according to the pericentric passage at which
theratiobetweenthetidalevolutionarytracksofcuspyandcoreddSphsas
particlesbecametidallyunbound.WemarkthecylindricaldistanceRtothe
givenbyEquation2,whichweplotwithadottedlineforeaseofreference.
galacticcentreofsegmentswithintherange20kpc(cid:54)R(cid:54)100kpc.Notice
theclearkinematicoffsetofthestreamsdependingontheDMhaloprofile.
creases at a faster pace (see Fig. 1) than the velocity dispersion
oftheassociatedstream.Hence,tidalstreamsappearkinematically
upper and lower panel reveals that tidal mass loss is more pro-
hotterwithrespecttototheprogenitor’svelocitydispersionasthey
nouncedindSphsembeddedincoredDMhaloes.Indeed,although
becomeolder2.Fig.3showsthatboththewidthandthevelocity
not shown here the cored dSph is fully disrupted during the 5th
dispersionoftidalstreamsarehighlydependentontheprogenitor’s
encounter,whereasthecuspydSphstillretainsaboundremnant.
orbit,thenumberoforbitalperiodscompleted,andthegalactocen-
At each snapshot we quantify the mass m /m . The width
h h,0
tricradiuswherethesequantitiesaremeasured.
wal2on=g(cid:104)tzh2e(cid:105)t−id(cid:104)azl(cid:105)t2aailnsdatrheemveealosucirteyddiinsptheresidoinreσctzioonfppaerrtpicelnedsicmuolavrintgo Interestingly,Fig.4showsthatplottingtheratiosσ˜core/σ˜cusp
theorbitalplaneatfixedcylindricaldistancesR=(cid:112)x2+y2 from and w˜core/w˜cusp at fixed segments collapses the degeneracy be-
tween these effects into a single relation, which roughly follows
thehostgalaxycentre.Thesequantitiesarethennormalizedbythe
the path defined by the tidal evolutionary tracks of the progeni-
half-lightradiusandthevelocitydispersionofthestreamprogeni-
torgalaxies,Equation2,evaluatedforthecorrespondingvaluesof
torasgivenbyEquation2forthecorrespondingvalueofm /m .
h h,0 m /m forthecuspyandcoredmodels(shownwithdottedlines
Toreducenoiseweapplythesameaveragingisitwasdonewith h h,0
for ease of reference). This result suggests that the evolutionary
thetracks.Fig.3showsthattidalstreamsbecomeverynarrowand
path of the stream in this plane is mainly driven by the disparate
kinematically hot at small distances from the host and get wider
structuralevolutionofgalaxiesembeddedincoredandcuspyDM
andcolderwithincreasingR,asalsoshowninFig.2,asonewould
haloes as a result of tidal mass loss (see Fig. 1). As shown in
expectfromLiouville’stheorem.
Fig.4,thereisanintrinsicoffsetbetweenthevariouspropertiesof
In order to understand the internal evolution of the stream
thestreamwhichcanbeunderstoodusingsimpledynamicalargu-
properties it is useful to distinguish between particles lost at dif-
ments.Ifweassume,asinAmorisco(2014),thatthestreamwidth
ferent pericentric passages. We define a wrap as the ensemble of
is proportional to the tidal radius of the progenitor at pericentre
particles stripped at the same pericentre encounter. Each wrap is
thendividedintosegmentsaccordingtotheircylindricaldistanceR rt ∝M(cid:112)1/3,andthatthevelocitydispersionofthestreamscalesas
tothegalacticcentre.Wrapsthatformedduringrecentpericentric σz ∝ m(<rt)/rt, one finds that for the orbits plotted in Fig. 4
passages tend to be found at close distances from the progenitor thewidthandvelocitydispersionratiosarert,core/rt,cusp(cid:39)1.7and
galaxy,asittakesafeworbitalperiodsfortheseparticlestopop- σz,core/σz,cusp(cid:39)1.7,respectively(seesection2).Fig.4showsthat
these simple analytical estimates, marked with a black cross for
ulatetheentireorbit.Incontraststarsstrippedatearliertimescan
ease of reference, faithfully describe the numerical results. It is
in some cases wrap around the host galaxy entirely. Comparison
straightforwardtoshowthatformodelswithsmallerstellarsegre-
between different wraps in Fig. 3 shows that streams associated
to dSphs embedded in cored DM haloes have similar widths but gationr(cid:63)/awiththesamevaluesofrhandσhthisoffsetincreases.
highervelocitydispersionsthantheircuspycounterparts.Thisisso This is in agreement with our models for r(cid:63)/a=0.1 (not shown
here).
regardlessofthegalactocentricradiiatwhichthesequantitiesare
measured. Also, wraps that form during early encounters tend to
havehighervelocitydispersionsthanthoseformedrecently.This 2 Stream‘age’istypicallydefinedasthetimeelapsedsincetheparticles
trendarisesbecausethevelocitydispersionofthedwarfgalaxyde- becometidallyunbound.
©2015RAS,MNRAS
ConstrainingDMindSphswithstellarstreams 5
5 CONCLUSIONS BattagliaG.,HelmiA.,TolstoyE.,IrwinM.,HillV.,JablonkaP.,2008,
ApJ,681,L13
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h
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McConnachieA.W.,2012,AJ,144,4
systempriortotidalstripping.Modelsthatreproducetheobserved
MiyamotoM.,NagaiR.,1975,PASJ,27,533
rh andσh leadtoMcore>Mcusp.Havingsettheinitialconditions NavarroJ.F.,EkeV.R.,FrenkC.S.,1996,MNRAS,283,L72
of the dwarf galaxy, the next step corresponds to modelling the NavarroJ.F.,FrenkC.S.,WhiteS.D.M.,1997,ApJ,490,493
orbit and the mass evolution of the progenitor system simultane- NipotiC.,BinneyJ.,2015,MNRAS,446,1820
ously in a given host potential. This can be done with the aid of PeñarrubiaJ.,BensonA.J.,Martínez-DelgadoD.,RixH.W.,2006,ApJ,
self-consistentN-bodymodels(e.g.Bonacaetal.2014)or,alterna- 645,240
tively, with efficient semi-analytical algorithms based on forward PeñarrubiaJ.,NavarroJ.F.,McConnachieA.W.,2008,ApJ,673,226
modellingofstellarstreams(e.g.Vargheseetal.2011;Sanders& Peñarrubia J., Benson A. J., Walker M. G., Gilmore G., McConnachie
A.W.,MayerL.,2010,MNRAS,406,1290
Binney 2013; Amorisco 2014; Gibbons et al. 2014; Fardal et al.
PeñarrubiaJ.,PontzenA.,WalkerM.G.,KoposovS.E.,2012,ApJ,759,
2014; Price-Whelan et al. 2014). Our results suggest that the ve-
L42
locitydispersionofstellarstreamsassociatedtocuspyhalomodels
PontzenA.,GovernatoF.,2012,MNRAS,421,3464
willliesystematicallybelowthatofthecoredmodels,whichinturn
PontzenA.,GovernatoF.,2014,Nature,506,171
canbeusedtoconstrainthemassprofileoftheprogenitorgalaxy Price-WhelanA.M.,HoggD.W.,JohnstonK.V.,HendelD.,2014,ApJ,
bycomparingthevelocitydispersionofthestreamagainstthatof 794,4
theremnantgalaxy. RichardsonT.,FairbairnM.,2014,MNRAS,441,1584
Todatetheonlydwarfspheroidalwithaknowntidalstream RochaM.,PeterA.H.G.,BullockJ.S.,KaplinghatM.,Garrison-Kimmel
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lokurov et al. 2014 for a recent data compilation.) As this dSph SandersJ.L.,BinneyJ.,2013,MNRAS,433,1826
Strigari L. E., Frenk C. S., White S. D. M., 2014, preprint,
iscurrentlylocatedclosetopericentre,wecan’tapplydirectlyour
(arXiv:1406.6079)
tidal evolutionary tracks, as these have been computed for dSphs
TremaineS.,GunnJ.E.,1979,PhysicalReviewLetters,42,407
that have reached equilibrium after each pericentre passage. The
VargheseA.,IbataR.,LewisG.F.,2011,MNRAS,417,198
useofN-bodysimulationswillberequiredtostudyperturbations
VogelsbergerM.,ZavalaJ.,LoebA.,2012,MNRAS,423,3740
fromtheequilibriumconfiguration.Anapplicationoftheproposed VogelsbergerM.,ZavalaJ.,SimpsonC.,JenkinsA.,2014,MNRAS,444,
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separatecontribution. WalkerM.G.,PeñarrubiaJ.,2011,ApJ,742,20
WalkerM.G.,MateoM.,OlszewskiE.W.,PeñarrubiaJ.,WynEvansN.,
GilmoreG.,2009,ApJ,704,1274
WolfJ.,MartinezG.D.,BullockJ.S.,KaplinghatM.,GehaM.,Muñoz
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©2015RAS,MNRAS