Constraining Self-Interacting Dark Matter with the Milky Way's dwarf spheroidals

0.7 MB·English

by  Jesus Zavala

Mon.Not.R.Astron.Soc.000,1–6(2012) Printed7January2013 (MNLATEXstylefilev2.2)
Constraining Self-Interacting Dark Matter with the Milky Way’s
dwarf spheroidals
Jesu´s Zavala1,2(cid:63), Mark Vogelsberger3† and Matthew G. Walker3‡,
1PerimeterInstituteforTheoreticalPhysics,31CarolineSt.N.,Waterloo,ON,N2L2Y5,Canada
2DepartmentofPhysicsandAstronomy,UniversityofWaterloo,Waterloo,Ontario,N2L3G1,Canada
3Harvard-SmithsonianCenterforAstrophysics,60GardenStreet,Cambridge,MA02138,USA
3
1 Accepted???.Received???;inoriginalform???
0
2
ABSTRACT
n
Self-InteractingDarkMatterisanattractivealternativetotheColdDarkMatterparadigmonly
a
J ifitisabletosubstantiallyreducethecentraldensitiesofdwarf-sizehaloeswhilekeepingthe
densities and shapes of cluster-size haloes within current constraints. Given the seemingly
4
stringent nature of the latter, it was thought for nearly a decade that Self-Interacting Dark

] Matter would be viable only if the cross section for self-scattering was strongly velocity-
O dependent.However,ithasrecentlybeensuggestedthataconstantcrosssectionperunitmass
C ofσT/m∼0.1cm2g−1issufficienttoaccomplishthedesiredeffect.Weexplicitlyinvestigate
thisclaimusinghighresolutioncosmologicalsimulationsofaMilky-Waysizehaloandfind
.
h that, similarly to the Cold Dark Matter case, such cross section produces a population of
p massivesubhaloesthatisinconsistentwiththekinematicsoftheclassicaldwarfspheroidals,
-
o inparticularwiththeinferredslopesofthemassprofilesofFornaxandSculptor.Thisproblem
r is resolved if σT/m∼1cm2g−1 at the dwarf spheroidal scales. Since this value is likely
t inconsistent with the halo shapes of several clusters, our results leave only a small window
s
a open for a velocity-independent Self-Interacting Dark Matter model to work as a distinct
[ alternativetoColdDarkMatter.

2 Keywords: cosmology:darkmatter–galaxies:halos–methods:numerical
v
6
2
4
6 1 INTRODUCTION modifytheinitialcuspydarkmatterdistributionintoacoredone
. (e.g.Navarroetal.1996;Pontzen&Governato2012).Currenthy-
1 It is now clear that observations of dark matter dominated sys-
1 drodynamical simulations have shown that such a mechanism is
temssuchaslow-mass(dwarf)andlowsurfacebrightness(LSB)
2 abletocreatelargecoresinintermediate-massgalaxies(Governato
galaxiesfavourthepresenceofdarkmattercoresofO(1kpc)(e.g.
1 etal.2010,2012),and,oncetidalstrippingistakenintoaccount,
Moore1994,KuziodeNarayetal.2008,deBlok2010,Walker&
: itmightsolvethetoobigtofailproblemaswell(Brooks&Zolo-
v Pen˜arrubia2011,Amorisco&Evans2012).Theseobservationsare
tov 2012). It is not clear, however, if such episodes of large gas
i achallengefortheColdDarkMatter(CDM)paradigmwheredark
X blow-outsareconsistentwiththestarformationhistoriesandstel-
matterhaloesarepredictedtohavedensitycusps,animprintofthe
r larpropertiesofLSBsanddwarfs(e.g.KuziodeNaray&Spekkens
collisionlessnatureofCDM(thecore-cuspproblem).Inapossibly
a 2011;Boylan-Kolchinetal.2012;Pen˜arrubiaetal.2012).
relatedissue,ithasbeenpointedoutrecentlythatthedarksatellites
ofMilky-Way(MW)sizehalosimulationsaretoodensetobecon- Given the large uncertainties regarding whether baryon
sistentwiththekinematicsoftheMWdwarfspheroidals(dSphs) physicscanreconciletheCDMmodelwithobservationsofdwarf
(thetoobigtofailproblem;Boylan-Kolchinetal.2011,2012). galaxies,itisprudenttoconsiderthealternative,whichistoques-
AlthoughthesearesignificantchallengestotheCDMmodel, tion the fundamental CDM hypotheses, namely, the collisionless
theirsolutioncouldnaturallylieinourincompleteunderstandingof andcoldnatureofCDMparticles.Thisalternativeisadditionally
thecomplexprocessofgalaxyformation.Eventhoughtheinternal encouraged by the null detection of several experiments that are
dynamicsofdwarfsisdominatedbydarkmattertoday,itiscon- pursuingthediscoveryofthefavouredCDMparticles,andwhose
ceivablethatearlierepisodesofstarformationandsubsequentgas sensitivity is reaching the natural values for the interaction cross
removalbysupernovafeedbackmighthavebeenviolentenoughto sectionsoftheparticlephysicsmodelsthatpredictthem(e.g.Su-
persymmetry,Abazajianetal.2012;Aprileetal.2012).
An exciting possibility is that of self-interacting dark mat-
(cid:63) CITANationalFellow,e-mail:[email protected]
† HubbleFellow ter(SIDM)originallyintroducedoveradecadeagobySpergel&
‡ HubbleFellow Steinhardt(2000).Self-scatteringbetweendarkmatterparticlesis
©2012RAS
2 J.Zavala,M.Vogelsberger&M.G.Walker
afeatureofpresenthidden-sectordarkmattermodelsthatpredict 103
theexistenceofnewgaugebosons.Thepresenceofthesebosonsis
invokedtoenhancetheannihilationand/orself-scatteringofdark
matterparticlestoexplainanumberofpuzzlingobservations(the 102
Sommerfeld enhancement, e.g. Arkani-Hamed et al. 2009, Buck-
ley&Fox2010).Collisionaldarkmatterisconstrainedbythere-
101
quirements from different astrophysical observations, such as the ]
1
ellipsoidal shape of haloes, the avoidance of subhalo evaporation g−
ingalaxyclusters,andtheavoidanceofthegravothermalcatastro- 100
2
phe(e.g.Miralda-Escude´ 2002;Gnedin&Ostriker2001;Firmani m
etal.2001).TheoriginalexcitementcausedbySIDMdiedoffby c
[
theapparentlystrongconstraintsonthescatteringcrosssectionset m10-1
particularly by X-ray and lensing observations of clusters in the /
T
analysis by Miralda-Escude´ (2002): σT/m(cid:54)0.02cm2g−1; such σ10-2 SIDM10
alowcrosssectionwouldhavenorelevantimpactforthedynam-
SIDM1 SIDM0.1
icsofgalaxiesattheO(1kpc)scale.Peteretal.(2012)havere-
vised this constraint and found that it was overestimated by over 10-3 vdSIDMa vdSIDMb
an order of magnitude suggesting that a current constraint is of
O(0.1cm2g−1).
10-4
SIDM is clearly a viable model if the cross section depends 100 101 102 103
ontherelativevelocityinsuchawaythatdarkmatterbehavesas v [km s−1]
acollisionalfluidindwarfs,andisessentiallycollisionlessatthe
scaleofclusters.Althoughthisideawasphenomenologicallypro- Figure1.Dependenceofthemomentum-transferweightedcross-section
posed(Yoshidaetal.2000)andexploredwithcosmologicalsimu- perunitmassontherelativevelocityforthedifferentSIDMmodelsconsid-
lations(Col´ınetal.2002)adecadeago,itstheoreticalsupporthas eredhere.TheconstantcrosssectioncaseswithσT/m(cid:62)1cm2g−1 are
likelyruledoutbyhaloshapesbasedonX-rayandlensingobservationsof
comeuponlyrecently(e.g.Ackermanetal.2009;Fengetal.2009,
clusters(Peteretal.2012).Themodelswithavelocity-dependentcross-
2010;Buckley&Fox2010;Loeb&Weiner2011;vandenAarssen
sectionaretunedtosatisfyallcurrentastrophysicalconstraintsandhave
etal.2012;Tulinetal.2012).Moreover,earliersimulationslacked
beenshowntobeconsistentwiththekinematicsofMWdSphs(VZL).
the resolution needed to reliably explore the sub-kpc region of
dwarf-sizehaloes.Itwasonlyuntilrecentlythatitwasexplicitly
shownthattheoreticallymotivatedvelocity-dependentSIDM(vd- range of interesting constant σ /m values is thus very narrow:
T
SIDM) models produce core sizes consistent with those found in 0.1cm2g−1<σ /m<1cm2g−1.
T
MW dSphs, and also solve the emergent too big to fail problem
(Vogelsbergeretal.2012,hereafterVZL).
On the other hand, Rocha et al. (2012) have suggested that
2 SIMULATIONSANDRESULTS
a velocity-dependent cross section is not essential since a SIDM
model with a constant σT/m=0.1cm2g−1 (allowed by cluster Ouranalysisisbasedonre-simulationsoftheAq-Ahalo(level3
constraints) is also consistent with the inner structure of dSphs. resolution)oftheAquariusproject(Springeletal.2008),whichisa
ThisseemstocontradictearlierestimatesmadebyYoshidaetal. setofrepresentativeMW-likehaloeswithintheCDMWMAP-1yr
(2000) who suggested that the average number of collisions per cosmology.ThishalohasavirialmassofM ∼1.8×1012M
200 (cid:12)
particleinthecentralcore,ncore,scalesasthecuberootofthehalo withinaradiusofr200∼246kpc(enclosinganaveragedensityof
mass.Sinceforthiscrosssection,ncore∼2foracluster-sizehalo 200timesthecriticaldensity).Theparticlemassinthesimulations
(within∼10% of the virial radius, see their Fig. 2), ncore would is mp∼4.9×104M(cid:12) and the Plummer equivalent gravitational
thusbesuppressedbyafactorofO(100)indwarf-sizehaloes,re- softeninglengthis(cid:15)∼120pc.Weuseanalgorithmthataddsdark
sultingincoresthataretoosmall.Thisscalingishoweverimprecise matter self-scattering to the N-body code GADGET-3 for gravita-
sinceforahaloofvirialmassM: tionalinteractions(lastdescribedinSpringel2005).Thealgorithm
(cid:16)σ (cid:17) (cid:16)σ (cid:17) usesaN-body/MonteCarloapproachtorepresentthemicrophysi-
ncore∼(cid:104)ρcore(cid:105) mT (cid:104)σvel(cid:105)tage ∝∆core mT M1/3tage, (1) calscatteringprocessinthemacroscopiccontextofthesimulation.
TheconnectionbetweenthistypeofapproachandtheBoltzmann
where(cid:104)ρ (cid:105)and(cid:104)σ (cid:105)aretheaveragedensityandvelocitydis- equationisnicelydescribedinAppendixAofRochaetal.(2012).
core vel
persion of dark matter particles, t is the formation time, and ThedetailsofthisalgorithmcanbefoundinVZL,aswellassim-
age
∆ is proportional to the density contrast relative to the back- plecontrolledteststhatshowtheagreementbetweentheoutcome
core
grounddensity;allofthesequantitiesaredefinedwithinthecoreof of the code and analytical expectations. All dark matter models
thehalo.Thus,thehigherconcentrationsandlargerformationtimes weresimulatedstartingwiththesameinitialconditionsandtheir
ofdwarf-sizehaloesreducetheM1/3 dependence.Itisimportant present-dayself-boundsubhalopopulationwasidentifiedusingthe
toremarkthatboth,Yoshidaetal.(2000)andRochaetal.(2012), SUBFINDalgorithm(Springeletal.2001).
extrapolatedtheregimestheycoulddirectlysimulatetotheregime In addition to CDM, we consider five SIDM cases (recently
ofdwarfs.InthisLetter,weresolvethisissuebyprovingexplic- presentedinVogelsberger&Zavala2012toanalysetheimpactof
itlythataconstantscatteringcross-sectionofσ /m=0.1cm2g−1 self-scattering in direct detection experiments): three with a con-
T
is not able to create O(1kpc) cores in the dark subhaloes where stantcrosssectionandtwowithavelocity-dependentonegivenby
theMWdSphsareexpectedtolive;itdeviatesonlyslightlyfrom aYukawa-likeinteraction(e.g.Loeb&Weiner2011).Thetransfer
theCDMpredictions.Unlessbaryonicprocessesareinvoked,the crosssectionscalingwiththerelativevelocitycanbeseeninFig.1.
©2012RAS,MNRAS000,1–6
ConstrainingSelf-InteractingDarkMatterwiththeMilkyWay’sdwarfspheroidals 3
50 theuncertaintyinmassthatisduetothisdegeneracyisminimised
ssssss
40 LeoIILeoIILeoIILeoIILeoIILeoII DracoDracoDracoDracoDracoDracoCarinaCarinaCarinaCarinaCarinaCarinaSculptSculptSculptSculptSculptSculptLeoILeoILeoILeoILeoILeoI UrsMinUrsMinUrsMinUrsMinUrsMinUrsMin CVnICVnICVnICVnICVnICVnI FornaxFornaxFornaxFornaxFornaxFornaxSextanSextanSextanSextanSextanSextan nvaelaurethoefheanlcfl-olisgehdtmraadsiussr,ewgahredrleesJseaonfsamniosdoetrlospteyn(de.tgo.gSitvreigtahreiseatmale.
2007;Walkeretal.2009;Wolfetal.2010).Observationscanthen
CDM SIDM10
beusedtoconstrainthemaximumdarkmatterdensitywithinthis
SIDM1 SIDM0.1
radius. CDM clearly predicts a population of massive subhaloes
30 vdSIDMa vdSIDMb that is inconsistent with all the 9 dSphs, whereas for SIDM this
] problemdisappearsaslongasσ /m(cid:38)1cm2g−1ondSphscales.
1 T
− Thecurrentlyallowedcasewithσ /m=0.1cm2g−1isveryclose
s T
m toCDM,onlyreducingslightlytheinnerpartofthesubhaloveloc-
k ityprofiles.Onthecontrary,thevdSIDMmodelsclearlysolvethe
[20 toobigtofailproblem.Wenotethattheextentofthetoobigtofail
c
cir probleminCDMdependsonthemassoftheMWhalo,ifitisin
V thelowendofcurrentestimates,(cid:46)1012M ,theproblemmaybe
(cid:12)
resolved(e.g.Wangetal.2012),althoughalowhalomassmaygen-
erateotherdifficultiessuchasexplainingthepresenceoftheMag-
ellanicClouds.InthecontextofSIDM,thelowerthemassofthe
MWhalo,theweakertheargumentagainstσ /m=0.1cm2g−1.
T
Asimplestatisticaltestoftheagreementbetweenthesubhalo
10 distributionsoftwomodelsandthe9dSphsistocomputethechi-
0.1 1.0 square difference associated to the likelihood of having n+(n−)
r [kpc]
data points above (below) the median of the distribution of each
model. Assuming that the probability distribution of finding n±
Figure2.Thecircularvelocityprofilesatz=0encompassingthe1stand datapointsisPoissonian:
3rdquartilesofthedistributionofthe15subhaloeswiththelargestvalues
ofVmax(z = 0).Thesymbolswitherrorbarsareestimatesofthecircu- ∆χ2 =2(ln(n+1! n−1!)−ln(n+2! n−2!)). (2)
larvelocitywithinthehalf-lightradiifor9MWdSphs(Walkeretal.2009;
Wolfetal.2010).Clearly,themostmassiveCDMsubhaloesareinconsis- Comparing SIDM1 and the vdSIDM models with SIDM0.1,
tentwiththekinematicsoftheMWdSphs.SIDMcanalleviatethisproblem the difference is driven solely by Draco with the former pre-
onlyforaconstantscatteringcross-sectionσT/m(cid:38)1cm2g−1(SIDM10 ferred over the latter with ∆χ2∼4.4 (2.1σ). Using an interpo-
andSIDM1)orifithasavelocitydependence(vdSIDMaandvdSIDMb). lation of our three constant cross section cases, we estimate that
Currentconstraintsfromclustersputanupperlimittotheconstantcross σ /m∼0.6cm2g−1 istheminimumvalueforwhich∆χ2 = 0
T
sectioncaseclosetoσT/m∼0.1cm2g−1 (SIDM0.1).Thisvalueistoo relativetoSIDM1.
lowtosolvethetoobigtofailproblem.Theobservationaldatainthebot-
Toshowthetypicalcoresizeandcentraldensitiesthatarepre-
tomrightcanbefittedbylowermasssubhaloes,notshownheresincethey
dictedbythedifferentSIDMmodels,weplotinFig.3thedensity
areaffectedbythelimitedresolutionofoursimulations.
profileofthe15subhaloeswiththelargestV (z = 0)values.
max
Avalueofσ /m∼1cm2g−1 isneededforaconstantcrosssec-
T
tionSIDMmodeltomimictheeffectofthevdSIDMmodelsand
We note that the formula for σ /m for the velocity-dependent produce∼1kpccoreswithcentraldensitiesofO(0.1M pc−3).
T (cid:12)
cases is only valid in the classical regime, once quantum effects If the transfer cross section is reduced to 0.1cm2g−1, then the
are important, the finite interaction length of the Yukawa poten- subhaloesareonlyslightlylessdensethaninCDM,havingcores
tialcutsoffthezero-velocitydivergenceofthecrosssection(see (centraldensities)thatareatleasttwicesmaller(higher)thanthose
e.g.Fengetal.2010).Forourpurposes,thequantityofrelevance intheotherSIDMcases.
is (σ /m)v which goes to zero at zero velocity. It is clear that VZLshowedthattheSIDM10andvdSIDMmodelshavecon-
T
for the vdSIDM models, σ /m(cid:29)0.1cm2g−1 at the character- vergentdensityandcircularvelocityprofileswithinthecentralden-
T
isticvelocitiesinMWdSphs(theobservedvelocitydispersionof sitycore;wehavefoundthesameforSIDM1andtolesserextent
starsalongthelineofsightis∼10kms−1,e.g.Walkeretal.2009). forSIDM0.1.ConvergenceishardertoachieveforCDMsince,ata
ThisfactalonealreadycastsadoubtonthepossibilityofSIDM0.1 fixedradius,thetwo-bodyrelaxationtimeisshorterthanforSIDM
(σ /m=0.1cm2g−1) producing similar results as the vdSIDM (duetothereduceddensitiesinthelattercase).Poweretal.(2003)
T
casesthatwereshowntobeconsistentwiththekinematicsofthe showed that the density profile converges at a given radius when
MW dSphs in VZL. We note that there is a change in nomen- thetwo-bodyrelaxationtimeislargerthantheHubbletimeatthis
clature relative to VZL: RefP0≡CDM, RefP1≡SIDM10, RefP2- radius.Attheresolutionlevelofoursimulations,theconvergence
3≡vdSIDMa-b. radiusforCDMis∼600pc,whichimpliesthattheCDMcircular
Fig.2showstheinter-quartilerange(i.e.,25-75%)ofthedis- velocityanddensityprofilesshowninFigs.2and3underestimate
tributionofthepresent-daycircularvelocityprofilesofthe15sub- thetruedarkmattercontentwithin∼600pc(Springeletal.2008),
haloes with the largest values of V (z = 0) (the maximum whereasforSIDMisatleasthalfofthisvalue.Inanycase,theex-
max
ofthecircularvelocity)within300kpchalocentricdistance.The pectationisthatifthedensityprofileofSIDM0.1hasnotconverged
symbols with error bars correspond to estimates of the circular yet,higherresolutionwoulddriveittowardshigherdensities,not
velocitywithinthehalf-lightradiiofthesampleof9MWdSphs lower,bringingitevenclosertoCDM(thisisatrendconfirmedfor
usedbyBoylan-Kolchinetal.(2011,2012).Sincecurrentdatafor thecasesanalysedinVZL,seetheirFig.9).
thestarsinthedSphsprovideanincompletedescriptionofthe6- By using the fact that some MW dSphs have chemo-
dimensionalphase-spacedistribution,thederivedmassprofilesare dynamically distinct stellar subcomponents that independently
typicallydegeneratewiththevelocityanisotropyprofile.However, tracethesamegravitationalpotential,Walker&Pen˜arrubia(2011)
©2012RAS,MNRAS000,1–6
4 J.Zavala,M.Vogelsberger&M.G.Walker
Name ρ(r=200pc)[M(cid:12)kpc−3] rs[kpc] rc[kpc]
CDM SIDM10
vdSIDMa 1.37×108 0.94 0.75
SIDM1 SIDM0.1
vdSIDMb 1.37×108 0.94 0.73
vdSIDMa vdSIDMb
SIDM1 1.16×108 0.96 1.33
] SIDM0.1 2.31×108 0.97 0.41
3
−
c108
p
k Table1.BestfitparametersforthemedianoftheSIDMdensityprofilesof
fl
M the15subhaloeswiththelargestVmax(z = 0)values.Thelasttwohave
[ aconstantcrosssectionwhiletheothershaveavelocity-dependentcross

ρ section (see Fig. 1). SIDM1.0 is likely ruled out by cluster observations
(seeRochaetal.2012).Thedensityprofileusedforthefitsisgivenby
Eq.(3)forSIDM1andthevdSIDMmodels,andbyEq.(4)forSIDM0.1.
fit parameters for the median of the subhalo population for each
SIDMmodel(exceptforSIDM10whichhasbeenruledout).We
107 notethatPen˜arrubiaetal.(2012)alreadyusedEq.(4)toestimate
10-1 100 r (cid:38)1kpcforFornaxandSculptor.Coresofthissizearetoolarge
c
r [kpc]
tobeconsistentwithmostofthesubhaloesinSIDM0.1.
To test the consistency of the different SIDM models, we
Figure3.Densityprofileofthe15subhaloeswiththelargestVmax(z = use the parameters of the fits to compute the slope of the inner
0) values within CDM and different SIDM models (see Fig. 1). We
massprofilebetweenthepairofhalflightradii(themedianlike-
show the median and 1st and 3rd quartiles of the subhalo distribution
lihood values) of the two distinct stellar subcomponents in For-
for each case. The velocity-dependent SIDM cases produce cores of ap-
nax and Sculptor. We then test whether this slope is as steep as
proximately600pc.OftheconstantcrosssectionSIDMmodelsweex-
the lower limit set by the data. The confidence level at which
plored,theonethatiscurrentlyallowedbyclusterconstraints,SIDM0.1
(σT/m=0.1cm2g−1),onlydeviatesslightlyfromCDM;theassociated a given slope is said to be excluded is determined by the frac-
coresizesarelessthan300pc. tion of the posterior distribution fp of allowed slopes that are
larger.Forσ /m=0.1cm2g−1,allbut2subhaloesareexcluded
T
at>95(90)%confidenceforFornax(Sculptor);theremainingtwo
showedthatitispossibletoconstraintheslopesoftheirinnermass subhaloeshavevaluesoff (cid:38) 0.86(0.81)forFornax(Sculptor).
p
profiles.TheyfoundthatFornaxandSculptorareconsistentwith
Onthecontrary,theotherSIDMmodels(exceptforSIDM10that
coreddensityprofileswhilecuspyprofileswithρ∝r−1areruled
was not analysed) are clearly more consistent with the data with
outwithasignificance(cid:38) 96%and(cid:38) 99%,respectively.Weuse
onlyfoursubhaloesexcludedat90%confidenceforFornax(fiveof
thismethodtotesttheconsistencyoftheSIDMmodelsexplored
thesubhaloesactuallyhavef <0.8),whileonlythreesubhaloes
p
here. We found that all SIDM models, except for SIDM0.1, are
areexcludedat>80%confidenceforSculptor.Wefoundnoclear
wellfittedbythefollowingthree-parameterformula:
preferencebetweenthevdSIDMmodelsandthecasewithconstant
ρ(r)= ρ0rs3 , (3) σT/m=1cm2g−1. To consider the impact of the non-spherical
(r+r )(r2+r2) morphologiesofFornaxandSculptor,werepeatedtheanalysisfor
c s
ellipticalratherthancircularradiiforthestarsusedtoestimatethe
whichissimilartotheBurkertprofile(Burkert1995)butwithtwo
slope of the mass profiles (see sect. 6.1 of Walker & Pen˜arrubia
scaleradiir andr .Theremainingcase,SIDM0.1,isbetterfitted
s c 2011).WefindthatforallmodelsFornaxbecomesslightlymore
by:
exclusivewhileSculptorisconsiderablylessexclusive.
ρ r3
ρ(r)= 0 s . (4)
(r+r )(r+r )2
c s
3 DISCUSSIONANDCONCLUSIONS
Usingtheseformulae,wefoundthebestfitparametersforthemas-
sivesubhaloesineachoftheSIDMmodels.Suchfitsarerestricted Self-Interacting Dark Matter (SIDM) offers a promising solution
to a radial range between the softening length of our simulations to the dwarf-scale challenges faced by the otherwise-remarkably
∼120pcandtheradiuswheretidalstrippinghasmadetheouter successfulColdDarkMatter(CDM)model.Theoriginalideaofa
logarithmicslopeofthedensityprofilesteeperthan−3.Thelatter velocity-independent, elastically scattering cross section died off
restrictionisofrelevanceonlyforfoursubhaloesthatareaffected quickly, mostly due to the apparently stringent constraint found
significantly by tidal stripping within ∼ 5kpc. Two of these are byMiralda-Escude´(2002)requiringthatthecross-sectionperunit
clearlyaffectedwithin∼1kpcandshouldlikelyberemovedina masswasσ /m(cid:54)0.02cm2g−1.Thisvalueisuninteresting,with
T
moredetailedanalysis;theyaretheleastconsistentwiththedata. earlier estimates requiring σ /m to be at least of O(1cm2g−1)
T
Tofindthebestfitparametersweminimise: tocreate∼1kpccoresindwarf-sizehaloes(Yoshidaetal.2000;
Q2 = N1 (cid:88)(lnρi(ri)−lnρfit(ri))2, (5) cDoanvse´treatinatls.o2n00c1o)l.liPsieotenraletdaarl.k(m20a1tt2e)rhaanvdefroeucnedntltyhermevitsoedbeeaorvleier-r
bins
i estimated by over an order of magnitude; the current constraint
wherethesumgoesoverallradialbins.Thusdefined,Qgivesan isσ /m(cid:46)0.1cm2g−1.Moreover,theseauthorshaverevived,in
T
estimate of the goodness of the fit. In Table 1, we give the best a companion paper (Rocha et al. 2012), the velocity-independent
©2012RAS,MNRAS000,1–6
ConstrainingSelf-InteractingDarkMatterwiththeMilkyWay’sdwarfspheroidals 5
1011 ofσT/mvalues.Thechallengestomakeadefinitivetestofthishy-
pothesisaretwofold:thecluster-constraintsneedberefined,andthe
impact of conservative baryonic processes needs to be estimated.
] CDM SIDM10
fl AlthoughaddinggasphysicsisthenextstepofSIDMsimulations,
M SIDM1 SIDM0.1
a challenge to make SIDM an even more attractive alternative to
[ vdSIDMa vdSIDMb
) CDM is the prospect of explaining the observed scarcity of MW
b
u satellites and field dwarfs (e.g. Klypin et al. 1999; Zavala et al.
Ms
2009)withoutinvokingextremebaryonicprocesses.Asweshow
d
/ inFig.4,allallowedelasticSIDMmodelsessentiallyproducethe
N
sameabundanceofdwarf-sizehaloesasinCDM.Apromisingpos-
d
( sibilityisthatofexothermicinteractionsbetweenexcitedandnon-
b
2Msu1010 excitedstatesofdarkmatter(e.g.Loeb&Weiner2011).Theve-
locitykickimpartedduringthecollisionmightbelargeenoughto
causetheevaporationoflow-masshaloes.
106 107 108 109 1010
M [M ]
sub
fl ACKNOWLEDGEMENTS
Figure4.SubhalomassfunctionforaMW-sizehalowithinCDManddif-
WethankVolkerSpringelforgivingusaccesstoGADGET-3,Ni-
ferentelasticSIDMmodels.Theonlymodelthatleadstoadifferencerel-
ayeshAfshordi,ManojKaplinghatandPaulSteinhardtforfruitful
ativetoCDMhasaconstantcrosssectionofσT/m=10cm2g−1,which discussions, Mike Boylan-Kolchin, Fabio Governato, Lars Hern-
isclearlyruledoutbyclusterobservations.
quist,AviLoeb,JorgePen˜arrubiaandSimonWhiteforusefulsug-
gestions. JZ is supported by the University of Waterloo and the
SIDMmodelbysuggestingthatavalueofσ /m=0.1cm2g−1is PerimeterInstituteforTheoreticalPhysics.ResearchatPerimeter
T
seeminglyconsistentwiththeinnerstructureoftheMWdSphs. Institute is supported by the Government of Canada through In-
Motivated by the prospect of a viable constant cross section dustry Canada and by the Province of Ontario through the Min-
SIDMmodel,weinvestigatetheclaimsfromRochaetal.(2012) istry of Research & Innovation. JZ acknowledges financial sup-
using high resolution cosmological SIDM simulations of a MW- portbyaCITANationalFellowship.M.G.W.iscurrentlysupported
sizehalo.ContrarytoRochaetal.(2012),weareabletoresolve byNASAthroughHubbleFellowshipgrantHST-HF-51283.01-A,
the sub-kpc structure of the massive subhalo population to suffi- awardedbytheSpaceTelescopeScienceInstitute,whichisoper-
cientlysmallradiiforcomparisonwiththeMWdSphs.Wefindthat atedbytheAssociationofUniversitiesforResearchinAstronomy,
avelocity-independentSIDMmodelisconsistentwiththekinemat- Inc., for NASA, under contract NAS5-26555. MV acknowledges
icsofdSphsonlyifσ /m≈1cm2g−1(seeFig.2),i.e.,avalueof support from NASA through Hubble Fellowship grant HST-HF-
T
thisorderisrequiredtosolvethetoobigtofailproblem(Boylan- 51317.01.
Kolchinetal.2011,2012).Ifthecrosssectionislowerbyanorder
ofmagnitude,thesubhalopopulationisstilltoodensetobecon-
sistentwiththeMWdSphs.Ontheotherhand,asshownalready
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